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\section{ { \large Introduction} }
Our aim in this paper is to propose a logical framework for formally
mode\-ling how the information stored in a database can get captured progressively,
by an agent/adversary querying repeatedly the database. The data can be of any
following types: numerical, non-numerical, or literal.
In practice however, some of the literals representing `sensitive data' could be in a
taxonomical relation; moreover, part of the data could be presented, for `anonymization'
purposes, as finite intervals or sets, over the basic types. We shall therefore agree to
consider the types of the data in an extended `overloaded' sense. Cf. Example 1 below.
(Only tree-structured taxonomies will be considered in this work.)
We assume given a data base $D$, with its attributes set ${\mathcal{A}}$, usually divided in
three disjoint groups: the subgroup ${\mathcal{A}}^{(i)}$ of {\em identifiers}, ${\mathcal{A}}^{(qi)}$ of
{\em quasi-identifiers}, and ${\mathcal{A}}^{(s)}$ of {\em sensitive attributes}. The tuples of
the base $D$ will be generally denoted as $t$, and their attributes
denoted respectively as $t^{i}, t^{qi},$ and $t^{s}$ in the three subgroups of ${\mathcal{A}}$.
The attributes $t^{i}$ on any tuple $t$ of $D$ are conveniently viewed as defining a
`user' or a `client' of the database $D$.
Quasi-identifiers\footnote{A formal definition of quasi-identifier attributes does
not seem to be known. For our purposes, it suffices to see them as those that
are not identifiers nor sensitive.} are informally defined in general, as a set of public
attributes, which in combination with other attributes and/or external information,
can allow to re-identify all or some of the users to whom the information refers.
The base $D$ itself could be `distributed probabilistically' over a finite set
(referred to then, as `universe', and its elements named as possible `worlds').
By a {\em privacy policy} $P = P_A(D)$ on $D$ with respect to a given
agent/adversary $A$ is meant the stipulation that for a certain {\em given set} of
tuples $\{t \in P \subset D\}$, the sensitive attributes $t^{s}$ on any such $t$ shall
remain inaccessible (`even after further deduction' -- see below) to $A$. It is assumed
that $A$ is not the user identified by the attributes $t^{i}$ on these $t$'s.
The logical framework we propose in this work, to model the evolution of the `knowledge'
that an adversary $A$ can gain by repeatedly querying the given database $D$ -- with a view
to get access to sensitive data meant to remain hidden for him/her under the given privacy
policy $P$ --, will be called {\em Distributed Labeled-Tagged Transition System} (DLTTS);
The underlying logic for DLTTS is first-order, with countably many variables and finitely
many constants (including certain usual dummy symbols like `$\star, \$, \#$').
In this work, the basic signature $\Sigma$ for the framework is assumed to have no
non-constant function symbols.
By `knowledge' of $A$ we shall mean the data that $A$ retrieves as answers to his/her
successive queries, as well as other data that can be deduced/derived, under relational
operations on these answers; and in addition, some others derivable from these, using
relational combinations with data (possibly involving some of the users of $D$) from
finitely many {\em external DBs given in advance}, denoted as $B_1, \dots, B_m$, to
which the adversary $A$ is assumed to have free access. These relational and querying
operations are all assumed done with a well-delimited fragment of the language SQL ;
{\em it is assumed that this fragment of SQL is part of the signature $\Sigma$ underlying
the DLTTSs.} In addition, if $n \ge 1$ is the length of the tuples forming the data in $D$,
finitely many predicate symbols ${\mathcal{K}}_i, 1 \le i \le n$, each $K_i$ of arity $i$, will be part
of the signature $\Sigma$; in the work presented here they will be the only predicate
symbols in $\Sigma$. The role of these symbols is to allow us to see any data tuple of
length $r, 1 \le r \le n$, as a variable-free first-order formula with top symbol ${\mathcal{K}}_r$,
with all arguments assumed typed implicitly (with the help of the headers of the base
$D$). In practice however, we shall choose to drop these top symbols ${\mathcal{K}}_i$, and see
any data tuple that is not part of the given privacy policy $P_A(D)$, directly as a
first-order variable-free formula over $\Sigma$; data tuples $t$ that are elements
of the policy $P_A(D)$ will in practice be just written as $\neg t$.
As we shall see, the DLTTS framework is well suited for capturing the ideas on acquiring
knowledge and on policy violation, in an elegant and abstract setup. A preliminary
definition of this framework (Section~\ref{DLTTS}) considers only the case where the
data, as well as the answers to the queries, do not involve any notion of `noise'.
(By `noise' we shall mean the perturbation of data by some external random
(probabilistic mechanism.)
But we shall extend this definition in a later section, as an option to also handle
noisy data.The notion of violation of any given privacy policy on a database can
then be (optionally) extended into a notion of violation up to some given
$\epsilon \ge 0$ ($\epsilon$-violation, for short). In the first part of the work, we
will be modeling the lookout for the sensitive attributes of certain given users, by
a single adversary. In the second part of the work (Section~\ref{TwoRuns} onwards),
we propose a method for {\em comparing the evolution of knowledge} of an adversary
at two different nodes on a given run, or on two different possible runs; the same method
also applies for comparing the evolution of knowledge of two different adversaries
$A_1, A_2$, both querying repeatedly (and independently) the given database.
But before formally defining the DLTTS, a couple of examples might help. They will in
particular throw some light on how to delimit properly the fragment of SQL that we want
included in our logical setup.
\subsection{A couple of Examples}
\vspace*{1mm}\noindent
{\bf Example 1}. Table~\ref{1} below is the record kept by the central Hospital of a
Faculty, with three Departments, in a University, on recent consultations by
the faculty staff. In this record,
`Name' is an identifier attribute, `Ailment' is sensitive, the others are QI;
`Ailment' is categorical with 3 branches: Heart-Disease, Cancer, and
Viral-Infection; this latter in turn is categorical too, with 2 branches: Flu and CoVid.
By convention., such taxonomical relations are assumed known to public,
(For simplicity of the example, we assume that all Faculty staff are on the
consultation list of the Hospital.)
\begin{table
\centering
\begin{tabular}{|c | c| c| c| c|}
\hline
Name & Age & Gender & Dept. & Ailment \\
\hline
Joan & 24 & F & Chemistry & Heart-Disease \\
Michel & 46 & M & Chemistry & Cancer \\
Aline & 23 & F & Physics & Flu \\
Harry & 53 & M & Maths & Flu \\
John & 46 & M & Physics & CoVid \\
\hline
\end{tabular}
\caption{\label{1} Hospital's `secret' record }
\end{table}
The Hospital intends to keep `secret' information concerning CoVid infected
faculty members; the tuple $\neg(John, 46, M, \#, CoVid)$ therefore constitutes
its privacy policy. The following Table~\ref{2} is then published for the public,
where the `Age' attributes have been anonymized as (integer) intervals,
the `Ailment' attribute is anonymized by an upward push in the taxonomy.
A certain person $A$, who met John at a faculty banquet, suspected John to have
been infected with CoVid; (s)he thus decides to consult the published record of the
hospital for information.
\begin{table}[h]
\centering
\begin{tabular}{| c| c| c| c|c|}
\hline
Age & Gender & Dept. & Ailment \\
\hline
$\ell_1$ & $[20-30]$ & F & Chemistry & Heart-Disease \\
$\ell_2$ & $[40-50]$ & M & Chemistry & Cancer \\
$\ell_3$ & $[20-30]$ & F & Physics & Viral-Infection \\
$\ell_4$ & $[50-60]$ & M & Maths & Viral-Infection \\
$\ell_5$ & $[40-50]$ & M & Physics & Viral-Infection \\
\hline
\end{tabular}
\caption{\label{2} Hospital's published record }
\end{table}
Knowing that the `John' (s)he met is a `man' and that the table~\ref{2} must contain
John's health bulletin), $A$ has as choice lines 2, 4 and 5 ($\ell_2, \ell_4, \ell_5$)
of Table~\ref{2}.
$A$ being in the lookout for a `CoVid-infected' man, this choice is reduced to the last
two tuples of the table -- a priori indistinguishable because of the `anomymization'
(as `Viral-Infection'). Now, $A$ had the impression that the John (s)he met `was not too
old', so feels that the last tuple is twice more likely; (s)he thus `decides that John must
be from the Physics Dept.', and goes to consult the CoVid-cases statement kept
publicly visible at that Dept.; which reads: \par
\hspace*{1cm} Recent CoVid-cases in the Dept: \; Female 0 ; \hspace*{8mm} Male 1.
\par\noindent
And that confirms $A$'s suspicion concerning John.
In this case, the DLTTS framework would function as follows: At the starting state
$s$ a transition with three branches would a priori be possible, corresponding to
the three (`M') lines 2, 4 and 5 of Table~\ref{2}, which represent the knowledge that
would be acquired respectively along these branches. Now $A$ is on the lookout for a
possible CoVid case, so rules out the `line 2 branch' (i.e., gives this branch probability
$0$). As for the remaining two branches (corresponding to lines 4 and 5 on
Table~\ref{2}), $A$ chooses to go by the line 5 branch, considering it twice more likely
to be successful, than the other ($A$ had the impression that `John was not too old').
That leads to the probability distribution $0, 1/3, 2/3$ assigned respectively on
the three possible branches for the transition. If $s_0, s_1, s_2$ are the respective
successor states for the transition considered, the privacy policy of the Hospital
(concerning John's CoVid information) would thus be violated at state $s_2$ (with
probability $2/3$), it wouldn't be at $s_1$ (probability $1/3$); no information
deduced at state $s_0$.
As just seen, modeling an adversary's search for some specific information on a
given data base $D$ -- as `runs' on a suitable DLTTS and probability distributions over
the successor steps along the runs --, depends in general on the nature(structure) of the
information looked for. The probability distributions on the transitions along the runs
would generally depend on some random mechanism, which could also reflect
the choices the adversary might make. \hfill$\Box$
\vspace*{1mm}
The role of our next example is to point out that specifying Privacy policy policies
will in general have some serious side effects on the functioning of the primitives and
aggregate procedures of SQL. If the policies are to have some `content', operationally
speaking, the DBMS may have to stipulate that the queries employing these primitives
either should have `void outputs' in certain contexts, or `get filtered by the Privacy
policy'.
\noindent {\bf Example 2}. Table~\ref{3} below is an imaginary record $D$ of a bank ${\mathcal{L}}$,
containing a list of its clients: with client\_ids, their names, and their monthly
balances. (Client\_id is the identifier attribute, Monthly--balance is sensitive.)
The privacy policy $P$ of the bank is that client {\em Jean}'s Monthly--balance
should `be invisible' to others; formally, the policy $P$ is the negated
formula $\neg (Jean, \ge 420)$.
On the other hand, the bank is obliged administratively to render public
a monthly statement, on its minimum total Monthly--balance; that is
Table~\ref{4}.
\begin{table}[h]
\centering
\begin{tabular}{|c | c| c|}
\hline
Client\_id & Name & Monthly-balance \\
\hline
1 & Claude & 320 \\
2 & Paul & 270 \\
3 & Jean & 420 \\
4 & Martin & 150 \\
5 & Michel & 420 \\
\hline
\end{tabular}
\caption{\label{3} ${\mathcal{L}}$'s (secret) client record }
\vspace*{1em}
\begin{tabular}{|c | c|}
\hline
Number of Clients & Minimum Total Monthly--balance \\
\hline
5 & $\ge 1580$ \\
\hline
\end{tabular}
\caption{\label{4} Bank ${\mathcal{L}}$'s Monthly public statement}
\end{table}
\vspace*{-1mm}
An adversary $A$ wants to know if Jean is a client of the bank, and if
so, with a monthly balance among the highest. So $A$ first queries the
bank to get the list of its clients with their Monthly-balances. The Bank-DBMS's
answer to $A$'s query will be, say, as in Table~\ref{5} below, where $\star$ stands for
the anonymization of Jean's sensitive data, as a `mask' or as an interval,
say of the form $[330-450]$.
\begin{table}[h]
\centering
\begin{tabular}{| c| c|}
\hline
Name & Monthly-balance \\
\hline
Claude & 320 \\
Jean & $\star$ \\
Paul & 270 \\
Michel & 420 \\
Martin & 150 \\
\hline
\end{tabular}
\caption{\label{5} DBMS's Answer to $A$'s query}
\end{table}
\vspace*{-1mm}
The external Table~\ref{4} is freely accessible to $A$; so, if the functio\-nalities
{\tt COUNT} and {\tt SUM} are applied `without any filter', $A$ can easily deduce that
{\em Jean}'s Monthly--balance at ${\mathcal{L}}$ is $\ge 420$; the bank's Privacy policy is
thus violated. \hfill $\Box$
{\bf Remark}~1: In the above example, if the external DB (Table~\ref{4}) was
unavailable to $A$, the DBMS could have answered his/her query with a Table 5' where
the entire tuple on Jean is deleted; in such a case, the privacy policy $P$ on $D$
(concerning Jean) would a priori remain unviolated; {\em except} if we assume
that the DBMS accepts queries with aggregate operations on the database $D$ that
`do not explicitly look' for Jean's sensitive attribute: For instance $A$
could first retrieve the SUM on the entire Monthly--balance column, then ask for
SUM(Monthly--balance) where `Name $<>$ Jean'. A relational deduction then
leads to the violation of the policy $P$.
The above two Examples show that the violation of privacy policies
needs, in general, some additional `outside knowledge'. \hfill $\Box$
\vspace*{1mm}
We may assume wlog that the given external bases $B_1, \dots, B_m$ -- to which $A$
could resort, with relational operations for deducing additional information -- are also
of the same signature $\Sigma$ as $D$; so all the knowledge $A$ can deduce/derive
from his/her repeated queries can be expressed as a first-order variable-free formula
over the signature $\Sigma$.
\vspace*{-1mm}
\section{{\large Distributed Labeled-Tagged Transition Systems}}~\label{DLTTS}
\vspace*{-1em}
The DLTTS framework presented in this section synthesizes ideas coming from
various domains, such as the Probabilistic Automata of Segala (\cite{Segala95b},
Probabilistic Concurrent Systems, Probabilistic labelled transition systems
(\cite{Fast2018,PTS2019}. Although the underlying signature for the DLTTS can be
rich in general, for the purposes of our current work we shall be working with a
limited first-order signature (as mentioned in the Introduction) denoted $\Sigma$,
with countably many variables, finitely many constants (including some `standard
dummies'), no non-constant function symbols, and a finite limited set of predicate
(propositional) symbols. Let ${\mathcal{E}}$ be the set of all variable-free formulas over
$\Sigma$, and $\mathtt{Ext}$ a given subset of ${\mathcal{E}}$. We assume given a decidable
procedure ${\mathcal{C}}$ whose role is to `saturate' any finite set $G$ of variable-free formulas
into a finite set $\overline{G}$, by adding a finite (possibly empty) set of variable-free
formulas, using {\em relational operations} on $G$ and $\mathtt{Ext}$.
This procedure ${\mathcal{C}}$ will be internal at every node on a DLTTS; in addition, {\em there
will also be a `blackbox' mechanism ${\mathcal{O}}$, acting as an oracle} telling if the given
privacy policy on a given database is violated at the current node. In a later paragraph
(Section~\ref{TwoRuns}) more details will be given on an additional role the oracle
will play, in a privacy analysis schema, on any given DB.
\begin{defn}
A Distributed Labeled-Tagged Transition System (DLTTS), over a given
signature $\Sigma$, is formed of:
\begin{itemize}
\item[-] a finite (or denumerable) set $S$ of states, an `initial' state $s_0 \in S$,
and a special state $\otimes \in S$ named `fail':
\item[-] a finite set $Act$ of action symbols (disjoint from $\Sigma$), with a
special action $\delta \in Act$ called `violation';
\item[-] a (probabilistic) transition relation ${\mathcal{T}} \subset S\times Act \times Distr(S)$,
where $Distr(S)$ is the set of all probability distributions over $S$, with finite
support.
\item[-] a tag $\tau(s)$ attached to every state $s \in S\smallsetminus\{\otimes\}$,
formed of finitely many first-order variable-free formulas over $\Sigma$;
the tag $\tau(s_0)$ at the initial state is the singleton set $\{\top\}$.
\item[-] at every state $s$ a special action symbol $\iota = \iota_s \in Act$,
said to be {\em internal} at $s$, completes/saturates $\tau(s)$ into a set $\overline{\tau}(s)$
with the procedure ${\mathcal{C}}$, by using relational operations between the formulas in
$\tau(s)$ and $\mathtt{Ext}$.
\end{itemize}
\end{defn}
\vspace*{-0.5em}
A (probabilistic) transition ${\mathfrak t} \in {\mathcal{T}}$ will generally be written as a triple
$(s, a, {\mathfrak t}(s))$; and ${\mathfrak t}$ will be said to be `from' (or `at') the state $s$,
the states of ${\mathfrak t}(s)$ will be the `successors' of $s$ under ${\mathfrak t}$.
The formulas in the tag $\overline{\tau}(s)$ attached to any state $s$
will all be assigned the same probability as the state $s$ in $Distr(S)$.
If the set $\overline{\tau}(s)$ of formulas turns out to be inconsistent, then the oracle
mechanism ${\mathcal{O}}$ will (intervene and) impose $(s, \delta, \otimes)$ as the only
transition from $s$, standing for `violation' and `fail', by definition,
Nondeterminism of transitions can be defined without difficulty on DLTTS, as a
nondeterministic choice between the possible probabilistic transitions at any given
state. We shall assume that nondeterminism is managed by the choice of a
suitable scheduler; and in addition, that at most one probabilistic transition
is firable from any state $s \in S\smallsetminus\{\otimes\}$, and none from the
halting state $\otimes$.
\vspace*{1mm}
\noindent {\bf DLTTS and Repeated queries on a database}:
The states of the DLTTS will stand for the various `moments' of the querying sequence,
while the tags attached to the states will stand for the knowledge $A$ has acquired
on the data of $D$ `thus far'. This knowledge consists partly in the answers to the
queries (s)he made so far, then completed with additional knowledge using the
internal `sa\-turation' procedure ${\mathcal{C}}$ of the framework.
In the context of DBs, this procedure would consist in relational algebraic
operations between the answers retrieved by $A$ for his/her repeated queries on
$D$, all seen as tuples (variable-free formulas), and suitable tuples from the given
external databases $B_1, \dots, B_m$.
If the saturated knowledge of $A$ at a current state $s$ on the DLTTS (i.e., the tag
$\overline{\tau}(s)$ attached to the current state $s$) is not inconsistent, then the transition
from $s$ to its successor states represents the probability distribution of the likely
answers $A$ would expect to get for his/her next query.
Note that we make no assumption on whether the repeated queries by $A$ on
$D$ are treated {\em interactively, or non-interactively}, by the DBMS. It appears
that the logical framework would function exactly alike, in both cases.
\vspace*{1mm}
{\bf Remark}~2: (a) Suppose ${\mathfrak t}$ is a transition from a state $s$, on the DLTTS corresponding
to a querying sequence by an adversary $A$, and $s'$ is one of the successors of $s$ under
${\mathfrak t}$; then, by definition, the `fresh' knowledge $\tau(s')$ of $A$ at $s'$ resulting from
this transition, is the addition to $A$'s saturated knowledge $\overline{\tau}(s)$ at $s$, the part
of the response of the DBMS's answering mechanism for $A$'s current
query, represented by the branch of ${\mathfrak t}$ going from $s$ to $s'$.
(b) As already mentioned, we assume that the relational operations needed for gaining
further knowledge are done using a well delimited finite subset of the functionalities
of SQL; and that `no infinite set can get generated from a finite set' under these
functionalities, assumed included in the signature $\Sigma$. (This corresponds to the
{\em bounded inputs outputs} assumption, as in e.g., \cite{BarthePOPL12,BartheLICS20}.)
\hfill$\Box$
\begin{propn}~\label{exact}
Suppose given a database $D$, a finite sequence of repeated queries on $D$ by an
adversary $A$, and a first-order relational formula $P = P_A(D)$ over the signature $\Sigma$
of $D$, expressing the privacy policy of $D$ with respect to $A$. Let ${\mathcal{W}}$ be the DLTTS
modeling the various queries of $A$ on $D$, and the evolution of the knowledge of $A$
on the data of $D$, resulting from these queries and the internal actions at the states of
${\mathcal{W}}$, as described above.
(i) The given privacy policy $P_A(D)$ on $D$ is violated if and only if the failure state
$\otimes$ on the DLTTS ${\mathcal{W}}$ is reachable from the initial state of ${\mathcal{W}}$.
(ii) The satisfiabiliity of the set of formulas $\overline{\tau}(s) \cup \{\neg P\}$ is decidable,
at any state $s$ on the DLTTS, under the assumptions of Remark~2(b).
\end{propn}
\vspace*{-0.5mm}\noindent
{\em Proof}: Assertion (i) is restatement. Observe now, that at any state $s$ on
${\mathcal{W}}$, the tags $\tau(s)$, $\overline{\tau}(s)$ are both {\em finite sets of first-order variable-free
formulas} over $\Sigma$, without non-constant function symbols. For, to start
with, the knowledge of $A$ consists of the responses received for his/her queries,
in the form of a finite set of data tuples from the given databases, and some
subtuples. And by our assumptions of Remark-2~(b), no infinite set can be generated
by saturating this initial knowledge with procedure ${\mathcal{C}}$.
Assertion (ii) follows then from the known result that the inconsistency of any given
finite set of variable-free first-order Datalog formulas is decidable, e.g., by the
analytic tableaux procedure. (Only the absence of variables is essential.) \hfill$\Box$
\vspace*{-1em}
\section{{\large $\epsilon$-indistinguishability, $\epsilon$-local-differential
privacy}}~\label{LDP}
\vspace*{-2em}
Our objective now is to extend the result of Proposition~\ref{exact} to the case when
the violation to be considered can be {\em up to some given $\epsilon \ge0$}, in a
sense to be made precise. We stick to the same notation as above. The set ${\mathcal{E}}$ of all
variable-free formulas over $\Sigma$ is thus a disjoint union of subsets of the form
${\mathcal{E}} = \cup \{{\mathcal{E}}^{{\mathcal{K}}}_i \mid 0 < i \le n, {\mathcal{K}} \in \Sigma\}$, the index $i$ in ${\mathcal{E}}^{{\mathcal{K}}}_i$
standing for the common length of the formulas in the subset, and ${\mathcal{K}}$ for the
common root symbol of its formulas; each set ${\mathcal{E}}^{{\mathcal{K}}}_i$ will be seen as a
database of $i$-tuples.
We shall first look at the situation where the queries intend to capture certain
(sensitive) values on a given tuple $t$ in the database $D$. Two different tuples
in ${\mathcal{E}}$ might correspond to two likely answers to such a query, but with possibly
different probabilities in the distribution assigned for the transitions, by the
probabilistic mechanism ${\mathcal{M}}$ (e.g., as in Example 1).
Given two such instances, and a real $\epsilon \ge 0$, we can also define a notion
of their $\epsilon$-local-indistinguishabilty, wrt the tuple $t$ and the mechanism
${\mathcal{M}}$ answering the queries.
This can be done in a slightly extended setup, where the answering mechanism
may, {\em as an option}, also add `noise' to certain numerical data values, for several
reasons among which the safety of data. We shall then assume that the internal
procedure ${\mathcal{C}}$ of the DLTTS at each of its states (meant to saturate the current
knowledge of the adversary querying the database) incorporates the following
three well-known noise adding mechanisms: the Laplace, Gauss, and exponential
mechanisms. With the stipulation that this optional noise additions to numerical values
can be done in a {\em bounded} fashion, so as to be from a finite prescribed domain
around the values; it will then be assumed that tuples formed of such noisy data are
also in ${\mathcal{E}}$.
\vspace*{-1mm}
\begin{defn}~\label{eps-locindistinguish}
(i) Suppose that, while answering a given query on the base $D$, at two
instances $v, v',$ the probabilistic answering mechanism ${\mathcal{M}}$ outputs the same
tuple $\alpha \in {\mathcal{E}}$. Given $\epsilon \ge 0$, these two instances are said to be
$\epsilon$-local-indistinguishable wrt $\alpha$, if and only if: \par
\hspace*{2.5cm} $ Prob[{\mathcal{M}}(v) = \alpha] \le e^{\epsilon} Prob[{\mathcal{M}}(v') = \alpha]$ and \par
\hspace*{2.5cm} $ Prob[{\mathcal{M}}(v') = \alpha] \le e^{\epsilon} Prob[{\mathcal{M}}(v) = \alpha]$.
(ii) The probabilistic answering mechanism ${\mathcal{M}}$ is said to satisfy
{\em $\epsilon$-local differential privacy} {\em($\epsilon$-LDP)} for $\epsilon \ge 0$,
if and only if: For any two instances $v, v'$ of ${\mathcal{M}}$ {\em that lead to the same
output}, and any set ${\mathcal{S}} \subset Range({\mathcal{M}})$, we have \par
\hspace*{2.5cm} $ Prob[{\mathcal{M}}(v) \in {\mathcal{S}} ] \le e^{\epsilon} Prob[{\mathcal{M}}(v') \in {\mathcal{S}}]$.
\end{defn}
\vspace*{-1mm}
We shall also be needing the following notion of $\epsilon$-indistinguishability (and of
$\epsilon$-distinguishability) of two different outputs of the mechanism ${\mathcal{M}}$:
These definitions -- as well that of $\epsilon$-DP given below -- are essentially
reformulations of the same (or similar) notions defined in \cite{Dwork2006,Dwork2014}.
\begin{defn}~\label{eps-distinguish}
Given $\epsilon \ge 0$, two outputs $\alpha, \alpha'$ of the probabilistic
mechanism ${\mathcal{M}}$ answering the queries of an agent $A$, are said to be
$\epsilon$-indistinguishable, if and only if: For every pair $v, v'$ of inputs
for ${\mathcal{M}}$, such that $Prob[{\mathcal{M}}(v) = \alpha] = p$ and $Prob[{\mathcal{M}}(v') = \alpha'] = p'$,
we must have: $p \le e^{\epsilon} p'$ and \,$p' \le e^{\epsilon} p$.
\noindent
Otherwise, the outputs $\alpha, \alpha'$ will be said to be $\epsilon$-distinguishable.
\end{defn}
\vspace*{-1mm}
{\bf Remark}~3: Given an $\epsilon \ge 0$, one may assume as an option, that
at every state on the DLTTS {\em the retrieval of answers to the current query
(from the mechanism ${\mathcal{M}}$) is done up to $\epsilon$-indistinguishabilty}; this will
then be implicitly part of what was called the saturation procedure ${\mathcal{C}}$ at that state.
The procedure thus enhanced for saturating the tags at the states, will then be
denoted as $\epsilon{\mathcal{C}}$, when necessary (it will still be decidable, under the
finiteness asumptions of Remark-2~(b)). Inconsistency of the set of formulas,
in the `$\epsilon{\mathcal{C}}$-saturated' tag at any state, will be checked up to
$\epsilon$-indistinguishabilty, and referred to as $\epsilon$-inconsistency, or
$\epsilon$-failure. The notion of privacy policy will not need to be modified; that
of its violation will be referred to as $\epsilon$-violation, Under these optional
extensions of $\epsilon$-failure and $\epsilon$-violation, it must be clear that the
statements of Proposition~\ref{exact} continue to be valid. \hfill$\Box$
\vspace*{1mm}
Two small examples of $\epsilon$-local-indistinguishability, before closing this section.
(i) The two sub-tuples ([50--60], M, Maths) and ([40--50], M, Physics), from the last
two tuples on the Hospital's published record in Example 1 (Table~\ref{2}), both
point to Viral--Infection as output; they can thus be seen as
$log(2)$-local-indististinguishable, for the adversary $A$.
(ii) The `Randomized Response' mechanism $RR$~(\cite{Warner65}) can be
modelled as follows. Input is ($X, F_1, F_2$) where $X$ is a Boolean, and $F_1, F_2$
are flips of a coin ($H$ or $T$). $RR$ outputs $X$ if $F_1=H$, $True$ if
$F_1=T$ and $F_2=H$, and $False$ if $F_1=T$ and $F_2=T$. This mechanism is
$log(3)$-LDP : the instances ($True, H, H$), ($True, H, T$), ($True, T,
H$) and ($True, T, T$) are $log(3)$-indistinguishable for output $True$.
($False, H, H$), ($False, H, T$), ($False, T, H$)and ($False, T, T$) are
$log(3)$-indistinguishable for output $False$.
\vspace*{-1em}
\section{ {\large $\epsilon$-Differential Privacy} }~\label{DP}
\vspace*{-2em}
The notion of {\em $\epsilon$-indistinguishability of two given databases} $D, D'$
for an adversary, is more general than that of $\epsilon$-local-indistinguishability
(of pairs of instances of a probabilistic answering mechanism giving the same
output, defined in the previous section). $\epsilon$-indistinguishability is usually
defined only for pairs of databases $D, D'$ that are {\em adjacent} in a certain sense
(cf. below).
There is no uniquely defined notion of adjacence on pairs of databases; in fact,
several are known, and in use in the literature. Actually, a notion of adjacence can
be defined in a generic parametrizable manner (as in e.g., \cite{dpMetrics2013}),
as follows. We assume given a map $\mathbf{f}$ from the set ${\mathcal{D}}$ of all databases
of $m$-tuples (for some given $m > 0$), into some given metric space $(X, d_X)$.
The binary relation on pairs of databases in ${\mathcal{D}}$, defined by $\mathbf{f}_{adj}(D, D') =
d_X(\mathbf{f}(D), \mathbf{f}(D'))$ is then said to define a measure of {\em adjacence} on these
databases. The relation $\mathbf{f}_{adj}$ is said to define an `adjacency relation'.
\begin{defn}~\label{eps-indistinguish}
Let $\mathbf{f}_{adj}$ be a given adjacency relation on a set ${\mathcal{D}}$ of databases, and
${\mathcal{M}}$ a probabilistic mechanism answering queries on the databases in ${\mathcal{D}}$.
- Two databases $D, D' \in {\mathcal{D}}$ are said to be $\mathbf{f}_{adj}$-indistinguishable
under ${\mathcal{M}}$, if and only if, for any possible output ${\mathcal{S}} \subset Range({\mathcal{M}})$, we have
\disp{$ Prob[{\mathcal{M}}(D) \in {\mathcal{S}} ] \le e^{\mathbf{f}_{adj}(D, D')} Prob[{\mathcal{M}}(D') \in {\mathcal{S}}]$.}
- The mechanism ${\mathcal{M}}$ is said to satisfy {\em $\mathbf{f}_{adj}$-differential privacy}
($\mathbf{f}_{adj}$-DP), if and only if the above condition is satisfied for {\em every
pair of databases} $D, D'$ in ${\mathcal{D}}$, and any possible output ${\mathcal{S}} \subset Range({\mathcal{M}})$.
\end{defn}
\noindent
{\em Comments}: (i) Given $\epsilon \ge 0$, the `usual' notions of {\em
$\epsilon$-indistinguishability and $\epsilon$-DP} correspond to the choice of
adjacency $\mathbf{f}_{adj} = \epsilon d_h$, where $d_h$ is the Hamming metric
on databases -- namely, the number of `records' where $D$ and $D'$ differ,
plus the assumption $d_h(D, D') \le 1$ (cf. \cite{dpMetrics2013}).
(ii) In Section~\ref{NewDefn}, we propose a more general notion of adjacency,
based on a different metric defined `value-wise', to serve other purposes as well.
(iii) On disjoint databases, one can work with different adjacency relations, using
different maps to the same (or different) metric space(s),
(iv) The mechanism $RR$ described above is actually $log(3)$-DP, not only
$log(3)$-LDP. To check $DP$, we have to
check all possible pairs of numbers of the form $(Prob[{\mathcal{M}}(x) = y], Prob[{\mathcal{M}}(x') = y])$,
$(Prob[{\mathcal{M}}(x) = y'], Prob[{\mathcal{M}}(x') = y])$, $(Prob[{\mathcal{M}}(x) = y], Prob[{\mathcal{M}}(x') = y'])$, etc.,
where the $x, x'. ...$ are the input instances for $RR$, and $y, y',
...$ the outputs. The mechanism $RR$ has $2^3$ possible input instances for
($X, F_1, F_2$) and two outputs ({\em True, False}); thus 16
pairs of numbers, the distinct ones being $(1/4, 1/4), (1/4, 3/4), (3/4,
1/4)$, $(3/4, 3/4)$; if $(a, b)$ is any such pair, obviously $a \le e^{log(3)} b$.
Thus $RR$ is indeed $log(3)$-DP. \hfill$\Box$
\vspace*{-1mm}
\section{ {\large Comparing Two Nodes on one or more Runs} }~\label{TwoRuns}
\vspace*{-2em}
In the previous two sections, we looked at the issue of `quantifying' the
indistinguishability of two data tuples or databases, under repeated queries
of an adversary $A$. In this section, our concern will be in a sense `orthogonal':
the issue will be that of quantifying how different the probabilistic mechanism's
answers can be, at different moments of $A$'s querying sequence. Remember that
the knowledge of $A$, at any node on the DLTTS of the run corresponding
to the query sequence, is represented as a set of tuples; and also that the data forming
any tuple are assumed implicitly typed, `labeled with' (i.e., under) the headers of the
database $D$. To be able to compare two tuples of the same length, we shall
assume that there is a natural, injective, {\em type-preserving} map from
one of them onto the other; this map will remain implicit in general; two such tuples
will be said to be {\em type-compatible}. If the two tuples are not of the same length,
one of them will be projected onto (or restricted to) a suitable subtuple, so as to
be type-compatible and comparable with the other; if this turns out to be impossible,
the two tuples will be said to be uncomparable.
The quantification looked for will be based on a suitable notion of `distance'
between two {\em sets of type-compatible tuples}. For that, we shall first define
`distance' between any two type-compatible tuples; more precisely, define such
a notion of distance between any two data values under every given header of $D$.
As a first step, we shall therefore begin by defining, for every given header of $D$,
a binary `distance' function on the set of all values that get assigned to the
{\em attributes under that header}, along the sequence of $A$'s queries.
This distance function to be defined will be a {\em metric}: non-negative,
symmetric, and satisfying the so-called Triangle Inequality (cf. below).
The `{\em direct-sum}' of these metrics, taken over all the headers of $D$,
will then define a metric $d$ on the set of all type-compatible tuples of data
assigned to the various attributes, under all the headers of $D$, along the
sequence of $A$'s queries.
The `distance' $d(t, t')$, from any given tuple $t$ in this set to another
type-compatible tuple $t'$, will be defined as the value of this direct-sum
metric on the pair of tuples $(t, t')$; it will, by definition, be calculated
`column-wise' on the base $D$, and also on the intermediary databases along
$A$'s query sequence; note that it will give us a priori an $m$-tuple of numbers,
where $m$ is the number of headers (or columns) in the database $D$.
A single number can then be derived as the sum of the entries in the
$m$-tuple $d(t, t')$. This sum will be denoted as $\overline{d}(t, t')$, and defined
as the distance from the tuple $t$ to the tuple $t'$ in the database $D$.
Finally, if $S, S'$ are any two given finite sets of type-compatible tuples, of data
that get assigned to the various attributes (along the queries), we shall define
the distance from the set $S$ to the set $S'$ as the number
$\rho(S, S') = min \{\, \overline{d}(t, t') \mid t \in S, \, t' \in S' \, \}$
\vspace*{1mm}
Some preliminaries are needed before we can define the `distance' function between the
data values under every given header of $D$. We begin by dividing the headers of the
base $D$ into four classes classes, for clarity of presentation:
\vspace*{-1em}
\begin{itemize}
\item[.] `Nominal': identities, names, attributes receiving literal data
{\em not in any taxonomy} (e.g., gender, city, \dots), finite sets of such data;
\vspace*{-1mm}
\item[.] `Numerval' : attributes receiving numerical values, or bounded
intervals of (finitely many) numerical values;
\item[.] `Numerical': attributes receiving single numerical values (numbers).
\vspace*{-1mm}
\item[.] `Taxoral': attributes receiving literal data in a taxonomy relation.
\end{itemize}
\vspace*{-1mm}
For defining the `distance' between any two values $v, v'$ assigned to an attribute
under a given `Nominal' header of $D$, for the sake of uniformity we agree to
consider every value as a {\em finite set} of singleton values. (In particular, a
singleton value `$x$' will be seen as the set $\{x\}$.) Given two such values
$v, v'$, note first that the so-called {\em Jaccard Index} between them is the number
$jacc(v, v') = |(v \cap v') / (v \cup v') |$, which is a `measure of their similarity';
but this index is not a metric: the {\em triangle inequality} is not satisfied; however,
the Jaccard metric $d_{Nom}(v, v') = 1 - jacc(v, v') = |(v \Delta v') / (v \cup v')|$
does satisfy that property, and will suit our purposes. Thus defined, $d_{Nom}(v, v')$
is a `measure of the dissimilarity' between the sets $v$ and $v'$.
Let $\Tau_{Nom}$ be the set of all data assigned to the attributes under the
`Nominal' headers of $D$, along the sequence of $A$'s queries. Then the above
defined binary function $d_{Nom}$ extends to a metric on the set of all
type-compatible data-tuples from $\Tau_{Nom}$, defined as the `direct-sum'
taken over the `Nominal' headers of $D$.
If $\Tau_{Num}$ is the set of all data assigned to the attributes under the `Numerval'
headers along the sequence of queries by $A$, we also define a `distance' metric
$d_{Num}$ on the set of all type-compatible data-tuples from $\Tau_{Num}$, in a
similar manner. We first define $d_{Num}$ on any couple of values $u, v$
assigned to the attributes under a given `Numerval' header of $D$, then extend it
to the set of all type-compatible data-tuples from $\Tau_{Num}$ (as the direct-sum
taken over the `Numerval' headers of $D$). This will be done exactly as under
the `Nominal' headers: suffices to visualize any finite interval value as a particular
way of presenting a set of numerical values (integers, usually). (In particular, a
single value `$a$' under a `Numerval' header will be seen as the interval value
$[a]$.) Thus defined the (Jaccard) metric distance $d_{Nom}([a, b], [c, d])$ is a
measure of `dissimilarity' between $[a, b]$ and $[c, d]$. .
Between numerical data $x, x'$ under the `Numerical' headers, the distance we shall
work with is the euclidean metric $|x - x'|$, {\em normalized as}:
$d_{eucl}(x, x') = |x - x'| / D$, where $D > 0$ is a fixed finite number, bigger than
the maximal euclidean distance between the numerical data on the databases
and on the answers to $A$'s queries.
On the data under the `Taxoral' headers, we choose as distance function the metric
$d_{wp}$, defined in Lemma~\ref{wpmetric} (cf. {\em Appendix}) between the
nodes of any Taxonomy tree.
Note that the `datawise distance functions' defined above are {\em all with values in
the real interval} $[0, 1]$. (This is also one reason for our choice of the distance
metric on Taxonomy trees.) This fact is of importance, for comparing the metric $\rho$
we defined above with the Hamming metric, cf. Section~ \ref{NewDefn}.
\vspace*{1mm}\noindent
{\bf An additonal role for Oracle ${\mathcal{O}}$}:
In Section~\ref{CompScheme} below, we present a procedure for comparing the
knowledge of an adversary $A$ at different nodes of the DLTTS that models the
`distributed sequence' of $A$'s queries on a given database $D$. The comparison
can be with respect to any given `target' dataset $T$ (e.g., a privacy policy
$P$ on $D$). In operational terms, so to say, the oracle mechanism ${\mathcal{O}}$ of
the DLTTS keeps the target dataset `in store'; and as said earlier, a first role
for the oracle ${\mathcal{O}}$ of the DLTTS is to keep a watch on the deduction of the target
dataset by the adversary $A$ at some node. The additional second role that we
assign now to the oracle ${\mathcal{O}}$, is to publish information on the distance of $A$'s
saturated knowledge $\overline{\tau}(s)$, at any given node $s$, to the target dataset $T$.
This distance is calculated wrt the distance $\rho$, defined above as the minimal
distance $\overline{d}(t, t')$ between the tuples $t \in \overline{\tau}(s), t' \in T$, where $\overline{d}$
is the direct sum of the `column-wise distances' between the data on the tuples.
Before presenting the comparison schema, here is an example to illustrate how
the notions developed above operate in practice.
\vspace*{1mm}\noindent
{\bf Example 1 bis}. We go back to the Hospital-CoVid example seen earlier,
more particularly its Table~2, reproduced here:
\begin{table}[h]
\centering
\begin{tabular}{| c| c| c| c|c|}
\hline
Age & Gender & Dept. & Ailment \\
\hline\hline
$\ell_1$ & $[20-30]$ & F & Chemistry & Heart-Disease \\
$\ell_2$ & $[40-50]$ & M & Chemistry & Cancer \\
$\ell_3$ & $[20-30]$ & F & Physics & Viral-Infection \\
$\ell_4$ & $[50-60]$ & M & Maths & Viral-Infection \\
$\ell_5$ & $[40-50]$ & M & Physics & Viral-Infection \\
\hline
\end{tabular}
\caption{Hospital's public record recalled}
\end{table}
\noindent
`Gender' and `Dept.'. are the `Nominal' headers in this record, `Age' is `Numerval'
and `Ailment' is `Taxoral'. We are interested in the second, fourth and fifth tuples on
the record, respectively referred to as $l_2, l_4, l_5$. The `target set' of
(type-compatible) tuple in this example is taken as the (negation of the) privacy policy
specified, namely the tuple $T = (John, 46, M, \#, CoVid)$.
We compute now the distance $\overline{d}$ between the target $T$, and the
three tuples $l_2, l_4, l_5$. This involves only the subtuple $L = (46, M, \#, CoVid)$
of $T$: \par
. $\overline{d}(l_2, L) = d_{Num}(l_2, L) + d_{Nom}(l_2, L) + d_{wp}(L_2, L) $ \par
\hspace*{1.5cm} $ = (1 - 1/10) + 0 + (1 - 2/5) = 9/10 + 3/5 = 15/10 $ \par
. $\overline{d}(l_4, L) = d_{Num}(l_2, L) + d_{Nom}(l_4, L) + d_{wp}(L_4, L) $ \par
\hspace*{1.5cm} $ = (1 - 0) + 0 + (1 - 4/5) = 1 + 1/5 = 6/5 $ \par
. $\overline{d}(l_5, L) = d_{Num}(l_5, L) + d_{Nom}(l_5, L) + d_{wp}(L_5, L) $ \par
\hspace*{1.5cm} $ = (1-1/10) + 0 + (1 - 4/5) = 9/10 + 1/5 = 11/10$ \par
\noindent
The tuple $l_2$ is the farthest from the target, while $l_5$ is the closest. This
`explains' that the adversary can choose the branch on the transition that leads
to a state where $l_5$ is added to his/her knowledge. This is more formally
detailed in the procedure presented below. \hfill$\Box$
\vspace*{-1em}
\subsection{{\small A (Non-Deterministic) Comparison Procedure}}~\label{CompScheme}
\vspace*{-2em}
\noindent
$\cdot$ Given: DLTTS associated with a querying sequence, by adversary $A$
on given database $D$; and {\em a Target set} of tuples $T$.
\noindent
$\cdot$ Given: Two states $s, s'$ on the DLTTS with their saturated tags
$l = \overline{\tau}(s)$, $l' = \overline{\tau}(s')$ at $s, s'$. Target $T$ {\em assumed} not in the saturated
tags $l$ or $l'$. \\ (i.e. Distances to the target $T$ are non-informative.)
\vspace*{1mm}\noindent
$\cdot$ Objective: {\em Continue under $s$, or under $s'$ ?}
- $config_1$: successor states $s_1, \dots, s_n$ for a transition from $s$,
with probability distribution $p_1, \dots, p_n$; and $l_1, \dots, l_n$
are the tags at $s_1, \dots, s_n$.
- $config_2$: successor states $s'_1, \dots, s'_m$ for a transition from $s'$,
with probability distribution $p'_1, \dots, p'_m$; and $l'_1, \dots, l'_m$
are the tags at $s'_1, \dots, s'_m$.
\vspace*{1mm}\noindent
(i) Compute $d_i = \rho(l_i, T), i \in 1 \cdots n$, \,and\, $d'_j =
\rho(l'_j, T), j \in 1 \cdots m$. ~ Define:
\disp{$d_{min}(s, T) = min\{d_i \mid 1 \le i \le n\}, \,
\; \; \; d'_{min}(s', T) = min\{d'_j \mid 1 \le j \le m\}$}
\vspace*{1mm}\noindent
(ii) {\em Select $config_1$, and discard $config_2$}, IF the following
{\em two conditions hold}:
\disp{
$ d_{min}(s, T) \, \le \, d'_{min}(s', T)$ \par
$\exists$ an $i, 1 \le i \le n$, such that $d_i = d_{min}(s, T)$ and \par
$p_i \ge \, p'_j$ \, for any \, $j, 1 \le j \le m$, where $d'_j = d'_{min}(s', T)$
}
\vspace*{1mm}\noindent
iii) IF {\em conditions} are not satisfied, EXIT.
\vspace*{-1em}
\section{{\large New Metric for Indistinguishability and DP}}~\label{NewDefn}
\vspace*{-1.5em}
Given a randomized/probabilistic mechanism ${\mathcal{M}}$ answering the queries on databases,
and an $\epsilon \ge 0$, recall that the $\epsilon$-indistinguishability of any two given
databases under ${\mathcal{M}}$, and the notion of $\epsilon$-DP for ${\mathcal{M}}$, were both defined
in Definition~\ref{eps-indistinguish} (Section~\ref{DP}), based first on a
hypothetical map $\mathbf{f}$ from the set of all the databases concerned, into some
given metric space $(X, d_X)$, and an `adjacency relation' on databases defined as
$ \mathbf{f}_{adj}(D, D') = d_X(\mathbf{f} D, \mathbf{f} D')$, which was subsequently instantiated to
$\mathbf{f}_{adj} = \epsilon d_h$, where $d_h$ is the Hamming metric between databases.
It must be observed here, that {\em the Hamming metric is defined only between databases
with the same number of columns}, and usually only with all data of the same type.
In this subsection, our objective is to propose a more general notion of adjacency, based on
the distance metric $\rho$ defined above, between type-compatible tuples on databases
with data of multiple types. In other words, our ${\mathcal{D}}$ here will be the set of all
databases, {\em not necessarily all with the same number of columns, and with data of
several possible types} as mentioned in the Introduction. We define then a binary
relation $\mathbf{f}^{\rho}_{adj}(D, D')$ between databases $D, D'$ in the set ${\mathcal{D}}$ by
setting $ \mathbf{f}^{\rho}_{adj}(D, D') = \rho(D, D')$, visualizing $D, D'$ as sets of
type-compatible data tuples.
Given $\epsilon$, we can then define the notion of $\epsilon_{\rho}$-indistinguishabilty of
two databases $D, D'$ under a (probabilistic) answering mechanism ${\mathcal{M}}$, as well as the
notion of $\epsilon_{\rho}$-DP for ${\mathcal{M}}$, exactly as in Definition~\ref{eps-indistinguish}, by
replacing $\mathbf{f}_{adj}$ first with the relation $ \mathbf{f}^{\rho}_{adj}$, and subsequently with
$\epsilon\rho$. The notions thus defined are {\em more general} than those presented
earlier in Section~\ref{DP} with the choice $\mathbf{f}_{adj} = \epsilon d_h$.
An example will illustrate this point.
\vspace*{1mm}\noindent
{\bf Example 4}. We go back to the `Hospital's public record' of our
previous example, with the same notation. For this example, we shall
assume that the mechanism ${\mathcal{M}}$ answering a query for `ailment information
involving men' on that record, returns the tuples $l_2, l_4, l_5$ with the
probability distribution $0, 2/5, 3/5$, respectively.
Let us look for the minimum value of $\epsilon \ge 0$, for which these three tuples
will be $\epsilon_{\rho}$-indistinguishable under the mechanism ${\mathcal{M}}$.
The output $l_2$, with probability $0$, will be $\epsilon_{\rho}$-distinguishable
for any $\epsilon\ge 0$. Only the two other outputs $l_4, l_5$ need to be considered.
We first compute the $\rho$-distances between these two tuples:
$ \overline{d}(l_4, l_5) = (1 - \frac{1}{20}) + 0 + 1 + 0 = 39/20$. The condition for $l_4$ and
$l_4$ to be $\epsilon_{\rho}$-indistinguishable under ${\mathcal{M}}$ is thus:
\disp{ $ (2/5 ) \le e^{(39/20) \epsilon}*(3/5) \;\; and \;\; (3/5) \le e^{(39/20)
\epsilon}*(2/5)$,}
i.e., $\epsilon \ge (20/39)*ln(3/2)$.
In other words, for any $\epsilon \ge (20/39)*ln(3/2)$, the two tuples $l_4$
and $l_5$ will be $\epsilon_{\rho}$-indistinguishable; and for values of $\epsilon$ with
$0 \le \epsilon < (20/39)*ln(3/2)$, these tuples will be $\epsilon_{\rho}$-distinguishable.
For the $\epsilon$-indis\-tinguishabilty of these tuples wrt the Hamming metric $d_h$,
we proceed similarly: the distance $d_h(l_4, l_5)$ is by definition the number
of `records' where these tuples differ, so $d_h(l_4, l_5) = 2$. So the condition on
$\epsilon \ge 0$ for their $\epsilon$-indistinguishabilty wrt $d_h$ is:
$(3/5) \le e^{2 \epsilon}*(2/5)$,\, i.e., \, $\epsilon \ge (1/2)*ln(3/2)$ .
In other words, if these two tuples are $\epsilon_{\rho}$-indistinguishables wrt $\rho$
under ${\mathcal{M}}$ for some $\epsilon$, then they will be $\epsilon$-indistinguishable wrt
$d_h$ for the same $\epsilon$. But the converse is not true, since
$(1/2)*ln(3/2) < (20/39)*ln(3/2)$. Said otherwise: {\em ${\mathcal{M}}$ $\epsilon$-distinguishes
more finely with $\rho$, than with $d_h$}. \hfill$\Box$
\vspace*{1mm}
{\bf Remark}~4: The statement!``${\mathcal{M}}$ $\epsilon$-distinguishes more finely with
$\rho$, than with $d_h$'', is {\em always true} (not just in Example~4). For the following
reasons: The records that differ `at some given position' on two bases $D, D'$ are
always at distance $1$ for the Hamming metric $d_h$, by definition, whatever be
the type of data stored at that position.
Now, if the data stored at that position `happened to be' numerical, the usual
euclidean distance between the two data could have been (much) bigger than
their Hamming distance $1$; precisely to avoid such a situation, our definition of
the metric $d_{eucl}$ on numerical data `normalized' the euclidean distance,
to ensure that their $d_{eucl}$-distance will not exceed their Hamming distance.
Thus, all the `record-wise' metrics we have defined above have their values in
$[0,1]$, as we mentioned earlier; so, whatever the type of data at corresponding
positions on any two bases $D, D'$, the $\rho$-distance between the records will
never exceed their Hamming distance. That suffices to prove our statement above.
The Proposition below formulates all this, more precisely:
\begin{propn}
Let ${\mathcal{D}}_m$ be the set of all databases with the same number $m$ of columns,
over a finite set of given data, and ${\mathcal{M}}$ a probabilistic mechanism answering
queries on the bases in ${\mathcal{D}}$. Let $\rho$ be the metric (defined above) and $d_h$
the Hamming metric, between the databases in ${\mathcal{D}}$, and suppose given
an $\epsilon \ge 0$.
- If two databases $D, D' \in {\mathcal{D}}_m$ are $\epsilon_{\rho}$-indistinguishable under ${\mathcal{M}}$
wrt $\rho$, then they are also $\epsilon$-indistinguishable under ${\mathcal{M}}$ wrt $d_h$.
- If the mechanism ${\mathcal{M}}$ is $\epsilon_{\rho}$-DP on the bases in ${\mathcal{D}}_m$ (wrt $\rho$),
then it is also $\epsilon$-DP (wrt $d_h$) on these bases.
\end{propn}
The idea of `normalizing' the Hamming metric between numerical databases (with the
same number of columns) was already suggested in \cite{dpMetrics2013} for the same
reasons. When only numerical databases are considered, the metric $\rho$ that
we have defined above is the same as the `normalized Hamming metric' of
\cite{dpMetrics2013}. Our metric $\rho$ must actually be seen as a generalization
of that notion, to directly handle bases with more general types of data:
anonymized, taxonomies, \dots
\section{ {\large Related Work and Conclusion} }
A starting point for the work presented here was the observation that databases
could be distributed over several `worlds' in general, and querying such bases
leads to answers which would also be distributed. Conceivably, to such distributed
answers one could assign probability distributions of relevance or pertinence to
the query. The probabilistic automata of Segala (\cite{Segala95a,Segala95b}) are
perhaps among the first logical structures proposed to model such a vision, in
particular with outputs. Distributed Transition Systems (DTS) appeared a little
later; most of them had as objective the behavioral analysis of the distributed
transitions, based on traces or on simulation/bisimulation. Quasi- or pseudo-
or hemi- metrics, suitably defined, were essential for the reasonings
employed, e.g., as in~\cite{Fast2018,PTS2019,LBr-SystMetrics09}.
Our quest for a metric based vision for privacy analysis has certainly been
influenced by these works, although not for the same objectives.
As the developments presented in our work show, our lookout was for a
{\em syntax}-based metric that can directly handle data of
`mixed types'; they can be numbers or literals , but can also be `anonymized'
as intervals or sets; they can also be taxonomically related to each other
(in a tree structure). Moreover, the metric we were looking for was intended as a
syntactic measure to express how far or how close a querying process on a database
gets to a given privacy policy on that base. Part of future work could be
to define a `divergence measure' (as a quasi-metric?) between two given nodes
on a DLTTS that models a querying process, in terms of the respective knowledge
distributions at the two nodes, independently of any notion of a given target data set.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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\section{Introduction}
What are the conditions that force a matrix of differentiable functions to commute with its elementwise derivative?
This problem, discussed in a letter from I. Schur to H. Wielandt \cite{Sch34}, has been
discussed in a large number of papers \cite{Ama54,Asc50,Asc52,BogC59,Die74,Eps63,Eru46,Gof81,Hel55,KotE82,
Kuz76,Mar65,Mar67,Par72,Pet79,Ros65,Sch52,Ter55}. However, these authors were unaware of Schur's letter and did not find some of its principal results. A summary and a historical discussion of the problem and several extensions thereof are presented by Evard in \cite{Eva85,Eva95}, where the study of the topic is dated back to the 1940s and 1950s, but
Schur's letter shows that it already appeared in Schur's lectures in the 1930s, if not earlier.
\if {
We do not know which set of functions Schur had in mind,
whether Schur meant this to be the set of analytic functions
or meromorphic functions in one variable. He
may even have had the rational functions in one variable over the
complex numbers in mind. And we do not know which arguments Schur used to reach conclusions concerning matrices of small size at the end of his letter. Though our arguments remain close to those of Schur, we will take an algebraic approach and discuss the results in Schur's letter in differential fields.
This is also the approach that was taken in \cite{AdkEG93} and in unpublished notes of Guralnick~\cite{Gur05}, where results related to ours using differential fields were discussed.
This approach has also been taken in
} \fi
The content of the paper is as follows.
In Section~\ref{letter} we present a facsimile of Schur's letter to
Wielandt and its English translation. In Section~\ref{sec:discussion} we discuss Schur's letter and we motivate our use of differential fields.
In Section~\ref{sec:prelim} we introduce our notation and reprove Frobenius result on Wronskians. In Section~\ref{sec:ct1} we discuss the results that characterize
the matrices of Type~1 in Schur's letter and in our main Section~\ref{sec:triandia} we discuss
the role played by diagonalizability and triangularizability of the matrix in the commutativity of the matrix and its derivative.
We also present several illustrative examples in Section~\ref{sec:exs}
and we state an open problem in Section~\ref{conclusion}.
\section{A letter from Schur to Wielandt}\label{letter}
Our paper deals with the following letter from Issai Schur to his PhD
student Helmut Wielandt. See the facsimile below.
\begin{figure}
\scalebox{.8}{\includegraphics{schur_brief_voll}}
\vspace{0.5cm}
\label{FigOne}
\end{figure}
\begin{figure}
\scalebox{.8}{\includegraphics{schur_brief_voll2}}
\vspace{0.5cm}
\label{FigTwo}
\end{figure}
\begin{figure}
\scalebox{.8}{\includegraphics{schur_brief_voll3}}
\vspace{0.5cm}
\label{FigThree}
\end{figure}
\begin{figure}
\scalebox{.8}{\includegraphics{schur_brief_voll4}}
\vspace{0.5cm}
\label{FigFour}
\end{figure}
Translated into English, the letter reads as follows:
{\it
Lieber Herr Doktor!\hfill Berlin, 21.7.34
You are perfectly right. Already for $3\leq n<6$
not every solution of the
equation $M M'=M'M$ has the form
\eq{1} M_1 =\sum_{\lambda} f_\lambda C_\lambda, \en
where the $C_\lambda$ are pairwise commuting constant matrices. One
must also consider the type
\eq{2} M_2=(f_\alpha g_\beta), \quad (\alpha,\beta=1,\ldots n), \en
where $f_1,\ldots f_n$, $ g_1,\ldots,g_n$ are arbitrary functions
that satisfy the conditions
$$ \sum_\alpha f_\alpha g_\alpha= \sum_\alpha f'_\alpha g_\alpha=0$$
and therefore also
$$ \sum_\alpha f_\alpha g'_\alpha=0.$$
In this case we obtain
$$ M^2 =M M'=M'M=0.$$
In addition we have the type
\eq{3} M_3=\phi E+M_2, \en
with $M_2$ of type (\ref{2}). \footnote{Note that $E$ here denotes the identity matrix.}
From my old notes, which I did not present correctly in my lectures,
it can be deduced that for $n<6$ every solution of $M M'=M'M$
can be completely decomposed by means of constant similarity
transformations into matrices of type (\ref{1}) and (\ref{3}).
Only from $n=6$ on there are also other cases.
This seems to be correct.
But I have not checked my rather laborious
computations (for $n=4$ and $n=5$).
I concluded in the following simple manner that one can restrict oneself to
the case where $M$ has only one characteristic root (namely $0$): If $M$
has two different characteristic roots, then one can determine
a rational function $N$ of $M$ for which $N^2=N$ but
not $N=\phi E$. Also $N$ commutes with $N'$. It follows from $N^2=N$
that $2NN'=N'$, thus $2N^2N'= 2NN'=NN'$. This yields
$2 NN'=N'=0$, i.e., $N$ is constant.
Now one can apply a constant similarity transformation to $M$ so that
instead of $N$ one achieves a matrix of the form
$$\mat{cc} E & 0 \\ 0 & 0 \rix.$$
This shows that $M$ can be decomposed completely
by means of a constant
similarity transformation.
One is led to type (\ref{2}) by studying the case $M^2=0$, $\rank M=1$.
Already for $n=4$ also the cases $M^2=0$, $\rank M=2$, $M^3=0$ need to be
considered.
Type (\ref{1}) is completely characterized by the property
that $M,M',M'', \ldots $ are pairwise
commuting. This is not only necessary but also sufficient.
For, if among the $n^2$ coefficients $f_{\alpha \beta}$ of $M$ exactly
$r$ are linearly independent over the domain of constants,
then one can write
$$ M=f_1 C_1+\cdots +f_rC_r,$$
($C_s$ a constant matrix), where $f_1, \ldots, f_r$ satisfy no
equation $\sum_{\alpha} \mbox{\rm const}\ f_\alpha=0$.
Then
$$ M^{(\nu)}= f_1^{(\nu)} C_1+ \cdots +f_r^{(\nu)} C_r,
\quad (\nu=1,\ldots,r-1).$$
Since the Wronskian determinant
$$\left |\mat{ccc} f_1 &\ldots& f_r \\
f_1' &\ldots& f_r'\\
& \vdots & \rix\right |
$$
cannot vanish identically, one obtains equations of the form
$$ C_s=\sum_{\sigma=0}^{r-1} \phi_{s \sigma} M^{(\sigma)}.$$
If $M,M',M'', \ldots, M^{(r-1)}$ are pairwise
commuting, then the same is true also for
$C_1,\ldots C_r$ and thus $M$ is of type (\ref{1}). This implies
furthermore that $M$ belongs to type (\ref{1}) if
$M^n$ is the highest\footnote{We think that Schur means \emph{lowest} here.} power of $M$ that equals $0$.
In the case $n=3$ one therefore only needs to consider type (\ref{2}).
\hfill With best regards
\hfill Yours, Schur
}
\bigskip
\section{Discussion of Schur's letter}\label{sec:discussion}
This letter was found in Helmut Wielandt's mathematical Nachlass when it was collected by Heinrich Wefelscheid and Hans Schneider not long after Wielandt's death in 2001. We may therefore safely assume that Schur's recent student Wielandt is the "Herr Doktor" to whom the letter is addressed. Schur's letter begins with a reference to a previous remark of Wielandt's which corrected an incorrect assertion by Schur. We can only guess at this sequence of events, but perhaps a clue is provided by Schur's reference to his notes which he did not present correctly in his lectures. Could Wielandt have been in the audience and did he subsequently point out the error? And what was this error? Very probably it was that every matrix of functions that commutes with its derivative is given by (1) (matrices called Type 1), for Schur now denies this and displays another type of matrix commuting with its derivative (called Type 2). He recalls that in his notes he claimed that for matrices of size 5 or less every such matrix is of Type 1, 2 or 3, where Type 3 is obtained from Type 2 by adding a scalar function times the identity. This is not correct because there is also the direct sum of a size 2 matrix of Type 1 and a size 3 matrix of Type 2, we prove this below.
We do not know why Schur was interested in the topic of matrices of functions that commute with their derivative, but
it is probably a safe guess that this question came up in the context of solving differential equations, at least this is
the motivation in many of the subsequent papers on this topic.
As one of the main results of his letter, Schur shows that an idempotent that commutes with its derivative is a constant matrix and, without further explanation, concludes that one can restrict oneself to matrices with a single eigenvalue. The latter observation raises several questions. First, Schur does not say which functions he has in mind. Second, his argument follows from a standard decomposition of a matrix by a similarity into a direct sum of matrices {\em provided that} the eigenvalues of the matrix are functions of the type considered. But this is not true in general, for example the eigenvalues of a matrix of rational functions are algebraic functions.
We wonder whether Schur was aware of this difficulty and we shall return to it at the end of this section.
Then Schur shows a matrix of size $n$ is of Type 1 if and only if it and its first $n-1$ derivatives are pairwise commutative. His proof is based on a result of Frobenius \cite{Fro1874} that a set of functions is linear independent over the constants if and only if their Wronskian determinant is nonzero. Frobenius, like Schur, does not explain what functions he has in mind. In fact, Peano \cite{Pea1889} shows that there exist real differentiable functions that are linearly independent over the reals whose Wronskian is $0$. This is followed by Bocher \cite{Boc00} who shows that Frobenius' result holds for analytic functions and investigates necessary and sufficient conditions in \cite{Boc01}. A good discussion of this topic can be found in \cite{BosD10}.
We conclude this section by explaining how our exposition has been influenced by some of the observation above. As we do not know what functions Schur and Frobenius had in mind, we follow \cite{AdkEG93} and some unpublished notes of Guralnick \cite{Gur05} and set Schur's results and ours in terms of differential fields (which include the field of rational functions and the quotient field of analytic functions over the real or complex numbers). Since we do not know how Schur concludes that it is enough to consider matrices with a single eigenvalue, we derive our results from standard matrix decomposition (our Lemma \ref{decomp} below) which does not assume that all eigenvalues lie in the differential field under consideration.
\section{Notation and preliminaries}\label{sec:prelim}
A {\em differential field} $\mathbb F$ is an (algebraic) field together
with an additional operation (the derivative), denoted by ${}'$ that satisfies $(a+b)' = a'
+ b'$ and $(ab)' = ab' + a'b$ for $a,b \in \mathbb F$. An element $a
\in \mathbb F$ is called a {\em constant} if $a' = 0$. It is easily
shown that the set of constants forms a subfield $\mathbb K$ of $\mathbb F$
with $1 \in \mathbb K$. Examples are provided by the rational functions over the real or complex numbers
and the meromorphic functions over the complex numbers.
In what follows we consider a (differential) field $\mathbb F$
and matrices $M=[m_{i,j}]\in \mathbb F^{n,n}$.
The main condition that we want to analyze is when $M\in \mathbb F^{n,n}$
commutes with its derivative,
\begin{equation}\label{c1}
MM'=M'M.
\end{equation}
As $M\in \mathbb F^{n,n}$, it has a minimal and a characteristic polynomial, and $M$ is called {\em nonderogatory} if the characteristic polynomial is equal to the minimal polynomial, otherwise it is called {\em derogatory}. See \cite{HorJ85}.
In Schur's letter the following
three types of matrices are considered.
%
\begin{definition}
Let $M\in \mathbb F^{n,n}$. Then $M$ is said to be of
\begin{itemize}
\item {\em Type 1\/} if
\[
M =\sum_{j=1}^{k} f_j C_j,
\]
where $f_j\in \mathbb F$, and $C_j\in \mathbb K^{n,n}$, for $j=1,\ldots,k$,
and the $C_j$ are pairwise commuting;
\item {\em Type 2\/} if
\[
M=f g^T,\
\]
with $f,g\in \mathbb F^{n}$, satisfying $f^Tg=f^Tg'=0$;
\item {\em Type 3\/} if
\[
M=hI+\widetilde M,
\]
with $h\in \mathbb F$ and $\widetilde M$ is of Type~2.
\end{itemize}
\end{definition}
Schur's letter also mentions the condition that all derivatives of $M$ commute, i.e.,
\begin{equation}\label{c6}
M^{(i)}M^{(j)}=M^{(j)}M^{(i)}\ \mbox{\rm for all nonnegative integers}\ i,j.
\end{equation}
To characterize the relationship between all these properties, we first recall
several results from Schur's letter and from classical algebra.
\begin{lemma} \label{insight} Let $\mathbb F$ be a differential field with field of constants
$\mathbb K$. Let $N$ be an idempotent matrix in
$\mathbb {F}^{n,n}$ that commutes with $N'$. Then $N \in \mathbb K^{n,n}$.
\end{lemma}
\proof (See Schur's letter.) It follows from $N^2 = N$ that $2NN' =
N'$. Thus $2NN' = 2N^2N' = NN'$ and this implies that $0 = 2NN' = N'$.
\eproof
Another important tool in our analysis will be the following result which in its original form
is due to Frobenius~\cite{Fro1874}, see Section~\ref{sec:discussion}.
We phrase and prove the result in the context of differential fields.
\begin{theorem}\label{frob}
Consider a differential field $\mathbb F$ with field of constants $\mathbb K$. Then
$y_1,\ldots,y_r\in \mathbb F$ are linearly dependent over $\mathbb K$ if and only if the columns of the \emph{Wronski matrix}
\[
Y=\left[ \begin{array}{cccc} y_1 & y_2 & \dots & y_r \\
y_1' & y_2' &\dots & y_r'\\
\vdots & \vdots & \ddots & \vdots\\
y_1^{(r-1)} & y_2^{(r-1)} &\dots & y_r^{(r-1)}
\end{array} \right ],
\]
are linearly dependent over $\mathbb F$.
\end{theorem}
\proof
We proceed by induction over $r$. The case $r=1$ is trivial.
Consider the Wronski matrix $Y$ and the lower triangular matrix
\[
Z=\left[ \begin{array}{cccc} z & 0 & \dots & 0 \\
c_{2,1}z' & z &\dots & 0\\
\vdots & \vdots & \ddots & \vdots\\
c_{n,1}z^{(n-1)} & c_{n,2}z^{(n-2)} &\dots & z
\end{array} \right ],
\]
with $c_{i,j}$ appropriate binomial coefficients such that
\[
ZY=\left[ \begin{array}{cccc} z y_1& z y_2& \dots & z y_r \\
(z y_1)' & (z y_2)' &\dots & (z y_r)'\\
\vdots & \vdots & \ddots & \vdots\\
(z y_1)^{(n-1)} & (z y_2)^{(n-1)} &\dots & (z y_r)^{(n-1)}
\end{array} \right ].
\]
Since $\mathbb F$ is a differential field, we can choose $z=y_1^{-1}$ and obtain
that
\[
ZY=\left[ \begin{array}{cccc} 1& y_1^{-1} y_2& \dots & y_1^{-1} y_r \\
0 & (y_1^{-1} y_2)' &\dots & ( y_1^{-1} y_r)'\\
\vdots & \vdots & \ddots & \vdots\\
0 & (y_1^{-1} y_2)^{(n-1)} &\dots & ( y_1^{-1} y_r)^{(n-1)}
\end{array} \right ].
\]
It follows that the columns of $Y$ are linearly dependent over $\mathbb F$ if and only if the columns
of
\[
\left[ \begin{array}{ccc}
(y_1^{-1} y_2)' &\dots & ( y_1^{-1} y_r)'\\
\vdots & \ddots & \vdots\\
(y_1^{-1} y_2)^{(n-1)} &\dots & ( y_1^{-1} y_r)^{(n-1)}
\end{array} \right ]
\]
are linearly dependent over $\mathbb F$, which, by induction, holds
if and only if $(y_1^{-1} y_2)' ,\dots , ( y_1^{-1} y_r)'$
are linearly dependent over $\mathbb K$, i.e., there exist coefficients
$b_2,\ldots,b_r\in \mathbb K$, not all $0$,
such that
\[
b_2 (y_1^{-1} y_2)'+\cdots +b_r( y_1^{-1} y_r)'=0.
\]
Integrating this identity, we obtain
\[
b_2 (y_1^{-1} y_2)+\cdots +b_r( y_1^{-1} y_r)=-b_1
\]
for some integration constant $b_1\in \mathbb K$, or equivalently
\[
b_1 y_1+\cdots + b_r y_r=0.
\]
{}\vskip -1cm\hskip 12cm \eproof
Theorem~\ref{frob} implies in particular that the columns of the Wronski matrix $Y$
are linearly independent over $\mathbb F$ if and only if they are linearly independent over $\mathbb K$.
\begin{remark}{\rm
Theorem~\ref{frob} is discussed from a formal algebraic point of view, which however includes the cases of complex analytic functions and rational functions over a field, since these are contained in differential fields. Necessary and sufficient conditions for Theorem~\ref{frob} to hold for other functions were proved in \cite{Boc01} and discussed in many places, see, e.g., \cite{BosD10,Mei61} and \cite[Ch. XVIII]{Mui33}.
}
\end{remark}
\section{Characterization of matrices of Type~1} \label{sec:ct1}
In this section we discuss relationships among the various properties introduced in Schur's letter and in the previous section. This will give, in particular, a characterization of matrices of Type~1.
In his letter, Schur proves the following result.
\begin{theorem}\label{th:allcommute}
Let $\mathbb F$ be a differential field. Then $M\in {\mathbb F}^{n,n}$
is of Type~1 if and only if it satisfies condition (\ref{c6}), i.e., $M^{(i)}M^{(j)}=M^{(j)}M^{(i)}$ for all nonnegative integers $i,j$.
\end{theorem}
\proof (See Schur's letter.)
If $M$ is of Type~1, then $M =\sum_{j=1}^{k} f_j C_j$ and the $C_j\in \mathbb K^{n,n}$ are pairwise commuting, which immediately implies (\ref{c6}). For the converse,
Schur makes use of Theorem~\ref{frob}, since if among the $n^2$ coefficients
$m_{i,j}$ exactly $r$ are linearly independent over $\mathbb K$, then
\[
M=f_1C_1+\cdots+f_rC_r,
\]
with coefficients $C_i\in \mathbb K^{n,n}$, where
$f_1,\ldots,f_r$ are linearly independent over $\mathbb K$.
Then
\[
M^{(i)}=f_1^{(i)}C_1+\cdots +f_r^{(i)}C_r,\qquad i=1,\ldots,r-1.
\]
By Theorem~\ref{frob}, the columns of the associated Wronski matrix
are linearly independent, and hence each of the $C_i$ can be expressed
as
\[
C_i=\sum_{j=0}^{r-1} g_{i,j} M^{(j)}.
\]
Thus, if condition~(\ref{c6}) holds, then the $C_i$, $i=1,\ldots,r$,
are pairwise commuting and thus $M$ is of Type~1.
\eproof
Using this result we immediately have the following Theorem.
\begin{theorem}\label{th:nondero}
Let $\mathbb F$ be a differential field with field of constants
$\mathbb K$. If $M\in \mathbb F^{n,n}$ is nonderogatory and $MM' = M'M$,
then $M$ is of Type~1.
\end{theorem}
\proof
If $M$ is nonderogatory then all matrices that commute with $M$ have the form $p(M)$, where $p$ is a polynomial with coefficients in $\mathbb F$, see \cite{DraDG51,HorJ85}. Thus $MM' = M'M$ implies that $M'$ is a polynomial in $M$.
But then every derivative $M^{(j)}$ is a polynomial in $M$ as well and
thus (\ref{c6}) holds which by Theorem~\ref{th:allcommute} implies that $M$ is of Type~1.
\eproof
The following example from \cite{Asc52,Eva85} of a Type~2 matrix shows that one cannot easily drop the
condition that the matrix is nonderogatory.
\begin{example}\label{eva3x3}
{\rm Let
\[ f =\mat{c} 1\\ t \\ t^2\rix,\qquad g =\mat{c} t^2\\ -2 t\\ 1
\rix,
\]
then $f^T g=0$ and $f^T g'=0$, hence
\begin{equation}\label{evaM}
M_a := g f^T= \mat{ccc} t^2 & t^3& t^4\\
-2 t& -2 t^2 & -2 t^3\\
1& t & t^2\rix,
\end{equation}
is of Type~2. Since $M_a$ is nilpotent with $M_a^2=0$ but $M_a\neq 0$ and the rank is $1$,
it is derogatory. One has
\[
M_a'=
\mat{ccc} 2t & 3t^2& 4t^3\\
-2 & -4t& -6t^2\\
0 & 1 & 2 t
\rix,\qquad
M_a''= \mat{ccc} 2 & 6t & 12 t^2 \\
0 & -4 & -12 t \\
0 & 0 & 2\rix,
\]
and thus $ M_a M_a'=M_a' M_a=0$. By the product rule
it immediately follows that $M_a M_a''=M_a''M_a$, but
\[
M_a' M_a''= \mat{ccc}
4t& 0& -4t^3\\
-4 & 4t &12t^2\\
0 & -4 & -8t
\rix \neq M_a'M_a''=\mat{ccc}
-8t &-6t^2 & -4t^3\\
8 & 4t & 0\\
0 & 2 & 4t\rix.
\]
Therefore, it follows from Theorem~\ref{th:allcommute} that $M_a$ is not of Type~1.
For any dimension $n\geq 3$, one can construct an example of Type~2 by choosing $f \in {\mathbb F}^n$, setting $F = [f,f']$ and then choosing $g$ in the nullspace of $F^T$.
Then $fg^T$ is of Type~2.
}
\end{example}
Actually every nilpotent matrix function $M$ of rank one
satisfying $MM' = M'M$ is of the form $M=fg^T$ and hence of Type~2.
This follows immediately because if $M=fg^T$ and $M^2=0$ then $g^Tf=0$
and hence $g^Tf'+(g^T)'f=0$. Then it follows from $MM' = M'M$
that $fg^T(f(g^T)' + f'g^T) = (g^Tf')fg^T= (f(g^T)' + f'g^T)fg^T = (g^T)'f fg^T$
which implies that $g^Tf' = f^Tg'$ and hence $g^Tf' = f^Tg' = 0$.
\section{Triangularizability and Diagonalizability}\label{sec:triandia}
In his letter Schur claims that it is sufficient to consider the case
that $M\in \mathbb F^{n,n}$ is triangular with only one eigenvalue. This follows from his argument
in case the matrix has its eigenvalues in $\mathbb F$, which could be guaranteed by assuming that this
matrix is $\mathbb F$-diagonalizable or even $\mathbb F$-triangularizable. Clearly a sufficient condition
for this to hold is that $\mathbb F$ is algebraically closed, because then for every matrix in $\mathbb F^{n,n}$ the characteristic polynomial splits into linear factors.
\if{
To do this, an essential property discussed in Schur's letter is whether there exists a similarity
transformation to triangular or diagonal form with nonsingular matrices in $\mathbb F^{n,n}$ or
$\mathbb K^{n,n}$.
}\fi
\begin{definition}\label {triangularizable}
Let $\mathbb F$ be a differential field and let $\mathbb H$ be a subfield of $\mathbb F$.
Then $M\in \mathbb F^{n,n}$ is called
{\em $\mathbb H$-triangularizable (diagonalizable)} if there exists a nonsingular $T\in \mathbb H^{n,n}$ such that $T^{-1} M T$ is upper triangular (diagonal).
\end{definition}
Using Lemma~\ref{insight}, we can obtain the following result for
matrices $M\in \mathbb F^{n,n}$ that commute with their derivative $M'$, which is most likely well known
but we could not find a reference.
\begin{lemma}\label{decomp}
Let $\mathbb F$ be a differential field with field of constants $\mathbb K$, and suppose that $M \in {\mathbb F}^{n,n}$ satisfies $MM' = M'M$. Then there
exists an invertible matrix $T\in \mathbb K^{n,n}$ such that
\eq{dirsum}
T^{-1} M T= \diag (M_1,\ldots,M_k),
\en
where the minimal polynomial of each $M_i$ is a power of a
polynomial that is irreducible over $\mathbb F$.
\end{lemma}
\proof
Let the minimal polynomial of $M$ be $\mu(\lambda) = \mu_1(\lambda)\cdots \mu_k(\lambda)$,
where the $\mu_i(\lambda)$ are powers of pairwise distinct polynomials that are
irreducible over $\mathbb F$. Set
\[
p_i(\lambda) = \mu(\lambda)/\mu_i(\lambda),\qquad i = 1,\ldots,k.
\]
Since the polynomials $p_i(\lambda)$ have no common factor, there exist polynomials
$q_i(\lambda)$, $i = 1,\ldots,k$, such that the polynomials $\epsilon_i(\lambda) = p_i(\lambda)q_i(\lambda)$, $i = 1,\ldots,k$, satisfy
\begin{equation}\label{epscomp}
\epsilon_1(\lambda) + \cdots + \epsilon_k(\lambda) = 1.
\end{equation}
Setting $E_i = \epsilon_i(M)$, $i = 1, \ldots, k$ and using the fact that
$\mu(M) =0$ yields that
\begin{eqnarray}\label{comp}
E_1 + \cdots + E_k &=& I, \\
\label{ortho}
E_iE_j &=& 0,\qquad
\; \, i,j = 1,\ldots,k,\quad i\neq j,\\
\label{idem}
E_i^2 &=& E_i,\qquad i = 1,\ldots,k.
\end{eqnarray}
The last identity follows directly from (\ref{comp}) and (\ref{ortho}).
Since the $E_i$ are polynomials in $M$ and $MM' = M'M$, it follows that the $E_i$ commute with $E'_i$, $i = 1,\ldots k$. Hence, by Lemma~\ref{insight}, $E_i \in \mathbb K^{n,n}$, $i = 1,\ldots,k$. By (\ref{comp}), (\ref{ortho}), and (\ref{idem}), $\mathbb K^n$ is a direct sum
of the ranges of the $E_i$ and we obtain that, for some nonsingular $T\in \mathbb K^{n,n}$,
\[
\widetilde{E_i}:= T^{-1}E_iT = \diag(0, I_i,0),\qquad i = 1,\ldots,k,
\]
where the $I_i$ are identity matrices of the size equal to the dimension to the
range of $E_i$. This is a consequence of the fact that $E_i$ is diagonalizable with eigenvalues $0$ and $1$.
Since each $E_i$ commutes with $M$,
we obtain that
\begin{eqnarray*}
\widetilde{M_i}&:=& T^{-1}E_iMT \\
&=& T^{-1}E_iME_iT\\
&=& \diag(0,I_i,0) T^{-1}MT \diag(0,I_i,0)\\
&=&\diag(0,M_i,0) ,\qquad i = 1, \ldots, k.
\end{eqnarray*}
Now observe that
\[
\widetilde{E_i}\mu_i(\widetilde{M}_i) \widetilde{E_i}= T^{-1} \epsilon_i(M)\mu_i(M) \epsilon_i(M)T = 0,
\]
since
$\epsilon_i(\lambda)\mu_i(\lambda )= \mu(\lambda)q_i(\lambda)$. Hence $\mu_i(M_i)=0$ as well.
We assert that $\mu_i(\lambda)$ is the minimal polynomial of $M_i$, for if
$r(M_i) = 0$ for a proper factor $r(\lambda)$ of $m_i(\lambda)$ then $r(M)\Pi_{j \neq i} \mu_j(M) = 0$,
contrary to the assumption that $ \mu(\lambda)$ is the minimal polynomial of $M$.
\eproof
Lemma~\ref{decomp} has the following corollary, which has been proved in a different way
in \cite{AdkEG93} and \cite{Gur05}.
\begin{corollary}\label{th:diagonal}
Let $\mathbb F$ be a differential field with field of constants
$\mathbb K$. If $M\in \mathbb F^{n,n}$ satisfies $MM' = M'M$ and is $\mathbb F$-diagonalizable, then $M$ is $\mathbb K$-diagonalizable.
\end{corollary}
\proof
In this case, the minimal polynomial of $M$ is a product of distinct linear factors and hence, the minimal polynomial of each $M_i$ occurring in the proof of Lemma~\ref{decomp} is linear. Therefore, each $M_i$ is a scalar matrix.
\eproof
We also have the following Corollary.
\begin{corollary}\label{cor:diag_type1}
Let $\mathbb F$ be a differential field with field of constants
$\mathbb K$. If $M\in \mathbb F^{n,n}$ satisfies $MM' = M'M$ and is $\mathbb F$-diagonalizable, then $M$ is of Type~1.
\end{corollary}
\proof
By Corollary~\ref{th:diagonal}, $M=T^{-1} \diag (m_1,\ldots,m_n)T$ with $m_i\in \mathbb F$
and nonsingular $T\in \mathbb K^{n,n}$. Hence
\[
M=\sum_{i=1}^n m_{i}T^{-1} E_{i,i} T
\]
where $E_{i,i}$ is a matrix that has a $1$ in position $(i,i)$ and zeros everywhere else. Since all the matrices $E_{i,i}$ commute,
$M$ is of Type~1.
\eproof
\begin{remark}\label{refrem} {\rm Any $M\in \mathbb F^{n,n}$ that is of rank one, satisfies $MM' = M'M$ and is not nilpotent, is of Type~1, since in this case $M$ is $\mathbb F$-diagonalizable. This follows by Corollary~\ref{cor:diag_type1}, since
the minimal polynomial has the from $(\lambda-c)\lambda$ for some $c\in \mathbb F$. This means in particular for a rank one matrix $M\in \mathbb F^{n,n}$ to be of Type~2 and not of Type~1 it has to be nilpotent.}
\end{remark}
For matrices that are just triangularizable the situation is more subtle. We have the following theorem.
\begin{theorem} \label{th:triangularize} Let $\mathbb F$ be a differential field with an algebraically closed field of constants $\mathbb K$. If $M \in \mathbb F^{n,n}$ is Type~1, then $M$ is $\mathbb K$-triangularizable.
\end{theorem}
\proof
Any finite set of pairwise
commutative matrices with elements in an algebraically closed field may be simultaneously triangularized, see e.g.,
\cite[Theorem 1.1.5]{RadR00}. Under this assumption on $\mathbb K$, if $M$ is Type~1, then it follows that the matrices $C_i \in \mathbb K^{n,n}$ in the representation of $M$ are simultaneously triangularizable by a matrix
$T \in \mathbb K^{n,n}$. Hence $T$ also triangularizes $M$.
\eproof
Theorem~\ref{th:triangularize} implies that Type~1 matrices
have $n$ eigenvalues in $\mathbb F$ if $\mathbb K$ is algebraically closed and it further immediately
leads to a Corollary of Theorem~\ref{th:nondero}.
\begin{corollary}\label{cor:triangularize}
Let $\mathbb F$ be a differential field with field of constants
$\mathbb K$. If $M\in \mathbb F^{n,n}$ is nonderogatory, satisfies $MM' = M'M$ and
if $\mathbb K$ is algebraically closed, then $M$ is $\mathbb K$-triangularizable.
\end{corollary}
\proof
By Theorem~\ref{th:nondero} it follows that $M$ is Type~1 and thus the assertion follows
from Theorem~\ref{th:triangularize}.
\eproof
\section{Matrices of small size and examples}\label{sec:exs}
Example~\ref{eva3x3} again shows that it is difficult to drop
some of the assumptions, since this matrix is derogatory, not of Type~1, and not $\mathbb K$-triangularizable.
One might be tempted to conjecture that any $M\in \mathbb F^{n,n}$ that is $\mathbb K$-triangularizable and satisfies (\ref{c1}) is of Type~1 but this is so only for small dimensions and
is no longer true for large enough $n$, as we will demonstrate below.
Consider small dimensions first.
\begin{proposition}\label{2x2}
Consider a differential field $\mathbb F$ of functions with field of constants
$\mathbb K$.
Let $M=[m_{i,j}]\in {\mathbb F}^{2,2}$ be upper triangular and satisfy $M\, M'=M'\, M$. Then
$M$ is of Type~\ref{1}.
\end{proposition}
\proof
Since $M\, M'=M'\, M$ we obtain
\[
m_{1,2}(m_{1,1}'-m_{2,2}')-m_{1,2}'(m_{1,1}-m_{2,2})=0,
\]
%
which implies that $m_{1,2}=0$ or $m_{1,1}-m_{2,2}=0$ or
both are nonzero and ${ d \over dt}({m_{1,1}-m_{2,2}\over m_{1,2}})=0$, i.e.,
$c m_{1,2}+ (m_{1,1}-m_{2,2})=0$ for some nonzero constant $c$.
If $m_{1,1}=m_{2,2}$ or $m_{1,2}=0$, then $M$, being triangular, is obviously of Type~1.
Otherwise
\[
M=m_{1,1} I + m_{1,2}\mat{cc} 0 & 1 \\ 0 & c \rix.
\]
and hence again of Type~1 as claimed.
\eproof
Proposition~\ref{2x2} implies that $2\times2$ $\mathbb K$-triangularizable matrices
satisfying (\ref{c1}) are of Type~1.
\begin{proposition}\label{2x2type}
Consider a differential field $\mathbb F$ with an algebraically closed field of constants $\mathbb K$.
Let $M=[m_{i,j}]\in {\mathbb F}^{2,2}$ satisfy $M\, M'=M'\, M$.
Then $M$ is of Type~1.
\end{proposition}
\proof If $M$ is $\mathbb F$-diagonalizable, then the result follows by Corollary~\ref{cor:diag_type1}. If $M$ is not $\mathbb F$-diagonalizable, then it is nonderogatory and the result follows by Corollary~\ref{cor:triangularize}.
\eproof
\begin{example}{\rm
In the $2\times2$ case, any Type~2 or Type~3 matrix is also of Type~1 but not every
Type~1 matrix is Type~3.
Let $M=\phi I_2 +f g^T$ with
\[\phi\in \mathbb F,\quad f=\mat{c} f_1 \\ f_2\rix ,\quad g=\mat{c} g_1 \\ g_2\rix\in {\mathbb F}^2\]
be of Type~3, i.e.,
$f^Tg={f'}^Tg= f^T{g'}=0$.
If $f_2=0$, then $M$ is upper triangular and hence by Proposition~\ref{2x2}, $M$ is of Type~\ref{1}.
If $f_2\neq 0$, then with
\[
T=\mat{cc} 1 & -f_1/f_2 \\ 0 & 1 \rix.
\]
we have
\[
T MT^{-1}= \phi I_2 +\mat{cc} 0 & 0 \\ f_2 g_1 & 0 \rix=
\phi I_2 +f_2g_1\mat{cc} 0 & 0 \\ 1 & 0 \rix,
\]
since $ f_1g_1+f_2 g_2=0$, and hence $M$ is of Type~1.
However, if we consider
\[
M=\phi I_2+ f\mat{cc} 0 & c \\ 0 & d\rix
\]
with $\phi,f$ nonzero functions and $c,d$ nonzero constants,
then $M$ is Type~1 but not Type~3.
}
\end{example}
\begin{proposition}\label{3x3type}
Consider a differential field $\mathbb F$ of functions with field of constants
$\mathbb K$.
Let $M=[m_{i,j}]\in {\mathbb F}^{3,3}$ be $\mathbb K$-triangularizable and satisfy $M\, M'=M'\, M$. Then $M$ is of Type~\ref{1}.
\end{proposition}
\proof
Since $M$ is $\mathbb K$-triangularizable, we may assume that it is upper triangular already and consider different cases for the diagonal elements. If $M$ has three distinct diagonal elements, then it is $\mathbb K$-diagonalizable and the result follows by
Corollary~\ref{cor:diag_type1}. If $M$ has exactly two distinct diagonal elements,
then it can be transformed to a direct sum of a $2\times 2$ and $1\times1$ matrix and hence the result follows by Proposition~\ref{2x2}. If all diagonal elements are equal, then, letting $E_{i,j}$ be the matrix that is zero except for the position $(i,j)$, where it is $1$, we have
$M=m_{1,1} I+ m_{1,3} E_{1,3}+ \widetilde M$, where $\widetilde M=m_{1,2} E_{1,2}+ m_{2,3} E_{2,3}$ also satisfies (\ref{c1}). Then it follows that $m_{1,2} m'_{2,3}= m'_{1,2} m_{2,3}$. If either
$m_{1,2}=0$ or $m_{2,3}=0$, then we immediately have again Type~1, since $\widetilde M$ is a direct sum of a $2\times 2$ and a $1\times 1$ problem.
If both are nonzero, then $\widetilde M$ is nonderogatory and the result follows
by Theorem~\ref{th:nondero}. In fact, in this case $m_{1,2}=c m_{2,3}$ for some $c\in \mathbb K$ and therefore
\[
M=m_{1,1} I+ m_{1,3} E_{1,3}+ m_{2,3}\mat{ccc} 0 & c & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \rix,
\]
which is clearly of Type~\ref{1}.
\eproof
In the $4\times 4$ case, if the matrix is $\mathbb K$-triangularizable, then we either have at least two different eigenvalues, in which case we have reduced the problem again to the case of dimensions smaller than $4$, or there is only one eigenvalue,
and thus without loss of generality $M$ is nilpotent. If $M$ is nonderogatory then we again have Type
$1$. If $M$ is derogatory then it is the direct sum of blocks of smaller dimension. If these dimensions are smaller than $3$, then we are again in the Type~1
case. So it remains to study the case of a block of size $3$ and a block of size $1$.
Since $M$ is nilpotent, the block of size $3$ is either Type~1 or Type~2. In both cases the complete matrix is also Type~1 or Type~2, respectively.
The following example shows that $\mathbb K$-triangularizability is not enough
to imply that the matrix is Type~1.
\begin{example}{\rm
Consider the $9\times 9$ block matrix
\[
\hat M=\mat{ccc} 0 & M_a & 0 \\ 0 & 0 & M_a \\ 0 & 0 & 0 \rix,
\]
where $M_a$ is the Type~2 matrix from Example~\ref{eva3x3}.
Then $\hat M$ is nilpotent upper triangular and not of Type~1, 2, or 3, the latter two
facts due to its $\mathbb F$-rank being $2$.
}
\end{example}
Already in the $5\times 5$
case, we can find examples that are none of the (proper) types.
\begin{example}{\rm
Consider $M=T^{-1} \diag(M_1,M_2) T$ with $T\in \mathbb K^{n,n}$,
$M_1\in \mathbb F^{3,3}$ of Type~2 (e.g., take $M_1=M_a$ as in Example~\ref{eva3x3})
and $M_2=\mat{cc} 0&1\\ 0& 0\rix$. Then clearly $M$ is
not of Type~1 and it is not of Type~2, since
it has an $\mathbb F$-rank larger than $1$. By definition it is not of Type~3 either.
Clearly examples of any size can be constructed by building direct sums
of smaller blocks.
}
\end{example}
Schur's letter states that for $n\geq 6$ there are other types. The following example demonstrates this.
\begin{example}{\rm Let $M_a$ be the Type~2 matrix in Example~\ref{eva3x3}
and form the block matrix
\[
A =\mat{cc} M_a & I \\ 0 & M_a\rix .
\]
Direct computation shows $AA' = A'A$ but $A'A'' \not = A''A$. Furthermore $A^3 = 0$ and $A$ has $\mathbb F$-rank $3$. Thus $A$ is neither Type~1, Type~2 nor Type 3 (the last case need not be considered, since $A$ is nilpotent). We also note that $\rank(A'') = 6$. We now assume that $\mathbb K$ is algebraically closed and we show that $A$ is not $\mathbb K$-similar to the direct sum of Type~1 or Type~2 matrices.
To obtain a contradiction we assume that (after a $\mathbb K$-similarity)
$A = \diag(A_1,A_2)$ where $A_1$ is the direct sum of
Type~1 matrices (and hence Type~1) and $A_2$ is the direct sum of Type~2 matrices that are not Type~1. Since $A$ is not Type~1, $A_2$ cannot be the empty matrix. Since the minimum size of a Type~2 matrix that is not Type~1 is $3$ and its rank is $1$ it follows that $A$ cannot be the sum of Type~2 matrices that are not Type~1. Hence the size of $A_1$ must be larger or equal to $1$ and, since $A_1$ is nilpotent, it follows that $\rank(A_1) < \size(A_1)$. Since
$A_1$ is $\mathbb K$-similar to a strictly triangular matrix, it follows that
$\rank(A_1'') < \size(A_1)$. Hence $\rank(A'') = \rank(A_1'') + \rank(A_2'') < 6$, a contradiction.
}
\end{example}
\begin{example}{\rm
If the matrix $M=\sum_{i=0}^r C_i t^i\in \mathbb F^{n,n}$ is a polynomial with coefficients $C_i\in \mathbb K^{n,n}$, then from (\ref{c1}) we obtain a specific set of conditions on
sums of commutators that have to be satisfied. For this we just compare coefficients
of powers of $t$ and obtain a set of quadratic equations in the $C_i$, which has a
clear pattern. For example, in the case $r=2$, we obtain the three conditions $C_0C_1-C_1C_0=0$, $C_0C_2-C_2C_0=0$ and $C_1C_2-C_2C_1=0$, which shows that $M$ is of Type~1.
For $r=3$ we obtain the first nontrivial condition $3(C_0C_3-C_3C_0)+(C_1C_2-C_2C_1)=0$.
We have implemented
a Matlab routine for Newton's method to solve the set of quadratic matrix equations in the case $r=3$ and ran it for many different random starting coefficients
$C_i$ of different dimensions $n$. Whenever Newton's method converged (which it did in most of the
cases) it converged to a matrix of Type~1. Even in the neighborhood of a Type~2 matrix it converged to a Type~1 matrix. This suggests that the matrices of Type~1 are generic in the set of matrices satisfying~(\ref{c1}). A copy of the Matlab routine is available from the authors upon request.
}
\end{example}
\section{Conclusion}\label{conclusion}
We have presented a letter of Schur's that contains a major contribution
to the question when a matrix with elements that are functions in one variable
commutes with its derivative. Schur's letter precedes many partial results
on this question, which is still partially open. We have put Schur's result in perspective with later results and extended it in an algebraic context to matrices over a differential field. In particular, we have presented several results that characterize
Schur's matrices of Type~1. We have given examples of matrices that commute with their derivative which are of none of the Types~1,~2 or~3.We have shown that matrices of Type~1 may be triangularized over the constant field (which implies that their eigenvalues lie in the differential field) but we are left with an open problem already mentioned in Section \ref{sec:discussion}.
\begin{openproblem} {\rm Let $M$ be a matrix in a differential field $\mathbb F$, with an algebraically closed
field of constants, that satisfies $MM' = M'M$. Must the eigenvalues of $M$ be elements of the field $\mathbb F$?}
\end{openproblem}
For example, if $M$ is a polynomial matrix over the complex numbers must the eigenvalues be rational functions?
We have found no counterexample.
\section*{Acknowledgements}
We thank Carl de Boor for helpful comments on a previous draft of the paper and Olivier Lader for his careful reading of the paper and for his suggestions. We also thank an anonymous referee for pointing out the observation in Remark~\ref{refrem}.
\bibliographystyle{plain}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 4,794
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|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 668
|
fullybooked2017
PAST TIMES – OLD CRIMES
NINE ELMS . . . Between the covers
ate Marshall lectures in criminology at a university in the south west of England, but when she speaks to her students it is not as an academic, making judgments based purely on the research of others; neither does she approach the subject as an outsider, albeit one who is well read and well prepared. Fifteen years earlier, when she was a humble detective constable with London's Metropolitan Police, she brought to justice one of the country's most prolific and perverted serial killers. In doing so, she paid a heavy price; only skilled surgeons prevented her death from terrible injuries, but her career – and personal reputation – were both beyond saving.
Fifteen years on, the former police officer dubbed The Nine Elms Cannibal is serving multiple life sentences in a secure mental institution, and Kate Marshall, if not exactly dining out on her experiences, uses her involvement in the case as part of the course she delivers. She lives alone and while not exactly lonely, she is a changed woman from her days as part of London's police force. She battles alcoholism, but with the support of Alcoholics Anonymous and, in particular, a local AA member called Myra, Kate sips her iced tea and pretends it contains a hefty shot of Jack Daniels.
Kate Marshall has a rather distinctive connection with The Nine Elms Cannibal, aka Peter Conway, but to elaborate further would be to spoil your fun. Suffice it to say that when a series of copycat killings – young women found dead with savage bite marks on their bodies – Kate is drawn into the investigation despite the misgivings of some police officers, who are only too aware of her back-story.
Of course the new killer can't be Peter Conway – he is held under Hannibal Lecter – style restraints in prison, but what is his mother – author of a best-selling lurid true crime book called No Son Of Mine – up to? Is she acting as malignant go-between, a conduit between her son and an admirer who seems to have studied Conway's modus operandi, and is proving the old adage that imitation is the sincerest form of flattery?
ith her research assistant Tristan Harper, Kate tries to reassemble the pieces of an increasingly complex puzzle, but it is not until events take a spectacular turn that she comes face to face with both the apprentice New Elms Cannibal – and his master – in a fast and furious finale which is not for the faint of heart.
Author Robert Bryndza is British, but lives and works in Slovakia. He has a successful series featuring Detective Erika Foster already under his belt. Nine Elms is published by Sphere, and will be out on 9th January.
I have an unopened hardback copy of Nine Elms up for grabs. Watch the Fully Booked Twitter feed for a prize draw competition – coming soon.
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|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 7,148
|
Sorry, all seats have been filled for this event. Please contact us if you'd like to be placed on the wait list.
Join Us for our Annual Wine Club Member Appreciation Events!
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|
{
"redpajama_set_name": "RedPajamaC4"
}
| 8,108
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Theorem. If the sequence (1) is contractive, it is a Cauchy sequence .
Proof. Suppose that the sequence (1) is contractive. Let ε be an arbitrary positive number and m,n some positive integers from which e.g. n is greater than m, n=m+δ.
when n>m. Consequently, (1) is a Cauchy sequence.
tends to 1 as n→∞.
Cf. sequences of bounded variation (http://planetmath.org/SequenceOfBoundedVariation).
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 6,388
|
\section{Motivation}
The crust of a mature neutron star shields the high-density fluid
core from the thin atmosphere. It provides a heat-blanket that
determines the link between the neutrino-driven cooling of the core
and the evolution of the observed surface temperature
\citep{heatblanket}. The physics of the crust is also of key
importance for neutron star dynamics. The presence of a superfluid
component, and the associated rotational vortices, is central to our
understanding of pulsar glitches \citep{espinoza}. The coupling
between the neutron-rich nuclei in the crust and the superfluid
neutrons also affect global oscillations involving the crust, as in
the case of the quasi-periodic oscillations observed in the tails of
magnetar flares \citep{magnetars}. On the one hand, our
understanding of the crust physics is quite good. The equation of
state for matter has been modelled in detail. In particular, we have
a clear idea of how the composition changes with density which
allows us to work out the elastic properties of the lattice of
nuclei \citep{chamelLR}. This also provides us with the fraction of
neutrons that have dripped out of nuclei and which may considered
free to move relative to the lattice. However, our understanding of
the dynamics of the coupled crust-superfluid system is quite poor.
This is somewhat surprising given the relevance of the involved
issues (e.g. in the context of glitches), but it is nevertheless the
case.
To make progress we need to develop a theoretical framework that
allows us to model the dynamics of the inner-crust region. Such a
model has to consider the key physics, like elasticity, the magnetic
field and superfluidity. It must account for the presence of
superfluid vortices, potential pinning and mutual friction. It is
also important that the model is adaptable, in order to faciliate
further development concerning, for example, finite temperature
effects and heat propagation. This is obviously a major challenge.
The aim of the present work is to develop a ``complete'' model for
linear perturbations of a (moderately) realistic neutron star crust.
Working within the Lagrangian perturbation framework (the natural
way to view the perturbed crust, and a necessity if one wants to
consider the stability of the system from the formal point of view
\citep{fs78}), we provide a two-component model that accounts for
the key physics. The model also complements previous work on the
outer-core region \citep{kirsty} by discussing the role of the
superfluid entrainment and the magnetic field \citep{maglag}. We
also consider the conditions that need to be implemented at the
crust-core transition. The theory is developed to the point where
the results can be applied to a range of interesting astrophysics
problems. Having said that, there is massive room for future
refinements as our understanding of the relevant physics improves.
\section{The two-fluid model}
The conditions in the inner crust, with an elastic lattice of
increasingly neutron-rich nuclei immersed in a neutron superfluid
has (at least) two dynamical degrees of freedom; the superfluid
neutrons may flow relative to the lattice. In essence, this is an
example of a two-``fluid'' system, although in this case one of the
components is also affected by elastic restoring forces. Our model
for this system is based on the variational approach to multi-fluid
dynamics developed by \citet{prix} and \citet{monster} (see also
\citet{brynform}, which represents the Newtonian limit of the
fully relativistic convective variational model designed by \citet{carter}, see also
\citet{livrev}. The elastic sector builds on the relativistic model
developed by \citet{maxlars}, and the inclusion of superfluidity
follows the strategy set out by \citet{casa,cacho}.
\subsection{Hydrodynamics, magnetic fields and elasticity}
In order to model the conditions in the inner crust of a neutron
star, we take as the starting point the equations for two-fluid
hydrodynamics \citep{prix,monster,brynform}. Assuming that the
individual components are conserved (and working in a coordinate
basis where vectors are represented by their components, with
indices $i,j,k$ as usual), we then have the usual conservation laws
for the number densities $n_{\mathrm{x}}$, where ${\mathrm{x}}$ is a constituent index
labeling the components,
\begin{equation}
\partial_t n_{\mathrm{x}} + \nabla_i (n_{\mathrm{x}} v_{\mathrm{x}}^i) = 0 \ .
\label{conti}\end{equation}
Note that a repeated species index x does not imply summation, in contrast to the spatial indices like $i$
for which the Einstein summation convention applies.
In the outer core of a neutron star, the
distinction between the two components is fairly clear. On the one
hand, we have the superfluid neutrons. On the other hand, we have a
conglomerate of (most likely superconducting) protons and electrons.
On scales larger than the electron screening length and timescales
longer than the inverse of the plasma frequency \citep{mendell,supercon}, these form a single, charge neutral, fluid. The two-fluid
model simply distinguishes the neutrons (represented by $n_{\rm n}$, say)
from the protons/electrons (given by $n_{\rm p}$). The situation in the
crust is similar yet different. At densities beyond neutron drip, some neutrons
remain bound in nuclei but there is also a ``gas'' of free neutrons.
The assignation of neutrons to each component follows from the
equation of state, once the nature of the ions in the lattice is
established \citep{chamelLR}. However, if we consider the dynamics of the system it
is not clear to what extent the ``confined'' neutrons are able to
move \citep{cacha}. This depends on how strongly bound they are, to what extent
they can tunnel through the relevant interaction potentials
etcetera. The upshot is that one can choose to work in different
chemical ``gauges''. This issue has been discussed in detail by
\citet{cacha} (and we will return to it later). The choice of chemical gauge affects the
interpretation of the involved quantities (number densities, etc),
but the two-fluid model remains unchanged conceptually. To make a
distinction from the outer core problem, we will refer to the two
components in the crust as ``free'' neutrons, with density $n_\f$,
and ``confined'' baryons, represented by $n_\I$. This notation may
represent a slight bias towards to description advocated by \citet{cacha} and \citet{casa}, but at this point we
basically want to keep the options open by not linking the
discussion too much to established results for the outer core.
The ``free'' neutrons can flow relative to the crust lattice once the system cools below the transition to
$^1S_0$ neutron superfluidity (see \citet{nphysa} for typical transition temperatures). We then have two coupled
equations of momentum balance. Assuming that the large scale system comprises a sufficient number of
quantized vortices that macroscopic averaging is meaningful (this should, indeed,
be the case for all astrophysical systems of interest) the two momentum equations can be written \citep{prix}
\begin{equation}
(\partial_t + v_{\mathrm{x}}^j \nabla_j ) (v^{\mathrm{x}}_i+\varepsilon_{\mathrm{x}} w^{{\mathrm{y}}{\mathrm{x}}}_i) +\nabla_i (\tilde{\mu}_{\mathrm{x}}+\Phi)\\
+ \varepsilon_{\mathrm{x}} w^j_{{\mathrm{y}}{\mathrm{x}}} \nabla_i v^{\mathrm{x}}_j
= f^{\mathrm{x}}_i/\rho_{\mathrm{x}}
\label{Eulers}\end{equation}
where ${\mathrm{x}}=\{\f,\I\}$, the velocities are $v_{\mathrm{x}}^i$, the relative velocity is defined as $w_{{\mathrm{x}}{\mathrm{y}}}^i = v_{\mathrm{x}}^i-v_{\mathrm{y}}^i$ and
$\tilde{\mu}_{\mathrm{x}}=\mu_{\mathrm{x}}/m_{\mathrm{x}}$ represents the
chemical potential scaled to the nucleon mass (we will assume that the neutron and proton masses are equal, $m_\mathrm{c}=m_{\rm n}=m_{\mathrm{B}}$). The mass densities are
given by
$\rho_{\mathrm{x}}=m_{\mathrm{B}} n_{\mathrm{x}}$ and $\Phi$ represents the gravitational potential, which means that we have
\begin{equation}
\nabla^2 \Phi = 4 \pi G (\rho_\f + \rho_\I)
\end{equation}
and, finally, the parameter
$\varepsilon_{\mathrm{x}}$ encodes the entrainment. The entrainment can be expressed in terms of a single parameter
$\alpha$ such that \citep{prix}
\begin{equation}
\rho_{\mathrm{x}} \varepsilon_{\mathrm{x}} = 2 \alpha
\end{equation}
To close the system, we need to provide an equation of state. In the present formalism, the equation of state takes the
form of an energy functional $E$, the functional form of which determines the chemical potentials
\begin{equation}
\mu_{\mathrm{x}} = \left( {\partial E \over \partial n_{\mathrm{x}}}\right)_{n_{\mathrm{y}},w^2} \ ,
\end{equation}
and the entrainment parameter
\begin{equation}
\alpha = \left( {\partial E \over \partial w^2}\right)_{n_{\mathrm{x}},n_{\mathrm{y}}} \ .
\end{equation}
The forces on the right-hand side
of (\ref{Eulers}) can be used to represent various other interactions, including dissipative terms \citep{monster,brynform}. If we focus on the
conditions in the neutron star crust, then we need to account for elasticity and the large-scale magnetic field.
The latter is described by the usual electromagnetic Lorentz
force. That is, we have
\begin{equation}
f_i^\I = \frac{1}{c} \epsilon_{ijk} J^j B^k
\label{lorentz0}
\end{equation}
Eliminating the total current with the help of Amp\'ere's law,
i.e. $J^i = (c/4\pi) \epsilon^{ijk} \nabla_j B_k$,
this becomes
\begin{equation}
f_i^\I = { B^j \over 4\pi } (\nabla_j B_i - \nabla_i B_j )\
\label{lorentz1}
\end{equation}
In order to use this in \eqref{Eulers} we also need to know $n_\I$, i.e., to what extent the baryons are affected
by the magnetic field. It is natural to assume that all baryons that are confined to nuclei are involved, but
the exact meaning of this is (as we will discuss later) somewhat fuzzy in a dynamical situation in regions of the stars
where some of the neutrons are free.
The elastic force is different in that it only serves to restore deviations from a relaxed state of the lattice.
This means that it is natural to discuss elasticity at the linear perturbation level. We will do this later, in Section~4.2.
In that discussion, we will assume that the background configuration is relaxed, in which case there is
no leading order elastic force in \eqref{Eulers}. This assumption is not quite realistic; the crust of an astrophysical
neutron star is likely to be strained due to the regular electromagnetic spin-down of the system.
It is, in principle, straightforward to account for this strain but in the interests of clarity we have chosen
not to do so here.
Before we move on, it is worth noting that the incorporation of elasticity requires us to track given
``fluid'' elements relative to the relaxed configuration. This motivates us to
use a Lagrangian framework. This approach is, of course, advantageous for a number of reasons.
In particular, if we are interested in considered rotating neutron stars. Our model for the inner crust
builds on the two-fluid perturbation framework developed by \citet{kirsty}, adds the magnetic field according to the
analysis of \citet{maglag} and provides a model for elasticity which represents the Newtonian limit of
the theory developed by \citet{casa}.
\subsection{Superfluidity and vortex dynamics}
Let us turn to our attention to the superfluid aspects of the problem. Doing this, we note that
\eqref{Eulers} accounts for the presence of a (macroscopically averaged) vortex array. In order to
discuss issues concerning, for example, vortex pinning and mutual friction it is useful to
consider \eqref{Eulers} in more detail. Following \citet{supercon} we introduce the momentum
\begin{equation}
p^\f_i = m \left( v^\f_i + \varepsilon_\f w^{\I\f}_i \right)
\end{equation}
In a superfluid, the momentum arises as the gradient of the condensate wavefunction. The upshot of this is that the superfluid is irrotational. However, this is only true on the microscopic scale. On the scale of hydrodynamics, the superfluid can rotate by forming vortices and when these are averaged over the system mimics a system with bulk rotation (as evidenced by \eqref{Eulers}). The rotation is, however, quantized and the vorticity is given by
\begin{equation}
\mathcal{W}_\f^i = { 1 \over m} \epsilon^{ijk} \nabla_j p^\f_k = n_{\rm v} \kappa_\f^i
\label{circolo}\end{equation}
where $n_{\rm v}$ is the number of vortices per unit surface area and $\kappa_\f^i = \kappa \hat{\kappa}^i$ (with $\hat{\kappa}^i$ a unit vector along the direction of the vortex array and $\kappa=h/2 m \approx 2 \times 10^{-3}$ cm$^2$ s$^{-1}$ the quantum of circulation).
From equation (\ref{circolo}) one can derive the equation that governs the vorticity.
Assuming that the vortex density is conserved we have
\begin{equation}
\partial_t n_{\rm v} +\nabla_i (n_{\rm v} v^i_{\rm v}) =0\label{circolo2}
\end{equation}
where $v^i_{\rm v}$, in fact, \underline{defines} the macroscopically averaged vortex velocity. The fact that the vortices move with
$v^i_{\rm v}$ also means that (in terms of the Lie derivative $\mathcal{L}_{v_{\rm v}}$ along $v_{\rm v}^i$) we have
\begin{equation}
\left( \partial_t + \mathcal{L}_{v_{\rm v}} \right) \kappa^i = 0 \label{vortlie}
\end{equation}
Given these relations, it follows that
\begin{equation}
\partial_t \mathcal{W}^\f_i+\epsilon_{ijk} \nabla^j \left( \epsilon^{klm} \mathcal{W}^\f_l v^{\rm v}_m \right) =0\label{circolo1}
\end{equation}
In order to make contact with the macroscopic description, we now rewrite the relevant Euler equation, c.f. \eqref{Eulers}, as
\begin{equation}
\partial_t p^\f_i + \nabla_i \left( \mu_\f - {m\over 2} v_\f^2 + v_\f^j p^\f_j \right) - m \epsilon_{ijk}
v_\f^j \mathcal{W}_\f^k = f^\f_i/n_\f
\label{eulern}\end{equation}
This expression makes it clear that, in the absence of vortices and external forces, the superfluid motion follows from the gradient of a scalar potential.
Moreover, it is now easy to compare \eqref{circolo1} and \eqref{circolo2}. As discussed by \citet{supercon}, we then find that
the models are consistent provided we account for the ``Magnus force'' on the right hand side of equation \eqref{eulern}.
This force takes the form
\begin{equation}
\frac{f_i^\f}{\rho_\f}= n_{\rm v} \epsilon_{ijk} \kappa^j (v_\f^k-v_{\rm v}^k)
\label{magnus}\end{equation}
and an equal and opposite force will act on the vortex array. In the simple case of a single condensate at zero temperature, force balance on the vortices
requires them to flow with $v_\f^i$ (here and in the following we ignore the inertia of the vortices \citep{mendell}). In a more general situation,
we can still use the above strategy to account the forces that act on the vortices. We ``simply'' solve the force balance equation for the vortices for
$v_{\rm v}^i$ and use the result in \eqref{magnus}. In the case of resistive scattering off of the vortex cores, e.g. by phonons, this leads to the
usual representation of the vortex-mediated mutual friction \citep{trev}. We will now consider this problem in the context of the crust.
\section{Mutual friction and vortex pinning}
To discuss the various vortex forces, we takes as our starting point the equation of force balance for a
single vortex;
\begin{equation}
\epsilon^{ijk} \hat{\kappa}_j (v^{\rm v}_k - v^\f_k) + \mathcal{R} (v_\I^i - v_{\rm v}^i) + \mathcal{F}^i = 0
\end{equation}
This accounts for (i) the Magnus force, (ii) a resistive friction
associated with the normal component (e.g. nuclei, electrons and phonons in the crust), with coefficient $\mathcal{R}$, and (iii) a general force which we leave unspecified
at this point. This force will later be taken to represent the ``pinning'' of vortices to the nuclei in the crust.
Note that the different terms all have the dimension of velocity. In order to obtain
an expression for the force per unit length of a vortex, as required in the macroscopic Euler equations, we need to multiply by $\rho_\f \kappa n_{\rm v}$.
This step assumes that the vortices form a recti-linear array (the usual Abrikosov lattice). It is the simplest set-up, essentially since it make the averaging over vortices trivial,
but there is no guarantee that this situation prevails in a real system. In particular, it may be relevant to worry about the
formation of vortex tangles and superfluid turbulence \citep{trevturb,peralta}. We will not consider this problem here. Neither will we account for contributions like the
vortex tension or the elasticity of the vortex array.
These effects are readily incorporated in our framework (see \citet{haskell} for a recent discussion of the elasticity of the vortex lattice) but we leave them out in the interest of clarity.
Finally, we assume that there are no force contributions along $\hat{\kappa}^i$, the direction of the vortex axis.
Solving for the vortex velocity in the standard way, we find
\begin{equation}
v_{\rm v}^i = v_\mathrm{c}^i + { 1 \over 1 + \mathcal{R}^2} \left(
\mathcal{R} f^i + \epsilon^{ijk} \hat{\kappa}_j f_k \right)
\label{vv}\end{equation}
where
\begin{equation}
f^i = \epsilon^{ijk} \hat{\kappa}_j w^{\mathrm{c} \f}_k + \mathcal{F}^i
\end{equation}
Now, the reaction force acting on the normal component will be
\begin{multline}
{ f_\mathrm{c}^i \over \rho_\f \kappa} = - \mathcal{R} (v_\mathrm{c}^i - v_{\rm v}^i) - \mathcal{F}^i
\\
= { \mathcal{R} \over 1 + \mathcal{R}^2} \left(
\mathcal{R} f^i + \epsilon^{ijk} \hat{\kappa}_j f_k \right)
+ { 1 \over
\left(1 + \mathcal{R}^2 \right) } \hat{\kappa}^i \left( \hat{\kappa}_j \mathcal{A}^j \right) - \mathcal{F}^i \\
= { \mathcal{R}\over 1 + \mathcal{R}^2 } \epsilon^{ijk} \hat{\kappa}_j \left[ \mathcal{R} w^{\mathrm{c}{\rm n}}_k + \mathcal{F}_k \right] - {1 \over 1 + \mathcal{R}^2 }\perp^i_j
\left[ \mathcal{R} w_{\mathrm{c}\f}^j+ \mathcal{F}^j \right]
\end{multline}
where we have defined the projection orthogonal to the vortices;
\begin{equation}
\perp^i_j = \delta^i_j - \hat{\kappa}^i \hat{\kappa}_j
\end{equation}
The force acting on the neutrons will naturally be equal and opposite;
\begin{equation}
{ f_\f^i \over \rho_\f \kappa}=-\epsilon^{ijk} \hat{\kappa}_j (v^{\rm v}_k - v^\f_k) =-{ f_\mathrm{c}^i \over \rho_\f \kappa}
\end{equation}
For later convenience, it is natural to introduce basis vectors along the macroscopic relative flow (in the plane orthogonal to the vortex).
That is, we use
\begin{equation}
\hat{w}^i = w^i/w
\end{equation}
where
\begin{equation}
w^i = \perp^i_j w_{\mathrm{c}\f}^j \quad \mbox{ and } \quad w^2 = \left( \perp^i_j w_{\mathrm{c}\f}^j \right) w^{\mathrm{c}\f}_i
\end{equation}
together with the decomposition
\begin{equation}
\mathcal{F}^i = a_\parallel \hat{w}^i + a_\perp \epsilon^{ijk} \hat{\kappa}_j \hat{w}_k
\label{acomp}\end{equation}
This means that we get
\begin{multline}
{ \left( 1 + \mathcal{R}^2 \right) \over \rho_{\rm n} \kappa} f_\mathrm{c}^i \\
= \left[ \mathcal{R}^2 w + a_\parallel \mathcal{R} - a_\perp \right] \epsilon^{ijk} \hat{\kappa}_j \hat{w}_k \\
- \left[ \mathcal{R} w + a_\perp \mathcal{R} + a_\parallel \right] \hat{w}^i
\end{multline}
Expressing the result in the usual form \citep{trev} we have
\begin{equation}
{ f_\mathrm{c}^i \over \rho_\f \kappa}
= w \mathcal{B}'_\mathrm{eff} \epsilon^{ijk} \hat{\kappa}_j \hat{w}_k - w \mathcal{B}_\mathrm{eff} \hat{w}^i
\label{f1}\end{equation}
where
\begin{equation}
\mathcal{B}_\mathrm{eff} = { 1 \over 1 + \mathcal{R}^2 } \left[ \mathcal{R} + { a_\parallel + a_\perp \mathcal{R} \over w } \right]
\label{bb1}\end{equation}
and
\begin{equation}
\mathcal{B}'_\mathrm{eff} = { 1 \over 1 + \mathcal{R}^2 } \left[ \mathcal{R}^2 + { a_\parallel \mathcal{R} - a_\perp \over w } \right]
\label{bb2}\end{equation}
The first term in each bracket represents the standard mutual friction. The second terms illustrate how a pinning force may be accounted for
in the macroscopic multi-fluids model. It is worth noting that this model can also be applied to the problem of (potentially strong) interaction
between neutron vortices and proton fluxtubes in the outer core of a neutron star, c.f. \citet{supercon}.
\subsection{Perfect pinning}
Having discussed the general model, we are equipped to consider the limiting case of perfect ``pinning''. The interaction between the
vortex lines and the crustal nuclei may be strong enough to ``pin'' the vortices and force them to move with along with the crust \citep{pierre}.
This has profound
implications for the macroscopic dynamics of the system. Given that the vortex lines are no longer free to move, the superfluid neutrons cannot spin down (or up).
Hence, a lag will build up between the two components as the crust slows down due to magnetic braking. When this lag develops, the Magnus force will tend to
push the vortices out (or in),
c.f. \eqref{magnus}. Eventually, the force will be strong enough to overcome the pinning and break the vortices free. This leads to a transfer of angular momentum,
that could explain
large pulsar glitches (see \citet{andrea} for a recent discussion). Vortex pinning may also have a severe effects on neutron star precession. By acting as a gyroscope, the pinned vortices are expected to lead to
extremely short period precession, of the order of the rotation period (rather than the several months to years period expected from a typical crustal deformation)
\citep{jones,linkprec}. While this general picture is
supported by a range of theoretical models, we are still quite far from a detailed understanding of the nature and strength of vortex pinning. However,
for the present study it is sufficient to assume that a pinning force is acting.
Let us assume that there is ``perfect'' pinning, $v_{\rm v}^i=v_\mathrm{c}^i$. In this case the equation of force balance for a single vortex takes the form
\begin{equation}
\epsilon^{ijk} \hat{\kappa}_j (v^\mathrm{c}_k - v^\f_k) + \mathcal{F}^i = 0
\end{equation}
As long as the system remains below the unpinning limit, this provides us with the required pinning force $\mathcal{F}^i$.
Given this, we find that the force acting on the neutrons is:
\begin{equation}
{ f_\f^i \over \rho_\f \kappa}=-\epsilon^{ijk} \hat{\kappa}_j (v^\mathrm{c}_k - v^\f_k)
\end{equation}
while the reaction force on the charged component will be
\begin{equation}
{ f_\mathrm{c}^i \over \rho_\f \kappa}=\epsilon^{ijk} \hat{\kappa}_j (v^\mathrm{c}_k - v^\f_k)
\end{equation}
The main conclusion from this exercise is that, if the lag between the two components is sufficiently small to allow us to consider the vortices as perfectly ``pinned'',
the exact form of the pinning force does not appear explicitly in the equations of motion.
\subsection{Vortex creep}
Let us now consider the situation where the lag between the two components is close to the critical value for unpinning. This regime is of great physical interest as it is at the heart
of many theoretical models for pulsar glitches. If one assumes that parts of the system are always slightly subcritical, one may
allow for a population of thermally excited vortices to unpin randomly and transfer angular momentum to the crust. This is usually refered to as ``vortex creep'' \citep{alpar84}.
Describing this behaviour is clearly a challenging task, both from the microscopic and the macroscopic point of view.
On the one hand, there have been efforts to calculate the pinning ``force'' and the barrier that the thermally excited
vortices would have to overcome to unpin \citep{linkpaper}.
On the other hand, there have been attempts to incorporate the concept of vortex creep in a
macroscopic hydrodynamical description, by assuming that only a fraction of the vortices, on average, participates in the dynamics \citep{jahanmiri}.
Here we adopt a phenomenological approach aimed at exploring the hydrodynamics of the creep regime.
We start by noting that vortex creep would correspond to motion such that $v_{\rm v}^i \approx v_\mathrm{c}^i$. Assuming that \eqref{acomp} describes the ``pinning force''
completely, i.e. that there is no component along $\hat{\kappa}^i$, we can rewrite \eqref{vv} as
\begin{multline}
v_\mathrm{cr}^i = v_{\rm v}^i - v_\mathrm{c}^i
= {1 \over 1 + \mathcal{R}^2 } \left[ a_\parallel \mathcal{R} - w_{\mathrm{c}\f} - a_\perp \right] \hat{w}_{\mathrm{c}\f}^i
\\
+ {1 \over 1 + \mathcal{R}^2 } \left[ a_\parallel + \left( w_{\mathrm{c}\f} + a_\perp \right) \mathcal{R} \right] \epsilon^{ijk} \hat{\kappa}_j \hat{w}^{\mathrm{c}\f}_k
\end{multline}
From this expression we see that there are two ways of enforcing vortex creep. One would be to let $\mathcal{R} \to \infty$. This model has recently been
used in studies of precession and the unstable r-modes \citep{glitchlett}. However, with the ``pinning'' force explicitly in the problem we have another option.
Focussing on the $\mathcal{R}\ll 1$ case, which should be relevant in the crust \citep{feibelman,bildsten}, we can demand that
\begin{equation}
a_\parallel \mathcal{R} - w_{\mathrm{c}\f} - a_\perp \equiv v_\parallel \ll v_\mathrm{c}
\end{equation}
and
\begin{equation}
a_\parallel + \left( w_{\mathrm{c}\f} + a_\perp \right) \mathcal{R} \equiv v_\perp \ll v_\mathrm{c}
\end{equation}
With these definitions the creep velocity is given by
\begin{equation}
v^i_\mathrm{cr} = v_\parallel \hat{w}^i + v_\perp \epsilon^{ijk} \hat{\kappa}_j \hat{w}_k
\end{equation}
and we have
\begin{equation}
v^2_\mathrm{cr} = v_\parallel^2 + v_\perp^2
\end{equation}
This model is, obviously, more complicated since we now have three coefficients to specify; we need $\mathcal{R}$, $a_\parallel$ and $a_\perp$. However,
this provides more flexibility and
could allow us to, for example, consider a specific form for the ``pinning'' force or, indeed, the creep rate $v_\mathrm{cr}$. An important point is that, in this model you do not
have to have strong drag, $\mathcal{R} \gg 1$, to effect pinning. This may be particularly
relevant if we want to make our neutron star precession models more realistic,see \citet{link}.
Let us conclude by writing down the force that enters in the hydrodynamics.
After some straightforward algebra we have
\begin{equation}
a_\parallel \approx v_\perp + v_\parallel \mathcal{R}
\end{equation}
and
\begin{equation}
a_\perp \approx -w - v_\parallel + v_\perp \mathcal{R}
\end{equation}
This means that the force becomes
\begin{equation}
{ f_\mathrm{c}^i \over \rho_{\rm n} \kappa} \approx - v_\perp \hat{w}^i + (w + v_\parallel) \epsilon^{ijk} \hat{\kappa}_j \hat{w}_k
\end{equation}
which means that
\begin{equation}
f_\mathrm{c}^2 \approx v_\perp^2 + \left( w+v_\parallel\right)^2 \approx w^2
\end{equation}
The required hydrodynamical force follows once we multiply by $\rho_\f n_{\rm v} \kappa$.
It is important to remember that the ``pinning'' force discussed here does not describe the realistic interaction between the vortices and the nuclei.
We have discussed a purely phenomenological model which allows us to describe the motion when vortices are not yet completely free so that the drag
force cannot be approximated as linear in the velocities \citep{linkpaper}. Our simple ``pinning'' model
allows us to consider the dynamical implications of this regime.
\section{Lagrangian perturbations}
So far, we have discussed the general conditions that prevail in the inner neutron star crust and a two-fluid ``hydrodynamics''
model that accounts for the key features. We will now take an important step towards astrophysical applications by developing a
framework for Lagrangian perturbations of this system. The aim is to provide a model that can be applied to a range of important problems in
neutron star dynamics, from pulsar glitches to the gravitational-wave driven instability of the r-modes and magnetar oscillations.
These problems are all naturally approached within perturbation theory. Moreover, they all represent scenarios where the
sensitive interplay between the crust, the superfluid and the magnetic field is expected to be important.
\subsection{The unentrained two-fluid problem revisited}
\label{unentrained}
Since the two-fluid problem has two dynamical degrees of freedom it is natural to introduce
two distinct Lagrangian displacement vectors $ {\xi}^i_{\mathrm{x}} $ \citep{kirsty}. In order to distinguish between these
displacements, we use
variations $\Delta_{\mathrm{x}}$ such that (for any, scalar or vectorial, quantity $Q$)
\begin{equation}
\Delta_{\mathrm{x}} Q = \delta Q + \mathcal{L}_{\xi_{\mathrm{x}}} Q \ ,
\end{equation}
where $\delta$ represents an Eulerian perturbation.
The perturbed continuity equations, c.f. \eqref{conti}, then take the form \citep{fs78}
\begin{equation}
\Delta_{\mathrm{x}} n_{\mathrm{x}} = - n_{\mathrm{x}} \nabla_i \xi_{\mathrm{x}}^i \longrightarrow
\delta n_{\mathrm{x}} = - \nabla_i (n_{\mathrm{x}} \xi_{\mathrm{x}}^i) \ .
\label{super:continuity}
\end{equation}
This means that the equation that describes the perturbed gravitational potential is
\begin{equation}
\nabla^2 \delta \Phi
= 4 \pi m_{\mathrm{B}} G (\delta n_{\mathrm{x}} + \delta n_{\mathrm{y}})\\
= - 4 \pi m_{\mathrm{B}} G \nabla_i (n_{\mathrm{x}} \xi^i_{\mathrm{x}} + n_{\mathrm{y}} \xi^i_{\mathrm{y}})
\label{super:poisson}
\end{equation}
Considering the simplest case of vanishing entrainment and no ``external'' forces, $f_i^\f=f_i^\mathrm{c}=0$, the
results of \citet{kirsty} show that
\begin{equation}
\left( \partial_t + \mathcal{L}_{v_{\mathrm{x}}}\right)\Delta_{\mathrm{x}} v^{\mathrm{x}}_i + \nabla_i
\left(\Delta_{\mathrm{x}} \Phi + \Delta_{\mathrm{x}} \tilde{\mu}_{\mathrm{x}} - { 1\over 2} \Delta_{\mathrm{x}} v_{\mathrm{x}}^2\right)
= 0
\label{sfpeul1}\end{equation}
After some algebra, this leads to
\begin{multline}
\partial_t^2 \xi^{\mathrm{x}}_i +
2 v_{\mathrm{x}}^j \nabla_j \partial_t \xi^{\mathrm{x}}_i + (v_{\mathrm{x}}^j \nabla_j)^2 \xi^{\mathrm{x}}_i +
\nabla_i \delta \Phi \\ +
\xi_{\mathrm{x}}^j \nabla_i \nabla_j \Phi
- (\nabla_i \xi_{\mathrm{x}}^j) \nabla_j\tilde{\mu}_{\mathrm{x}}
+\nabla_i \Delta_{\mathrm{x}} \tilde{\mu}_{\mathrm{x}}
= 0 \ .
\label{sfpeul2}
\end{multline}
Here, the Lagrangian perturbation of the chemical potential can be written (with ${\mathrm{y}}\neq{\mathrm{x}}$)
\begin{multline}
\Delta_{\mathrm{x}} \tilde{\mu}_{\mathrm{x}}
= \delta \tilde{\mu}_{\mathrm{x}}
+ \xi^j_{\mathrm{x}} \nabla_j \tilde{\mu}_{\mathrm{x}} \\
= \left( {\partial \tilde{\mu}_{\mathrm{x}} \over \partial n_{\mathrm{x}}}
\right)_{n_{\mathrm{y}}} \delta n_{\mathrm{x}}
+ \left( {\partial \tilde{\mu}_{\mathrm{x}} \over \partial n_{\mathrm{y}}}
\right)_{n_{\mathrm{x}}} \delta n_{\mathrm{y}}
+ \xi^j_{\mathrm{x}} \nabla_j \tilde{\mu}_{\mathrm{x}} \\
= - \left( {\partial \tilde{\mu}_{\mathrm{x}} \over \partial n_{\mathrm{x}}}
\right)_{n_{\mathrm{y}}}
\nabla_j (n_{\mathrm{x}} \xi^j_{\mathrm{x}})
- \left( {\partial \tilde{\mu}_{\mathrm{x}} \over \partial n_{\mathrm{y}}}
\right)_{n_{\mathrm{x}}}
\nabla_j (n_{\mathrm{y}} \xi^j_{\mathrm{y}}) + \xi^j_{\mathrm{x}} \nabla_j \tilde{\mu}_{\mathrm{x}}
\end{multline}
using the fact that $\tilde{\mu}_{\mathrm{x}} = \tilde{\mu}_{\mathrm{x}} (n_\f, n_\mathrm{c})$.
Hence, we arrive at the following final form for the perturbed
Euler equations;
\begin{multline}
\partial_t^2 \xi^{\mathrm{x}}_i +
2 v_{\mathrm{x}}^j \nabla_j \partial_t \xi^{\mathrm{x}}_i + (v_{\mathrm{x}}^j \nabla_j)^2 \xi^{\mathrm{x}}_i +
\nabla_i \delta \Phi
+ \xi_{\mathrm{x}} ^j \nabla_i \nabla_j (\Phi + \tilde{\mu}_{\mathrm{x}})
\\
- \nabla_i \left[ \left( {\partial \tilde{\mu}_{\mathrm{x}} \over \partial n_{\mathrm{x}}}
\right)_{n_{\mathrm{y}}} \nabla_j (n_{\mathrm{x}}\xi_{\mathrm{x}}^j) +
\left( {\partial \tilde{\mu}_{\mathrm{x}} \over \partial {n_{\mathrm{y}}}} \right)_{n_{\mathrm{x}}}
\nabla_j (n_{\mathrm{y}}\xi_{\mathrm{y}}^j)
\right] = 0
\label{sfpeul3}
\end{multline}
\citet{kirsty} demonstrated how one can proceed further and derive useful conserved quantities,
extending the single-fluid analysis of \citet{fs78} to the two-fluid arena. The importance of the
obtained canonical
energy $E_c$ stems from the fact that it can be used to
assess the stability of the system. In order for the evolution to be dynamically unstable, i.e.
for a perturbation to blow up in absence of additional forces, we must have $E_c=0$.
A secular (viscosity or radiation driven) instability requires $E_c<0$, provided that the energy lost
through dissipation is positive (which makes sense). A particularly nice feature of the
analysis of \citet{kirsty} was the proof that the standard instability criterion for gravitational-wave instabilities, that a normal mode of oscillation becomes
unstable when its pattern speed changes sign (eg. when an originally backwards retrograde mode in a rotating
star becomes prograde \citep{gwreview}), holds also in the two-fluid problem. This had previously been assumed to be the case,
but there was no formal proof.
In the following, we will not attempt to address the issue of the canonical energy
for more complex systems; our focus is entirely on the perturbed equations of motion. A stability
analysis for these equations would be interesting, but as this may well be prohibitively complicated we
leave the problem for future considerations.
\subsection{Accounting for elasticity and the magnetic field}
The equation that represents that crust dynamics must account for both elastic and magnetic contributions.
The former leads to the well-known contribution
\begin{equation}
\Delta_\mathrm{c} \left( f^\mathrm{c}_i/\rho_\mathrm{c} \right) = { 1 \over \rho_\mathrm{c}} \nabla^j \sigma_{ij}
\end{equation}
where the shear tensor is given by
\begin{equation}
\sigma_{ij} = \check \mu ( \nabla_i \xi^\mathrm{c}_j + \nabla_j \xi^\mathrm{c}_i) - { 2 \over 3} \check \mu (\nabla^l \xi_l^\mathrm{c}) \delta_{ij}
\end{equation}
(here one should not confuse the shear modulus $\check \mu$ with the chemical potentials $\mu_{\mathrm{x}}$). It is important to keep in mind that
these expressions are only valid for unstrained background configurations.
In the case of the magnetic field, we need the Lagrangian perturbation of \eqref{lorentz1}.
The required results have already been derived by \citet{maglag}, so we simply restate them here.
The perturbations are determined from
\begin{equation}
\Delta_\mathrm{c} \left( {B^j \over \rho_\mathrm{c}} \right) = 0
\label{ind1}
\end{equation}
which leads to
\begin{equation}
\Delta_\mathrm{c} B^i = -B^i \nabla_j \xi^j_\mathrm{c}
\label{db1}\end{equation}
and
\begin{equation}
\Delta_\mathrm{c} B_i = B_j \nabla_i \xi_\mathrm{c}^j - B_i (\nabla_j \xi_\mathrm{c}^j) + B^j \nabla_j \xi^\mathrm{c}_i
\label{db2}\end{equation}
Finally, using
\begin{equation}
\Delta_\mathrm{c} ( \nabla_j B_i) = \nabla_j ( \Delta_\mathrm{c} B_i) - B_l \nabla_j \nabla_i \xi_\mathrm{c}^l
\end{equation}
we obtain from (\ref{lorentz1})
\begin{equation}
\Delta_\mathrm{c} \left( f^\mathrm{c}_i/\rho_\mathrm{c} \right) = {B^j \over 4 \pi \rho_\mathrm{c}} [ \nabla_j ( \Delta_\mathrm{c} B_i) - \nabla_i (\Delta_\mathrm{c} B_j)]
\end{equation}
It is straightforward to express the magnetic perturbations in terms of the displacement $\xi_\mathrm{c}^i$, but since expressions that result are
quite involved we have decided not to do so here.
\subsection{Entrainment}
The elastic and magnetic forces take relatively simple forms. However, the fluid part of the problem becomes much more complex
if we consider the generic situation where the entrainment is not vanishing.
In the unentrained case the two equations of motion are
coupled \underline{chemically} through the equation of state (e.g. through various interactions) and \underline{gravitationally}
since variations in the number density
of one fluid affect the gravitational potential and hence the motion of the other fluid.
In contrast, the entrainment parameter $\alpha$
encodes how the internal energy of the system depends on the \underline{relative velocity} of the two fluids. This usually leads to a stronger coupling of the components.
Since the entrainment encodes the effective dynamical mass of each matter constituent, it will affect most scenarios that involve
the superfluid regions of the star.
Including the entrainment, the Euler equations take the form \eqref{Eulers}. However, since
\begin{equation}
v_{\mathrm{x}}^j \nabla_j \( \varepsilon_{\mathrm{x}} w_i^{\Y\X} \)
= \mathcal{L}_{v_{\mathrm{x}}}\(\varepsilon_{\mathrm{x}} w_i^{\Y\X}\) - \varepsilon_{\mathrm{x}} w_j^{\Y\X} \nabla_i v_{\mathrm{x}}^j
\end{equation}
these can be rewritten as
\begin{equation}
\left(\partial_t + \mathcal{L}_{v_{\mathrm{x}}} \right) \left(v^{\mathrm{x}}_i + \varepsilon_{\mathrm{x}} w_i^{{\mathrm{y}}{\mathrm{x}}} \right)
+ \nabla_i \left(\Phi + \widetilde{\mu}_{\mathrm{x}} - \frac{v_{\mathrm{x}}^2}{2} \right) = 0
\label{euler2}\end{equation}
We want to consider Lagrangian perturbations of this system.
The derivation follows
the same approach as in the unentrained case, described by \citet{kirsty} and summarised in Section~\ref{unentrained}.
First we note that the continuity equations and the Poisson equation
are not affected by entrainment, so we can still use equations (\ref{super:continuity}) and (\ref{super:poisson}).
Secondly, perturbing the Euler equations we have
\begin{multline}
\left(\partial_t + \mathcal{L}_{v_{\mathrm{x}}} \right) \left[ \Delta_{\mathrm{x}} v^{\mathrm{x}}_i + \Delta_{\mathrm{x}} \(\varepsilon_{\mathrm{x}} w_i^{{\mathrm{y}}{\mathrm{x}}} \) \right] \\
+ \nabla_i \left(\Delta_{\mathrm{x}} \Phi + \Delta_{\mathrm{x}} \widetilde{\mu}_{\mathrm{x}} - \frac{\Delta_{\mathrm{x}} v_{\mathrm{x}}^2 }{ 2} \right) = 0
\label{lageqn}
\end{multline}
This follows immediately since the Lagrangian variation commutes with $\partial_t + \mathcal{L}_{v_{\mathrm{x}}} $.
Most of the terms in this equation were already considered in the unentrained problem.
A key difference now is that $ \delta \tilde{\mu}_{\mathrm{x}}$ depends on the entrainment. This is obvious
since the chemical potential, $\mu_{\mathrm{x}}$, is the
partial derivative of the energy functional, $E$, with respect to the number density, $n_{\mathrm{x}}$. Since $E$ depends on the
entrainment the Eulerian variation of the chemical potential also depends on the entrainment. In general, we have
\begin{multline}
\delta \tilde{\mu}_{\mathrm{x}} = - \( {\partial \tilde{\mu}_{\mathrm{x}} \over \partial n_{\mathrm{x}}}\)_{n_{\mathrm{y}}, w^2}\nabla_j \(n_{\mathrm{x}} \xi_{\mathrm{x}}^j \) \\
- \( {\partial \tilde{\mu}_{\mathrm{x}} \over \partial n_{\mathrm{y}}}\)_{n_{\mathrm{x}}, w^2}\nabla_j \(n_{\mathrm{x}} \xi_{\mathrm{x}}^j \)
+ \( {\partial \tilde{\mu}_{\mathrm{x}} \over \partial w^2}\)_{n_{\mathrm{x}},n_{\mathrm{y}}} \delta w^2
\end{multline}
where
\begin{equation}
\( {\partial \tilde{\mu}_{\mathrm{x}} \over \partial w^2}\)_{n_{\mathrm{x}},n_{\mathrm{y}}}
= {1 \over m_{\mathrm{B}} } \( {\partial \alpha \over \partial n_{\mathrm{x}}}\)_{n_{\mathrm{y}}, w^2} \equiv {1 \over m_{\mathrm{B}} } \mathcal{A}_{\mathrm{x}}
\end{equation}
and
\begin{equation}
\delta w^2 = 2 w_j^{\Y\X} \delta w^j_{\Y\X}
\end{equation}
giving
\begin{multline}
\delta \tilde{\mu}_{\mathrm{x}} = - \( {\partial \tilde{\mu}_{\mathrm{x}} \over \partial n_{\mathrm{x}}}\)_{n_{\mathrm{y}}, w^2}\nabla_j \(n_{\mathrm{x}} \xi_{\mathrm{x}}^j \) \\
- \( {\partial \tilde{\mu}_{\mathrm{x}} \over \partial n_{\mathrm{y}}}\)_{n_{\mathrm{x}}, w^2}\nabla_j \(n_{\mathrm{y}} \xi_{\mathrm{y}}^j \)
+ {2 \over m_{\mathrm{B}}} \mathcal{A}_{\mathrm{x}} w_j^{\Y\X} \delta w^j_{\Y\X}
\label{eq:cf1}
\end{multline}
At this point it is worth noting that
\begin{multline}
\delta w_{{\mathrm{y}}{\mathrm{x}}}^i =
\partial_t \xi_{\mathrm{y}}^i + v_{\mathrm{y}}^j \nabla_j \xi_{\mathrm{y}}^i - \xi_{\mathrm{y}}^j \nabla_j v_{\mathrm{y}}^i
- \partial_t \xi_{\mathrm{x}}^i - v_{\mathrm{x}}^j \nabla_j \xi_{\mathrm{x}}^i + \xi_{\mathrm{x}}^j \nabla_j v_{\mathrm{x}}^i \\
= \partial_t \left( \xi_{\mathrm{y}}^i - \xi_{\mathrm{x}}^i \right) + v_{\mathrm{x}}^j \nabla_j \left( \xi_{\mathrm{y}}^i - \xi_{\mathrm{x}}^i \right) \\
- \left( \xi_{\mathrm{y}}^j - \xi_{\mathrm{x}}^j \right) \nabla_j v_{\mathrm{x}}^i
+ w_{{\mathrm{y}}{\mathrm{x}}}^j \nabla_j \xi_{\mathrm{y}}^i - \xi_{\mathrm{y}}^j \nabla_j w_{{\mathrm{y}}{\mathrm{x}}}^i \\
= \left( \partial_t + \mathcal{L}_{v_{\mathrm{x}}} \right) \left( \xi_{\mathrm{y}}^i - \xi_{\mathrm{x}}^i \right) - \mathcal{L}_{w_{{\mathrm{y}}{\mathrm{x}}}} \xi_{\mathrm{y}}^i
\end{multline}
The only other piece of equation \eqref{lageqn} that was not present in the unentrained problem can be written
\begin{multline}
\left(\partial_t + \mathcal{L}_{v_{\mathrm{x}}} \right)\Delta_{\mathrm{x}} \(\varepsilon_{\mathrm{x}} w_i^{\Y\X} \) \\
= \varepsilon_{\mathrm{x}} \left(\partial_t + \mathcal{L}_{v_{\mathrm{x}}} \right)\Delta_{\mathrm{x}} w_i^{\Y\X}
+ w_i^{\Y\X} \left(\partial_t + \mathcal{L}_{v_{\mathrm{x}}} \right)\Delta_{\mathrm{x}} \varepsilon_{\mathrm{x}}
\label{eq:remain}
\end{multline}
The first term follows easily from
\begin{equation}
\Delta_{\mathrm{x}} w_i^{\Y\X} = \delta w_i^{{\mathrm{y}}{\mathrm{x}}} + \xi^j_{\mathrm{x}} \nabla_j w^{{\mathrm{y}}{\mathrm{x}}}_i + w^{{\mathrm{y}}{\mathrm{x}}}_j \nabla_i \xi_{\mathrm{x}}^j
\end{equation}
The second term in \eqref{eq:remain} is worth discussing in more detail.
We first consider
\begin{equation}
\Delta_{\mathrm{x}} \varepsilon_{\mathrm{x}} =
\delta \varepsilon_{\mathrm{x}} + \xi_{\mathrm{x}}^j \nabla_j \varepsilon_{\mathrm{x}}
\end{equation}
Using the definition for $\varepsilon_{\mathrm{x}}$, and the perturbed continuity equation, we find
\begin{equation}
\Delta_{\mathrm{x}} \varepsilon_{\mathrm{x}} =
{2 \over \rho_{\mathrm{x}}} \left[ \delta \alpha + \nabla_i \(\alpha \xi_{\mathrm{x}}^i \) \right]
\end{equation}
In the general case, the entrainment parameter
$\alpha$ is a function of the two number densities, e.g. $n_\f$ and $n_\mathrm{c}$, and $w^2$. This means that
\begin{equation}
\delta \alpha = \mathcal{A}_\f \delta n_\f + \mathcal{A}_\mathrm{c} \delta n_\mathrm{c} + 2 \mathcal{A}_w w^{\mathrm{c}\f}_j \delta w_{\mathrm{c}\f}^j
\end{equation}
where we have defined
\begin{equation}
\label{eq:aw}
\mathcal{A}_w = \({\partial \alpha \over \partial w^2 } \)_{n_\f, n_\mathrm{c}}
\end{equation}
We can also use
\begin{equation}
\nabla_i \alpha = \mathcal{A}_\f \nabla_i n_\f + \mathcal{A}_\mathrm{c} \nabla_i n_\mathrm{c} + 2 \mathcal{A}_w w_j^{\mathrm{c}\f} \nabla_i w_{\mathrm{c}\f}^j
\end{equation}
This means that
we can write $\delta \alpha$ as,
\begin{multline}
\delta \alpha = - \mathcal{A}_\f \nabla_i \(n_\f \xi_\f^i \) - \mathcal{A}_\mathrm{c} \nabla_i \( n_\mathrm{c} \xi_\mathrm{c} ^i \)
\\
+ 2 \mathcal{A}_w w^{\mathrm{c}\f}_j \[ \partial_t \xi_\mathrm{c}^j - \partial_t \xi_\f^j + v_\mathrm{c}^i \nabla_i \xi_\mathrm{c}^j
- v_\f^i \nabla_i \xi_\f^j - \xi_\mathrm{c}^i \nabla_i v_\mathrm{c}^j + \xi_\f^i \nabla_i v_\f^j \]
\end{multline}
After some algebra, we finally find that
\begin{multline}
\Delta_{\mathrm{x}} \varepsilon_{\mathrm{x}} =
{2 \over \rho_{\mathrm{x}}} \Big\{ \(\alpha - \mathcal{A}_{\mathrm{x}} n_{\mathrm{x}} \) \nabla_i \xi_{\mathrm{x}}^i
- \mathcal{A}_{\mathrm{y}} n_{\mathrm{y}} \nabla_i \xi_{\mathrm{y}}^i \\
+ 2 \mathcal{A}_w w_j^{\Y\X} \left[ \partial_t \left( \xi_{\mathrm{y}}^j - \xi_{\mathrm{x}}^j \right) - v_{\mathrm{x}}^i \nabla_i \xi_{\mathrm{x}}^j + v_{\mathrm{y}}^i \nabla_i \xi_{\mathrm{y}}^j
- \left( \xi_{\mathrm{y}}^i - \xi_{\mathrm{x}}^i \right)\nabla_i v_{\mathrm{y}}^j \right] \Big\}
\label{dex}\end{multline}
We can now combine the above results to get a general expression for the right-hand side of \eqref{eq:remain}
in terms of the two displacements. However, this expression will be rather lengthy and may not be particularly useful.
In most situations of interest a reduced version should suffice. In principle, one may consider different
simplifying assumptions. The most drastic would be to consider the entrainment parameter to be uniform.
The natural way to achieve this would be to take $\alpha=$~constant\footnote{It is worth noting that $\varepsilon_{\mathrm{x}}=\ $constant is only consistent for a
uniform density model.}. Then we have $\mathcal{A}_{\mathrm{x}} = \mathcal{A}_w =0$, and
the equations simplify greatly. In fact, from \eqref{dex} we are only left with
\begin{equation}
\Delta_{\mathrm{x}} \varepsilon_{\mathrm{x}} =
{2 \alpha \over \rho_{\mathrm{x}}} \nabla_i \xi_{\mathrm{x}}^i = \varepsilon_{\mathrm{x}} \nabla_i \xi_{\mathrm{x}}^i
\end{equation}
A more realistic model would be based on an expansion for small relative velocities \citep{gregexpand}. One would expect $w_{{\mathrm{y}}{\mathrm{x}}}$ to be
small in most cases, so it makes sense to use the approximate equation of state
\begin{equation}
E(n_\f, n_\mathrm{c}, w^2) \approx E_0 (n_\f, n_\mathrm{c}) + E_1 (n_\f, n_\mathrm{c}) w^2
\end{equation}
In this case, we simply have
\begin{equation}
\alpha = E_1
\end{equation}
and it is obviously the case that $\mathcal{A}_w=0$. Hence, we have
\begin{equation}
\Delta_{\mathrm{x}} \varepsilon_{\mathrm{x}} =
{2 \over \rho_{\mathrm{x}}} \left[ \(\alpha - \mathcal{A}_{\mathrm{x}} n_{\mathrm{x}} \) \nabla_i \xi_{\mathrm{x}}^i
- \mathcal{A}_{\mathrm{y}} n_{\mathrm{y}} \nabla_i \xi_{\mathrm{y}}^i \right]
\end{equation}
This expression completes our analysis of the perturbations of the inviscid problem for the coupled
crust-superfluid system.
\subsection{Perturbing the mutual friction}
The various contributions associated with the superfluid vortices add further complexity to the
problem. As an illustration of this we will focus on the mutual friction,
which follows from equation \eqref{f1}. To complete the perturbation equations, we need
\begin{equation}
\Delta_{\mathrm{x}}\left(\frac{f^i_\mathrm{c}}{\rho_\f}\right)=-\Delta_{\mathrm{x}} \left(\frac{f^i_\f}{\rho_\f}\right)=
\Delta_{\mathrm{x}} \left(\mathcal{B}'_\mathrm{eff} \epsilon^{ijk} n_{\rm v} {\kappa}_j {w}_k - \kappa n_{\rm v} \mathcal{B}_\mathrm{eff} {w}^i\right)
\end{equation}
where it is worth recalling that we defined
$\mathcal{W}_\f^i = n_{\rm v} \kappa^i$ in Section~2.2.
From equations (\ref{bb1}) and (\ref{bb2}) we see that the perturbations of the coefficients
$\mathcal{B}_\mathrm{eff}$ and $\mathcal{B}'_\mathrm{eff}$ will (in general) require a knowledge of
$\mathcal{R}$, $a_\parallel$ and $a_\perp$. The perturbations of these quantities can, obviously, be treated
in the same way as $\alpha$ in the previous section. However, in this case any simplifications would rely
on an understanding of the detailed microphysics. In addition to these quantities we need the variation
of the magnitude of the relative velocity, $w$. Determining this quantity is straightforward.
The main new piece of information required for the mutual friction is the perturbed vorticity.
In general, when the vortices are not moving with either of the macroscopic fluids, we need to perturb
\eqref{circolo}, after solving for the vortex velocity as in Section~3. The procedure is relatively straightforward,
but as the final expressions are messy, and not very instructive, we will not work out the details here.
Instead we consider the two extremes of free and pinned vortices.
In the first case, when the vortices are free so that $v_{\rm v}^i = v_\f^i$, we see that \eqref{circolo} leads to
\begin{equation}
\left(\partial_t + \mathcal{L}_{v_\f} \right) \mathcal{W}_\f^i + \mathcal{W}_\f^i (\nabla_j v_\f^j ) = 0 \ .
\end{equation}
Perturbing this, it is quite easy to show that (in the case of a stationary and axisymmetric background)
\begin{equation}
\left(\partial_t + \mathcal{L}_{v_\f} \right) \left[ \Delta_\f \mathcal{W}_\f^i + \mathcal{W}_\f^i (\nabla_j \xi_\f^j ) \right] = 0
\end{equation}
We need the trivial solution to this equation, which means that we have
\begin{equation}
\Delta_\f \mathcal{W}_\f^i = - \mathcal{W}_\f^i (\nabla_j \xi_\f^j )
\end{equation}
Finally, we perturb \eqref{circolo2} (which is completely analogous to the continuity equation for $n_{\mathrm{x}}$)
to get
\begin{equation}
\Delta_\f n_{\rm v} = - n_{\rm v} \nabla_j \xi_\f^j \ .
\end{equation}
Given these results, and the discussion in Section~3.1, it is easy to
work out what happens when the vortices are (perfectly) pinned. In that case, we have $v_{\rm v}^i = v_\mathrm{c}^i$ and
as a result we find that
\begin{equation}
\Delta_\mathrm{c} \mathcal{W}_\f^i = - \mathcal{W}_\f^i (\nabla_j \xi_\mathrm{c}^j )
\end{equation}
and
\begin{equation}
\Delta_\mathrm{c} n_{\rm v} = - n_{\rm v} \nabla_j \xi_\mathrm{c}^j \ .
\end{equation}
\section{The crust-core interface}
In order for the developed perturbation framework to be useful for neutron star astrophysics, we need to
consider the crust-core interface. This region is known to be
important for a range of problems, especially since the associated viscous boundary layer may
provide efficient dissipation of large-scale flows in the core. We will not consider the viscous problem here,
but it is worth keeping in mind that a key issue concerns to what extent the velocity
perturbations are continuous across the interface. If they are not, then viscosity works to smooth out
the discontinuities (over some relatively short length scale) leading to damping of the bulk motion.
The magnetic field may play a similar role. When a magnetic field penetrates the interface, discontinuities
would induce Alfv\'en waves which would effect an efficient coupling between the crust and the core.
Another issue arising in this context is the potential appearance of nuclear pasta, that the nucleons form non-trivial topological clusters (e.g. rods or plates) rather than spherical nuclei arranged in a Coulomb lattice. Accounting for these structures is, in principle, straightforward once the properties of the various phases are understood. In most cases one would expect the system to remain ``isotropic'' on macroscopic scales owing to the fact that the pasta structures will ``freeze'' in a random fashion on some smaller scale, and the ``fluid model'' arises from a larger scale average. However, there are cases where these structures may be aligned on macroscopic scales (for instance due to a strong magnetic field or the existence of an ordered array of vortices). Then we may need to consider non-isotropic elasticity. The computation of the microscopic input parameters (equation of state, entrainment, shear modulus, et c.) is very complicated in the pasta phase. It may, for instance, be that the densities exhibit discontinuous jumps across the crust-core interface, which could lead to discontinuities in the velocities [see e.g.\ equation \eqref{con1} below] and thus to enhanced viscous damping as discussed above. These are very important issues, but for simplicity we will ignore them in the following, assuming an isotropic solid and continuous densities across the crust-core interface.
\subsection{Chemical gauge}
As before, we consider a system where a charge-carrying component is coupled to a neutral superfluid.
Furthermore, we assume that the superfluid extends across the interface.
At this point we have to return to the issue of the ``chemical gauge''. That is,
we have to discuss the physical meaning of $n_\f$ and $n_\mathrm{c}$. In developing the model, we have taken
the view that $n_\f$ represents the neutrons that are not confined to nuclei in the crust, while
$n_\mathrm{c}$ represents all protons as well as the confined neutrons (making up the ions in the lattice).
This view leads to a natural description of the elastic and magnetic forces. However, it does not
lead to a straightforward connection to the core, where one would usually distinguish \underline{all} the
neutrons, $n_{\rm n}$, from the protons, $n_{\rm p}$. Problems arise from the fact that the analysis
requires variables that are ``meaningful'' across the crust-core interface. In principle, the problem would be
more straightforward if we were to use a two-fluid model based on $n_{\rm n}$ and $n_{\rm p}$ also in the crust.
The downside to this would be that we would then have to reconsider the Lorentz force and the elasticity contributions.
After all, some of the neutrons will be associated with the nuclei and hence should be affected by the crust motion.
Focussing on the generic case, we will connect the standard two-fluid model for the core with the
crust model we have developed. This forces us to consider the relevance of the chemical gauge
and serves to clarify some of the key issues.
The chemical gauge choice relates to the neutrons that are considered ``free''.
The issue is subtle since, in a dynamic situation, even the neutrons that are associated with the nuclei may be able to tunnel through
the relevant interaction potential. This makes concepts like the atomic number somewhat hazy. In general, one may introduce a new
basis such that
\begin{equation}
n_\f^i = n_{\rm n}^i + (1-a_\mathrm{c}) n_{\rm p}^i
\end{equation}
where $a_\mathrm{c}$ (which we will take to be constant in the following, a good approximation at the level of the individual fluid elements)
accounts for the fact that some of the neutrons move with the
(crust) protons. We also have
\begin{equation}
n_\mathrm{c}^i = a_\mathrm{c} n_{\rm p}^i
\end{equation}
Given these relations, it is easy to show that the neutron momentum is independent of the chemical gauge \citep{cacha}.
This follows immediately from the definition of the momentum \citep{monster};
\begin{equation}
p^{\mathrm{x}}_i = {\partial \mathcal{L} \over \partial n_{\mathrm{x}}^i}
\end{equation}
where $\mathcal{L}$ represents the relevant Lagrangian.
Hence, we have
\begin{equation}
p^{\rm n}_i = p^\f_i
\end{equation}
It also follows that
\begin{equation}
\mu_{\rm n} = \mu_\f
\end{equation}
However, these results also show that in general we must have $v_\f^i \neq v_{\rm n}^i$ and $\varepsilon_\f \neq \varepsilon_{\rm n}$.
Finally, in order to consider the vortices across the interface, it is natural to assume that
\begin{equation}
\mathcal{W}_\f^i = \mathcal{W}_{\rm n}^i
\end{equation}
The behaviour of the vortices may, of course, be more complicated than this but it makes sense to first consider the simplest
``reasonable'' model.
\subsection{The background configuration}
Following \citet{maglag} we represent the moving interface by a level set of a scalar function $f$ which can be extended
in a smooth fashion. Expecting the interface to move with the charged component, we require
\begin{equation}
[\partial_t + {\cal L}_{v_\mathrm{c}} ] f = 0 \ ,
\end{equation}
from which it is easy to show that
\begin{equation}
[\partial_t + {\cal L}_{v_\mathrm{c}}] \nabla_i f = 0 \ .
\end{equation}
In other words, the gradient $\nabla_i f$ is constant in the frame moving with $v_\mathrm{c}^i$. From this, it follows that
the perturbation $\Delta_\mathrm{c} f$ satisfies
\begin{equation}
[\partial_t + {\cal L}_{v_\mathrm{c}} ] \Delta_\mathrm{c} f = 0 \ .
\end{equation}
The trivial solution to this equation is $\Delta_\mathrm{c} f=0$, which essentially means that a fluid element
at the original surface remains at the perturbed surface. The normal to the surface can obviously be taken to be
$N_i = \nabla_i f$, and hence we have the unit normal
\begin{equation}
\hat{N}_i = { \nabla_i f / N } \ , \mbox{ where } \quad N = |\nabla f| = (g^{ij} \nabla_i f \nabla_j f)^{1/2}
\end{equation}
This means that
\begin{equation}
[\partial_t + {\cal L}_{v_\mathrm{c}} ] \hat{N}_i = N_i [\partial_t + {\cal L}_{v_\mathrm{c}} ] N \ .
\end{equation}
which shows that, even though $\hat{N}_i$ is not preserved by the flow,
any change in the unit normal is parallel to the normal itself. We will use this fact later.
These considerations are quite general. However, in the problem of interest we may restrict ourselves to
configurations (at the unperturbed level) that are stationary and axisymmetric. These assumptions mean that
we have $\partial_t N_i=0$ and $N_i v_{\mathrm{x}}^i=0$. The latter represents a no-penetration condition, simply
stating that (in the background configuration) the core fluids do not migrate into the crust.
In order to obtain the interface conditions, we identify a small cylinder of fluid aligned
with the normal to the interface, $\hat{N}_i$. Integrating the various equations over this small volume,
we will be able to deduce the relevant conditions to impose. Carrying out this exercise we need to make sure that the
equations we consider are valid in both the crust and the core. Given this, it is
natural to take as our starting point the conservation of baryon number. Assuming that the problem is stationary, the core equation
\begin{equation}
\nabla_i \left( n_{\rm n} v_{\rm n}^i + n_{\rm p} v_{\rm p}^i \right) = 0
\end{equation}
matches to the crust result;
\begin{equation}
\nabla_i \left( n_\f v_\f^i + n_\mathrm{c} v_\mathrm{c}^i \right) = 0
\end{equation}
Integrating these over the small volume, we see that we should impose
\begin{equation}
\hat{N}_i \left( n_{\rm n} v_{\rm n}^i + n_{\rm p} v_{\rm p}^i \right) = \hat{N}_i \left( n_\f v_\f^i + n_\mathrm{c} v_\mathrm{c}^i \right)
\end{equation}
at the interface. Noting that there are no chemical gauge issues concerning the protons, the
corresponding conservation law leads to (assuming that the densities are continuous
across the interface);
\begin{equation}
\hat{N}_i \left( v_{\rm p}^i - v_\mathrm{c}^i \right) = 0
\label{con1}\end{equation}
Given this, and the fact that the total number density is given by $n=n_{\rm p}+ n_{\rm n}= n_\f + n_\mathrm{c}$,
we can rewrite the first condition as
\begin{equation}
n_{\rm n} \hat{N}_i \left( v_{\rm n}^i - v_{\rm p}^i \right) = n_\f \hat{N}_i \left( v_\f^i - v_\mathrm{c}^i \right)
\label{con2}\end{equation}
The final conditions \eqref{con1} and \eqref{con2} are, of course, trivially satisfied for an axisymmetric system since $\hat{N}_i v_{\mathrm{x}}^i = 0$.
Moving on to the momentum equations, it is natural to work in the frame moving with the protons/crust. After all, the volume that we integrate
over is fixed in this frame. We can also safely treat any relative flow as planar, since the volume we consider is arbitrarily small.
These assumptions simplify the analysis greatly.
Let us first introduce the total momentum flux;
\begin{equation}
\pi_i = \rho_{\mathrm{x}} v^{\mathrm{x}}_i + \rho_{\mathrm{y}} v^{\mathrm{y}}_i
\end{equation}
where $({\mathrm{x}},{\mathrm{y}})$ is either $({\rm n},{\rm p})$ or $(\f,\mathrm{c})$, depending of whether we consider the core or the crust.
Combining the Euler equations in the appropriate way we find that \citep{monster}
\begin{equation}
\partial_t \pi_i + \nabla_j \left( v_{\mathrm{x}}^j \pi^{\mathrm{x}}_i + v_{\mathrm{y}}^j \pi^{\mathrm{y}}_i \right) + \nabla_i p + \rho\nabla_i\Phi = \nabla^j T_{ij} \ ,
\label{momtot}\end{equation}
where the pressure $p$ is defined such that
\begin{equation}
\nabla_i p = \sum_{\mathrm{x}} n_{\mathrm{x}}\nabla_i \mu_{\mathrm{x}} - \alpha \nabla_i w_{{\mathrm{x}}{\mathrm{y}}}^2 \ .
\end{equation}
The elastic and magnetic stresses are accounted for in $T_{ij}$.
Let us consider the problem on the crust side of the interface (the core follows simply from letting $\f\to{\rm n}$ and $\mathrm{c}\to {\rm p}$).
In the frame moving with the crust we have $v_\mathrm{c}^i=0$ (obviously), and we also need to replace $v_\f^i\to w_{\f\mathrm{c}}^i$. This leads to
\begin{equation}
\pi_i^\f \to \rho_\f (1-\varepsilon_\f) w^{\f\mathrm{c}}_i \ ,
\end{equation}
and the momentum equation takes the form
\begin{equation}
\partial_t \pi_i + \nabla_j \left[ \rho_\f (1-\varepsilon_\f) w_{\f\mathrm{c}}^j w^{\f\mathrm{c}}_i + \delta_i^j p \right] +\rho\nabla_i\Phi = \nabla^j T_{ij} \ ,
\end{equation}
We now integrate this equation over the small volume straddling the interface. As long as the total density is continuous across the interface, the
gravitational potential and its derivative will be smooth and therefore the corresponding integral vanishes as we let the volume shrink.
This exercise tells us that there will be no local force associated with the interface as long as
\begin{multline}
\hat{N}_j \left[ \rho_\f (1-\varepsilon_\f) w_{\f\mathrm{c}}^j w^{\f\mathrm{c}}_i + \delta_i^j p - T_i^j \right]_\mathrm{crust} \\
=
\hat{N}_j \left[ \rho_{\rm n} (1-\varepsilon_{\rm n}) w_{{\rm n}{\rm p}}^j w^{{\rm n}{\rm p}}_i + \delta_i^j p - T_i^j \right]_\mathrm{core}
\label{gencond}\end{multline}
This condition is quite general. In particular, it needs to hold also on the perturbative level. As far as the background
configuration is concerned, we obviously have $\hat{N}_j v_{\mathrm{x}}^j=0$, which means that we have (representing the change in a given quantity across the interface by
$\langle \ldots \rangle$ \citep{maglag});
\begin{equation}
\hat{N}_j \langle \delta_i^j p - T_i^{\ j} \rangle = 0 \ ,
\label{cond0}\end{equation}
These are the usual traction conditions.
For the vertical component see that
\begin{equation}
\langle p \rangle = \hat{N}^i \hat{N}^j \langle T_{ij} \rangle \ ,
\label{cond1}\end{equation}
while the horizontal components lead to
\begin{equation}
\perp^{li} \hat{N}^j \langle T_{ij} \rangle = 0 \ ,
\label{cond2}\end{equation}
where we have defined the projection (orthogonal to the normal)
\begin{equation}
\perp^{li} =
g^{li} - \hat{N}^l \hat{N}^i \ .
\end{equation}
It is relevant to note that
the pressure may now be affected by the presence of a relative flow.
If we assume that the background configuration is such that the crust is relaxed, we
only need to account for the magnetic stresses. Then we have
\begin{equation}
T_{ij} = - g_{ij} {B^2 \over 8\pi} + { 1 \over 4 \pi} B_i B_j \ .
\end{equation}
We also know that $\nabla_i B^i=0$, which implies that we must have
\begin{equation}
\langle \hat{N}_i B^i \rangle = 0 \ .
\label{bone}\end{equation}
In this case, condition \eqref{cond1} leads to
\begin{equation}
\langle p + {B^2 \over 8 \pi } \rangle = 0 \ ,
\end{equation}
while \eqref{cond2} becomes
\begin{equation}
\left( \hat{N}_j B^j \right) \perp^{li} \langle B_i \rangle = 0 \ .
\end{equation}
Combined with \eqref{bone}, this shows that if the magnetic field penetrates the interface then all
components of the background field $B_i$ must be continuous.
To complete the analysis of the interface, we need one more condition. We obtain this condition from the
momentum equation for the neutrons. This choice is natural since we need to consider a quantity that remains relevant on both sides of
the interface, and there are no chemical gauge issues concerning the momentum of the superfluid
(essentially since it follows from the phase of the macroscopic
quantum wavefunction). However, we still have to be careful. Basically, the presence of vortices and potential pinning
complicates the picture. To make progress we will take the view that the irrotational condensate and the vortices can be considered separately.
At the end of the day, the total momentum equation involves an average over these components. In effect, the interface
must reflect this large scale average. Our approach to the problem represents this, yet it is
admittedly rather naive. A number of issues need to be better understood, in particular concerning the way in which
vortices extend from the fluid core to the elastic environment of the crust.
Let us simply mention two problems: First of all, we know from low-temperature laboratory
superfluids that vortices connect orthogonally to solid walls. It is natural to ask if the
same is true for vortices that penetrate the neutron star crust-core interface. Secondly, the entrainment
in the core leads to the vortices being magnetised, due to the entrainment, but this effect
relies on the protons being superconducting so is not active in the crust. The upshot is that a magnetised v
ortex somehow connects to an unmagnetized one. How does this work? The answer may be linked to the
transition from superconducting protons to ones locked in nuclei. In this case, one would expect the
presence of a current sheet. Presumably, this may also resolve any issues concerning the magnetic vortices,
but the details have not yet been considered. These and other issues need to be resolved by
future work. In the following we will adopt the pragmatic view that really difficult problems are perhaps best ignored.
Anyway, considering first the irrotational part, we have
\begin{equation}
\partial_t \tilde{p}^{\mathrm{x}}_i + \nabla_i \left( \tilde{\mu}_{\mathrm{x}} - {1\over 2} v_{\mathrm{x}}^2 + v_{\mathrm{x}}^j \tilde{p}^{\mathrm{x}}_j \right) = 0
\end{equation}
where ${\mathrm{x}}=[{\rm n},\f]$ depending on whether we are in the core or the crust. Working in the crust frame, and integrating over a small
volume, this leads to the interface condition
\begin{equation}
\tilde{\mu}_\f - \left( {1 \over 2}-\varepsilon_\f\right) w_{\f\mathrm{c}}^2 = \tilde{\mu}_{\rm n} - \left( {1 \over 2}-\varepsilon_{\rm n}\right) w_{{\rm n}{\rm p}}^2
\label{mucon}\end{equation}
It should be noted that, in the particular choice of chemical gauge where we consider all the neutrons in the crust
we have $\f\to{\rm n}$. In that case, the neutron chemical potential must be continuous, as expected.
Moving on to the vortices, we still do not have to worry about chemical gauge issues. Basically, one would expect each vortex to penetrate into the crust
leading to the vortex density $n_{\rm v}$ being continuous. Hence, we consider \eqref{circolo1},
where we recall that the vortex velocity $v_{\rm v}^i$ depends on whether there is pinning or not.
Working in the crust frame (as before) and integrating, we arrive at
the condition
\begin{equation}
(\hat{N}_j \mathcal{W}_\f^j ) w_i^{{\rm v}\mathrm{c}} = (\hat{N}_j \mathcal{W}_{\rm n}^j ) w_i^{{\rm n}{\rm p}}
\end{equation}
where we have used the fact that (in the present analysis) we do not consider pinning in the core.
However, because of the chemical gauge invariance, we have $\mathcal{W}_\f^j = \mathcal{W}_{\rm n}^j$ which means that
our final interface condition is
\begin{equation}
v_i^{\rm v} = v_i^{\rm n}
\label{vortcon}\end{equation}
This result is extremely intuitive. If the crust vortices are free, moving with $v_\f^i$, then we must have
$v_\f^i = v_{\rm n}^i$ at the interface. Meanwhile, if the vortices are pinned, moving with $v_\mathrm{c}^i$, then the condition should be
$v_\mathrm{c}^i = v_{\rm n}^i$.
These results represent two limiting cases. In the general case, we would also need to keep track of the
vortex velocity. This is, in principle, straightforward but we will not discuss the results here. It may be worth noting
that such models may be considered from a three-fluid point-of-view, with the vortices forming a distinct ``species''.
This is an interesting strategy that could prove advantageous in some situations.
\subsection{The perturbed problem}
Let us now move on to the conditions that need to be imposed at the linear perturbation level.
We can think of two possible strategies. Either we take the view that the conditions derived in the previous
section are ``exact'', which means that we can perturb them directly, or we start from the relevant perturbation equations
and carry out the analysis for a small volume straddling the interface all over again. In principle, these two approaches should lead to
the same answer. In practice, we find it useful to use a combination of them.
We begin by considering particle conservation.
In general, Lagrangian variation of the continuity equations leads to
\begin{equation}
\left( \partial_t + \mathcal{L}_{v_{\mathrm{x}}} \right) \left( \Delta_{\mathrm{x}} n_{\mathrm{x}} + n_{\mathrm{x}} \nabla_i \xi_{\mathrm{x}}^i \right) = 0
\end{equation}
We require the trivial solution, i.e. take
\begin{equation}
\Delta_{\mathrm{x}} n_{\mathrm{x}} + n_{\mathrm{x}} \nabla_i \xi_{\mathrm{x}}^i = 0
\end{equation}
In the case of the protons, we can integrate this equation over the small cylinder across the interface.
Taking the volume small enough that variations in $n_{\rm p}$ can be neglected (we are not allowing for
density discontinuities), we then find that
\begin{equation}
N_i \left( \xi_{\rm p}^i - \xi_\mathrm{c}^i \right) = 0
\label{pcon10}\end{equation}
As one would have expected, the normal component of the proton displacement should be continuous.
This condition follows immediately if we want to avoid there being a void (or overlap) in the proton fluid at the interface.
To get the second condition , we perturb the equation for total baryon conservation. This leads to (in the crust)
\begin{equation}
\Delta_\mathrm{c} n = \Delta_\mathrm{c} (n_\f + n_\mathrm{c}) = - n_\mathrm{c} \nabla_j \xi_\mathrm{c}^j + \xi_\mathrm{c}^j \nabla_j n_\f - \nabla_j \left( n_\f \xi_\f^j \right)
\end{equation}
If we (again) assume that the densities are smooth, then we only need to consider
\begin{equation}
\Delta_\mathrm{c} n \approx - \nabla_j \left( n_\mathrm{c} \xi_\mathrm{c}^j + n_\f \xi_\f^j \right)
\end{equation}
After integration across the interface, we find that we must have
\begin{equation}
N_j \left[ n_{\rm n} \left( \xi_\mathrm{c}^j - \xi_{\rm n}^j \right) - n_\f \left( \xi_\mathrm{c}^j - \xi_\f^j \right) \right] = 0
\label{mixcon}\end{equation}
In the case of the comprehensive gauge, when $n_\f=n_{\rm n}$, this reduces to
\begin{equation}
N_j \left( \xi_{\rm n}^j - \xi_\f^j \right) = 0
\end{equation}
Again, this condition seems natural, and we learn that the more complicated nature of \eqref{mixcon} results from the
fact that not all neutrons in the crust are free. We also see that we must keep careful track of the
different number densities across the interface.
Next we need the perturbed versions of \eqref{cond1} and \eqref{cond2}.
To derive these, we assume (as in the standard level set method) that the general conditions can meaningfully be extended away from the interface, and be perturbed in the usual way. There may be some technical issues
associated with this approach, but we will not go into the details of this here.
To derive the relevant conditions we start from \eqref{gencond}
which leads to
\begin{multline}
\hat{N}_j \left[ \rho_\f (1-\varepsilon_\f) w_i^{\f\mathrm{c}} \partial_t (\xi_\f^j - \xi_\mathrm{c}^j) + \delta_i^j \Delta_\mathrm{c} p -\Delta_\mathrm{c} T_i^{\ j} \right] \\
=
\hat{N}_j \left[ \rho_{\rm n} (1-\varepsilon_{\rm n}) w_i^{{\rm n}{\rm p}} \partial_t (\xi_{\rm n}^j - \xi_{\rm p}^j) + \delta_i^j \Delta_{\rm p} p - \Delta_{\rm p} T_i^{\ j} \right] \ .
\end{multline}
It is easy to see that, for an axisymmetric background, the first term in each expression does not contribute to the
normal component. Contracting with $\hat{N}^i$ we are left with
\begin{equation}
\left[ \Delta_\mathrm{c} p - \hat{N}^i \hat{N}_j \Delta_\mathrm{c} T_i^{\ j} \right]_\mathrm{crust} =
\left[ \Delta_{\rm p} p - \hat{N}^i \hat{N}_j \Delta_{\rm p} T_i^{\ j} \right]_\mathrm{core} \ .
\end{equation}
That is, we arrive at the expected traction condition.
The horizontal result is (obviously) more complicated. A projection orthogonal to $\hat{N}^i$ leads to
\begin{multline}
\hat{N}_j \left[ \rho_\f (1-\varepsilon_\f) w_i^{\f\mathrm{c}} \partial_t (\xi_\f^j - \xi_\mathrm{c}^j) - (\delta^l_i-\hat{N}^l \hat{N}_i)\Delta_\mathrm{c} T_l^{\ j} \right]_\mathrm{crust} \\
=
\hat{N}_j \left[ \rho_{\rm n} (1-\varepsilon_{\rm n}) w_i^{{\rm n}{\rm p}} \partial_t (\xi_{\rm n}^j - \xi_{\rm p}^j) - (\delta^l_i-\hat{N}^l \hat{N}_i)\Delta_{\rm p} T_l^{\ j} \right]_\mathrm{core} \ .
\end{multline}
As in previous cases, the additional complications arise from the choice of chemical gauge.
In the magnetic field case, we need \eqref{db1} and \eqref{db2}.
It is also useful to note that \eqref{bone} leads to
\begin{equation}
\langle \hat{N}_i \Delta_\mathrm{c} B^i \rangle = 0 \ .
\end{equation}
From this we see that
\begin{equation}
\langle \hat{N}^i \Delta_\mathrm{c} B_i \rangle = \langle B^i \hat{N}^j \left( \nabla_i \xi^\mathrm{c}_j + \nabla_j \xi^\mathrm{c}_l \right) \rangle \ .
\end{equation}
We then have
\begin{multline}
\hat{N}_i \Delta_\mathrm{c} p - \hat{N}_j \Delta_\mathrm{c} T_i^{\ j}\\
= \hat{N}_i \left( \Delta_\mathrm{c} p + { 1 \over 8 \pi} \Delta_c B^2 \right) -
{1 \over 4 \pi} \hat{N}_j \left( B^j \Delta_\mathrm{c} B_i + B_i \Delta_\mathrm{c} B^j \right) \ .
\end{multline}
The vertical component becomes
\begin{equation}
\langle \Delta_\mathrm{c} p + { 1 \over 8 \pi} \Delta_c B^2 \rangle = { 1 \over 4 \pi} \left( \hat{N}_j B^j \right) \langle \hat{N}^i \Delta_\mathrm{c} B_i \rangle \ ,
\end{equation}
while the horizontal condition becomes
\begin{equation}
\perp^{li}\langle \hat{N}_j \left( B^j \Delta_\mathrm{c} B_i + B_i \Delta_\mathrm{c} B^j \right) \rangle = 0 \ .
\end{equation}
At the perturbation level, we also need to consider the elastic problem. As before, we assume that the background
configuration is relaxed (and the core is fluid!), in which case we have
\begin{equation}
\Delta_\mathrm{c} T_{ij} = \check \mu \left( \nabla_i \xi^\mathrm{c}_j + \nabla_j \xi^\mathrm{c}_i \right) - {2 \over 3} \check \mu g_{ij} \nabla_l \xi_\mathrm{c}^l \ ,
\end{equation}
and
\begin{equation}
\Delta_\mathrm{c} T_i^{\ j} = g^{jl} \Delta_\mathrm{c} T_{il} \ .
\end{equation}
In this case, the vertical condition becomes
\begin{equation}
\langle \Delta_\mathrm{c} p + {2 \over 3} \check \mu \nabla_j \xi_\mathrm{c}^j \rangle = 2 \langle \check \mu \hat{N}^i \hat{N}^j \nabla_i \xi^\mathrm{c}_j \rangle \ ,
\end{equation}
while the horizontal one can be written
\begin{equation}
\perp^{li} \langle \check \mu \hat{N}^j \left( \nabla_i \xi^\mathrm{c}_j + \nabla_j \xi^\mathrm{c}_i \right) \rangle = 0 \ .
\end{equation}
Combining the elastic and magnetic results to arrive at the conditions to impose in the general case is, of course, straightforward.
Finally, we consider the conditions relating to the superfluid component. Perturbing the scalar condition
\eqref{mucon} we see that we should require
\begin{multline}
\left[ \Delta_\mathrm{c} \tilde{\mu}_\f - w_{\f\mathrm{c}}^2 \Delta_\mathrm{c} \varepsilon_\f + \left( {1 \over 2} - \varepsilon_\f \right) \Delta_\mathrm{c} w_{\f\mathrm{c}}^2 \right]_\mathrm{crust} = \\
\left[ \Delta_{\rm p} \tilde{\mu}_{\rm n} - w_{{\rm n}{\rm p}}^2 \Delta_{\rm p} \varepsilon_{\rm n} + \left( {1 \over 2} - \varepsilon_{\rm n} \right) \Delta_{\rm p} w_{{\rm n}{\rm p}}^2 \right]_\mathrm{core}
\end{multline}
As far as the vorticity is concerned, it follows naturally from the discussion leading up to \eqref{vortcon} that we should have
\begin{equation}
\perp^i_j \left( \Delta_\mathrm{c} v_{\rm v}^j - \Delta_{\rm p} v_{\rm n}^j \right) = 0
\end{equation}
This condition is (obviously) satisfied if we have $\perp^i_j(\xi_\f^j-\xi_{\rm n}^j)=0$ in the free vortex case and $\perp^i_j(\xi_\mathrm{c}^j-\xi_{\rm n}^j)=0$ when perfect pinning prevails.
This ensures that there are no kinks in the vortices at the interface.
\section{Conclusions}
We have developed a Lagrangian perturbation framework relevant for the conditions
that apply in a mature neutron star, accounting for the presence of superfluid components,
the elastic crust and the magnetic field. The considered physics impacts on a wide range of astrophysical
phenomena, from pulsar glitches to magnetar seismology and various gravitational-wave emission mechanisms.
Hence, the reported theoretical developments provide us with a solid foundation to consider exciting applications.
There is also significant scope for future improvements of the theory. Most importantly, the effort should be extended to
relativistic gravity. This would open the door to truly quantitative considerations of realistic neutron star models, e.g.
based on a modern supranuclear equation of state with composition and thermal gradients. Developments in this
direction are in progress.
We also need to improve our understanding of the physics involved.
Our discussion highlights the need to know a wider set of parameters, like the superfluid entrainment both in the
star's core and in the elastic crust. The various interactions involving superfluid vortices, from pinning to mutual friction,
also need to be understood. While we can continue to advance our understanding of the phenomenology of these very complex systems,
we need to impose realistic constraints on our models. This requires, if not a precise knowledge of the involved parameters,
some idea of what the permissible ranges may be. To achieve this goal we need a continued dialogue across different branches of physics,
a challenging but ultimately rewarding exercise.
\section*{Acknowledgments}
NA would like to thank Bennett Link for useful conversations on neutron star superfluids in general
and vortex interactions in particular.
Our model for the pinning in the crust is heavily influenced by a talk that Bennett gave at the neutron star meeting at Nordita in Stockholm in 2009.
We are also grateful to Pierre Pizzochero for sharing his thoughts on the nuclear pinning force.
NA acknowledges support from STFC via grant number PP/E001025/1. LS is supported by the European Research Council under Contract No.\ 204059-QPQV,
and the Swedish Research Council under Contract No.\ 2007-4422. BH is supported by a Marie Curie Fellowship.
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Oakdale est une ville de la paroisse d'Allen, en Louisiane, aux États-Unis.
La ville est fondée en 1890 sous le nom de Dunnville. En 1893, elle change de nom pour devenir Oakdale lorsque le St. Louis, Iron Mountain and Southern Railway arrive dans la ville.
Références
Article connexe
Source de la traduction
Ville en Louisiane
Paroisse d'Allen
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| 4,633
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Q: Chatting about mathematics (with real-time LaTeX rendering) Do you know about some tools which can be used for online chat about mathematics? In particular, I am interested in software which would be able to render LaTeX formulas. (Since LaTeX is probably the fastest possibility to type mathematics.)
Have you tried some of them? What are their advantages and drawbacks?
NOTE 1: In this question I am asking only about solutions how to type mathematics in chat, not about possibility to use video and sound.
(For the purposes of this question, assume that only keyboard, mouse and display are plugged to your computer.)
NOTE 2: I will post some possibilities I am aware of in the answers. But I would be grateful if someone who tried these applications could expand these answers a little more.
A: Hopefully this is helpful; I have been programming a MathJax based online chat service in my spare time (there are some styling issues still). It is quite fast and has quite a few features. Here it is:
http://mathchat.x10.mx/
Enjoy!
A: ShareLaTeX had builtin chat with MathJax:
UPDATE: it was aquired by Overleaf. As almost all of ShareLaTeX, it was open source, and remains open source after aquisition!
Source moved here: [backend, frontend].
As of 2020 it's integrated into Overleaf.com, and all MathJax features seem to work fine:
This is a near-real-time collaborative LaTeX editor, so this is great for chatting around a writeup/paper, but you can also create empty project or file just to use chat/commenting, and gradually "spill over" into the editor for a more flexible collaboration...
P.S. Note that for review comments on particular points of the paper, Overleaf have dedicated feature for comment threads on particular points! These don't render math currently.
A: EDIT: This project seems to be abandoned. (At least the website does not work anymore.) If anyone has the knowledge that it has been moved to another location, please, edit this post with updated information.
TeXChat is a chat which uses Mathjax for rendering math.
I've learned about it from the website MathJax in Use.
Here's a screenshot:
You can copy a source of an individual message by hovering above it and selecting the text.
A: I work on Zulip, an open source team chat server. It supports LaTeX using $$…$$ for inline math and
```math
…
```
for displayed math. These are rendered on the server side using KaTeX.
A: There are scripts written by Valery Alexeev.
UPDATE: The new name for this plugin is TeX for Gmail. Now there is only one plugin which adds TeX-rendering to both Gmail and Gmail Chat. (IIRC, they used to be separate.)
Here is original version of this post:
They were mentioned in this answer: https://physics.stackexchange.com/questions/7809/online-physics-collaboration-tools/7811#7811
GmailTeX was mentioned in leo's comment. There is also GmailChatTeX.
This Firefox add-on http://thewe.net/tex/ seems to be similar.
A: Gitter which is generally programmer-optimized (markdown, syntax highlight, GitHub integration) also supports math with $$...$$ syntax.
It uses KaTeX which is very fast but not as feature-full as MathJax
Free public and private rooms up to 25 people.
A: Instabird with this MathJax addon:
A: If you want a wide platform support, including smartphones and want a mainstream messenger lots of people already use, then telegram with a latex bot can do this. If you are not familiar with telegram, it's basically like whatsapp.
Once you have telegram, you need to add a bot (just a contact) that would render LaTeX to image in your chats. Right now I have inlatexbot, but there are also others. https://github.com/vdrhtc/InLaTeXbot
It might not be as feature reach and perfect as latex plugins for jabber clients, for example, it is not capable of inline math, it just gives you an image with your formula in chat. If you need LaTeX only occasionally, this is ok.
However, I believe telegram is the only mainstream messenger that can do LaTeX and it is also available for all major platforms including mobile. It also has a superfast synchronization between your devices via cloud (yes, you can store your history on the server).
A: http://papertogether.com is a collaborative whiteboard app with chat that supports math surrounded by backticks:
Foo `a^2 + b^2 = c^2` bar baz.
Unfortunately there is no text tool to add formulas inside the drawing area, and the chat is a small subwindow in the corner.
KaTeX-powered so supports less constructs (e.g. no matrices).
Help, Background
A: LaTeX plugin in Pidgin:
http://sourceforge.net/projects/pidgin-latex/
This screenshot is taken from http://sourceforge.net/projects/pidgin-latex/screenshots/124729
A: I use Lyx to type LaTeX quickly. It is a WYSIWYG LaTeX editor.
You can then use screen sharing e.g with Skype so the other person can see what you are doing on Lyx.
Never tried the screen sharing part, just an idea.
A: Overleaf has a 'Chat' feature which is accessible in the top-right corner and is LaTeX-processed.
A: Mathim - online chat with the possibility to use of LaTeX syntax (the first result that google returned for latex online chat or latex online chat math)
http://mathim.com
Screenshot from my short experiment with this tool:
Mathim was also discussed here:
http://www.physicsforums.com/showthread.php?t=193510
http://www.physicsforums.com/showthread.php?t=196699
It is possible to copy the text of session (simply by selecting it) and put it into a TeX file.
A:
The web interface of hack.chat renders LaTeX, and there are some pre-made rooms for math, physics, etc.
It's also open source and can be installed on your own server if needed.
A: If you use Discord, invite TeXit to your server. (Go to that webpage, click "invite" and enter the name of your server.) Anytime you put dollar signs in a post, TeXit will interpret what you say as LaTeX and will repeat a TeX'd version of what you said. Here is an example of what you'll see
Mathbot is another bot with similar features, but you need to type =tex at the start of the line, which I find harder to remember.
A: Sorry for reviving a bit of an old question, however as of today, it is now possible to LaTeX over Facebook chat, automatic rendering. There are a few things to note:
$1:$ You will only be able to view this on desktop, mobile does not support it yet.
$2:$ You must enclose your message in either \(...\) for inline math (can be interspersed in text) or $$...$$ for display math (must be the sole content of a chat message, not recognized if preceded/followed by other text)
$3:$ There is a one-line size limit which isn't terribly generous.
$4:$ If KaTeX can't parse the math, it will stay unrendered text, but you can hover over it to see the error message.
So, a bit restricted, but there's a lot of potential, and the future is now. But yeah, again sorry for mentioning it on such an old message, but I think it's worth letting people know.
A: Deprecated: There are easier ways to render $\LaTeX$ in chat, such as the start ChatJax bookmarklet, which uses MathJax to render.
In the Mathematics chat, we often use the codecogs.com $\LaTeX$ Equation Editor: http://latex.codecogs.com/gif.latex?\sum_{k=1}^\infty\frac{1}{k^2}=\frac{\pi^2}{6} yields
You have to replace spaces with %20 since spaces are not allowed in URLs (actually, it is probably best to escape all reserved characters in URLs, but other than spaces, most characters seem to be passed through by a number of common browsers).
A: I haven't seen the easiest answer: Facebook Messager! If you write a message of the form:
$$ equation here $$
The whole message has to be only the formula, if you want an equation as a part of a longer message you can use:
Some text \( equation here \) and more text.
A: I use overleaf and screenshare it while talking over zoom. Or I use a chrome extension "TeX for Gmail & Inbox"
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Easton is an unincorporated community and census-designated place (CDP) in Kittitas County, Washington, United States. The population was 478 at the 2010 census.
History
Easton was platted in 1902. It was given its name by the Northern Pacific Railway due its location near the east end of the Stampede Tunnel through the Cascade Range.
Geography
Easton is located in western Kittitas County at (47.238368, -121.178327), in the Yakima River valley. Interstate 90 passes through the community, with access from Exits 70 and 71. I-90 leads northwest over Snoqualmie Pass to Seattle and southeast to Ellensburg, the Kittitas county seat.
According to the United States Census Bureau, the Easton CDP has a total area of , of which , or 0.46%, are water. Lake Easton, a reservoir at the junction of the Yakima and Kachess rivers, and Lake Easton State Park are at the west end of the community.
Climate
This region experiences warm (but not hot) and dry summers, with no average monthly temperatures above 71.6 °F. According to the Köppen Climate Classification system, Easton has a warm-summer Mediterranean climate, abbreviated "Csb" on climate maps.
Demographics
As of the census of 2000, there were 383 people, 151 households, and 104 families residing in the CDP. The population density was 227.3 people per square mile (88.0/km2). There were 228 housing units at an average density of 135.3/sq mi (52.4/km2). The racial makeup of the CDP was 91.91% White, 0.78% Native American, 6.53% from other races, and 0.78% from two or more races. Hispanic or Latino of any race were 9.14% of the population.
There were 151 households, out of which 35.1% had children under the age of 18 living with them, 54.3% were married couples living together, 7.3% had a female householder with no husband present, and 31.1% were non-families. 21.9% of all households were made up of individuals, and 4.0% had someone living alone who was 65 years of age or older. The average household size was 2.54 and the average family size was 2.94.
In the CDP, the population was spread out, with 28.7% under the age of 18, 7.3% from 18 to 24, 29.5% from 25 to 44, 23.0% from 45 to 64, and 11.5% who were 65 years of age or older. The median age was 35 years. For every 100 females, there were 124.0 males. For every 100 females age 18 and over, there were 125.6 males.
The median income for a household in the CDP was $37,708, and the median income for a family was $37,917. Males had a median income of $33,750 versus $20,357 for females. The per capita income for the CDP was $19,773. About 3.7% of families and 7.5% of the population were below the poverty line, including 2.7% of those under age 18 and 26.7% of those age 65 or over.
Notable people
Sherwood Egbert, president of the Studebaker-Packard and Studebaker corporations
Points of interest
Lake Easton State Park
Iron Horse State Park, former right-of-way for the Milwaukee Road which today serves as a path for bikers, hikers, cross-country skiers and horseback riders
See also
Kachess Lake
Stampede Pass
References
Census-designated places in Kittitas County, Washington
Census-designated places in Washington (state)
Populated places on the Yakima River
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{
"redpajama_set_name": "RedPajamaWikipedia"
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{"url":"http:\/\/moebiuscurve.com\/group-homomorphism-and-examples\/","text":"# Group\n\nA group is any set G with a defined binary operation (called the group law of $G$), written as 2 tuple (examples: $(G,*), (G,\\cdot), (G,+), ...$), satisfying 4 basic rules\n\n## Closure\n\nThe important point to be understood about a binary operation on $G$ is that $G$ is closed with respect to $*$ in the sense that if $a,b\\in G$ then $a*b\\in G$\n\n($a,b\\in{C}$ can be read as \"a,b element of C\" or \"a,b in C\")\n\n## Associativity\n\n$(a*b)*c = a*(b*c), \\forall a,b,c\\in{G}$\n\n($\\forall{a,b}\\in{C}$ can be read as \"for all a,b in C\" or \"for all a,b being element of C\" or \"for each a,b in C\" or \"for every a,b in C\", ...\u00a0 etc.)\n\n## Identity\n\nAn element $e\\in G$ (called identity of the Group $G$) that satisfies the condition $e*a=a*e = a, \\forall a\\in{G}$\n\n$G$ contains at most one identity element $e$\n\n## Inverse\n\n$\\forall a\\in{G}$ there exists an element $a^{-1}\\in{G}$ such that $a*a^{-1} = a^{-1}*a = e$\n\nGroups can be both finite and infinite.\n\n## Example 1\n\nThe set $\\mathbb{R}\\backslash\\{0\\}$ (set of all real numbers excluding $0$) with the binary operation of multiplication $((G,*))$\u00a0 forms a group.\n\nclosure criteria\n\n$\\forall a,b\\in \\mathbb{R}\\backslash\\{0\\} \\implies a*b\\in \\mathbb{R}\\backslash\\{0\\}$\n\nFor instance,\n\n5*6 =30 is an element of $R\\backslash\\{0\\}$\n\nassociativity criteria\n\n$\\forall a,b\\in \\mathbb{R}\\backslash\\{0\\} \\implies a*(b*c)= (a*b)*c=a*b*c$\n\nFor instance,\n\n2*(3*9)=(2*3)*9 = 2*3*9=54\n\nidentity Criteria\n\nnumber $1$ is identity for $*$ in $\\mathbb{R}\\backslash\\{0\\}$\n\n$\\forall a\\in \\mathbb{R}\\backslash\\{0\\}, a*1=1*a=a$\n\nFor instance,\n\n1*5=5*1=5\n\ninverse criteria\n\n$\\forall a\\in \\mathbb{R}\\backslash\\{0\\} \\implies a*a^{-1}=1$\n\nFor instance,\n\n$2*\\frac{1}{2}=2*0.5=1$\n\n## Example 2\n\nThe set $\\mathbb{R}$ with the binary operation of addition $((G,+))$ forms another group\n\nclosure criteria\n\n$\\forall a,b\\in \\mathbb{R} \\implies a+b\\in \\mathbb{R}$\n\nFor instance,\n\n5+6 =11 is an element of $\\mathbb{R}$\n\nassociativity criteria\n\n$\\forall a,b\\in \\mathbb{R} \\implies a+(b+c)= (a+b)+c=a+b+c$\n\nFor instance,\n\n2+(3+9)=(2+3)+9 = 2+3+9=14\n\nidentity Criteria\n\nnumber $0$ is identity for $+$ in $\\mathbb{R}$\n\n$\\forall a\\in \\mathbb{R}, a+0=0+a=a$\n\nFor instance,\n\n0+5=5+0=5\n\ninverse criteria\n\n$\\forall a\\in \\mathbb{R}\\implies a+a^{-1}=0$\n\nFor instance,\n\n$2+2^{-1}=2+(-2)=0$\n\n## Subgroup\n\nGiven a group $G$ under a binary operation $*$, a subset $H$ of $G$ is called a subgroup of $G$ if $H$ also forms a group under the operation $*$\n\nBoth Group($G$) and Subgroup($H$) share the same identity $e$.\n\n## Group Table\n\nGroup table describes the structure of a finite group by arranging all the possible products of all the group's elements in a square table (reminiscent of an addition or multiplication table). Many properties of a group - such as whether or not it is abelian, which elements are inverses of which elements, and the size and contents of the group - can be discovered from group table\n\nFor group $G_1=\\{1,-1\\}$ the multiplication table $((G_1,*))$ looks like:\n\nFor group $G_2 = \\{1, -1, i, -i\\}$, the multiplication table $((G_2,*))$ looks like:\n\n# Homomorphism of a Group\n\nif $G$ and $H$ are two groups with binary operations $*$ and $\\circ$, respectively, a function $f:G\\rightarrow{H}$ is a homomorphism if\n\n$f(a*b)= f(a)\\circ{f(b)}$, $\\forall a,b \\in{G}$\n\nSimply put, group homomorphism is a transformation of one Group into another that preserves (invariant) in the second Group the relations between elements of the first.\n\n## Examples of Group Homomorphism\n\n### Example 1\n\nLet $G$ be the group of all nonsingular, real, $N\\times{N}$ matrices with the binary operation of matrix multiplication. Let $H$ be the group $\\mathbb{R} \\backslash\\{0\\}$ with the binary operation of scalar multiplication. The function that is the determinant of a matrix is then a homomorphism from $G$ to $H$\n\nTo put this in symbolic context:\n\nLet $(G=\\{A,B,C,D,...\\},*)$ and let $(H=\\mathbb{R}\\backslash{\\{0\\}},\\times)$\n\nThen, $\\det(A*B)=\\det(A)\\times\\det(B)$\n\n## Endomorphism\n\nA homomorphism $f:G \\rightarrow{G}$ is called an endomorphism\n\n### Examples of Endomorphism\n\n#### Example 1\n\nLet $G$ be the group $\\mathbb{R}\\backslash\\{0\\}$ with the binary operation of multiplication. The function that takes the absolute value of a number is then an endomorphism of $G$ into $G$\n\nTo put this in symbolic context:\n\nLet $(G,*)$, $G=\\mathbb{R}\\backslash\\{0\\}$ Then,\n$|x*y|=|x|*|y|$, $\\forall x,y\\in{G}$\n\nFor instance,\n\n|-3*4|=|-3|*|4|=3*4=12\n\nAnd\n\n|-2| = |2|=2\n\n## Isomorphism\n\nA homomorphism $f :G \\rightarrow H$ is an isomorphism if $f$ is both one-to-one and onto (bijective).\n\n### Examples of Isomorphism\n\n#### Example 1\n\nLet $G$ be the group of positive real numbers with the binary operation of multiplication and let $H$ be the group of real numbers with the binary operation of addition. The $\\log_b$ function is an isomorphism between $G$ and $H$\n\nTo put this in symbolic context:\n\nLet $(G,*)$, $G ={\\{\\mathbb{R}^+\\}}$ and Let $(H,+)$, $H={\\{\\mathbb{R}\\}}$,\nThen,\n\n$\\log_{b}(x*y) = \\log_{b}(x) + \\log_{b}(y)$, $\\forall x,y\\in{G}$\n\n($\\mathbb{R}^+$ denotes set of all positive real numbers)\n\n## Automorphism\n\nAn isomorphism $f:G \\rightarrow{G}$ is called an automorphism.\n\n### Examples of Automorphism\n\n#### Example 1\n\nLet $G$ be the group $\\mathbb{R}^+\\backslash\\{0\\}$ with the binary operation of multiplication. The function that takes the absolute value of a number is then an automorphism of $G$ into $G$\n\nTo put this in symbolic context:\n\nLet $(G,*)$, $G=\\mathbb{R}^+\\backslash\\{0\\}$, Then, $|x*y|=|x|*|y|$, $\\forall x,y\\in{G}$\n\nFor instance,\n\n[3*4|=|3|*|4|=3*4=12\n\nIn this case both sides can use only positive real numbers. Note that this contrasts with an earlier example of Endomorphism where the Group\u00a0$G=\\mathbb{R}\\backslash\\{0\\}$\n\n# Kernel of Homomorphism\n\nThe kernel of a homomorphism $f:G \\rightarrow{H}$ is the subgroup $f^{-1}(e_0)$ of $G$.\n\nIn other words, the kernel of $f$ is the set of elements of $G$ that are mapped by $f$ to the identity element $e_0$ of $H$\n\nThe notation $K(f)$ can be used to denote the kernel of $f$\n\n## Examples of Kernel of homomorphism\n\n### Example 1\n\nLet $G$ be the group of all nonsingular, real, $N \\times N$ matrices with the binary operation of matrix multiplication. Let $H$ be the group $\\mathbb{R}\\backslash\\{0\\}$ with the binary operation of scalar multiplication. The function that is the determinant of a matrix is then a homomorphism from $G$ to $H$\n\nLet $(G=\\{A,B,C,D,...\\},*)$ and let $(H=\\mathbb{R}\\backslash{\\{0\\}},\\times)$\nThen,\n\n$\\det(A*B)=\\det(A)\\times\\det(B)$\n\nIn this case the kernel of $\\det$ consists of set of all $N \\times N$ matrices with determinant equal to the real number $1$\n\n### Example 2\n\nLet $(G,*)$, $G=\\mathbb{R}\\backslash\\{0\\}$, Then,\n\n$|x*y|=|x|*|y|$, $\\forall x,y\\in{G}$\n\nThe kernel of $|a|, \\forall{a}\\in{G}$ consists of set $\\{-1,1\\}$\n\n### Example 3\n\nLet $(G,*)$, $G=\\mathbb{R}^+\\backslash\\{0\\}$, Then,\n\n$|x*y|=|x|*|y|$, $\\forall x,y\\in{G}$\n\nThe kernel of $|a|, \\forall{a}\\in{G}$ consists of set $\\{1\\}$\n\n### Example 4\n\nLet $(G,*)$, $G ={\\{\\mathbb{R}^+\\}}$ and Let $(H,+)$, $H={\\{\\mathbb{R}\\}}$\n\nThen,\n\n$\\log_{b}(x*y) = \\log_{b}(x) + \\log_{b}(y)$, $\\forall x,y\\in{G}$\n\nThe kernel of $\\log_b$ is the set $\\{1\\}$ because identity $0$ of $H$ is mapped to set of all numbers whose $\\log_b$ produces $0$\n\n# Some simplified theorems derived from homomorphism\n\n(Note: I will not provide any proofs here, because the theorems are quiet simple and proofs can be worked out easily)\n\n## Theorem 1\n\nIf $f:G \\rightarrow{H}$ is a homomorphism, then $f(e)$ coincides with the identity element $e_0$ of $H$ and $f(a^{-1}) = f(a)^{-1}$\n\n### Example for Theorem 1\n\nLet $G$ be the group of all nonsingular, real, $N\\times{N}$ matrices with the binary operation of matrix multiplication. Let $H$ be the group $\\mathbb{R} \\backslash\\{0\\}$ with the binary operation of scalar multiplication. The function that is the determinant of a matrix is then a homomorphism from $G$ to $H$\n\nTo put this in symbolic context:\n\nLet $(G=\\{A,B,C,D,...\\},*)$ and let $(H=\\mathbb{R}\\backslash{\\{0\\}},\\times)$\n\nThen, $\\det(A*B)=\\det(A)\\times\\det(B)$\n\nIn this case the identity of Matrix is the Identity matrix (denoted by $I$).\n\nTherefore, $\\det(I*B)= \\det(I)\\times \\det(B)$, where: $\\det(I) =1$ and $1$ is identity of $\\mathbb{R}\\backslash\\{0\\}$\n\nNow For $N=2$, Let $A = \\left[\\begin{matrix}2 & 1 \\\\1 & 2\\end{matrix}\\right]$\n\nThen,\n\n$\\det(A)=3$ & $\\det(A)^{-1}=\\frac{1}{3}$\n\n$A^{-1} = \\left[\\begin{matrix}\\frac{2}{3} & -\\frac{1}{3} \\\\-\\frac{1}{3} & \\frac{2}{3}\\end{matrix}\\right]$\n\n$\\det(A^{-1})=\\frac{3}{9}=\\frac{1}{3}$\n\nWe can verify that, $\\det(A^{-1})=\\det(A)^{-1}$\n\n## Theorem 2\n\nIf $f:G\\rightarrow{H}$ is a homomorphism and if $G'$ is a subgroup of $G$, then $f(G')$ is a subgroup of H\n\n## Theorem 3\n\nIf $f:G\\rightarrow{H}$ is a homomorphism and if $H'$ is a subgroup of $H$ , then the preimage $f^{-1}(H')$ is a subgroup of $G$\n\n## Theorem 4\n\nA homomorphism $f:G\\rightarrow{H}$ is one-to-one if and only if $K(f) = {e}$.\n\n## Theorem 5\n\nIf $f:G\\rightarrow{H}$ is an isomorphism, then $f^{-1}:H\\rightarrow{G}$ is an isomorphism\n\n## Theorem 6\n\nA homomorphism $f:G\\rightarrow{H}$ is an isomorphism if it is onto and if its kernel contains only the identity element of G.","date":"2019-02-21 14:25:09","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 192, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 192, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9416847229003906, \"perplexity\": 279.92078600902863}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-09\/segments\/1550247504790.66\/warc\/CC-MAIN-20190221132217-20190221154217-00185.warc.gz\"}"}
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Q: Google Firebase Authentication: unrecognized selector sent to instance I am using Ionic2 with Cordova to authenticate a user in Firebase.
I can build the app and run it on iOS Simulator (Xcode). However, as soon as I try log in a user with the following code using ionic-native ("ionic-native": "2.2.11",) GooglePlus:
loginGoogleCordova(): void {
GooglePlus.login(['public_profile', 'email']).then(googleData => {
let provider = firebase.auth.GoogleAuthProvider.credential(googleData.authResponse.accessToken);
firebase.auth().signInWithCredential(provider).then((data) => {
this.signIn(data);
});
}, error => {
this.loading.dismiss();
console.error('loginGoogle: ' + error);
this.doAlert('loginGoogle: ' + error.message);
});
}
I get the following error:
2017-03-06 07:55:06.433 theWhoZoo[10489:868996] *** WebKit discarded
an uncaught exception in the
webView:decidePolicyForNavigationAction:request:frame:decisionListener:
delegate: -[__NSArrayM
objectForKeyedSubscript:]: unrecognized selector sent to instance
0x6100002471a0
More Info:
I can successfully authenticate a user in a browser with AngularFire2.
loginGoogleBrowser() {
this.auth.login({ provider: AuthProviders.Google, method: AuthMethods.Popup }).then((data: FirebaseAuthState) => {
this.signIn(data);
}).catch((error) => {
this.loading.dismiss();
console.error('loginGoogle', error);
this.doAlert('loginGoogle: ' + error.message);
});
}
Any help appreciated.
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
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It is an echo; a reminder of who we are. The redeemed imagination allows the believer to see the world, and his own life, through divine eyes. To play a role in the building of a Kingdom (in the already and the not yet) whose glory we can scarcely comprehend.
Artists and pastors play crucial parts in aiding the rest of us in this calling, but it is the calling of every Christian. Yet the separation of imagination from the church has left us with a disenchanted Christianity and a slew of vapid books, music, and movies.
The disenchanted, the lost, and the Church itself need a renaissance of the Christian imagination.
Your Imagination Redeemed in the Anselm Society's annual conference. From Friday night through Saturday night, April 26-27, we will seek inspiration and refreshment as we explore the redeemed imagination together.
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{
"redpajama_set_name": "RedPajamaC4"
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Sart is een studioalbum van Jan Garbarek. Het kwartet waarmee hij destijds speelde en opnam werd uitgebreid tot een kwintet door toevoeging van een pianist. Deze pianist, Bobo Stenson zou later als soloartiest een grote catalogus aan albums voor ECM Records opnemen. Het album werd opgenomen in de Bendiksen Studio te Oslo, met Jan Erik Kongshaug achter de knoppen. Het hoesontwerp was van Barbara Wojirsch.
In de volgende release van ECM verscheen het eerste soloalbum van Terje Rypdal, waarop een vervolg van Rypdals compositie Lontano staat. De samenstelling van het ensemble is in de basis hetzelfde.
Musici
Jan Garbarek – tenorsaxofoon, bassaxofoon, dwarsfluit
Bobo Stenson – piano
Terje Rypdal – gitaar
Arild Andersen – basgitaar
Jon Christensen – slagwerk
Muziek
Muziekalbum uit 1971
Jazzalbum
Muziekalbum van Jan Garbarek
Muziekalbum van Bobo Stenson
Muziekalbum van Terje Rypdal
Muziekalbum van Arild Andersen
Muziekalbum van Jon Christensen
Muziekalbum uitgegeven door ECM Records
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"redpajama_set_name": "RedPajamaWikipedia"
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{"url":"https:\/\/control.com\/textbook\/dc-electricity\/capacitors\/","text":"# Introduction to Capacitors and Capacitance\n\n## Chapter 4 - Basic Direct Current (DC) Theory\n\nAny two electrical conductors separated by an insulating medium possess the characteristic called capacitance: the ability to store energy in the form of an electric field created by a voltage between those two conductors. Capacitance is symbolized by the capital letter $$C$$ and is measured in the unit of the Farad (F). The relationship between capacitance, stored electric charge ($$Q$$), and voltage ($$V$$) is as follows:\n\n$Q = CV$\n\nFor example, a capacitance having a value of 33 microfarads charged to a voltage of 5 volts would store an electric charge of 165 microcoulombs.\n\nCapacitors are devices expressly designed and manufactured to possess capacitance. They are constructed of a \u201csandwich\u201d of conductive plates separated by an insulating dielectric. Capacitors have maximum voltage ratings as well as capacitance ratings. Here are some schematic symbols for capacitors:\n\nAlthough any two conductors separated from each other by an insulating medium possess capacitance, we may optimize the amount of capacitance by situating the conductors in a manner yielding more electric flux for any given amount of applied voltage. Placing the two conductors closer together (thus creating a more intense electric field between them, measured in volts per inch) is one way to increase capacitance. Increasing the overlapping area of the conductors (thus providing more area for parallel electric flux lines to form) is another way. Inserting a strongly dielectric (i.e. an exceptionally good insulating) material between the conductors is a third way to increase capacitance.\n\nThese three factors may be expressed in a single mathematical formula for capacitance:\n\n$C = {\\epsilon A \\over d}$\n\nWhere,\n\n$$C$$ = Capacitance in Farads\n\n$$A$$ = Overlapping area of conductors in square meters\n\n$$\\epsilon$$ = Permittivity of the dielectric substance\n\n$$d$$ = Distance separating the conductors in meters\n\nCapacitance is a non-dissipative quantity. Unlike resistance, a pure capacitance does not dissipate energy in the form of heat; rather, it stores and releases energy from and to the rest of the circuit. We may illustrate the energy-storing behavior of a capacitor by this simple voltage source, switch, and resistor circuit:\n\nNote how the capacitor alternately functions as a source and as a load, depending on what it\u2019s connected to. When connected to a source of voltage, the capacitor absorbs (stores) energy in the form of an electric field between its plates. Current flows through the voltage source in the same direction as though it were powering a load (e.g. a resistor). When the capacitor\u2019s voltage equals the source voltage, current stops in the circuit. Flipping the switch to the \u201cdischarge\u201d position connects the capacitor to a resistor, where it discharges its store of energy, acting as a source to the resistor\u2019s load.\n\nNote also how the capacitor maintains the same polarity of voltage during all three steps. Since energy is stored within an electric field inside the capacitor, and electric fields are a function of voltage, the stored energy manifests itself as a voltage with an unchanging polarity. The Law of Energy Conservation \u2013 which states energy cannot spontaneously vanish or appear but must be accounted for \u2013 tells us a capacitor\u2019s voltage cannot spontaneously vanish, appear, or change polarity. In other words, voltage is the conserved quantity in a capacitor as it transitions between acting as a source and acting as a load. Current through a capacitor, however, switches direction depending on whether the capacitor is charging (acting as a load) or discharging (acting as a source).\n\nCapacitance adds when capacitors are connected in parallel. It diminishes when capacitors are connected in series:\n\n$C_{parallel} = C_1 + C_2 + \\cdots C_n \\hbox{\\hskip 50pt} C_{series} = {1 \\over {1 \\over C_1} + {1 \\over C_2} + \\cdots + {1 \\over C_n}}$\n\nRecall that capacitance stores energy in the form of an electric field, as a function of the voltage applied to it. It we wish to increase capacitance by connecting multiple capacitors to each other, we need to do that in such a way that each capacitor receives the same (total) applied voltage so that each additional amount of capacitance included in the network will contribute a proportional amount of energy storage to the network. We know voltage is guaranteed to be equal only among parallel-connected components. If we were to connect multiple capacitors in series with one another, their individual voltages would be some fraction of the total voltage (series voltages always adding to equal the total voltage), thus diminishing the energy stored in each capacitor and similarly diminishing the total capacitance.\n\nAnother way to comprehend why capacitance increases in parallel and diminishes in series is to consider a network of capacitors as one equivalent capacitor in terms of aggregate plate area and separation distance. Examining the directions of change to the corresponding variables in the permittivity\/area\/distance formula for capacitance, we see how parallel-connected capacitances must add while series-connected capacitances must diminish:\n\nThe relationship between voltage and current for a capacitor is as follows:\n\n$I = C{dV \\over dt}$\n\nAs such, capacitors oppose changes in voltage over time by passing a current. This behavior makes capacitors useful for stabilizing voltage in DC circuits. One way to think of a capacitor in a DC circuit is as a temporary voltage source, always \u201cwanting\u201d to maintain voltage across its terminals as a function of the energy stored within its electric field.\n\nThe amount of potential energy ($$E_p$$, in units of joules) stored by a capacitor may be determined by altering the voltage\/current\/capacitance equation to express power ($$P = IV$$) and then applying some calculus (recall that power is defined as the time-derivative of work or energy, $$P = {dW \\over dt} = {dE \\over dt}$$):\n\n$I = C{dV \\over dt}$\n\n$P = IV = CV{dV \\over dt}$\n\n${dE_p \\over dt} = CV{dV \\over dt}$\n\n${dE_p \\over dt} \\> dt = CV \\> dV$\n\n$\\int{dE_p \\over dt} \\> dt = \\int CV \\> dV$\n\n$\\int dE_p = C \\int V \\> dV$\n\n$E_p = {1 \\over 2}CV^2$\n\nIn an AC circuit, the amount of capacitive reactance ($$X_C$$) offered by a capacitor is inversely proportional to both capacitance and frequency:\n\n$X_C = {1 \\over {2 \\pi f C}}$\n\nThis means an AC signal finds it \u201ceasier\u201d to pass through a capacitor (i.e. less ohms of reactance) at higher frequencies than at lower frequencies.\n\n\u2022 Share\nPublished under the terms and conditions of the Creative Commons Attribution 4.0 International Public License","date":"2021-01-25 17:58:24","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5739952921867371, \"perplexity\": 627.2771699859335}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-04\/segments\/1610703587074.70\/warc\/CC-MAIN-20210125154534-20210125184534-00028.warc.gz\"}"}
| null | null |
Check out page 46 in the July Hot Rod Magazine. Our fearless leader Jon gets credit for the authentication of the 69' Guldstrand T/A Camaro. How about a vintage photo of this car as it should look Jon?
it wasn't the #3 in front of it.
ago to show it to him.
Sports Car Graphic magazine a measly few decades ago. Little did he know the car was still "out there".
YEP, I always wondered if I would ever get to see that car in person. Now its in my garage and I have Jon to thank for that--THANKS again Jon.
I think Rob Kinnan wrote a fine short history on the car and gave the credit to whom it belongs.
This is the only color shot I have of the car. Maybe Robert's got something else he cares to share?
and black accents (the sides are mostly silver). It's a very nice looking car, in my opinion.
Nice to see Robert and the car get some attention, that's for sure!
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}
| 5,688
|
from collections import Sequence
from rest_framework.renderers import TemplateHTMLRenderer
class TemplateHTMLContextDictRenderer(TemplateHTMLRenderer):
"""Wrap serialized data in a dictionary for use in templates.
Otherwise, the serialized data will get dumped into the template
context without any namespacing.
The serialized data will be wrapped in a context dictionary like
this if the data is a list (or any other sequence type)::
{'object_list': data}
or like this if the data is a dict (or any other non-sequence
type)::
{'object': data}
To use a different wrapper name, set ``context_object_name`` on the
relevant view class::
class PantsView(ListAPIView):
# Access data via ``pants`` instead of ``object_list`` in
# template.
context_object_name = 'pants'
template_name = 'pants/list.html'
For view classes that have some methods that return lists and others
that return objects (e.g., ``ViewSets``), lists can be wrapped using
a different name by setting ``context_object_list_name``::
class HorseViewSet(ViewSet):
context_object_name = 'horse'
context_object_list_name = 'horses'
.. note:: If ``context_object_list_name`` or ``context_object_name``
is set to a name that's also set by a context processor
(like ``request`` or ``user``), the serialized data will
be shadowed and inaccessible in the template.
"""
context_object_name = 'object'
context_object_list_name = 'object_list'
def get_template_context(self, data, renderer_context):
wrapper_name = self.get_wrapper_name(data, renderer_context)
data = {wrapper_name: data}
return super().get_template_context(data, renderer_context)
def get_wrapper_name(self, data, renderer_context):
view = renderer_context['view']
if isinstance(data, Sequence):
name = (
getattr(view, 'context_object_list_name', None) or
getattr(view, 'context_object_name', None) or
self.context_object_list_name
)
else:
name = (
getattr(view, 'context_object_name', None) or
self.context_object_name
)
return name
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,880
|
'Birds Of Prey' TV Rewatch, Episode 7: 'Split'
CA Post-Show Team
CA Post-Show Team Published: August 16, 2016
Long before comic book superhero TV shows were as common as they are today, the WB launched a live-action Birds of Prey TV series that lasted just thirteen episodes. In an effort to determine what went wrong, our Bird Watching team of Meredith Tomeo and Caleb Mozzocco are watching and dissecting every episode. You can watch along on DVD, or digitally on iTunes or Amazon.
In this episode, The Huntress (Ashley Scott) teams with a new metahuman vigilante with whom she has much more in common with than her assigned romantic interest, Detective Jesse Reese. But could the mysterious Darkstrike (Kristoffer Polaha) have a dark and terrible secret? Spoiler alert: Yes, yes he could. "Split" originally aired on November 20 of 2002, and was written by Adam Armus, Kay Foster, Edward Kitsis and Adam Horowitz, and was directed by James Marshall.
Caleb: As we open this episode, Reese is trying to apprehend a bad guy in Crime Alley, aka the alley set in which 85% of the show's crimes seem to occur, and chases him onto the Main Street set... and directly into the foot of The Huntress, who is waiting atop a nearby car.
"You have the right to remain silent," he says, cuffing the dude. "Anything you say can and will be used against you in a court of law." He then turns to address The Huntress. Now, I'm no legal expert, and nothing I write in the column should be considered legal advice, but I think there may be slightly more to the Miranda rights than that.
Meredith: Oh, great. This episode opens with Reese. And Huntress. Sharing stilted banter. Again.
Caleb: But this time they're doing it in front of a perp that they caught together. That's new!
Meredith: And yet, they're still in the same place.
Caleb: She says this guy held up a store on Milller and Varley, no doubt named for Dark Knight Returns writer/artist Frank Miller, and DKR colorist Lynn Varley. Aha! An inside Batman comics joke!
Reese asks her to come in and make a statement about the crime, and she's like "Ha ha ha, whatever Reese." I foresee this dude totally walking.
Meredith: They are still talking about... something.
Caleb: Crime-fighting as a metaphor for their relationship, which still hasn't yet moved from occasional partners to romance! "What I want... doesn't matter," Reese says mournfully. What he wants is to kiss Huntress on the lips and go on dates and get married, I think. But he can't say that, he can only scold her for her violent, face-kicking ways.
Meredith: Babs consoles Huntress and gives her a location of some bad guys robbing a jewelry store. Good, she's looking for some heads to bash in.
Caleb: I am 100% sure that she executed a Trinity kick on one of those jewelry store robbers. Well, 99% sure. Now that it's 2016, I've completely forgotten how omnipresent The Matrix was in turn-of-the-millennium action filmmaking (and TV-making, I guess).
Meredith: In the midst of her fighting, a strange man crashes through the window. They are really carefree when it comes to breaking stuff. I hope the store owner has good insurance.
Caleb: Yeah, I'm beginning to wonder if the store would lose less money if they simply got cleaned out of jewels than they will from having to replace every single piece of glass in the joint.
So this guy has short black hair, and a long, flowing black trench coat over his tight black t shirt and tight black pants. I know that, because of the coats, fight music, and wire-work, I mention the Matrix every episode, and I just mentioned it due to the particularly Trinity-like kick Huntress executed on some hapless robber, but man, I did not expect Neo to guest-star in this episode.
teamup
"I guess from the outfit and and the moves you're in the life," Huntress banters. So I guess in The Birds of Prey-iverse, long black coats are the equivalent of capes.
Meredith: It looks like he's got sneaky cat powers like Helena. When he leaves, he ghosts her like she's always doing to Reese. I wonder how she likes it?
Caleb: Cut to a scene from a horror movie. On a lonely road, two kids are in a parked car with steamed-up windows, making out. A big, ugly guy (Brian Thompson, and by "ugly guy," I of course mean "character actor") also wearing a long dark coat appears, rips the car clean off and tosses it over his shoulder, grabbing at them.
Detective Reese investigates the crime scene, and a patrolmen is cynical, even when presented with the fact that a car door was literally torn off and thrown like thirty feet. He asks Reese who they should be looking for: King Kong, Sasquatch, meth heads, or a really big can-opener.
Apparently, this guy has never heard of metahumans or the weird crimes, like people being drowned to death by a water guy, or that janitor who was disintegrated by a fireball, or that corpse that was found encased in a block of ice, etc.
Meredith: Helena busts into the Clocktower, raging to Barbara (Dina Meyer) about the mysterious guy in the coat. She has no interest in sharing this city with any other vigilantes. And who happens to be there as well? Why, that very vigilante! Whose name turns out to be... Darkstrike?
Is Darkstrike a thing? Why isn't it a thing? Couldn't they have picked any of the hundreds of characters who are things in DC comics?
Caleb: Well, he's not a DC superhero I can think of. But "Dark" and "Strike" are two of the most basic superhero name components from the 1990s, so I wouldn't be surprised if there were, like, 15 characters named "Darkstrike" somewhere among the character catalogs of minor publishers or in the portfolios of aspiring amateur artists.
Meredith: He's in town pursuing a villain named The Crawler, who is also not a thing. Babs wants Helena to team up with Darkstrike to stop The Crawler from abducting women. So she's gonna be working with him now. A new lunkhead to distract from developing any sort of dynamic between the actual Birds of Prey.
Caleb: The Crawler is kind of a terrible name though, as he doesn't crawl at all. "The Abductor" or "The Lady-Grabber" are more accurate, I guess, and not any worse than The Crawler.
So Dinah (Rachel Skarsten) is immediately smitten with the new tall, dark and apparently gorgeous guy. I guess her teenage hormones are kicking in. Can we pause here to discuss her assessment? Meredith, what do you think? Darkstrike, hot or not?
Meredith: Very early 2000s dream boat. He's like a JV Tom Welling.
Caleb: Well, he's no Shemar Moore.
Meredith: I would assume you'd want to see his torso before you decided.
Caleb: We're only ten minutes in. Maybe there will be a scene later where the two of them both lose their shirts for, um, some reason. Maybe they have to hide from The Crawler in a steam bath, or the Crawler rips off their shirts in a fight, or they go shopping for tight t-shirts together, or they go do laps at the police pool together or…
Meredith: Alarms go off! But it's not an alert from Oracle's Delphi system. Nope, Oracle says it's Reese and he's activated "the bat-ring." Wait, no one on this show is a "bat" anything anymore.
bat ring alert
Caleb: And the ring doesn't have a bat-symbol on it, nor is it in the shape of a bat. It is in the shape of a bird. Babs isn't nearly as good at marketing herself and and brand extension as Batman was.
At Lover's Lane, which is full of more greenery than we've yet seen on this show, an attractive blonde assistant district attorney of Reese's acquaintance appears, and he looks her up and down and they exchange loaded dialogue. Say, Huntress has a new attractive partner on the very same night that Reese has a new attractive partner. What are the chances of that?
Meredith: Lurking in the bushes near the crime scene, Darkstrike and Helena decide this is the place to discuss her star-crossed love with Reese.
Caleb: I would just like to point out that as nice at it is to have a crime scene somewhere other than the, like, two streets and one warehouse set all crimes have so far been committed at, this park or wherever looks crazy fake. It seems to be half potted plants, and half fake vines. It seems like the sort of jungle set you would see in a cheap, black-and-white 1950s adventure flick, where in the hero would be wearing a safari outfit, someone would be dressed in a gorilla outfit and there would be rear-projected lions.
I'm not sure what the budget-per-episode was on this show, but based on the production values, I would not be at all surprised to learn that it is less than what Disney and Marvel Studios spent on Sebastian Stan's eyeliner in Civil War.
Anyway, Darkstrike says he's been tracking The Crawler "for years." Isn't that just another way of saying he's a terrible superhero? Can you imagine if Batman were working The Case of the Chemical Syndicate from, like, 1939-1943...?
Meredith: They keep pressing on the point that Helena always works alone, once again completely missing what should be the point of a Birds of Prey show.
The Crawler has the girl he grabbed from Lover's Lane and he's feeding her dinner. Well, not really. She's bound and gagged and he's planning on killing her. But he's eating dinner at the table in front of her chair.
Meanwhile, Huntress arrives at Darkstrike's hotel room, which is also in the middle of the jungle. It's trashed, so she switches on her Huntress Vision to get a better look.
huntress vision
Luckily, her Huntress Vision is able to let her know someone is loudly entering the room with their key.
Caleb: Huntress finds it suspicious that The Crawler has been to Darkstrike's hotel room, ransacked it, and left a mannequin with threatening words written all over it in Darkstrike's bed. Darkstrike explains that Cralwer does this all the time, that it's way of taunting him and daring him to capture him. Kind of like The Riddler does to Batman, only Darkstrike is apparently never smart enough to follow the clues back to the villain the way Batman is.
Actually, I'm suspicious too now, Huntress. I'm beginning to suspect that Darkstrike and The Crawler may be one and the same.
When Huntress pops up out of nowhere to start talking to Reese about the latest Crawler clues, he's irritated by her sudden appearance. I think that is the most realistic part of this show so far. Who wouldn't be surprised if you had a friend who began every conversation by leaping out of the shadows when you weren't expecting them, and ended every conversation by disappearing when you stopped making eye contact with them?
Anyway, Reese, like us, doesn't think that the new guy has a very good superhero codename. "Darkstrike? Who comes up with these names?" he asks Huntress incredulously.
"He strikes after dark," she shrugs. "It's descriptive." Whatever you say, Coat Woman.
lunkhead
Meredith: Darkstrike is anxious about finding the girl who was kidnapped, so Dinah makes him some tea. They have a heart to heart about being a crime-fighter. She's not sure she's ever going to be as good as her mom, who remember was the Black Canary, even if she does learn to handle her telekinetic powers (which I totally forgot she had until she mentioned them just this moment). Darkstrike takes the opportunity to mansplain being a superhero to her. It's not like she's been living under the same roof as two other crime-fighters who've been mentoring her or anything.
Caleb: Reese goes to Dr. Harleen Quinzel (Mia Sara) for some insight into the psychological profile of The Crawler. So, what is Harley wearing in this scene? Is that a... purse strap... tied around her neck like necklace…?
sweet bowtie
Meredith: The outfit needed a pop of color and it was all she had on hand.
Caleb: And then Darkstrike has a heart-to-heart with Huntress about how The Crawler killed his girlfriend. So now he's mainsplaining hurt to Huntress. While Mansplainer isn't a very good superhero name, I do like it better than Darkstrike.
I like how Dinah thinks Darkstrike is such a good match for Huntress, and isn't exactly shy about saying it over and over.
Meredith: Dinah's only purpose in this episode is to ship Huntress and Darkstrike.
Caleb: Putting on her Oracle glasses, which make her smarter, and using her computer kung fu, Barbara was able to trace a bit of hair taken from the mannequin to the abandoned caretaker's house at the old Gotham Arboretum.
Huntress checks the place out, but forget to uses her Huntress Vision, so Crawler attacks her with a huge 2x4 while heavy metal elevator music plays in the background. She trips on her coat. You know, these long coats that everyone wears look really inconvenient in a fight.
Before he delivers a killing blow, he says to her, "You're Darkstrike's little bitch."
"We're just friends," she says. But his misogyny has activated a well of reserve feminist strength in her, and she rallies. "And I'm nobody's bitch," she says, kicking The Crawler out the window.
And then, suspiciously, Darkstrike enters, breathless and suffering from a blow to the head. Hey, ever notice how they are never in the same place at the same time? Darkstrike and Crawler are totally the same person.
But at least they saved the captured girl. Dinah uses her psychic powers for the first time, in, like, episodes, to see inside the girl's mind, and there's a brief flash showing Darkstrike at the diner that The Crawler had with her earlier. Aha! They are the same guy.
Unfortunately, all the bad, scary feeelings overwhelm Dinah. Maybe she's right: She's never gonna fill Black Canary's shoes.
Meredith: While the Birds try to figure out what's going on with Crawler, I'll just take a moment to point out that Rachel Skarsten would be a really good Black Canary, but like, now, in 2016. Her show Lost Girl is over, so she's got some spare time.
Caleb: Agreed! Maybe someone should get to work developing a newer, much more improved Birds of Prey TV show, and cast Skarsten as Dinah Lance/Black Canary. Just not on the CW; they have like five Canaries in the CW-verse already, right?
Written on the walls of Darkstrike's room, apparently by The Crawler? "Your girlfriend is next."
In Oracle's chemistry lab --- the various beakers of colored water she keeps next to her computers --- she shows Dinah the weird thing about The Crawler's DNA, found on the clues left in Darkstrike's room. It changes back and forth, like "it can't decide what it wants to be." Everyone is with me now, right? We know what that is?
Just then, the bat-ring alert goes off! Since Huntress is away, Oracle calls Reese back. Hey, this is the first time they've "met," isn't it...?
Meredith: On a payphone.
Caleb: Payphones! I remember those! He tells Oracle, who he recognizes as the mysterious voice Huntress sometimes starts talking to, that he was talking to a friend on the force in Central City, home of The Flash. Could his friend at Central City PD be Barry Allen himself? Let's pretend yes.
Reese reveals some extremely confusing plot point. Apparently, about the time The Crawler started crawling, there was a mysterious killing that they never attached to The Crawler because there were two victims, not one; a young woman of the sort The Crawler generally kills, and another unidentified male. It looked as if the dead man was the one who killed the girl, though.
At this point, Oracle has put two and two and two and two together and correctly come up with eight. Really Oracle, this is Superhero 101 stuff. If two characters in a superhero story are never in the same place at the same time, they are more than likely the same person.
Meredith: Helena actually lives in an apartment over the bar, where she still works, apparently? Oh, snap! There's a weird morphing special effect and it is revealed that The Crawler is Darkstrike. I see we've got a Glory/Ben situation here.
Caleb: I have seen more challenging mysteries on Scooby-Doo. Like, any season of any Scooby-Doo show ever. Wait, wait, wait; even if their bodies can somehow morph back and forth, how come their coats morph too...?
Oracle kinda sorta explains what's going on, but, um, it doesn't actually make any sense. There's no comic book science here or anything. Darkstrike didn't get bitten by The Crawler under a full moon, or have a teleporter accident with him; they weren't around anything radioactive at any point, and no one seems to be a demon or anything. He just killed The Crawler, and then became him? Physically. Somehow.
Meredith: And he keeps killing more people because he's got guilt or something.
Caleb: Okay, so Huntress is stunned by the realization that The Crawler and Darkstrike are the same person, morphing back and forth between two bodies and identities. This is understandable, since it makes little sense. She is then stunned by The Crawler hitting her over the head.
She comes to, bound to a chair in her own apartment, where The Crawler tells her she must die because she's in love. He apparently... smells her love for Reese on her...?
But once again she is saved by the villain repeatedly running into her feet while she is chained up. She then uses the chain to Slave Leia The Crawler into unconsciousness, so he morphs back into Darkstrike. ("Slave Leia" is here a verb, meaning "to throttle a captor from behind with the very chains he was using to imprison you." Update your dictionaries!)
Meredith: And Darkstrike gets tossed into Arkham. But he's actually in his Crawler form now, and it looks like his attending physician... is Dr. Quinzel. Crawler knows about her other identity as the Joker's girlfriend, Harley Quinn, and also spills the beans that the person repeatedly thwarting her plans is known as "The Huntress."
Caleb: Yes, he knows who she is and her relationship with The Joker because of his never even vaguely defined love-smelling powers, right…?
This is another great example of just how small of a city New Gotham appears to be, despite all those whooshing, CGI shots of skyscrapers. Dr. Qunizel is like the only mental health professional in the city. She's Helena Kyle's therapist, she helps the police department build psych profiles on wanted criminals, and she also runs the home for the criminally insane.
This episode ends where it began, with Reese in the middle of cuffing another perp he had just chased down and Huntress appearing out of nowhere to flirt with him. They reveal that they were both jealous of one another's team-ups, he of Darkstrike, and she of the assistant ADA she saw him with at the crime scene, although he assures her that she was never anything else than an ADA to him... well that, and a really bad blind date.
Oh God, just kiss already you too! The season's half over!
Well, that was certainly an episode of Birds of Prey, wasn't it? I think this may surpass episode three, "Prey For The Hunter" --- you know, the one that seemed to be set in a version of the Marvel Universe, where they had simply swapped the word "mutant" for "metahuman" --- as my least favorite of the series so far.
It really had a perfect confluence of all the things I'm not fond of about this series: Non-costume superhero costumes, making up terrible new characters instead of using any from the comics (or even making up good new characters), seemingly leaving out a scene or even a few lines of important dialogue (explaining what the heck was going on, exactly, with Darkstrike/The Crawler) and, of course, being yet another episode about the trust issues between Huntress and the other Birds and their professed difficulties of working with others.
On the other hand, I did like all the Dinah business in this episode; her crushing on Darkstrike and her busting of Helena's chops regarding her will-they-won't-they romance with Reese.
But when we get to the end of the series, and review why there might not have been a season two, I imagine this episode is going to be Exhibit B, right behind "Prey For The Hunter."
Meredith: This is the second episode in a row that has left me cold. The focus on Helena and Reese teaming up to solve crimes is really not my favorite. Once again, I'm left wondering what is the point of making a Birds of Prey show when it's clear no one was interested in actually focusing on the Huntress/Oracle dynamic. It also doesn't help that the Darkstrike plot is confusing and half-assed. I ended up spending most of my time trying to figure out what was going on and wondering where Dinah was.
Speaking of Dinah, you may have liked her ragging on Helena, but she was barely in this episode. She only really appeared to use her psychic powers to move the plot forward. That's pretty much exactly what I was afraid would happen with her. They use her visions to crank the wheels of the story, but they don't actually involve her in any significant manner or do anything to develop her character further. It's a shame that "Dinah Lance" still hasn't gotten the on-screen treatment that she deserves.
Caleb: Well, there's always next episode. But now that we've surpassed the halfway point of the series, I guess I can only use that as an excuse so many more times.
Filed Under: barbara gordon, bird watching, birds of prey, huntress
Categories: DC, Opinion, Post-Show, Television, TV Recaps
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
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| 6,811
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Бен Саа́р (; 10 августа 1989, Холон, Израиль) — израильский футболист, нападающий клуба «Маккаби» (Хайфа). В сезоне 2015/16 вместе с командой завоевал звание чемпиона Израиля.
Клубная карьера
В свои 16 лет он играл уже второй год за лондонский «Челси». Под наблюдение скаутов «Челси» впервые он попал после игры молодёжной сборной Израиля до 16 лет в матче против Ирландии в 2004 году. До прихода в «Челси» получил польское гражданство (его мать Батья имеет польское происхождение), которое автоматически предоставило ему право играть в Великобритании, поскольку Польша часть ЕС.
Бен Саар перешёл в лондонский «Челси» в мае 2006 года из тель-авивского «Хапоэль» за 320 000 $. Первый свой матч за клуб он сыграл против «Маклсфилд Таун» в Кубке Англии 6 января 2007 года, заменив Саломона Калу на 76-й минуте. Четыре дня спустя Саар вышел на замену вместо Шона Райт-Филлипса на 60-й минуте в игре Кубка Футбольной лиги против «Уиком Уондерерс», закончившейся со счётом 1:1. Своё первое выступление в Премьер-лиге он совершил 13 января 2007 года, выйдя со скамейки запасных вместо Арьена Роббена на 82-й минуте в матче с «Уиганом». Позже в сезоне он ещё дважды выходил на поле против клубов «Манчестер Юнайтед» и «Эвертон».
4 июля 2011 года французский «Осер» взял в аренду Бен Саара. Первый матч за новый клуб он провёл 6 августа 2011 года, выйдя в стартовом составе против Монпелье.
19 июля 2012 года Бен Саар перешёл в клуб из Второй Бундеслиги «Герта» (Берлин). Дебют состоялся 16 сентября 2012 года, когда Бен Саар вышел на замену в матче против «Аалена».
В июле 2014 года Саар перешёл в нидерландский клуб «Виллем II» из Тилбурга.
С 8 июля 2015 года выступает за клуб «Хапоэль» (Беэр-Шева).
Карьера в сборной
Личная жизнь
Как гражданин Израиля, Саар обязан был пройти трёхлетнюю службу в армии Израиля. В 2010 году израильские юристы предприняли попытку помочь Саару избежать военной службы, внеся на рассмотрение в Кнессет специальный закон, по которому прохождение аналогичной гражданской службы в стране ЕС приравнивалось бы к военной службе в Израиле (этот закон так и был назван — «Закон Бен Саара»). Однако закон так и не был принят, вследствие чего Саар был призван в армию Израиля.
4 ноября 2010 года Саар после совещания с религиозными деятелями, решил поменять написание своей фамилии на иврите, и поменял первую букву самех (ס) на шин (ש). На произношение это никак не влияет, так как шин в данном случае произносится «с» (син).
Достижения
Чемпион Израиля (1): 2015/16
Примечания
Ссылки
Профиль игрока на сайте footballdatabase.com
Футболисты Израиля
Игроки сборной Израиля по футболу (до 21 года)
Игроки сборной Израиля по футболу
Игроки ФК «Челси»
Игроки ФК «Куинз Парк Рейнджерс»
Игроки ФК «Шеффилд Уэнсдей»
Игроки ФК «Де Графсхап»
Игроки ФК «Эспаньол»
Игроки ФК «Хапоэль» Тель-Авив
Игроки ФК «Осер»
Игроки ФК «Герта» Берлин
Игроки ФК «Арминия» Билефельд
Игроки ФК «Виллем II»
Игроки ФК «Хапоэль» Беэр-Шева
Игроки ФК АПОЭЛ
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{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 7,662
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{"url":"http:\/\/program.dengshilong.org\/","text":"github\u5730\u5740\n\nOperationalError: (2006, \u2018MySQL server has gone away\u2019)\u9519\u8bef\uff0c\u4f46\u6b63\u5f0f\u670d\u52a1\u5668\u5c31\u4e0d\u4f1a\uff0c\u5728\u7f51\u4e0a\u627e\u4e86\u5f88\u4e45\u8fd8\u662f\u6ca1\u627e\u5230\u89e3\u51b3\u7684\u529e\u6cd5\u3002\n\nIf you hit this problem and don\u2019t want to understand what\u2019s going on, don\u2019t reopen this ticket, just do this:\n\n\u2022 RECOMMENDED SOLUTION: close the connection with from django.db import connection; connection.close() when you know that your program is going to be idle for a long time.\n\u2022 CRAPPY SOLUTION: increase wait_timeout so it\u2019s longer than the maximum idle time of your program.\n\nIn this context, idle time is the time between two successive database queries.\n\ndocker pull wordpress\u62c9\u53d6\u6700\u65b0\u7248\u672c\u7684Wordpress\u540e\uff0c\u6267\u884c\u547d\u4ee4\u540e\u53f0\u542f\u52a8Wordpress\n\nMySQL\u63d0\u4f9b\u4e86count\u547d\u4ee4\u6765\u7edf\u8ba1\u8868\u4e2d\u7684\u8bb0\u5f55\u6570, \u4f7f\u7528\u8d77\u6765\u975e\u5e38\u65b9\u4fbf\u3002\u4f46\u52a0\u4e0awhere\u6761\u4ef6\u7684count\u547d\u4ee4\u6709\u65f6\u4f1a\u5f88\u6162\uff0c\u6b64\u65f6\u9700\u8981\u4f18\u5316\u3002","date":"2016-09-30 13:39:35","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.17637784779071808, \"perplexity\": 4187.24998394548}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-40\/segments\/1474738662197.73\/warc\/CC-MAIN-20160924173742-00010-ip-10-143-35-109.ec2.internal.warc.gz\"}"}
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Go To... Home Podcasts Empower Blogs Schedule Inspirations Heard on Empower VIP Club Info
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Solutions for Global Sustainability with Vincenzo DiDato
In the world of crisis, Vincenzo DiDato is an expert. Finding solutions to global conflict and challenges requires a mind willing to look beyond the obvious to find workable solutions for global and local problems.
Vincenzo Di Dato, President of XERDAN Ltd. provides consulting, seminars, and training for Comprehensive Sustainability, for communities, organizations, private companies, governmental entities. Comprehensive Sustainability considers environment-economy-society-culture as part of an ambiance including humans and their context as a whole: We firmly are convinced that to solve problems and crisis it is impossible to consider sep arately the single parts, and we want to reach the objectives with instruments that are more inclusive, thoughtful, synergetic and durable in time, with the lower impact on the environment and on humans.
Elaine M. Grohman has been working in the field of Energy Medicine for nearly 20 years. The experiences of her own Life brought her to delve into the Mystery of our Spirit, Body, Emotions and Mind, and through that search she has sought to help others appreciate their own Life in a greater way. Elaine works with people in the medical fields, as well as having a private practice. She is the author of two books, "The Angels and Me - Experiences of Receiving and Sharing Divine Communication," and "Spirit Awakening - Wisdom for Life and Living." As an Intuitive, Elaine helps others to look beyond the wounds they use to define themselves, so that new and perhaps greater understanding can become known. Through this, we can begin to Heal our World - And Ourselves.
Photos by Laurie Tennent
View Full/Desktop Version
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T-type calcium channels (Cav3) play a key role in generating rhythmic action potentials in excitable cells such as the heart pacemaker and sleep-wake cycles in the thalamus. T-type channels are low voltage-activated channels, which can be opened near rest to cause an inward current that leads to membrane voltage rising to threshold to generate rhythmic action potential ring. The upstroke of the ventricular action potential in the vertebrate heart is attributed mostly to the cardiac-specfi c voltage-gated sodium channel, Nav1.5. Sodium channels are not expressed in the invertebrate heart, such as Lymnaea stagnalis. Instead, the major inward conductances of the invertebrate heart are due to voltage-gated calcium channels. The invertebrate pond snail, Lymnaea stagnalis, heart expresses T-type calcium channel, LCav3, which is alternatively-spliced in exon 12, generating a highly sodium selective T-type channel (with exon 12a) compared to a more calcium ion selective channel isoform (with exon 12b). The sodium permeant, LCav3-12a channel is the only T-type channel expressed in the heart, while LCav3-12b is more exclusive to the secretory glands, such as prostate and albumen. Our goal is to understand the functional consequence of diff ering sodium and calcium ion selectivities of T-type channels for the generation of rhythmic pacemaking in native tissues by conducting elecrophysiology experiments on dissociated ventricle cells and constructing a qualitative mathematical model of the invertebrate ventricular action potential. Mathematical models for both LCav3-12a and LCav3-12b T-type currents were constructed and implemented using current models from the Kyoto model, a guinea pig ventricular action potential model, to reflect the currents found in Lymnaea stagnalis. LCav3-12b had a smaller pacemaking current and showed slower rate of spike generation opposed to LCav3-12a which had a larger current and faster pacemaking activity. Spiking activity was not abolished with simulated T-type current block but had the greatest e ffect on rate of pacemaking. Simulations involving reduced current conductance or varying ion concentration show that LCav3 was primarily responsible for generating pacemaking activity and initiating the action potential upstroke.
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"redpajama_set_name": "RedPajamaC4"
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Is there a right way to train kids to be better athletes?
VIDEO; Training young athletes Jerrell Howell
By Sheldon Haygood | June 18, 2019 at 12:42 PM CDT - Updated June 18 at 12:43 PM
BIRMINGHAM, Ala. (WBRC) - In the state of Alabama most kids grow up wanting to play for the Crimson Tide or the Auburn Tigers, mostly in football, but any sport would suffice.
The problem is not every child has the talent or the ability to be good enough. But there is a way. Sports training is big business in the state and a lot of kids are willing to put in the work.
Jerrell Howell is a trainer with D1 Training Birmingham. He works most of the time for D1 at the Gardendale Civic Center and earned a degree in Kinesiology from Mississippi State University.
"It's all about making the kids better," said Howell. "We are going to have some fun, but they are going to put in the work because to be good is not easy. and the only way to get better is to train and there is a right way and a wrong way to do that. We will do it right with correct technique and a solid work ethic."
D1 Training Birmingham is located at 1014 Montgomery Highway, Vestavia Hills, AL 35216 or can call 205-588-2734. To work with Howell you can also call the Gardendale Civic Center at 205-631-5679.
Sports Anchor/Reporter
Sheldon Haygood began his career as a Sports Reporter at WBRC FOX6 back in 1994. Since then, Sheldon has developed into one of the city's favorite weekend sports anchors.
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
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{"url":"https:\/\/computers.tutsplus.com\/tutorials\/how-to-calibrate-your-macs-display--mac-47072","text":"Advertisement\n\n# How to Calibrate Your Mac's Display\n\nRead Time: 13 min\n\nWhether you work as a graphic designer, photographer or web developer - ensuring your Mac\u2019s display is accurately representing colours can be the difference between the perfect edit and something that looks washed out! In this tutorial, we\u2019ll explain why your display should be calibrated and the methods to do this.\n\n## What is Colour Calibration?\n\nHave you ever printed a photograph or seen a website you\u2019ve created on another computer and noticed that the colours printed look different from those that you saw on your Mac\u2019s display? This can likely be because your Mac\u2019s display isn\u2019t colour calibrated.\n\nWhat is seen on your display and what the image should look like can be two quite different things\n\nWhat happened? You\u2019ve changed the cartridges in your printer and it\u2019s been thoroughly cleaned, why are the colours looking a little off? Although the photograph looked great on your Mac, some of the colours looked somehow different on the printed photo - the red looks slightly different, almost purple. The reason for this is that your Mac\u2019s display wasn\u2019t giving you an accurate representation of the colours, only a good approximation.\n\n## Why is Calibration Needed?\n\nIf you think of your Mac\u2019s display as similar to a home stereo, calibration is just like adjusting the treble or bass. If you just bought a new stereo, you\u2019d spend time adjusting all the different features (such as treble, bass or balance) until you hear what you assume is the best possible sound. Furthermore, as the music will sound different if you\u2019re using large or small speakers in a large room or small room, you must adjust the sound for the space available.\n\nJust like adjusting the treble and bass of your stereo can fine-tune the sound of your favourite band, the same must be done for your display. If you bought a stereo and it came from the factory with the treble and bass turned all the way down, everything would sound terrible! Computer displays aren\u2019t calibrated fully simply because each person will have a different requirement.\n\nTime for a little physics! Light is made up of many different colours - you probably know that white light is actually all the colours of the visible spectrum (the light that we can see). White isn\u2019t actually a colour - it\u2019s a combination of all colours put together. This means that black is the absence of colour.\n\nIf you take a look at this colour palette wheel, you\u2019ll see that the centre is white - where all the colours converge\n\nLet\u2019s take two different colour balls - red and black. The red ball appears red because all the different colours of light that make up the visible spectrum is absorbed - all except red. Red is being reflected back and our eyes are detecting this red part of the spectrum. The black ball appears black because all light is absorbed by it - no part of the visible spectrum is being reflected back and so with the absence of any reflected light, we are not seeing any colour. Now imagine if we looked at these same balls under the a blue lightbulb - the red ball would look black because there\u2019s no red light to reflect. The black ball will still look black because it absorbs all colour. It\u2019s this variance of what a light source can be that affects the colours we see on-screen.\n\nTip: Just as you wouldn\u2019t use a red or blue tinted lightbulb in your work environment, ensure that you have a good lighting source! Energy-saving bulbs can cast a yellow tint to the room so invest in some LED bulbs which are still good energy savers but offers a more neutral white light.\n\n## Methods of Calibrating a Display\n\nThere\u2019s two methods of calibrating your Mac\u2019s display:\n\n\u2022 By eye\n\u2022 A colour calibrating tool\n\nBefore we begin any colour calibration, ensure your Mac is in your preferred work environment and the room is a dark as possible - turn off any lights and close any blinds or curtains. The less outside light we have the better the calibration will be. This is because we don\u2019t have an external light source that could alter our perception of the colour on screen. I\u2019d also recommend setting your desktop background to something dark such as solid black just to avoid any extra eyestrain whilst you\u2019re calibrating your display.\n\nComputer displays aren\u2019t calibrated fully simply because each person will have a different requirement.\n\n### By Eye\n\nTo calibrate your display, open up System Preferences and then select Display. You might have a number of them in the list already - if you do, remember which one you currently use and then change it. You\u2019ll instantly see the difference and your Mac will appear to have a coloured tint to it - on my Mac it makes it look like my Mac has a purple tint! However, if I were to take a screenshot and change the profile back, it would look exactly the same - it only affects the output of the display. This is why a photograph can look different than what your Mac shows you.\n\nTo calibrate the monitor manually, you can do so using the Calibrate\u2026 button which opens up the Display Calibrator Assistant.\n\n#### The Display Calibrator Assistant\n\nThe assistant explains briefly what it does and gives you the option to proceed and calibrate the display.\n\nCalibrator Assistant\n\nIf you are attempting to calibrate an external 3rd party display, you will be given an additional option to make adjustments before the next step. You\u2019ll be prompted to adjust the display\u2019s contrast and brightness and then fine-tune it.\n\nCalibrator Assistant will prompt you to make adjustments to your display before continuing\n\nCalibrator Assistant will prompt you to adjust the slider to suit your display\u2019s Native Gamma\n\n#### Target Gamma\n\nGamma is quite a complex characteristic of display calibration. Briefly, gamma is the relationship between how bright a pixel will appear on the screen in relation to its numerical value. It has an affect on the contrast of an image and an incorrect gamma can make images look washed out or we may not see the level of detail in the image as it\u2019s too dark. It\u2019s such a complex subject that it would go beyond the scope of this tutorial. If you\u2019d like to learn more about what precisely Gamma does, you can learn so from the Wikipedia article on the subject.\n\nThe option for Gamma 2.2 is the agreed upon standard for what Gamma should be. Older Macs used to use Gamma 1.8 which was the same for the printing industry - this was one of the reasons why Macs were often commonplace in the design industry.\n\nCalibrator Assistant to select target gamma\n\nIf you\u2019re calibrating your Mac\u2019s built-in display, Apple already has a good approximation of its Native Gamma and skips the step. However, you can adjust this later in this tutorial.\n\n#### White Point\n\nSetting the white point (sometimes referred to as colour temperature) for your display adjusts the overall tint of the display. The white point scale refers to what appears as white to us, as we actually see many different shades of yellow or blue as white. For example, at the lower end of the scale at around 4100K is the colour temperature of moonlight. If you asked most people what colour is moonlight, they\u2019ll usually say \u201cwhite\u201d. That\u2019s actually not quite right, we just see it as white but in actual fact it\u2019s slightly yellow - we just can\u2019t tell the difference.\n\nAt the higher end of the scale, let\u2019s say 10,000K, this is the colour temperature of a television or computer display. This may appear as white but in fact it\u2019s slightly blue - again, it\u2019s so close we don\u2019t see the difference.\n\nThe purpose of the white point is to match your display\u2019s output of white to the white point of what you\u2019re working with - whether it\u2019s printed material or television. If you\u2019re only ever working online and not in print then you can usually leave this to the default setting which is usually 6500K or D65 - on the colour temperature scale it\u2019s known as \u201cmiddle of the day, overcast\u201d.\n\nCalibrator Assistant to select white point (or colour temperature)\n\n#### Name your Profile\n\nOnce you\u2019ve completed these steps, you will be able to save your adjusted profile.\n\nCalibrator Assistant will let you specify any name you wish\n\nChances are, you probably won\u2019t notice much of a difference - if any. That\u2019s because with the basic options, there isn\u2019t much to change. Let\u2019s start that again, but with the Expert Mode enabled.\n\n#### Native Response (Native Gamma)\n\nThe following steps are to determine your Mac display\u2019s native gamma. What we\u2019ll be doing is adjusting the brightness and contrast of your display by using a series of sliders.\n\nFor each step, the left (brightness) slider should be adjusted until the Apple logo looks almost blended in with the lined background. The second (tint) slider is to adjust the tint of the Apple logo further until it looks almost blended in completely. You will repeat these steps five times to ensure a fully consistent reading. In addition, you can also go back and forth between the sliders if you feel you need to make some further changes.\n\nCalibrator Assistant: Native Response\n\nCalibrator Assistant: Native Response\n\nCalibrator Assistant: Native Response\n\nCalibrator Assistant: Native Response\n\nCalibrator Assistant: Native Response\n\nAs you move the sliders, you\u2019ll notice that the tint, brightness and contrast of the screen change. Don\u2019t get distracted by this and focus only on the image.\n\n#### Target Gamma\n\nIn this part, we can adjust the gamma to a wider range of values that previously was offered. However, stick to Gamma 2.2 unless you have a very specific need to use another value.\n\nCalibrator Assistant: Target Gamma\n\nTip: Rather than trying to get exactly 2.2 on the Gamma slider, simply click where it says \u201c2.2\u201d and the slider will automatically jump to that exact value.\n\n#### Target White Point\n\nYou are presented with a wider range of values for the white point but it\u2019s still recommended to use the default values such as D50 or D65 as well as the native white point of your display.\n\nDescription\n\nPhew! That seems like a lot to do!\n\nNow, the good news is that once you\u2019ve calibrated the display properly then you wouldn\u2019t need to really change it again unless the working environment (such as new lighting, moved desk) changed. However, even changes to the ambient lighting of the room can be enough to slightly alter our perception of the colour. So what can we do to avoid this?\n\n### Colour Calibrators\n\nThankfully, there\u2019s a number of colour calibrators available on the market. These are small USB devices that will automatically do all of the above work for you and a lot more accurately!\n\nTip: There are a number of different calibrators out there but not all of them will work with Lion or Mountain Lion - make sure to check the requirements before purchasing!\n\nDevices such as the Spyder4 by Datacolor will cost anywhere between $150-$1000s depending on the features you require. For most users, the lower end of this price range are more than enough and will mean your display is correctly calibrated. Some photography equipment suppliers even rent them out for those on a budget.\n\nThe Spyder4 range is a very popular range that works on Mac and PC\n\n#### How Do Colour Calibrators Work?\n\nColour calibrators work in a very similar way to how display calibration works when we use our eyes. The calibration tool has a small sensor (called a colorimeter) built-in to it and software that communicates to the device via USB. colour calibrators are so sensitive that they can see discrepancies in the colours displayed that we otherwise would miss. The sensor acts as the software\u2019s \u201ceye\u201d and can determine if the colours on screen are accurate or if the display needs adjusting.\n\nThe sensor is placed over the display and colours are displayed, the sensor determining if the outputted colour is accurate and if not, adjusts the profile accordingly\n\nWhen you run the calibration software, an area will appear on the centre of the display that will be where to place your calibration tool (the calibrators tend to have a number of tiny suction pads to keep it attached). Once placed on the display, you\u2019ll then be advised to turn off and block out any outside light sources. Additionally, you\u2019ll be asked to alter your display\u2019s contrast and brightness since this isn\u2019t controlled by the operating system.\n\ncolour calibrators work as software and hardware together\n\n#### Calibrating the Display\n\nOnce the software begins it will display a number of colours on the display where the tool is located - this is why it\u2019s important to place the tool as accurately as possible. After a few minutes, the software checks the results. If the colours need adjusting, it will remember what adjustments are needed and continue.\n\nThe calibrator\u2019s software ensures the colours displayed are as accurate as possible\n\nOnce the calibration process is completed, you\u2019ll be presented with a new colour profile you can use in OS X. You\u2019ll likely be able to compare what the original profile looked like against the new one before saving the changes.\n\nTip: It\u2019s always a good idea to check everything looks in order. I had a colour calibration tool develop a fault which meant every calibration I performed had a horrible dark purple tint!\n\n#### Ongoing Calibration\n\nOnce you\u2019ve calibrated your display, you\u2019re ready to start editing again! It\u2019s recommended to calibrate your display every few weeks if you rely upon it to be consistently accurate all the time. The colours won\u2019t necessarily change on the screen but your environment might, such as new lightning or even a different time of year where sunlight is less or more.\n\nMost calibration software will provide the option of reminding you to recalibrate your display. For the sake of 10 minutes every few weeks, it\u2019s definitely worth it to keep your display up to date!\n\nIf you have multiple displays, you can also use the tool for each display\n\n#### Which Calibration Tool Should I Get?\n\nThis depends on how much you rely upon keeping colours as true as possible. There are some features that the higher end models offer that may be of use. These tend to include features such as more granular controls of settings such as Gamma or colour temperature. All of these sensors will usually work with multiple displays as well - the lower end models usually require a little bit more work.\n\nThere\u2019s a number of different companies that provide colour calibrators - I\u2019ve included a list at the end of this tutorial to get you started\n\nOne notable feature of higher-end models include ambient light sensors. Your portable Mac or iMac will have an ambient light sensor built-in - this is what controls your keyboard backlight and\/or adjusts the brightness of your display when the room gets darker. A calibration tool can include a similar sensor that would adjust the colour profile of your display automatically so that even as the light in the room changes, the sensor will continually adjust the colour profile to keep it as true as possible.\n\nFor users who aren\u2019t printing or designing with their Mac, a colour calibration tool isn\u2019t something to consider and manually calibrating your display once in a while will be more than enough.\n\n## Wrapping Up\n\nIn this tutorial, we\u2019ve shown you how to calibrate your Mac\u2019s display manually as well as the benefits of an optional colour calibration tool. If you rely upon colours being as true as possible, a colour calibration tool should be an essential piece of equipment in your workflow and are extremely inexpensive when compared to the problems it will avoid for you.\n\nAdvertisement\nDid you find this post useful?\nWant a weekly email summary?\nSubscribe below and we\u2019ll send you a weekly email summary of all new Computer Skills tutorials. Never miss out on learning about the next big thing.\nAdvertisement\nLooking for something to help kick start your next project?\nEnvato Market has a range of items for sale to help get you started.","date":"2023-03-26 02:01:21","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.20385868847370148, \"perplexity\": 1237.5119348604183}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-14\/segments\/1679296945381.91\/warc\/CC-MAIN-20230326013652-20230326043652-00220.warc.gz\"}"}
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Q: Multiple virtualhosts with the same servername I have an apache server, a unique domain name and multiple tomcat instances, here is my actual config :
<VirtualHost *:80>
ServerName my.domain.com
...
ProxyPass /sample_1 ajp://127.0.0.1:8009/sample_1
ProxyPass /sample_2 ajp://127.0.0.1:8009/sample_2
ProxyPass /sample_3 ajp://127.0.0.1:8014/sample_3
ProxyPass /sample_4 ajp://127.0.0.1:8019/sample_4
....
CustomLog logs/my_access_log combined
ErrorLog logs/my_error_log
</VirtualHost>
Now, I would like to use a CustomLog for each tomcat instance, I tried to put each ProxyPass directive in a separate virtualhost, but I got 403 error except for the virtualhost on the top according to httpd -S output.
I don't like to remove the ServerName directive, because the service will be available throug the IP address.
Help please
A: You can use the SetEnvIf directive in combination with conditional logging to log specific requests to different log files.
<VirtualHost *:80>
ServerName my.example.com
...
SetEnvIf Request_URI "/sample_1.*" sample_1
SetEnvIf Request_URI "/sample_2.*" sample_2
CustomLog logs/my_access_log_sample_1 combined env=sample_1
CustomLog logs/my_access_log_sample_2 combined env=sample_2
CustomLog logs/my_access_log combined
ErrorLog logs/my_error_log
</VirtualHost>
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\section{Introduction}
Ultracold quantum gases provide clean, controllable model systems for exploring quantum many-body physics \cite{Bloch2008}, and a powerful probe of these interacting quantum systems is the spectroscopy of low-energy excitations. For example, intriguing behaviors such as superfluidity, fermion pairing, and exotic weakly bound molecules can be revealed in their characteristic excitation
spectra. In many cases, measured spectra can be directly compared with many-body theory to test our understanding of these rich systems.
Any experiment designed to probe excitations requires the same
essential components: a way to excite the sample and a way to measure the response. To drive the excitations one applies a field to perturb the gas, and spectra are obtained by measuring the response of the ultracold gas as a function of the driving-field frequency. In ultracold atom experiments, this response is measured by imaging the atom cloud after the perturbation, and observing the response as some change in the density distribution of the imaged cloud.
There exists, however, in any excitation spectroscopy, an alternative way to measure the response of the quantum gas to a driving field. Just as the quantum gas has responded to the probe field, the probe field must have an equivalent response to the quantum gas. In this paper, we present a technique to measure this complementary information in Bragg spectroscopy by measuring the change in the number of photons in one of the laser fields used to drive the Bragg excitations. While in this work we use Bragg spectroscopy, this technique may more generally be applicable to other excitation spectroscopies as well \cite{Peden2009a}. For ultracold atoms where the number of atoms is typically small ($\sim 10^5$), the challenge, of course, is to have adequate signal-to-noise in measuring photon number to detect the Bragg response. For smallish atom samples, this will typically require a photon shot-noise limited measurement. To that end, we detail the experimental setup and the techniques of a heterodyne-based detection scheme used to realize shot-noise-limited photon counting. We also explore the advantages and limitations of this technique.
To motivate tackling the challenge of photon counting, we point out that this technique avoids some of the pitfalls inherent to spectroscopy measurements where the cloud is imaged. For example, strong interactions, which complicate the response seen in the density distribution of a Bose-Einstein condensate (BEC) \cite{Papp2008a}, provide no additional complications for the photon counting approach. Indeed, a primary motivation for this work is our desire to extend Bragg spectroscopy of BEC to the case where we have both strong interactions and low momentum excitations. Finally, we present a powerful new feature of our technique, which is that we can directly probe the time evolution of the excitation process, even during the course of a single laser pulse.
\section{Bragg Spectroscopy}
Conceptually, a Bragg excitation can be thought of as a coherent scattering process involving absorption of a photon from one of the Bragg beams and stimulated emission into the other: a two-photon transition. It is this process of either absorption or emission that we aim to measure with our photon-counting technique. The process leaves the excited atoms in the same internal state, but with a new momentum, $\textbf{k}$, determined by the geometry and wavelength of the Bragg beams. The two lasers have slightly different frequencies, to account for the energy of the excitation, and we vary this frequency difference, $\omega$, for our spectroscopy.
Typically, the Bragg response is measured by looking at the cloud using time-of-flight atom imaging, where the gas is suddenly released from the trap and allowed to expand before imaging. Bragg excitations in a weakly interacting BEC then appear as atoms in a distinct cloud outside of the main cloud. The position of the new cloud, which is seen after the expansion from the trap, reflects the momentum of the excitation. This new cloud's density reflects the strength of the excitation. Pioneering studies of weakly interacting BECs have been done with such measurements \cite{Kozuma1999a,Stenger1999b,Steinhauer2002a}, however, there are limitations. In particular, in the case of strong interparticle interactions \cite{Papp2008a,Veeravalli2008} or low-momentum excitations \cite{Steinhauer2002a}, the excitations no longer appear as a clearly distinguishable second cloud in the momentum-space image and the response becomes more difficult to quantify.
We show a measured Bragg lineshape for a weakly interacting $^{85}$Rb BEC in Fig.\ \ref{fig:lineshape}. On the horizontal axis, we have the frequency difference between the two Bragg beams, which sets the energy of the Bragg excitation. On the vertical axis, we have the Bragg signal, namely, the number of excitations due to the Bragg process. We define this signal such that it can be either positive or negative, reflecting the direction of the momentum transfer. The number of excitations due to the Bragg pulse are counted in two different ways, and one can see that the photon counting and the time-of-flight imaging signals agree well with each other. The two sets of data were acquired simultaneously, with each cycle of the experiment providing both a photon-counting and an atom-imaging data point. This demonstrates the complementary nature of the two techniques. The lines in Fig.\ \ref{fig:lineshape} are individual fits of the Bragg spectrum to two Gaussian functions. These fits can be used to extract a center frequency and an RMS width. In the rest of the paper we describe in detail the photon-counting technique demonstrated here.
\begin{figure}[h]
\begin{center}
\includegraphics[width=80mm]{Counting_fig_1_BW.eps}
\caption{Bragg spectrum of a $^{85}$Rb BEC of $5.5\times10^4$ atoms at k = 16 $\mu$m$^{-1}$, measured in two different ways. The horizontal axis shows the frequency difference between the Bragg beams. The vertical scale shows the number of excitations, which is measured using traditional absorption imaging of ejected atoms (hollow circles), as well as with the photon-counting technique presented here (black triangles). The error bars on black points represent the shot noise in the photon counting measurements. The photon counting measurements used three pulses of equal length. The first and the third pulses used only a single weak beam to make an average background measurement, with no Bragg excitation. During the second pulse, both Bragg beams illuminate the condensate to induce Bragg scattering and we subtract the averaged background to count the number of photons gained or lost in the weak beam due to the Bragg excitation.
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Q: Pandas - Groupby find groups within groups This is a repost from this link I started, but I have realized the problem is much more complex.
df = pd.DataFrame({'a': ['A1', 'A1', 'A1', 'A2', 'A2','A3','A3', 'A4', 'A3', 'A2', "A4", "A4", "A4"],
'value': ["7:00","10:00","20:00","9:00","7:00","9:00","8:00","15:00","19:00", "9:30", "15:30", "16:00", "16:30"],
"value2": [3,1,2,4,2,3,3,5,3,2,1,5,7],
'value3': ["Apple", "Orange", "Apple", "Kiwi", "Orange", "Orange", "Apple", "Apple", "Apple", "Apple", "Orange", "Orange","Apple"],
"value4": ["Throw", "Eat", 'Throw', "Keep", "Eat", "Eat", "Throw", "Throw", "Throw", "Throw", "Eat", "Eat", "Chuck"]})
What I want is: 1) By ID (variable "a"), select all instances under "value3" where it is "orange" and then "apple". They don't have to be back to back; there can be many other values between these two. But orange must come before apple in time.
2) Then count these instances of orange then apple into two groups: 1) one is when value2 is = 1 for orange; 2) is when orange does not equal 1 (so the rest are grouped as one group).
The problem is A4 where there is two oranges - 1 and 5. This should be categorized in the group value2 = 1 because it happened first in time.
Update: Sorry - my expected response did not cut and paste over it seems:
value2 value3 count
1 orange 2
all other orange 2
A: See if this works, however I will see if some others can give you a simple and short version of it,
df1 = df[['a','value3']].drop_duplicates()
##Merging the dataframes
merge =df1.merge(df,how = 'left',left_index=True, right_index=True)
##Selecting the only requried columns
merge = merge[['value2','value3_x']]
##Renaming the columns
merge = merge.rename(columns={'value3_x':'value3'})
##Filtering the data
merge = merge[merge.value3=='Orange']
##Converting te value to string
merge['value2']= df.value2.astype(str)
## Changing the value of value2
merge['value2'] = merge.value2.apply(lambda x: '1' if x == '1' else 'all other')
##Grouping the data
merge.groupby(['value2','value3']).value3.count()
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\section{Introduction}
\begin{figure}[t]
\centering\includegraphics[width=\linewidth]{assets/images/figure1.jpg}
\caption{Overview of our approach. PICCOLO minimizes a novel, point cloud-centric loss function called sampling loss.
After the initialization phase trims off local minima, PICCOLO minimizes the sampling loss with gradient descent.
}
\label{impactful_demo}
\vspace{-0.5em}
\end{figure}
With the recent advancements in 3D sensing technology, 3D maps of the environment are often available for download~\cite{matterport_scan} or can be easily captured with commodity sensors~\cite{bundlefusion}.
The 3D map and the accurate location of the user within the map provide crucial information for AR/VR applications or other location-based services.
Visual localization is a cheap localization method as it only uses an image input and utilizes the 3D map without additional sensors such as WIFI, GPS, or gyroscopes.
However, visual localization is fragile to changes in illumination or local geometric variations resulting from object displacements~\cite{change_vis_1, change_vis_2}.
Further, with the limited field of view, perspective cameras often fail to regress the camera pose when the observed image lacks visual features (e.g., a plain wall) or the scene exhibits symmetric or repetitive structure~\cite{lstm_vis_loc, inloc}.
Omnidirectional cameras, equipped with a $360^\circ$ field of view, provide a holistic view of the surrounding environment.
Hence these cameras are immune to small scene changes and ambiguous local features~\cite{benefits_of_omni}, which gives them the potential to dramatically improve the performance of visual localization algorithms.
However, the large field of view comes with a cost: significant visual distortion caused by the spherical projection equation.
This makes it difficult to directly apply conventional visual localization algorithms on omnidirectional cameras~\cite{omni_hard_why_1, omni_hard_why_2, omni_hard_why_3, omni_hard_why_4, spherenet}, as many visual localization algorithms~\cite{da4ad, inloc, lstm_vis_loc, score} do not account for distortion.
Furthermore, learning-based approaches are bound to the settings they are trained on, and cannot generalize to arbitrary scenes.
\input{assets/images/teaser}
In this paper, we introduce PICCOLO, a simple yet effective omnidirectional localization algorithm.
PICCOLO optimizes over \textit{sampling loss}, which samples color values from the query image and compares them with the point cloud color.
We only utilize the color information from point clouds, as it is usually available from raw measurements.
With a simple formulation, PICCOLO can be adapted to any scene with 3D maps in an off-the-shelf manner.
Further, PICCOLO can work seamlessly with any other point-wise information, such as semantic segmentation labels shown in Figure~\ref{qualitative_results}.
Sampling loss is \textit{point cloud-centric}, as every point is taken into consideration.
In contrast, conventional photometric loss widely used in computer vision~\cite{flownet, lsd_slam} evaluates the color difference at every pixel location~\cite{lsd_slam, dtam}, thus is \textit{image-centric}.
Our point cloud-centric formulation leads to a significant performance boost in omnidirectional localization, where the image-centric approach suffers from distorted omnidirectional images unless the distortion is explicitly considered with additional processing~\cite{sphere_cnn,omni_hard_why_4}.
The gradient of our proposed sampling loss can be efficiently obtained with differentiable sampling~\cite{spatial_transformer}.
While differentiable sampling is widely used to minimize discrepancies in the projected space, it is usually part of a learned module~\cite{flownet, flownet2}.
Instead, we utilize the operation in a stand-alone fashion, making our framework cheap to compute.
We further accelerate the loss computation by ignoring the non-differentiable, costly components of projection, such as occlusion handling.
These design choices make sampling loss very fast: it only takes 3.5 ms for $10^6$ points on a commodity GPU.
With the rich information of the global context in point cloud color, our efficient formulation is empirically robust against visual distortions and more importantly, local scene changes.
The algorithm quickly converges to the global minimum of the proposed loss function as shown in Figure~\ref{impactful_demo}.
Equipped with a light-weight search for decent starting points, PICCOLO achieves stable localization in various datasets.
The algorithm is extensively evaluated on indoor/outdoor scenes and scenes with dynamic camera motion, scene changes, and arbitrary point cloud rotation.
Several qualitative results of our algorithm are shown in Figure~\ref{teaser_img} and~\ref{qualitative_results}.
In addition, we introduce a new dataset called OmniScenes to highlight the practicality of PICCOLO.
OmniScenes contains diverse recordings with significant scene changes and motion blur, making it the first dataset targeted for omnidirectional localization where visual localization algorithms frequently malfunction.
PICCOLO consistently exhibits performance superior to the previous approaches~\cite{gosma, sphere_cnn} in all of the tested datasets under a fixed hyperparameter configuration, indicating the practical effectiveness of our algorithm.
\section{Related Work}
\label{related_work}
Before we introduce PICCOLO in detail, we clarify our problem setup and how it differs from previous visual localization algorithms~\cite{active_search_eccv, inloc, energy_landscape, dsac}.
Then we will further describe recent algorithms proposed for omnidirectional localization.
\paragraph{Learning-based Algorithms}
A large body of recent visual localization literature trains an algorithm on the database of RGB (and possibly depth) images annotated with ground truth poses~\cite{energy_landscape, dsac, hierarchical_scene, score, inloc, posenet, lstm_vis_loc, learned_loc_1, learned_loc_2, learned_loc_3, learned_loc_4}.
While such training facilitates highly accurate camera pose estimation~\cite{energy_landscape, dsac, inloc, active_search}, it limits the applicability of these algorithms.
To estimate camera pose in new, unseen environments, these algorithms typically require additional pose-labelled samples.
In order to develop an algorithm that could be readily used in an off-the-shelf manner, we make a slight detour from these previous setups: the camera pose must be found \emph{solely} using the point cloud and query image information.
One may opt to train these learning-based models~\cite{energy_landscape, dsac, hierarchical_scene} with synthesized views from the point cloud as in Zhang \etal~\cite{sphere_cnn}.
However, it is costly to obtain such rendered views, and one must devise a way to reduce the domain gap between synthesized images and real query images, which is a non-trivial task.
\paragraph{Feature-based algorithms}
Another line of work utilizes visual features for localization~\cite{active_search_eccv, active_search, snavely, synthetic_view_with_matching, loc_feat_1, loc_feat_2}.
Feature-based localization algorithms require each 3D point to be associated with a visual feature, typically SIFT~\cite{sift}, necessitating a structure-from-motion (SfM) point cloud.
Provided an efficient search scheme~\cite{active_search, active_search_eccv, snavely}, it is relatively straightforward to establish 2D-3D correspondences by matching features extracted from the query image with those in the SfM model.
Our input point cloud is not limited to a structure-from-motion (SfM) point cloud.
Due to the developments in RGB-D sensors and Lidar scanners, 3D point clouds of a scene could be obtained in a wide variety of ways other than SfM.
These point clouds do not contain associated visual features for feature-based localization.
Our setup also does not provide any explicit 2D-3D correspondences, thus disabling the direct usage of PnP algorithms~\cite{pnp_1, pnp_2}.
Further, many point clouds and query images used in our experiments contain repetitive structures or regions that lack features as shown in Figure~\ref{qualitative_results}.
This hinders the usage of sparse local features such as SIFT~\cite{sift} in our setup, where we report additional difficulties for using SIFT in the supplementary material.
To accommodate these challenges, PICCOLO incorporates information from dense RGB measurements, which are easy to obtain in practice, and are robust against local ambiguities.
\paragraph{Omnidirectional Localization}
Visual localization on omnidirectional images requires an algorithm specifically designed to account for the unique visual distortion~\cite{omni_hard_why_1, omni_hard_why_2, omni_hard_why_3, omni_hard_why_4}.
A number of techniques have been proposed in recent years that tackle visual localization with omnidirectional cameras.
These techniques could be divided into two groups, namely algorithms that utilize global optimization techniques and others that leverage deep learning.
Campbell \etal \cite{gopac, gosma} proposed a family of global optimization-based algorithms for camera pose estimation, GOSMA \cite{gosma} and GOPAC \cite{gopac}, that could be readily applied for omnidirectional localization in diverse indoor and outdoor environments.
While these algorithms have solid optimality guarantees and competitive performance, semantic labels should be fed to these algorithms as additional inputs for reasonable accuracy.
On the other hand, deep learning-based omnidirectional localization algorithms such as Zhang \etal\cite{sphere_cnn}, train neural networks that learn rotationally equivariant features to effectively process omnidirectional images.
Although such features enable omnidirectional localization under arbitrary camera rotations, these algorithms cannot generalize to unobserved scenes as they require training on pose-annotated images.
We compare the localization performance of PICCOLO with optimization-based localization algorithms GOSMA \cite{gosma}, GOPAC \cite{gopac}, and deep learning-based localization algorithms from Zhang \etal \cite{posenet, sphere_cnn, spherenet}.
\section{Method}
\label{method}
PICCOLO is a point cloud-centric omnidirectional localization algorithm, which finds the optimal $SE(3)$ camera pose with respect to the colored point cloud at which the $360^{\circ}$ panorama image is taken.
PICCOLO solely relies on the point cloud data and the input query image.
It does not require a separate training process or explicit 2D-3D correspondences, and therefore could be used in an off-the-shelf manner.
We first introduce the formulation of sampling loss, which is the objective function that PICCOLO aims to minimize.
Then we will describe our light-weight initialization scheme.
\input{assets/images/loss_surface}
\paragraph{Sampling Loss}
Given a point cloud $P=\{X, C\}$ and a \emph{single} query image $I \in \mathbb{R}^{H\times W \times 3}$, where $X, C \in \mathbb{R}^{N\times 3}$ are the point cloud coordinates and color values, the objective is to find the optimal rotation $R^* \in SO(3)$ and translation $t^* \in \mathbb{R}^{3}$ at which the $360^{\circ}$ panorama image $I$ is taken.
Denote $\Pi(\cdot):\mathbb{R}^{3}\rightarrow \mathbb{R}^{2}$ as the projection function that maps a point $\mathbf{x}=(x_1, x_2, x_3)$ in 3D to a point $\tilde{\mathbf{x}} \in [0,H)\times[0,W)$ in the $360^{\circ}$ panorama image's coordinate frame.
This could be explicitly written as follows,
\begin{equation}
\Pi(\mathbf{x}) =
\bigg(\frac{H}{\pi}\mathrm{atan}\bigg(\frac{x_3}{\sqrt{x_1^2+x_2^2}}\bigg),
\frac{W}{2\pi}\mathrm{atan}\bigg(\frac{x_2}{x_1}\bigg)\bigg).
\end{equation}
Furthermore, let $\Gamma(\cdot;I)$ indicate the sampling function that maps 2D coordinates $\tilde{\mathbf{x}} \in [0,W)\times[0,H)$ to pixel values $\mathbf{c}\in \mathbb{R}^3$ sampled from the query image $I$ under a designated sampling kernel.
Suppose $\Gamma(\cdot;I),\Pi(\cdot)$ could be `vectorized', i.e., if the input $\tilde{X}$ consists of $N$ points in $\mathbb{R}^2$, $\Gamma(\tilde{X};I) \in \mathbb{R}^{N\times 3}$ are the sampled image values at 2D coordinates $\tilde{X}$, and vice versa for $\Pi(\cdot)$.
Under this setup, $\Pi(X) \in \mathbb{R}^{N\times 2}$ could be regarded as tentative \emph{sampling locations}, and $\Gamma(\Pi(X);I) \in \mathbb{R}^{N\times 3}$ as the \emph{sampled image values}.
If the point cloud $P$ is perfectly aligned with the omnidirectional camera's coordinate frame, one could expect the sampled image values $\Gamma(\Pi(X);I)$ to be very close to the point cloud color values $C$.
Sampling loss is derived from this observation, where the objective is to minimize the discrepancy between $\Gamma(\Pi(X);I)$ and $C$.
Given a candidate camera pose $R, t$, this could be formulated as follows,
\begin{equation}
\label{samp_loss}
L_\mathrm{sampling}(R, t) = \|\Gamma(\Pi(R(X-t));I) - C\|_2.
\end{equation}
Note that $R(X - t)$ is the transformed point cloud under $R, t$.
Gradients with respect to $R, t$ could be obtained by differentiating through the sampling function $\Gamma(\cdot;I)$ using the technique from Jaderberg \etal~\cite{spatial_transformer}.
Once the gradients are known, any off-the-shelf gradient based optimization algorithm such as stochastic gradient descent \cite{sgd} or Adam \cite{adam} could be applied to minimize Equation~\ref{samp_loss}, as shown in Figure~\ref{impactful_demo}.
Unlike photometric loss which stems from an \emph{image-centric} viewpoint, sampling loss aims at assigning an adequate sampled color value to each point in the point cloud, thus providing a \emph{point cloud-centric} viewpoint.
Specifically, photometric loss also compares the colors of the point cloud with the query image, but in the image space, namely,
\begin{equation}
\label{second_photo}
L_\mathrm{photometric}(R, t) = \|\Psi(\{R(X-t), C\}) - I\|_2,
\end{equation}
where $\Psi(\cdot):\{\mathbb{R}^{N\times3},\mathbb{R}^{N\times3}\} \rightarrow \mathbb{R}^{H\times W\times 3}$ is a rendering function that receives the point cloud to produce a synthesized image.
The rendering function is necessary to apply photometric loss in our setup, as only a single image is given, unlike existing applications~\cite{lsd_slam, dtam} where multiple images are provided.
As photometric loss is evaluated in the image space, it suffers from the visual distortion of omnidirectional cameras.
To illustrate, in Figure~\ref{teaser_img}, one can observe that points near the pole (ceilings, floors) are `stretched', while they correspond to small areas in reality.
Since photometric loss makes direct image comparisons, it is severely affected by such artifacts and requires additional processing to account for the distortion~\cite{sphere_cnn, omni_hard_why_4}.
Sampling loss has numerous advantages over photometric loss.
First, as seen from Equation~\ref{samp_loss}, it fairly incorporates all points in the point cloud agnostic of whether it is closer to the pole, thus making it more suitable for 6-DoF pose estimation of omnidirectional cameras.
Second, sampling loss is cheap to compute, while still allowing for easy gradient computation~\cite{spatial_transformer}.
Each sampling operation consists of simple image indexing, and we ignore the non-differentiable, costly components of projection, such as occlusion handling.
The core part of PICCOLO consists of simple gradient descent on the sampling loss, which is very fast: $3 \times 10^8$ points can be processed per second.
Nonetheless, sampling loss can effectively handle the holistic view of the $360^\circ$ image and is robust to visual distortion or minor scene changes.
\label{sec:init}
\paragraph{Initialization Algorithm} While sampling loss has various amenable properties, it is non-convex as visualized in Figure~\ref{loss_surfaces}.
Depending on the initial position, optimization using gradient descent can stop at a local minimum, which can be a serious issue for large spaces.
To this end, we introduce a lightweight initialization algorithm, which outputs feasible starting points that are likely to yield global convergence.
We uniformly sample the space of possible camera positions, and filter them through a two-step selection process as presented in Algorithm~\ref{alg:PICCOLO}.
During the first step, we compute sampling loss values across $N_t \times N_r$ candidate camera poses and obtain the top $K_1$ smallest starting points (line 2).
Specifically, $N_t$ translations are chosen from the uniform grid on the point cloud bounding box, for which $N_r$ rotations, uniformly sampled from $SO(3)$, are selected.
Since sampling loss is very efficient, we can quickly compute the loss for all of the starting points.
Among the $K_1$ starting points, the second filtering process further selects $K_2$ $(K_2 \leq K_1)$ of them using color histogram intersections (line 3).
Top $K_2$ candidate poses with the highest color distribution overlap with the query image are chosen.
Finally, the resulting $K_2$ starting points are individually optimized for a fixed number of iterations with respect to the sampling loss in $SE(3)$ (line 7).
At termination, the optimized camera pose with the smallest sampling loss value is chosen (line 9).
\begin{algorithm}
\caption{Overview of PICCOLO}
\textbf{Inputs:} Point cloud P = $\{X, C\}$, query image $I$ \\
\textbf{Output:} Camera pose $\hat{R}, \hat{t}$.
\begin{algorithmic}[1]
\State $T \gets [(R_i, t_i) | i \in [1\mathrel{{.}\,{.}}\nobreak N_tN_r]]$
\Comment{Starting points}
\State $T \gets \texttt{\small getTopK}(\texttt{\small lossValue}(T,P,I), K_1)$
\State $T \gets \texttt{\small getTopK}(\texttt{\small histIntersect}(T,P, I), K_2)$
\State $V \gets [\:]$
\ForAll {$(R_i, t_i) \in T$}
\For {$\mathrm{iter} \in [1\mathrel{{.}\,{.}}\nobreak N_\mathrm{iter}]$}
\State $(R_i, t_i) \gets (R_i, t_i) - \alpha\nabla L_\mathrm{sampling}(R_i, t_i)$
\EndFor
\State $V.\texttt{\small append}(L_\mathrm{sampling}(R_i, t_i))$
\EndFor
\State $(\hat{R}, \hat{t}) \gets \argmin_{R, t} V$
\end{algorithmic}
\label{alg:PICCOLO}
\end{algorithm}
\section{Experimental Results}
\label{exp}
\subsection{Performance Analysis}
\label{perf}
\paragraph{Implementation Details}
PICCOLO is mainly implemented using PyTorch~\cite{pytorch}, and is accelerated with a single RTX 2080 GPU.
Once the starting point is selected as described in Section~\ref{sec:init}, we find the camera pose using Adam~\cite{adam} with step size $\alpha=0.1$ in all experiments.
PICCOLO is straightforward to implement, with the core part of the algorithm taking less than 10 lines of PyTorch code.
For results in which accuracy is reported, a prediction is considered correct if the translation error is below $0.1$~m and the rotation error is below $5.0^\circ$.
All translation and rotation errors reported are median values, following the convention of \cite{gosma, gopac}.
The full hyperparameter setup and additional qualitative results are available in the supplementary material.
\input{tables/stanford_all_table}
\input{tables/stanford_area3_table}
\paragraph{Stanford2D-3D-S}
We assess the localization performance of PICCOLO against existing methods using the Stanford2D-3D-S dataset~\cite{stanford2d3d}, as shown in Table~\ref{table:stanford_all} and~\ref{table:stanford_area_3}.
It is an indoor dataset composed of 1413 panoramic images subdivided into six different areas, and many scenes exhibit repetitive structure and lack visual features, as in Figure~\ref{qualitative_results}.
All areas are used for comparison except for GOPAC~\cite{gopac}, where we use a subset from Area 3 consisting of small rooms, as the algorithm's long runtime hinders large-scale evaluation.
PICCOLO outperforms all existing baselines by a large margin, showing an order-of-magnitude performance gain from its competitors.
GOSMA~\cite{gosma} and GOPAC~\cite{gopac} are optimization-based methods that do not utilize color measurements.
Instead, they require semantic labels for decent performance.
For fair comparisons with these algorithms, we make PICCOLO observe color-coded semantic labels as input, as shown in Figure~\ref{qualitative_results}, and report the numbers in Table~\ref{table:stanford_all} (PICCOLO Semantic) and~\ref{table:stanford_area_3}.
Semantic labels lack visual features, thus finding camera pose in this setup is closer to solving a blind-PnP problem~\cite{softposit}.
However, PICCOLO operates seamlessly and outperforms GOSMA and GOPAC without the aid of rich visual information such as RGB inputs, consistently succeeding around 1~cm error.
Although GOSMA and GOPAC are powerful algorithms that guarantee global optimality, they often fail in large scenes such as hallways, where the qualitative results are shown in the supplementary material.
PICCOLO also shows superior performance against deep learning methods~\cite{sphere_cnn, spherenet, posenet}.
Nevertheless, it should be noted that there is a subtle distinction in the search spaces of these methods.
The translation domain for deep learning-based methods is the entire Stanford2D-3D-S dataset, while it is confined to a particular area for PICCOLO, similar to GOSMA~\cite{gosma}.
However, deep learning-based methods are given very strong prior information to cope with the large search space; they are trained on synthetic pose-annotated images, which are generated within 30 cm proximity of the test images.
This means the training images are very close to the ground truth.
Nevertheless, it must be acknowledged that deep learning methods are capable of regressing the pose at wider scales, about 5 times the maximum search scale ($1000~\mbox{m}^2$) attainable with PICCOLO (Table~\ref{table:fukuoka}).
\paragraph{MPO}
Multi-Modal Panoramic 3D Outdoor (MPO)~\cite{fukuoka} dataset is an outdoor dataset which spans a large area ($1000\mbox{m}^2$) with many scenes containing repetition or lacking visual features.
As shown in Table~\ref{table:fukuoka}, PICCOLO performs competently with the same hyperparameter setting as Stanford2D-3D-S~\cite{stanford2d3d}, despite the large area of the dataset.
This validates our claim that PICCOLO could readily function as an off-the-shelf omnidirectional localization algorithm for both indoor/outdoor environments.
\input{tables/fukuoka_table}
\input{tables/omniscenes}
\paragraph{Practicality Assessment with OmniScenes}
Omnidirectional localization is expected to provide stable visual localization under scene changes or dynamic motion, and therefore promises practical applications in VR/AR or robotics.
We introduce a new dataset called OmniScenes collected to evaluate the performance on scenes with the aforementioned challenges.
We collect dense 3D scans of eight areas including wedding halls and hotel rooms using the Matterport3D Scanner~\cite{matterport_scan}.
Corresponding $360^\circ$ panoramic images are acquired with the Ricoh Theta $360^\circ$ camera~\cite{Ricoh} under two scenarios, handheld and mobile robot mounted.
Handheld scenarios are typically more challenging as unconstrained motion could take place and the capturer partially occludes scene details.
The images are taken at different times of day and include significant changes in furniture configurations and motion blurs.
Further details about the dataset are deferred to the supplementary material.
The evaluation results on the OmniScenes dataset are shown in Table~\ref{table:omniscenes}.
Unlike previous experiments, we assume that the gravity direction is known, as this is often available in practice.
PICCOLO exhibits competent error rates when there are no scene changes, agnostic of whether the input $360^\circ$ panorama is recorded in a handheld or robot-mounted manner.
As shown in Figure~\ref{qualitative_results}, PICCOLO can estimate camera pose even under severe handheld motion, thanks to the full incorporation of points from sampling loss.
Even though there is no functionality in PICCOLO that accounts for scene changes, there is a considerable amount of success cases given the accuracy in Table~\ref{table:omniscenes} and qualitative results shown in Figure~\ref{qualitative_results}.
As long as the global context provides enough amount of evidence from color samples, omnidirectional localization can succeed.
Nonetheless, there is a clear performance gap, and enhancing the robustness of PICCOLO against various scene changes is left as future work.
\subsection{Ablation Study}
In this section we ablate various components of PICCOLO.
Experiments are conducted using all areas of the Stanford2D-3D-S dataset~\cite{stanford2d3d}, unless specified otherwise.
\paragraph{Sampling Loss}
We compare PICCOLO with a variant that uses photometric loss from Equation~\ref{second_photo} in place of the sampling loss, to ablate the effect of sampling loss in our algorithm.
The rendering function is implemented as a simple projection of the 3D point cloud, similar to projections shown in Figure~\ref{qualitative_results}.
We use the warping function to obtain gradients with respect to $R, t$, as in previous works~\cite{lsd_slam, dtam, flownet}.
All other hyperparameter setups and the initialization algorithm are the same as PICCOLO.
The design choice of using sampling loss shows a large performance gain over photometric loss, as shown in Table~\ref{table:photometric}.
As sampling loss fairly incorporates all points in point cloud, it is free from visual distortion and thus more suitable than photometric loss for 6-DoF omnidirectional localization.
\input{tables/photometric_table}
\input{assets/images/ablation}
\paragraph{Gravity Direction}
If the gravity direction is known, the number of initial positions is significantly reduced and PICCOLO can perform highly accurate localization as shown in Table~\ref{table:photometric}.
Knowing the gravity direction is a reasonable assumption as many panoramic images or 3D scan datasets~\cite{stanford2d3d, fukuoka} contain the information.
In practice, one can easily infer the gravity direction of omnidirectional cameras using integrated gyroscopes, and that of 3D maps with RANSAC~\cite{ransac}-based plane fitting.
Nonetheless, PICCOLO stably performs without knowing the gravity direction as shown in Table~\ref{table:stanford_all} and~\ref{table:fukuoka}.
In case PICCOLO might be biased towards the gravity-aligned conventional data, we evaluate PICCOLO in flipped input images and arbitrarily rotated point clouds.
Under the same hyperparameter setup as Section~\ref{perf}, PICCOLO demonstrates consistent performance, as shown in Table~\ref{table:photometric}.
Such results imply that PICCOLO is amenable for novel scenes, and could be directly applied to a wide variety of non-standard inputs without training.
\paragraph{Initialization Pipeline}
We finally ablate various components of the initialization pipeline presented in Section~\ref{sec:init}.
The first main parameters to be examined are the number of initial points $N_t, N_r$ sampled from the range of possible transformations.
We evaluate the effect of different values of $N_t, N_r$ on auditoriums from Area 2 of the Stanford2D-3D-S dataset~\cite{stanford2d3d}.
As shown in Figure~\ref{ablation_nt_nr}, larger $N_t, N_r$ tend to improve the error values, but result in computational overhead.
An adequate set of $N_t, N_r$ should be chosen considering the trade-off.
We use $N_t=50, N_r=32$ for all our experiments.
This means we have about 1600 initial points to test, but the initialization finishes within a few seconds, thanks to the efficiency of sampling loss.
For runtime-critical applications, one may cache the projected point cloud coordinates at each candidate starting pose once for each scene and use it afterward.
This would significantly reduce the time spent on initialization.
We further examine the efficacy of our two-stage initialization scheme.
Recall the two-stage initialization in Section~\ref{sec:init} first selects $K_1$ candidate locations using \emph{loss values} followed by filtration to $K_2$ candidates using \emph{color histograms}.
We compare the performance of PICCOLO selecting $K_2$ initial poses from $N_t\times N_r$ candidates using (i) loss only, and (ii) the two-stage method presented in Section~\ref{sec:init}.
All rooms in Area 3 of the Stanford2D-3D-S dataset are selected for evaluation with $N_t=50, N_r=32, K_1=50, K_2=6$.
We display the results in Figure~\ref{ablation_initialization}.
Our two-stage initialization enables a significant performance boost with only a small increase in runtime.
\section{Conclusion}
In this paper, we present PICCOLO, a simple, efficient algorithm for omnidirectional localization.
We introduce sampling loss, which enforces each point in the 3D point cloud to correctly \emph{sample} from the query image.
Sampling loss is clearly beneficial for omnidirectional localization, as it is a \emph{point cloud-centric} formulation, free from spherical distortion, and computationally efficient.
In experiments conducted on various indoor and outdoor environments, PICCOLO outperforms existing algorithms by a significant margin.
Furthermore, when evaluated on our newly proposed dataset, OmniScenes, PICCOLO shows competent performance even amidst diverse camera motion and scene changes.
We expect PICCOLO to be applied in a wide variety of virtual reality / robotics applications where omnidirectional cameras are present.
\section{Additional Implementation Details}
In this section, we provide several additional details in PICCOLO that are not provided in the original paper.
The majority of the description of PICCOLO is provided in Section 3.
\subsection{Gradient Step Size Scheduling}
To foster convergence, we adaptively decay the gradient step size $\alpha$ (line 7 of Algorithm 1) similarly to learning rate scheduling widely used in neural network training.
In our experiments, we decay the step size by a factor of 0.8 if the loss function value does not decrease for 5 consecutive iterations.
\section{Hyperparameter Setup}
We report the hyperparameter setups of PICCOLO, where the configurations vary only depending on the providence of gravity direction.
As shown in Algorithm 1, we first sample $N_r \times N_t$ initial poses, out of which we select $K_1$ poses through loss value-based filtering, which are consecutively reduced into $K_2$ poses using color histogram intersection.
Then we run gradient descent for $K_2$ starting points for $N_{iter}$ steps.
The quantitative results are reported in Section 4.1.
\subsection{Unknown Gravity Direction}
For inputs where the gravity direction is unknown, we use $N_r=32, N_t=50, N_{iter}=100, K_1=50, K_2=6$.
Such a setup is used in Table 1, 2, 3, and 5 (excluding `gravity direction').
This setup shows effective performance in both indoor / outdoor datasets (Stanford2D-3D-S~\cite{stanford2d3d}, MPO~\cite{fukuoka}), and generalizes to arbitrary point cloud rotations and flipped images.
The capacity of PICCOLO to generalize in such diverse inputs under a fixed hyperparameter configuration alludes to its potential as an off-the-shelf omnidirectional localization algorithm.
\subsection{Known Gravity Direction}
We use the following setup for inputs where the gravity direction is known: $N_r=8, N_t=50, N_{iter}=100, K_1=50, K_2=6$.
Such a setup is used in Table 4 and 5 (`gravity direction').
Since the gravity direction is known, the search space can be dramatically reduced, and PICCOLO can perform highly accurate localization, as shown in Table 4 and 5.
\setcounter{table}{0}
\setcounter{figure}{0}
\section{Dataset Details}
Here we report minor experimental details about the datasets used in Section 4.
For all datasets, we remove panoramas where the ground truth camera position is outside the point cloud's bounding box.
\subsection{Stanford2D-3D-S}
For GOSMA~\cite{gosma}, if the room size exceeds a certain limit, segmentation fault occurs and the algorithm terminates.
We exclude those cases when computing the accuracy.
We additionally describe the 33 rooms used for creating Table 2.
These rooms are chosen using the criterion of Campbell \etal~\cite{gosma}: (i) distance to the closest point is greater than 50 cm, (ii) number of labeled pixels should be greater than 2000, (iii) number of 3D points should be greater than 2000.
\subsection{MPO}
A peculiar aspect of the MPO dataset is that all the ground truth values are the same: they are fixed to $R^*=I, t^*=\mathbf{0}$.
Therefore, we apply random rotation and translation to the point cloud to make the dataset more challenging.
For rotation, we randomly rotate the point cloud along the z-axis by an angle $\theta \sim \mathcal{U}(0, \pi)$, where $\mathcal{U}(\cdot)$ denotes the uniform distribution.
For translation, we randomly apply translations along the $x, y, z$ directions, where $x, y, z, \sim \mathcal{U}(0, 3)$. Note that the units for $x, y$, and $z$ are in meters.
\subsection{OmniScenes}
In this section, we report the acquisition process of our newly proposed OmniScenes dataset.
OmniScenes dataset is composed of 3D scans of 8 scenes accompanied by omnidirectional images.
3D scans are collected using the Matterport 3D scanner~\cite{matterport_scan}.
The corresponding omnidirectional images are collected with the Ricoh Theta $360^\circ$ camera~\cite{Ricoh} under two scenarios: handheld and mobile robot-mounted.
For the handheld case, we have the capturer to take $360^\circ$ videos while walking around the eight scenes.
For the mobile robot-mounted case, we use a TurtleBot3 Waffle~\cite{turtle} that is manually controlled.
To obtain 6DoF pose annotations for each omnidirectional image, we apply SfM (Structure from Motion), as in Kendall~\etal~\cite{posenet}.
COLMAP~\cite{colmap_1, colmap_2} and OpenMVG~\cite{openmvg} are used to obtain dense SfM reconstructions, which are then manually aligned with the Matterport 3D scans, similar to Valentin~\etal~\cite{energy_landscape}.
The aligned SfM model contains omnidirectional camera poses with respect to the Matterport 3D scans.
We further remove invalid pose estimates from SfM through manual inspection.
The resulting dataset, OmniScenes, contains a wide variety of pose-annotated omnidirectional images.
The statistical properties of our dataset are displayed in Table~\ref{table:omniscenes_supp}.
Also, we show qualitative samples from OmniScenes in Figure~\ref{sup_omni_scene1_hand}, ~\ref{sup_omni_scene1_robot}, ~\ref{sup_omni_scene2_hand}, ~\ref{sup_omni_scene2_robot}.
\input{tables/omniscenes_supp}
\setcounter{table}{0}
\setcounter{figure}{0}
\section{Difficulties of Using SIFT}
The main factor that hinders the use of SIFT~\cite{sift} on our problem setup is the abundance of scenes with repetitive structure or lacking visual features.
For the Stanford2D-3D-S dataset~\cite{stanford2d3d}, 660 out of 1413 panoramic images are hallways, bathrooms, and auditoriums, which exhibit the aforementioned characteristics, as shown in Figure~\ref{stanford_hallway}, ~\ref{stanford_bathroom}, ~\ref{stanford_auditorium}.
Further, once the visual inputs are given as semantic labels as in Figure~\ref{stanford_semantic}, it is impossible to use SIFT~\cite{sift} since the colored labels don't have any distinct features.
For the MPO dataset~\cite{fukuoka}, 229 out of 650 panoramic images are coasts and forests, which are also very difficult to establish sparse visual correspondences, as shown in Figure~\ref{mpo_supp_sift}.
\input{assets/images/sift_hard}
\setcounter{table}{0}
\setcounter{figure}{0}
\section{Qualitative Comparison with GOSMA~\cite{gosma}}
We make a qualitative comparison of PICCOLO and GOSMA in Figure~\ref{comparison}.
While GOSMA is successful in small rooms such as offices, it often fails in large areas such as auditoriums.
PICCOLO is capable of performing stable omnidirectional localization under diverse challenging environments.
Further, recall that semantic labels were given as input, to ensure fair comparison with GOSMA~\cite{gosma}.
This indicates that PICCOLO can function seamlessly with any other point-wise information.
\input{assets/images/compare_gosma}
\setcounter{table}{0}
\setcounter{figure}{0}
\section{Runtime Analysis}
\input{tables/runtime}
In this section, we examine the runtime properties of PICCOLO.
Experiments are conducted with a single RTX 2080 GPU and an Intel Core i7-9700 3.00GHz CPU.
We report the amount of time it takes for initialization and gradient descent in Table~\ref{table:runtime}, with a varying number of points in the input point cloud.
We use the same configuration used for unknown gravity direction: $N_r=32, N_t=50, N_{iter}=100, K_1=50, K_2=6$.
Table~\ref{table:runtime} shows that initialization (line 2, 3 of Algorithm 1) terminates within a few seconds, and gradient descent (line 7 of Algorithm 1) finishes on the scale of milliseconds.
Note that both initialization and gradient descent are easily parallelizable.
Thus PICCOLO can directly benefit from the presence of multiple GPUs, similar to GOSMA~\cite{gosma} and GOPAC~\cite{gopac}.
Furthermore, while the number of points is increased by a factor of 10, the runtime only shows a modest increase.
Sampling loss scales seamlessly to large point clouds, as no costly operations such as visibility computation take place.
\section{Additional Ablation Study}
In this section, we perform additional ablation study on PICCOLO.
We examine the number of starting points on initialization runtime and the effect of point cloud density on pose error.
The results are displayed in Figure~\ref{ablation}.
\paragraph{Number of Starting Points} PICCOLO is tested with varying numbers of translation and rotation starting points $N_t, N_r$ on offices from Area 2 of the Stanford2D-3D-S~\cite{stanford2d3d} dataset.
The median initialization runtime is reported with either $N_t$ or $N_r$ modified from the original setup.
Figure~\ref{time} indicates that while increasing $N_t, N_r$ leads to enhanced performance as shown in Figure 4, this also incurs longer runtime.
An appropriate $N_t, N_r$ that balances the trade-off should be chosen.
We use $N_t=50, N_r=32$ in all our experiments, which shows competent performance yet maintains fast runtime.
\paragraph{Point Cloud Density} PICCOLO is evaluated with varying point cloud sampling rates on the Stanford2D-3D-S~\cite{stanford2d3d} dataset.
As seen in Figure~\ref{sp}, PICCOLO is robust against point cloud density: pose estimation error is very small even when less than $5\%$ of the entire point cloud is used.
\begin{figure}
\centering
\begin{subfigure}[t]{1.0\linewidth}
\centering
\includegraphics[width=\linewidth]{nt_nr_time.pdf}
\caption{Effects of $N_t$, $N_r$ on initialization runtime.}
\label{time}
\end{subfigure}
\newline
\begin{subfigure}[t]{0.9\linewidth}
\centering
\includegraphics[width=\linewidth]{sp_e.pdf}
\caption{Effect of point cloud sampling rate on localization error.}
\label{sp}
\end{subfigure}
\caption{Additional ablation study on PICCOLO.}
\label{ablation}
\end{figure}
\onecolumn
\newpage
\setcounter{table}{0}
\setcounter{figure}{0}
\section{Additional Qualitative Results}
\subsection{Stanford2D-3D-S RGB Input}
\input{assets/images/sup_stanford}
\newpage
\subsection{Stanford2D-3D-S Semantic Input}
\input{assets/images/sup_semantic}
\newpage
\subsection{MPO}
\input{assets/images/sup_fukuoka}
\newpage
\subsection{OmniScenes Handheld}
\vspace{-1em}
\input{assets/images/sup_omni_scene1_hand}
\subsection{OmniScenes Robot-Mounted}
\vspace{-1em}
\input{assets/images/sup_omni_scene1_robot}
\newpage
\subsection{OmniScenes Handheld with Scene Change}
\vspace{-1em}
\input{assets/images/sup_omni_scene2_hand}
\subsection{OmniScenes Robot-Mounted with Scene Change}
\vspace{-1em}
\input{assets/images/sup_omni_scene2_robot}
\twocolumn
\bibliographystyle{ieee}
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{"url":"http:\/\/mathforlove.com\/blog\/","text":"1\n\n## QAMA \u2013 the calculator that won\u2019t make you lazy\n\nI got a call months ago from someone with what sounded like like a bizarre idea: he claimed he\u2019d invented a special calculator to use as a pedagogical device in the classroom. I was about to dismiss the call as being a crank, when I realized that what he was describing, if it worked, was potentially a brilliant idea.\n\nI bought myself a calculator, and began to check it out. It\u2019s called QAMA, and it\u2019s now available as an app, which is a much better deal, and you won\u2019t accidentally kill the batteries if you leave the calculator on, as I did after the first time I used it. Nevertheless, I\u2019m blown away by QAMA, since it elegantly solves one of the central problems of using calculators in the classroom: the problem of students handing all the thinking to the calculator.\n\nHere\u2019s how it works.\n\nYou plug in whatever equation you want to solve. For example, I entered \u201c65.86 x 21.\u201d\n\nThen you hit the equals button. And the calculator doesn\u2019t give you an answer. And therein lies its genius, its usefulness, and also, according to my conversation with the designer, the great technical difficulty in creating it in the first place.\n\nTo get an answer, you have to enter an estimate. If it\u2019s just an arbitrary number, the calculator won\u2019t accept it. Your estimate must prove that you were thinking. And the calculator expects that you can work at a pretty decent level. It requires perfect answers for single digit multiplication for example\u2014it is no help with memorizing your multiplication tables. For this particular problem, I figured that 1300 would be a decent estimate. I entered it, and the calculator showed me the real answer: 1383.06.\n\nIt can be fun to play around with how good the estimates need to be. I tried 13\/21. First estimate: 1.6, and this turned out to be an excellent guess. Second estimate: 1.5. QAMA wouldn\u2019t accept it. Third estimate: 1.55. That was acceptable. The promise of this innovation is no doubt obvious to middle and high school teachers. QAMA has reinforced in its architecture the process of thoughtful calculator use, by making the tool that much more difficult to use mindlessly. Here\u2019s what students should do when they use a calculator:\n\n1. Decide if the problem actually requires a calculator.\n2. If it does, get a rough sense of what a reasonable answer might be, then enter the problem on the calculator.\n3. Pay attention to whether the answer the calculator gave you makes sense.\n\nHere\u2019s what students too often do once they have easy access to calculators:\n\n1. Grab a calculator whenever they have an arithmetic problem to do.\n2. Take whatever comes out as fact, and move on.\n\nI\u2019ve seen eighth graders reach for a calculator to solve 100 \u2013 98. I\u2019ve seen college students accept total gibberish from their calculator after mis-keying, without considering whether the answer makes sense on a gut level. (\u201cThe swimming pool costs\u2026 53 billion dollars.\u201d) Any teacher who gives their students access to calculators knows who pervasive these problems can become. \u201cDoes your answer make sense?\u201d we ask, repeatedly, and often to no avail. But QAMA prevents students from having the option to be lazy. Their motto is: \u201cThe calculator that thinks only if you think too.\u201d And that seems true.\n\nPersonally, I\u2019ve come down against having students use calculators until middle school (except for occasional use in 4th-5th grade). But I think QAMA could take all the worst parts (mindlessness, laziness, etc.) of calculator use out of the middle and high school classroom. I think they\u2019re on to something.\n\n1\n\n## Book Reviews\n\nI read pop math books. Quite a few, in fact. Also, sometimes publishers send me advance copies and ask for reviews. I generally read these too. What makes me a bad reviewer is that I then wait for 6 \u2013 20 months before I actually write anything down.\n\nTime to remedy this situation! Here are a batch of quick reviews for books on or related to math that I\u2019ve read in the past couple of years.\n\n##### How Not to Be Wrong: The Power of Mathematical Thinking\n\nJordan Ellenberg has written one of the finest books on mathematics in decades. How Not to Be Wrong belongs in the pop-math canon, alongside Simon Singh\u2019s best works (The Code Book; Fermat\u2019s Enigma) and Robert Dantzig\u2019s Number: The Language of Science.\n\nThere are two qualities that make How Not to Be Wrong exceptional. The first is how much news it contains. So many math books are rehashes of classic stories: Zeno, Archimedes, Pythagoras, Newton & Leibnitz, Euler, Gauss, and so on. Read a few accounts of the history of math and the stories, fun as they are, start to run into each other. Ellenberg begins with Abraham Wald studying bullet holes in airplane fuselages during WWII and goes off in all sorts of new directions from there. I was shocked at how much I had never seen before, and how seamlessly Ellenberg ties together statistics, mathematics, and common sense.\n\nFourth from the top is How Not to Be Wrong\n\nThe second quality that makes this book necessary reading is the sense of humor. The asides and footnotes are laugh-out-loud funny, and Ellenberg is a masterful and delightful writer to read. Bill Gates picked How Not to Be Wrong as one of his top five recommendations for reading this summer, and it\u2019s at the top of my list too. Don\u2019t miss it.\n\n##### Love and Math: The Heart of Hidden Reality\n\nHow I wanted to like this book. It\u2019s name is almost identical to this website\u2019s, and Ed Frenkel had been on a tear, speaking on the Colbert Report and other TV and radio shows about the book, which promised to share what he loved about math. I started reading hopefully, and the first five or so chapters didn\u2019t disappoint. Frenkel\u2019s story of learning math despite anti-semitism in Soviet Russia is compelling and readable. Soon enough he\u2019s invited to the West, and the story loses its dramatic tension: Frenkel\u2019s career heads up, and the sailing is smooth. Frenkel tries to create dramatic tension around whether an important mathematician might show up at a conference or not, but the stakes just feel too low.\n\nWisely, with little narrative left to mine from his own story, Frenkel pivots in the second half of the book mainly to explaining the math and the story behind the Langlands Program, an ambitious and collaborative mathematical undertaking. While points of this project are interesting, the complexity of the mathematics exceeds Frenkel\u2019s ability (and possibly anyone\u2019s ability) to explain it to a lay audience. I\u2019d estimate the necessary mathematical background for much of the second half of this book to be roughly graduate school level, and the layperson who tries to read it may find themselves scared off.\n\nMeanwhile, there are two undermining details that become more glaring as the book goes on. First, Frenkel\u2019s presentation of the mathematical world is deeply male. The female characters appear as charming wives who serve tea to their hardworking mathematician husbands, then disappear. Frenkel seems to have no problem with this, and his video project (looking for the equation for love) in the last chapter doesn\u2019t do a lot to present a more positive space for women in mathematics. While professional math continues to be dominated by men, it feels more important than ever to celebrate female mathematicians and make clear that women belong in the field. Frenkel seems happy with his Mad-Men-esque vision of the field.\n\nSecond, Frenkel\u2019s self regard unbalances the story. He\u2019s a master of the humble-brag, and the longer you read, the more you have a sense that the story he\u2019s really interested in telling is the one about how great Ed Frenkel is. Frenkel is taking on more and more of a place in the conversation around popular mathematics, and I think he has something important to share about the passion and beauty of mathematics. If he can make a little more room for underrepresented groups and a little less room for himself, I think his contributions will be that much more valuable.\n\n##### The Math Olympian\n\nThis is a peculiar and kind of wonderful book. It reads like a soap opera, almost: a sort of Slum Dog Millionaire for a female Canadian Math Olympian, who, in the course of a 5-question test, flashes back through all her preparation and through important life moments.\n\nThere\u2019s some solid math throughout this book, and, compared with Frenkel, a very clear place for women in math, along with a clear-eyed view of some of the specific difficulties they might face. What makes the book exceptional, though, is the diverse picture it paints of great math mentoring, and the emphasis on what really matters in mathematics\u2014not the contests, it turns out, but the work of doing math itself. A book\n\n##### The New York Times Book of Mathematics\n\nThe Times sent me a review copy of their Book of Mathematics last year, and I\u2019ve been slowly reading it since then. There\u2019s a lot here: over 100 years of reporting on mathematics. Overall, it\u2019s a pretty impressive collection. More than anything else, it\u2019s amazing to see what they got right: in so many articles, they\u2019re interviewing the pivotal players, and capturing the most important breakthroughs just as they\u2019re happening. Reading through the book gives you a sense of what the news was in 20th century mathematics: chaos theory, cryptography, computers, mathematicians and their major breakthroughs (Wiles, Perelman, Erdos, Conway, Godel and others make appearances throughout the book). There are some whimsical sections too, like an interview with the real Monty Hall, who takes the writer to school.\n\nIf you want to get a sense of what the news in mathematics actually was this past century, this is a great place to start.\n\n##### The Mathematics Devotional\n\nClifford Pickover has written a number of big, beautiful, coffee-table-grade books on mathematics and physics, and I\u2019ve been a fan. But when his publisher sent me this one, I was skeptical. A Devotional? As in, read an inspirational quote and ponder a picture? Indeed, that\u2019s exactly what this book is: one quote and one image per day of the calendar year. And yet, I\u2019ve had it for over a year now, and find myself opening it up all the time, and using it exactly how it\u2019s meant to be used. It\u2019s exactly what it set out to be, and I continue to be a fan.\n\nHere\u2019s today\u2019s quote: \u201cThe thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was \u2018out there\u2019 all along I just couldn\u2019t see it. And now I can! This is really what keeps me in the math game\u2014the chance that I might glimpse some kind of secret underlying truth, some sort of message from the gods.\u201d \u2014Paul Lockhard, A Mathematician\u2019s Lament, 2009\n\nSo there\u2019s some reading to check out this summer! I\u2019ll return now to my stack of books and start reading. Next summer is coming fast.\n\n## Tiny Polka Dot has funded!\n\nWe\u2019re thrilled to announce that our Kickstarter campaign for Tiny Polka Dot has funded! This means we\u2019ll be bringing this game into the world before the end of the year.\n\nThere are still 66 hours in the campaign, and you can still support the project, help us reach our stretch goals to make the game even better, and get your own copy locked down.\n\nA friend of mine\u2014a homeschooling mom and long-time K-2 teacher\u2014said recently that:\n\nEvery time we sit and play I think how really with pattern blocks, some beans and a Tiny Polka Dot set\u2026\u00a0 you could cover math from k-2 and have lots of fun doing it.\n\nWhile it is impossible to know how these things will go in the long run, I\u2019m hopeful that Tiny Polka Dot has will be the kind of game that ushers mathematical play into classrooms and families that much more quickly.\n\nSpeaking of which, Emily Grosvenor, author of Tessalation, just interviewed me (and some fantastic colleagues) in a piece on mathematical play in Parent Map. Take a look!\n\n## Pyramid Puzzle\n\nThis Pyramid Puzzle was recently featured in a post in Forbes about our Tiny Polka Dot campaign.\n\nTake two suits\u2013that\u2019s 22 cards, with 0 \u2013 10 each occurring twice. The puzzle is to make a pyramid using 10 cards of those 22 cards, so that each number in the pyramid is the sum of the two below it. Here\u2019s a near-solution: every card is the sum of the two dots below it; the only problem is that there\u2019s no third 1 to go in the last space on the bottom. (Excess cards are on the right.)\n\nI just received this email from a friend who\u2019s been play-testing Tiny Polka Dot with her kids.\n\n\u201c[my daughter] couldn\u2019t make it work [with 10] with two sets then decided \u201cOK let\u2019s try 9.\u201d Off to verify 10 really doesn\u2019t work\u201d\n\nHere\u2019s the photo she attached with the email (note: spoiler below!)\n\nI actually convinced myself that 10 couldn\u2019t work at the top of the pyramid\u2026 for a while. Turns out, I was wrong! More ends up being possible with this puzzle than meets the eye.\n\nBut I love this puzzle for precisely the reason that it worked so well for my friend\u2019s daughter: 10 doesn\u2019t seem to work, so she takes a leap of faith and tries 9 at the top of the pyramid; the puzzle rewards the courageous step of trying an even harder puzzle!\n\nIs it possible to put an even smaller number at the top of the Pyramid?\n\n[Sidenote: you can now get Prime Climb and Tiny Polka Dot together at a big discount if you support our campaign. Pledge here!]\n1\n\n## What are the aims and goals of math education, K-2?\n\nAs part of the Math for Future Elementary School Teachers class we\u2019re teaching at the UW, we regularly ask our students to reflect on what they\u2019re learning in the class. This particular student reflection felt so dense and comprehensive that I thought it would be worth sharing here (with her permission, and her name removed).\n\nThe prompt: What do you think are the aims and goals of math education for grades K-2? Include topics, values, and outcomes.\n\nWhat do you think?\n\nSo you want your kid to know math? Of course you do. Math is an important tool, used widely in many disciplines, and helps us make sense of our world. It\u2019s also beautiful, fun, and interesting, especially for young children.\n\nKids are just entering the world of patterns and numbers, and their love of math is ready to bloom. They are ready and excited to count, classify, name, and look for patterns. But too often, parents unintentionally do damage, either by neglecting their kids\u2019 mathematical development, or by pushing them too hard, too quickly. It\u2019s important to find the right balance, but many parents aren\u2019t sure how.\n\nThis is an issue now, as more attention is being paid to the development of a human intellect. Pre-Kindergarten education, Head Start, Common Core, and the achievement gap are all looming large in public discourse right now because we care so much about educating our children. Research has shown the best education begins at home, with a thoughtful approach to nurturing your child\u2019s natural math instincts.\n\nThe following guide is adapted from our new math game deck for three to eight year olds, Tiny Polka Dot. These ideas are, essentially, the keys to nurturing the natural mathematical instinct that is growing in every child.\n\n##### Guide for Grown-ups\n\n1. Play! Play is the engine of learning for young children. Provide your kids with a rich environment to play in, and let them take the lead. What makes for a rich math environment?\n\n\u2022 Blocks \u2013 pattern blocks, legos, tangrams, and other blocks for building, sorting, and playing are the best.\n\u2022 Games \u2013 Classics like Uno, concentration, war, dots and boxes, and Tiny Polka Dot are great as soon as kids are ready for them. Winning is irrelevant at first, and many games can be played collaboratively. Keep it light, and have fun yourself!\n\u2022 A mathematical perspective \u2013 a walk in the woods, a pile of buttons, an old egg carton\u2026 these all hold rich mathematical structure if you look at them with the right eyes. Any pile of assorted object can become an opportunity to group by color, by number of holes, or by size. Walks become a chance for counting steps or physical challenges that involve gut estimations and intuitions.\n\nEXAMPLE\nYou: How many steps do you think it will take to get to that tree?\nYou: Let\u2019s find out!\n[You walk and count. The answer, it turns out, was 15.] You: How many steps to that next tree?\nYou: Let\u2019s find out!\n\nMath teachers in elementary, middle and high school know how hard it is to get kids to intuitively understand whether their answers make sense. Connecting numbers up to the world with fun guess-and-check challenges pays off big time later.\n\nAs for egg cartons, check out the patterns emerging from kids playing with colored plastic eggs and egg cartons at Math-on-a-Stick at the Minnesota State fair. (These taken from Christopher Danielson\u2019s aptly titled blog post, Let the Children Play.)\nYou might not recognize this as mathematical play, but sorting, symmetry, and grouping by equal numbers is precisely the foundation of the more abstract mathematics that will come later in school. And most importantly, it\u2019s fun!\n\n2. Learning takes time! The process of learning and mastering a new skill can be slow and complex. This is not a test. Do not to rush your child or expect them to know something after they have seen it once or twice. You may find a child makes the same mistake over and over again. As long as they are having fun, trust that your child is learning! It\u2019s easy to over-help. Take a breath, and make sure you are letting your child take as active a role in the game as possible. It doesn\u2019t matter if they get the answer right. Because it isn\u2019t a test.\n\n\u2022 WRONG QUESTION: \u201cIs my child smart?\u201d\n\u2022 RIGHT QUESTION\u00a0\u00a0 \u201cHow is my child thinking?\u201d\n\n3. Think out loud. Your child is imitating everything you do, and the more you can narrate your thoughts, the better a model of thinking you can be. Slow down, find reasons to count slowly and clearly, and use mathematical language to describe what\u2019s happening in your head. Never say, \u201cMommy (or Daddy) is terrible at math!\u201d If you don\u2019t have the ideal relationship to math, now\u2019s your chance take a fresh look.\n\nThe happy truth about doing math with your kids is that it\u2019s way more fun than you\u2019re expecting it to be. It\u2019s not about right answers, and it\u2019s not about speed. It\u2019s about playing, counting, building, sorting, and studying the wonderful, colorful world around us.\n\nIf you\u2019re interested in more ways to explore math with your three- to eight-year-olds, our new math game, Tiny Polka Dot, is on Kickstarter now. It provides multitudes of ways to play with number and pattern in a colorful and fun family game.\n\nBecause really, we should all be having way more fun.\n\n## Tiny Polka Dot \u2013 the colorful math game for young kids\n\nWe\u2019re happy to announce that our newest math game, Tiny Polka Dot, is now on Kickstarter!\n\nTiny Polka Dot is a math game deck for 3- to 8-year-old children and their families. Over the past several years we\u2019ve designed series of games through our work with pre-K and K-2 teachers. Tiny Polka Dot is the culmination of that work: a deck of colorful cards that pulls together the best of those games.\n\nIf you or anyone you know would like this game to exist, please support the campaign now. Learn more here.\n\n##### Why Tiny Polka Dot?\n\nThe most common question we get asked about Prime Climb is: \u201ccan my 4 (or 5 or 6 or 7) year old play this game?\u201d And although some people have reported having fun playing the game with young children, Prime Climb was designed with older kids in mind.\n\nWe had some great card games to recommend, but the most mathematically relevant ones usually involved removing the face cards or a bunch of elaborate rules. (Cribbage jumps to mind.) And the design of standard playing cards makes simple games like memory or war or their variations less mathematical than they ought to be.\n\nWhy is there no deck of cards that\u2019s expressly designed to bring out the mathematical nature of these games? Three- and four-year-old kids often need practice counting different arrangements of objects, while Kindergarten-aged kids transition from counting to adding and subtracting; the right series of games and a thoughtfully-designed deck of cards could back up the entire sequence of early numeracy.\n\nAnd, in the pivotal moment that often occurs in these stories, we suddenly realized that we should build it.\n\nAnd so we did!\n\nIf you have a 3- to 8-year-old in your life, please consider backing the campaign, and spread the word to folks you know who would be interested! We\u2019re really excited about this game, and with your help we can get it produced before the year is out.\n\n## Math Festival, TEDx Talk, Fraction Talks\n\nSo much is coming up!\n\nFirst, Seattle\u2019s Julia Robinson Math Festival is this Sunday. It\u2019s a festival celebrating collaborative, beautiful, non-competitive mathematics. If you\u2019re interested in signing your child up (4th grade or older), there\u2019s still time! You can learn more about the festival here.\n\nSecond, my TEDx Talk, Five Principles of Extraordinary Math Teaching, if finally out. I\u2019d love to know what you think of it.\n\nAnd third, I\u2019ve been having a blast exploring the new website fractiontalks.com. This is a tremendous resource, a kind of one-stop-shopping experience to find fraction images to use with students of all ranges of experience. For example, what fraction of each shape below is green\/yellow\/blue\/etc.?\n\nMore coming soon, including a new Kickstarter game for 3-8 year-old kids. Stay tuned!\n\n4\n\n## Thoughts on linear equations\n\nI recently received this email from a teacher I work with:\n\n\u201cDan, I have a question for you. I just introduced my [pre-algebra students] to slope and then to slope-intercept form of linear equations and wanted to explore with them some word problems which could be written in that form. (Ex: . For babysitting, Anna charges a flat fee of $10, plus$5 per hour. Write an equation for the cost, C, after h hours of babysitting. What do you think the slope and the y-intercept represent? How much money will she make if she baby-sits 5 hours?)\n\nDo you have any ideas how to make this kind of lesson more fun, hands-on and exploratory for students?\u201d\n\nHere\u2019s my response:\n\n\u201cThis is a great question. Fortunately, there\u2019s a large community online that\u2019s working to solve it. I\u2019ve got some ideas too \ud83d\ude42\n\nStrategies for making linear equations more relevant, more interesting, more exploratory:\n\n1. Same problems, slicker delivery\nAn example might be the 100\u00d7100 cheeseburger problem. Same idea as the babysitting problem, but real life, involves a menu, and a compelling premise.\n2. Slick delivery, unanticipated result\nYou can sometimes grab students attention with a problem that seems easy, but has a twist, like this stacking cups activity.\n3. Pared down delivery\nFor example, visual patterns has the same info and the same question each time: here\u2019s steps 1-4, and you can get step 43 as a hint. Write the equation. Purely visual, so students can begin immediately, and there\u2019s actually more thinking work for them to do. It\u2019s harder for them to just use a recipe approach.\n4. Give two options to compare.\nFor example, a Would You Rather structure, as in, \u201cWould you rather charge $5 base rate plus$7 per hour, or $15 base rate plus$5 per hour to babysit? Defend with algebra.\u201d This is a harder question, and involves actually having to make an argument, which is a more compelling, more social reason to do something, and usually generates a deeper understanding.\n5. Use Desmos.\nI know a number of teachers who really like what they can do with this tool in the classroom. It basically allows kids to explore and solve problems with their computers or tablets, in some creative ways. There are some clever lessons in the teacher portal.\n6. Raise the ceiling.\nIf you were to show the sequence of dominoes in a growth pattern below, there are natural questions that you (or the kids!) might ask:\n-How many columns will there be in the nth stage?\n-How many dominoes will there be in the nth stage (double n dominoes)?\n-How many dominoes will be in the tallest column of this organization in the nth stage?\n-how many dots total on all the dominoes in the nth stage?\n\nSome of these questions go beyond linear equations, but provide a natural stretch questions, and can actually help kids understand how to model with equations even better.\u201d\n\nThe teacher who wrote me closed by say \u201cI have a few ideas, but would love to hear yours.\u201d I feel exactly the same way. What else goes on this list?\n\n## Phi is the new root 2\n\nMy knowledge about the foundation history of irrational numbers was challenged today, and I\u2019m pretty happy about it.\n\nI had recently tweeted a Vi Hart video that gave a fun, geometric proof of the classic first proof of irrationality: $\\sqrt{2}$ is irrational. If it weren\u2019t, that would mean you could build a square that had integer sides and an integer diagonal, and that would allow you to build a smaller square with the same process. To get a contradiction, repeat until you run out of integers.\n\nAfter I tweeted the video, I got a response claiming that\u2026\n\nI was somewhat taken aback. In source after source, I\u2019ve seen $\\sqrt{2}$ named as the first number ever proved irrational. Variations on the same proof abound. And here was a claim that $\\phi$, the golden ratio, actually holds the rightful place in history as humankind\u2019s first brush with \u201cthe unnameable.\u201d There seems to be a historical argument; but how complicated is the proof?\n\nIn fact, it\u2019s so wonderfully simple that there\u2019s a pedagogical argument to be made for teaching that $\\phi$ is irrational before we even mention the Pythagorean Theorem or square roots. You need to know how to find angles in regular polygons and chase them around diagrams, and know how Isosceles triangles work. The thrust of the proof is the same as for $\\sqrt{2}$, but it sidesteps the parity argument that can sometimes feel less tangible.\n\nLet\u2019s imagine, as the Pythagoreans might have, that every number is rational. An equivalent way to state this is there is always some scaling of any pair of lengths that allows them both to be positive integers. (To the Pythagoreans, the relationship between any two lengths was identical to the relationship between two whole numbers, axiomatically.) So suppose we have a regular pentagon with integer side length a and integer diagonal b.\nThe ratio of b to a, is precisely the golden ratio, by the way. But we don\u2019t even need to know what it is. We\u2019ll just try to show that a and b can\u2019t both be integers.\n\nFirst off, chase some angles around and you\u2019ll see pretty much every angle is either 36, 72, or 108 degrees. This gives a bunch of Isosceles triangles. It follows quickly that\n\n$x = 2a - b$ $y = b - a$ [I\u2019ll leave that piece as an exercise. It\u2019s pretty satisfying to chase angles around and have everything come out nicely.] This implies that x and y are positive integers. But they are the side and diagonal of a regular pentagon again, so the argument repeats! And this is the crux of the problem: positive integers can get smaller for only so long before they run less than 1. (Just like the infinite regress that was hinted at in that error-laden but inspiring work, Donald in Mathemagic Land.)\n\nConclusion? The original pentagon couldn\u2019t have been drawn with integer sides to start with. And that means it couldn\u2019t have been drawn with two rational sides, or else we would have scaled them up to whole numbers. And that means the relationship between the side and diagonal of the regular pentagon is irrational.\n\nAnd there we have it. Irrational numbers without actually dealing with numbers at all. Or evenness and oddness of numerators and denominators.\n\nA delightful discovery. We\u2019ll likely never know for sure what length the Pythagoreans proved irrational first, but that\u2019s a strong claim for $\/phi$ over $\/sqrt{2}$.\n\nEspecially because, as Donald found out, the Pythagoreans were all over pentagons and the golden ratio.","date":"2016-06-25 07:04:38","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 9, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.25406599044799805, \"perplexity\": 1496.7780257700329}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-26\/segments\/1466783392159.3\/warc\/CC-MAIN-20160624154952-00065-ip-10-164-35-72.ec2.internal.warc.gz\"}"}
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Q: Can SharePoint 2007 install on Windows 7? I have a 32 bit Windows 7 Ultimate N, will MOSS 2007 install on it?
A: this blog says you can, and shows you how.
A: If you can, you'll really benefit from creating a virtual environment to host MOSS and develop against it. I highly suggest against installing it on your home O/S.
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Q: Read content of RAR files using C# Is there any way to read the content of a RAR file (support for multi-file RAR is a must)?
I don't want to extract the content to the disk, just read it like a stream.
A: Install NUnrar from nuget
RarArchive file = RarArchive.Open("rar file path");//@"C:\test.rar"
foreach (RarArchiveEntry rarFile in file.Entries)
{
string path = "extracted file path";//@"C:\"
rarFile.WriteToDirectory(path);
}
A: Low level lib to work with 7z.dll (supports rar archives, incliding multi-part, works with .net streams):
C# (.net) interface for 7-Zip archive dlls
And more high-level lib based on the first one:
SevenZipSharp
A: Chilkat Rar library
More specific: link
A: My unrar project, http://nunrar.codeplex.com/ aims to be very .NETty and has streaming support. If you need something else, please suggest or give me a patch.
A: Another possibility is using including the rar command-line executable as application ressource and call it via System.Diagnostics.Process.
You may want to redirect the input/output stream.
A: If you want to directly access files stored in uncompressed rar files, then this answer might be of use.
ReScene is a project for recreating
rar archives from the extracted files.
You need a .srr file for this. The
source code is available. You may want
to take a look at RarStream.cs.
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By Identify Types
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The copyright of the received article shall be assigned to the journal as the publisher of the journal. The intended copyright includes the right to publish the article in various forms (including reprints). The journal maintains the publishing rights to the published articles.
Article Submission: 0.00 (IDR)
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\section{Introduction}\label{sec01}
\section{Introduction}\label{sec01}
Our topic in this paper is the compatibility of abstraction principles and relative categoricity. The most famous example of an abstraction principle is Hume's Principle, which asserts that the number~of~$X$'s is the same as the number~of~$Y$'s if and only if~$X$ and~$Y$ are equinumerous, where this just means that there is a bijection between the $X$'s and $Y$'s. In this, the ``number~of'' operator is understood to be a type-lowering operator which takes second-order entities and returns first-order entities. Much of the interest in Hume's Principle stems from the fact that it, in conjunction with certain axioms for second-order logic,
recovers the now standard Peano axiomatization for arithmetic (\cite{Wright1983} Chapter~4, cf. \cite{Walsh2012aa} \S{2.2} pp. 1688~ff). Wright vivified this in \cite{Wright1998ab} by asking us to consider the perspective of ``Hero,'' who using Hume's Principle recovers all the laws of pure and applied arithmetic using Frege's definitions for zero, successor, and natural number.
The motivation for relative categoricity is likewise often conveyed by considering the perspective of agents. Parsons in his seminal essay \cite{Parsons1990a} and later book \cite[\S{49}]{Parsons2008} asks us to consider interlocutors~$h$ and~$c$, each having access to her own structure satisfying the axioms for arithmetic, but whose access to the other's number structure comes primarily from the other's literal utterances. Initially it might appear that the incompleteness of arithmetic could allow for intractable disagreement: perhaps the which structure agent~$h$ has in mind witnesses the arithmetized version of the consistency of some theory, while the structure agent~$c$ has in mind does not.
However, Parsons notes that this can't happen so long as each interlocutor can in addition perform mathematical induction on concepts defined in terms of the other's natural number structure. If this is granted, then the map~$\Gamma$ defined by~$\Gamma(0_h)=0_c$ and~$\Gamma(s_h(n))=s_c(\Gamma(n))$ is an isomorphism, wherein~$0_i$ and~$s_i$ denote the zero and successor of agent~$i$'s number structure. Since isomorphisms preserve truth-values, the two agents will agree on all sentences of the pure arithmetical vocabulary in which zero and successor are taken as primitive.
So it's natural to ask whether there is similar agreement when it comes to abstraction principles. To expand upon Wright's example, we might envision Hero as well as an interlocutor Claudio, and ask whether their agreement upon Hume's Principle leads to an agreement on other numerical truths. Frege famously noted in the \emph{Grundlagen} one potential source of disagreement: Hero and Claudio might disagree about whether everything is a number, or whether this-or-that object is a number (\cite{Frege1884aa}, \cite{Frege1980} \S{56}, \S{66}). But it's still natural to ask what happens when we restrict attention to each
agent's \emph{pure numbers}, that is, to the range of each's ``number~of'' operator. One important species of agreement has been stressed in the recent literature under the heading of the principle `Nq'. In terms of our scenario, Hero and Claudio would both think that the number~of~$Y$'s is equal to~$n$, as defined in terms of their respective ``number~of'' operators, if and only if~$\exists^{=n} \; x \; Yx$, wherein this is the exact numerical quantifier defined in the usual first-order way
(cf. \cite{Hale1987aa} pp.~223-224, \cite{Wright1999} p.~18, \cite{Hale2001} p.~322, \cite{Cook2007aa} p.~32, \cite{Walsh2014aa} p. 92).
It turns out that this agreement extends to the truth-values of \emph{all} pure
numerical statements, where again we understand by ``pure'' the restriction to the range of each ``number~of'' operator. For, our interlocutors, just like Parsons', have a natural way of translating between their individual pure number discourse. Designating Hero's ``number~of'' with ``$\#_h$'' and Claudio's with ``$\#_c$,'' we see that
whenever Claudio utters a statement about his pure numbers, we may replace each instance of~$\#_c$ by~$\#_h$ and obtain a truth about Hero's pure numbers. This is due to the fact that the map~$\Gamma(\#_h(X))=\#_c(X)$ is an isomorphism between Hero's and Claudio's ``pure number'' structures, so that we can again appeal to the fact that isomorphisms preserve the relevant truth-values. So not only will Hero and Claudio agree about all the truths of number theory, they will agree also, for instance, that the number~of evens is the same as the number~of natural numbers.
This result about Hume's Principle was proven in the earlier paper \cite{Walsh2012aa} (Proposition 14 p. 1687).
However, this earlier work left open the question of whether this phenomena persists when one considers other abstraction principles. For, Wright and Hale \cite{Hale2001} have emphasized that Hume's Principle is just one abstraction principle amongst many. Other principles can be obtained by replacing the equinumerosity relation with another equivalence relation on second-order entities and by introducing a new type-lowering operator for each such equivalence relation. So an \emph{abstraction principle} is a principle of the following form:
\begin{myequation}\label{eqn:AE}
A[E]: \hspace{10mm} \forall \; X, Y \; (\partial(X)=\partial(Y) \leftrightarrow E(X,Y))
\end{myequation}
In this, the quantifiers range over second-order entities and the operator~$\partial$ takes second-order entities and returns first-order entities. Moreover, the type-lowering operator $\partial$ is understood to depend on the equivalence relation~$E$. The case of the two agents is thus well-formalized by the following principle:
\begin{myequation}
A^2[E]: \hspace{5mm} \forall \; X, Y \; [(\partial_1(X)=\partial_1(Y) \leftrightarrow E(X,Y)) \wedge (\partial_2(X)=\partial_2(Y) \leftrightarrow E(X,Y))] \label{eqn:AE2}
\end{myequation}
Let's call the objects in the range of the $\partial_i$-operator \emph{the abstracts} of interlocutor~$i$, and let's denote this by $\mathrm{rng}(\partial_i)$. Then we say that the abstraction principle~$A[E]$ is \emph{naturally relatively categorical} if it can be proved from this principle $A^2[E]$ (and the axioms governing the second-order logic) that the map $\Gamma(\partial_1(X))=\partial_2(X)$ is an isomorphism between the abstracts of the two interlocutors. For a more formal statement of natural relative categoricity, see Definition~\ref{eqn:defn:NRC}, which we provide after carefully setting up the particulars of the background second-order logic.
The present paper answers the question of what abstraction principles are naturally relatively categorical by presenting various equivalent characterizations in terms of sameness of cardinality and invariance under injections. These characterizations then allow us to ascertain easily whether a given abstraction principle is naturally relatively categorical (see \S\ref{sec04} for examples). Let us build up to the statement of these equivalent characterizations by introducing some key definitions we deploy in this paper. First, let us say that the abstraction principle $A[E]$ is \emph{cardinality coarsening on abstracts} if the following is provable from the abstraction principle and the associated principles of the second-order logic:
\begin{myequation}\label{eqn:defn:CC}
\forall \; X, Y\; ((Y\approx X \; \& \; X\subseteq \mathrm{rng}(\partial)) \rightarrow E(X,Y))]
\end{myequation}
In this, $Y \approx X$ is an abbreviation for the notion of equinumerosity operative in Hume's Principle, while $\mathrm{rng}(\partial)$ is the collection of objects in the range of the type-lowering operator~$\partial$; as above, we sometimes refer to these as the \emph{abstracts}. Note that in~(\ref{eqn:defn:CC}), the concept $Y$ is not required to be subconcept of $\mathrm{rng}(\partial)$. Further, let us say that the abstraction principle $A[E]$ is \emph{injection invariant on abstracts} if the following is provable from the abstraction principle and the associated principles of the ambient second-order logic:
\begin{myequation}\label{eqn:defn:II}
\forall \; \mbox{ injection } \iota\hspace{-.5mm}:\hspace{-.5mm}V\hspace{-1mm}\rightarrow\hspace{-1mm} V \; \forall \; X\subseteq \mathrm{rng}(\partial) \;E(X,\overline{\iota}(X))
\end{myequation}
wherein $V=\{x: x=x\}$ is an abbreviation for the concept of all objects and $\overline\iota (X)$ means $\{\iota(x): x \in X\}$. With this terminology in place, our primary characterization of natural relative categoricity can be stated as follows:
\begin{thm}\label{thm:ncr=iia=cca}
The following are equivalent:
\begin{myenumerate}
\item[] 1. The abstraction principle~$A[E]$ is naturally relatively categorical.\label{eqn:RC1}
\item[] 2. The abstraction principle~$A[E]$ is injection invariant on abstracts.\label{eqn:RC2}
\item[] 3. The abstraction principle~$A[E]$ is cardinality coarsening on abstracts.\label{eqn:RC3}
\end{myenumerate}
\end{thm}
\noindent This theorem is proven in \S{\ref{sec03}. Prior to establishing this theorem, in \S\ref{sec02} we define the particulars of the second-order logic which we're employing-- in short, we're assuming full impredicative comprehension and strong forms of the axiom of choice. Then in \S\ref{sec02.5} we present the official definition of natural relative categoricity in Definition \ref{eqn:defn:NRC}.
As mentioned above, Frege observed that abstraction principles like Hume's Principle don't determine whether or not everything is an abstract.
The idea behind the natural relative categoricity of Hume's Principle is that this is the only kind of statement-- expressible in the language of Hume's Principle-- whose truth-value is left undetermined by Hume's Principle. So in natural relative categoricity we restrict attention down to the abstracts. A complementary idea is to restrict attention to the case where the abstraction operator is assumed to be a surjective map from concepts to objects. To this end, let us call an abstraction principle $A[E]$ \emph{surjectively relatively categorical}
if it can be proved (in the background logic) from $A^2[E]$, and the claim that $\partial_1$ and $\partial_2$ are surjective, that the map $\Gamma(\partial_1(X))=\partial_2(X)$ is an isomorphism between the abstracts of the two interlocutors.
In analogy with our first main Theorem~\ref{thm:ncr=iia=cca}, our second main theorem establishes the following equivalent characterization of surjective relatively categorical abstraction principles:
\begin{thm}\label{thm:coverthm}
The following are equivalent:
\begin{myenumerate}
\item[] 1. The abstraction principle $A[E]$ is surjectively relatively categorical.
\item[] 2. The abstraction principle $A[E]$ is permutation invariant,
under the assumption that the abstraction operator is surjective.
\item[] 3. The abstraction principle $A[E]$ is bicardinality coarsening, under the assumption that the abstraction operator is surjective.
\end{myenumerate}
\end{thm}
\noindent In analogy to injection invariance on abstracts~(\ref{eqn:defn:II}), we say that $A[E]$ is \emph{permutation invariant} if
\begin{myequation}\label{eqn:defn:piI}
\forall \; \mbox{ bijection } \pi\hspace{-.5mm}:\hspace{-.5mm}V\hspace{-1mm}\rightarrow\hspace{-1mm} V \;\; \forall \; X \;E(X,\overline{\pi}(X))
\end{myequation}
Further, in analogue to cardinality coarsening on abstracts~(\ref{eqn:defn:CC}), we say that $A[E]$ is \emph{bicardinality coarsening} if
\begin{myequation}\label{eqn:defn:biC}
\forall \; X, Y\; (Y\approx X \; \& \; V\hspace{-.5mm}\setminus\hspace{-.5mm}X\approx V\hspace{-.5mm}\setminus\hspace{-.5mm}Y) \rightarrow E(X,Y)
\end{myequation}
In this, $V\setminus X$ denotes the concept of all objects which are not in $X$. It's worth emphasizing that in the statement of Theorem~\ref{thm:coverthm}, the
last two conditions occur under the hypothesis that the abstraction operator~$\partial$ is surjective: for every object~$b$ there is a concept~$F$ such that $\partial(F)=b$. Hence there is no restriction to abstracts in the formulations of permutation invariance~(\ref{eqn:defn:piI}) and bicardinality coarsening~(\ref{eqn:defn:biC}).
As with our earlier theorem, Theorem~\ref{thm:coverthm} is proven in \S{\ref{sec03}; the formal definition of surjective relative categoricity is given in Definition~\ref{eqn:defn:NRC:covered}, subsequent to our treatment of the background second-order logic in the next section.
The aim of our Theorem~\ref{thm:ncr=iia=cca} and Theorem~\ref{thm:coverthm} is to answer the question of what abstraction principles are relatively categorical in the specified senses, and in the coarsest of terms these theorems indicate that such abstraction principles look a lot like Hume's Principle, so that relative categoricity amongst abstraction principles is the exception rather than the rule. This obviously doesn't directly imply that there's a problem with appeals to either abstraction principles or relative categoricity considerations. But it indicates that a choice must be made: the advocate of relative categoricity arguments will find her preferred route to determinacy of truth value blocked in the case of most abstraction principles, and the advocate of abstraction principles might be pressed to find some other means by which to secure determinacy of truth value. That said, it's obviously non-trivial to spell out precisely what philosophical concern or question is intended to be assuaged by securing determinacy of truth-value (cf. \cite{Button2014ab}), and there are similarly problems with making out the case that abstraction principles can secure knowledge of our foundational theories of arithmetic and set theory (cf. \cite{Walsh2014aa}). This is not the place to adjudicate these larger philosophical issues. Rather, the aim of this paper is limited to showing that the tools which one segment of the philosophy of mathematics community have been using are largely incompatible with the tools employed by another part of the community. And this despite the fact that both relative categoricity and abstraction principles can be seen as latter-day descendants of the idea that the subject-matter of mathematics is given by implicit definitions of its fundamental concepts (cf. \cite{Hale2000}, \cite{Shapiro2005aa} p. 13, pp. 168-169, \cite{Shapiro1991} p. 190, \cite{Shapiro2000ac} pp. 132 ff).
The present paper is organized as follows. In \S\ref{sec02} we set out the particulars of the background second-order logic which we're employing. Then in \S\ref{sec02.5} we make a preliminary study of the map $\Gamma(\partial_1(X))=\partial_2(X)$, which we there call \emph{the natural bijection}. In the subsequent section \S\ref{sec03} we prove Theorem~\ref{thm:ncr=iia=cca} and Theorem~\ref{thm:coverthm}, as well as note some related results on the underlying equivalence relations. In \S\ref{sec04}, we use these theorems to determine quickly whether some well-known abstraction principles are
relatively categorical in the senses we have adumbrated. In \S\S\ref{sec05stable}-\ref{sec07} we contrast the nature of the requirement of relative categoricity to other constraints on abstraction principles related to invariance and determinacy of truth-value studied by authors such as Cook, Antonelli, Fine, and Hodes. In particular, in \S\ref{sec05stable} we indicate where relatively categorical abstraction principles fit into the stability hierarchy that has arisen in response to the Bad Company problem. In \S\ref{sec05:aldo}, we distinguish our notion of permutation invariance~(\ref{eqn:defn:piI}) from notions studied by Antonelli and Fine and related to the Tarski-Sher thesis on logicality. Finally, in \S\ref{sec05:hodes} we note that the determinacy of truth value ideas coming out of our notions of relative categoricity might be orthogonal to the determinacy ideas coming out of Hodes' supervaluationism (cf. Question~\ref{eqn:Q2}).
\section{Background Second-Order Logic}\label{sec02}
We work in a background second-order signature which contains a sort for objects as well as a sort for~$n$-ary relations for each~$n\geq 1$. Objects are written with lower-case roman letters~$a,b,c,d,x,y,z,\ldots$. The unary relations are called \emph{concepts} and written with upper-case roman letters~$A,B,C,X,Y,Z$, while~$n$-ary relations for~$n>1$ are written with upper-case roman letters~$R,S$. The predication relation is written~$Xa$ or~$a\in X$ for objects~$a$ and concepts~$X$; and it is typically written~$R(a_1, \ldots, a_n)$ for~$n$-ary relations. For the sake of definiteness, let us then stipulate:
\begin{defn}\label{defn:L000}
The background second-order signature $L_0$ is the many-sorted signature which consists merely of (i) sorts for objects and $n$-ary relations for each $n\geq 1$, and (ii) for each $n\geq 1$, the $(n+1)$-ary predication relations $R(x_1, \ldots, x_n)$ wherein $R$ is an $n$-ary relation and $x_1, \ldots, x_n$ are objects.
\end{defn}
\noindent The models of $L_0$ thus have the following form:
\begin{myequation}\label{eqn:defn:models}
\mathcal{M}=(M, S_1[M], S_2[M], \ldots)
\end{myequation}
wherein~$M$ is a non-empty set and~$S_1[M]\subseteq P(M^n)$, and wherein the predication relations are interpreted with the membership relation from the ambient set-theoretic metatheory. Often in what follows we will be discussing isomorphisms of $L_0$-structures and related expansions. In this connection, it's useful to explicitly note that $L_0$ itself does not contain any constant or function symbols and does not contain any relation symbols besides the predication relation symbols.
Suppose that~$L$ is an expansion of~$L_0$. An $L$-structure~$\mathcal{M}$ whose $L_0$-reduct is written as in~(\ref{eqn:defn:models}) is called \emph{standard} if~$S_n[M]=P(M^n)$; we do \emph{not} assume here that all structures are standard. The \emph{full comprehension schema} for concepts in~$L$ is the collection of all the following axioms:
\begin{myequation}\label{eqn:fullcomp}
\exists \; X \; \forall \; x \; (Xx \leftrightarrow \Phi(x))
\end{myequation}
wherein~$\Phi(x)$ is an~$L$-formula and~$X$ does not appear free in~$\Phi(x)$, but where~$\Phi(x)$ may contain other free variables which are reserved for parameters. There are similar comprehension schemas for the~$n$-ary relations.
In this paper, it is assumed that all theories contain the full comprehension schema in their signature for~$n$-ary relations for all~$n\geq 1$. Our primary motivation for working with the full comprehension schema in this paper is that it is presupposed by the statement of natural relative categoricity, as we will make clear in the formal presentation of this notion below. The comprehension schema allows us to use usual boolean connectives~$A\cap B$,~$A\cup B$,~$A\setminus B$,~$A\subseteq B$ with their usual meanings on both concepts and~$n$-ary relations for~$n>1$. Likewise, we use $A\times B$ to denote the binary concept consisting of pairs $(a,b)$ where $a$ is from $A$ and $b$ is from $B$. Sometimes in what follows we use the disjoint union notation~$A=B\sqcup C$, which of course just means that~$A=B\cup C$ and~$B\cap C=\emptyset$. In this paper,~$\emptyset$ and~$V$ are reserved for the concept of no objects and the concept of all objects, respectively:
\begin{myequation}\label{eqn:defnV}
\emptyset = \{x: x\neq x\}, \hspace{10mm} V = \{x:x=x\}
\end{myequation}
In what follows, we often employ various abbreviations for formulas in second-order logic. In particular, we use bracket notation~$\{x: \Phi(x)\}$ as short-hand for the unique concept~$X$ determined by~$\Phi(x)$ from the comprehension axiom in equation~(\ref{eqn:fullcomp}), and likewise we write~$\{(x_1, \ldots, x_n): \Phi(x_1, \ldots, x_n)\}$ in the case of~$n$-ary relations.
Functions are identified with their graphs, so that~$G:A\rightarrow B$ is an abbreviation for the claim that the binary relation~$G$ is such that for all~$a$ from~$A$ there is unique~$b$ from~$B$ with~$G(a,b)$. Likewise we have the following abbreviations for cardinality-related notions:
\begin{myenumerate}
\item ~$X\approx Y$ or~$\left|X\right|=\left|Y\right|$ is an abbreviation for there being a bijection~$F:X\rightarrow Y$.\label{eqn:cardinalityabb:1}
\item $\left|X\right|\leq \left|Y\right|$ is an abbreviation for there being an injection~$F:X\rightarrow Y$. \label{eqn:cardinalityabb:2}
\item $\left|X\right|<\omega$ is an abbreviation for the claim that~$X$ is Dedekind-finite, i.e. any injection~$F:X\rightarrow X$ is also a surjection; and we abbreviate~$\left|X\right|\geq \omega$ for its negation.\label{eqn:cardinalityabb:3}
\end{myenumerate}
Another abbreviation which we shall employ repeatedly in what follows pertains to images of concepts under maps on objects. Suppose that $f:X\rightarrow Y$ is a map and suppose $X_0\subseteq X$. Then we define the image of $X_0$ under $f$ as $\overline{f}(X_0)=\{f(x): x\in X_0\}$, which is a concept by full comprehension when $f\in S_2[M]$. Typically we apply this in the case where $f:V\rightarrow V$, so that $\overline{f}(X)$ is defined for any concept $X$.
The other definitions that we need in order to state our results are two forms of the axiom of choice. The first form is designated as ${\tt AC}$, and it is the following schema:
\begin{myequation}\label{eqn:AC}
[\forall \; \overline{x} \; \exists \; R^{\prime} \; \varphi(R^{\prime},\overline{x})]\rightarrow \exists \; R \; [\forall \; \overline{x} \; \varphi(R[\overline{x}],\overline{x})]
\end{myequation}
wherein $R[\overline{x}]=\{\overline{y}: R\overline{x}\overline{y}\}$, which exists by full comprehension. Intuitively this says that if for every $n$-tuple of objects $\overline{x}$ there is an $m$-ary concept $R^{\prime}$ witnessing the condition $\varphi(R^{\prime},\overline{x})$, then there is an $(n\mbox{+}m)$-ary concept $R$ such that for all $n$-tuples $\overline{x}$ the $m$-ary concept $R[\overline{x}]$ is a witness. More intuitively still, this version of the axiom of choice says that if for each object there is a concept satisfying a certain condition, then there is a uniform way to select these concepts. This version of the axiom of choice was used frequently in the earlier papers (\cite{Walsh2012aa} Definition 5 p. 1683, \cite{Walsh2014ac}) since in the setting of limited comprehension it is a natural component of a sufficient condition for the so-called $\Delta^1_1$-comprehension schema.
The other form of the axiom of choice that we employ is a form of global choice. Suppose that~$T$ is a theory in one of our signatures. Then we let~$T\mbox{+}{\tt GC}$ be the expansion of~$T$ by a new binary relation symbol~$<$ on objects in the signature, with axioms saying that~$<$ is a linear order of the first-order objects, and we additionally have a schema in the expanded signature saying that any instantiated formula~$\varphi(x)$ in the expanded signature, perhaps containing parameters, that holds of some first-order object~$x$ will hold of a~$<$-least element:
\begin{myenumerate}
\item~$[\exists \; x \; \varphi(x)]\rightarrow [\exists \; x \; \varphi(x) \; \& \; \forall \; y<x \; \neg \varphi(y)]$ \label{eqn:gcschema}
\end{myenumerate}
Since all our theories~$T$ contain full comprehension~(\ref{eqn:fullcomp}), we have that the graph of~$<$ forms a binary concept in ~$T\mbox{+}{\tt GC}$. Of course the postulated binary relation~$<$ does not necessarily have anything to do with the the usual ``less than'' relation on the natural numbers. This form of global choice was also defined and employed in the paper \cite{Walsh2014ac} where it was likewise designated as ${\tt GC}$. So in contrast to equation~(\ref{eqn:defn:models}), models of our global choice principle ${\tt GC}$ have the form:
\begin{myequation}\label{eqn:defn:models2}
\mathcal{M}=(M, S_1[M], S_2[M], \ldots, <)
\end{myequation}
where $<$ is a linear order on $M$ such that any non-empty $\mathcal{M}$-definable subset has a least element.
It's worth stressing that $L_0$ does \emph{not} include the global well-order (cf. Definition~\ref{defn:L000}). For, the equivalence relations that we will consider will all be $L_0$-formulas, and in \S\ref{sec05:aldo}, we will note that this implies that the equivalence relations are logical in the sense of Tarski-Sher, and this would be not be true if they included the global well-order. However, as far as theories and structures go, in what follows, it is assumed that all theories and structures contain ${\tt AC}$ and ${\tt GC}$. This of course may be taken to hold for standard structures by recourse to the axiom of choice in the metatheory. Since we are additionally assuming full comprehension, our models in effect look and act a lot like standard models. However, the advantage of working with arbitrary models of these axioms-- instead of restricting ourselves to the standard models-- is that we have the the benefits of the completeness theorem (cf. \cite{Enderton2001}~Chapter~4, \cite{Manzano1996}~Chapter~VII.2). So even though we are working model-theoretically, everything can in principle be turned into a concrete deduction by recourse to this theorem. Because the semantics for second-order logic are a contentious affair
(cf. \cite{Linnebo2011aa} for overview), and because relative categoricity arguments have been traditionally motivated by concerns with the standard semantics for second-order logic (\cite{Parsons2008} p. 270, \cite{McGee1997aa} pp. 45-47, \cite{Lavine1999aa} p. 5), it is useful to adopt a framework in which our results do not depend on the choice of semantics for second-order logic.
Our use of ${\tt AC}$~(\ref{eqn:AC}) is rather limited in this paper: we appeal to it to establish the implication recorded in Figure~\ref{diagram1} in \S\ref{sec03} which allows us to go from conditions on an equivalence relation to conditions on the associated abstraction principle; and we appeal to it a final time to treat notions of finiteness in our discussion of the examples in \S\ref{sec04}. As for global choice ${\tt GC}$~(\ref{eqn:gcschema}), the reason why we assume it in this paper is that it permits us to transfer the usual properties of cardinal arithmetic to our deductive setting. In particular, in what follows we make use of the following three properties:
\begin{myenumerate}
\item \emph{Cardinal Comparability} :~$\forall \; X,Y \; (\left|X\right|\leq \left|Y\right| \vee \left|Y\right|\leq \left|X\right|)$\label{eqn:CC}
\item \emph{Infinite Sums are Maxs}:~$\forall \; X \; \left|X\right|\geq \omega \rightarrow [\forall \; Y, Z \; (X=Y\sqcup Z \rightarrow \left|X\right|=\max\{\left|Y\right|, \left|Z\right|\})]$\label{eqn:InfSumMax}
\item \emph{Infinite Products are Maxs}:~$\forall \; Y,Z \; (\left|Y\right|\geq \omega \vee \left|Z\right|\geq \omega)\rightarrow \left|Y\times Z \right| = \max\{\left|Y\right|, \left|Z\right|\}$\label{eqn:InfProdMax}
\end{myenumerate}
Of course, by Cardinality Comparability~(\ref{eqn:CC}), the maximum expressions make good sense. For instance, the clause~$\left|X\right|=\max\{\left|Y\right|, \left|Z\right|\}$ is just an abbreviation for the following conjunction of conditionals, and Cardinality Comparability~(\ref{eqn:CC}) implies that one of the two antecedents is satisfied:
\begin{myequation}
(\left|Y\right|\geq \left|Z\right| \rightarrow \left|X\right|= \left|Y\right|) \wedge (\left|Z\right|\geq \left|Y\right| \rightarrow \left|X\right|= \left|Z\right|)
\end{myequation}
Note that Cardinality Comparatibility~(\ref{eqn:CC}) follows from global choice ${\tt GC}$: for, the global well-order restricted to any two concepts yields two well-orders, and we can then use the traditional proof that well-orders are either order-isomorphic or one is isomorphic to an initial segment of the other (cf. \cite{Hrbacek1999aa} p. 105, \cite{Kunen1980} p. 15); and this result trivially implies that each is comparable to the other in terms of cardinality as well. Similarly, we can transfer the usual proof of Infinite Sums are Maxs and Infinite Products are Maxs (\ref{eqn:InfSumMax})-(\ref{eqn:InfProdMax}) as expressed in the language of set theory to our framework for second-order logic, since this proof proceeds by transfinite induction, which we can emulate with our global well-order (cf. \cite{Hrbacek1999aa} pp. 134 ff, \cite{Kunen1980} p. 29, \cite{Kunen2011aa} p. 73).
Another use of the global well-order $(V,<)$ that we employ is in giving an equivalent characterization of Dedekind-finiteness~(\ref{eqn:cardinalityabb:3}). First, let's introduce the following notation for the initial segments:
$I_a=\{b: b<a\}$ and $\overline{I}_a=\{b: b\leq a\}$. Further, since~$(V,<)$ is a non-empty well-order, it has a least element, which we designate as zero or~$0$. There's also a natural partial successor function~$s$ defined as follows:
\begin{myequation}\label{eqn:defnsucconord}
s(a)=\min_{<}(V\setminus \overline{I}_a)=\min_<\{b: b>a\}
\end{myequation}
This function~$s$ might be partial because there might be a greatest element in well-order\; $(V,<)$. Finally, let's say that a \emph{limit point} in~$(V,<)$ is a point~$a>0$ such that~$b<a$ implies~$s(b)<a$. As in the theory of ordinals, the well-order~$(V,<)$ splits into zero, successors, and limits. Finally, let's say that $a$ is \emph{finite} if $a$ is strictly below the all the limit points, and let's say that $X$ is \emph{finite} if $X$ is bijective with $I_a$ or $\overline{I}_a$ for some finite $a$. Then one can show using induction that:
\begin{prop}\label{eqn:equivchardedfin}
(i) $X$ is finite if and only if $\left|X\right|<\omega$. (ii) If there is a least limit, and the least limit point is designated as $\omega$, then $X$ is infinite iff there is an injection $\iota:I_{\omega}\rightarrow X$, which happens iff $\left|X\right|\geq \omega$.
\end{prop}
\noindent Hence, $\left|X\right|\geq \omega$ (as defined in (\ref{eqn:cardinalityabb:3})) aligns extensionally with $\left|I_{\omega}\right|\leq \left|X\right|$ as defined in~(\ref{eqn:cardinalityabb:2}).
Sometimes in what follows we use some standard terminology for describing equivalence relations on a set. So suppose that $E$ is an equivalence relation on a set $P$. Usually in what follows $P$ will be the power set $P(M)$ of some set $M$. Then we use $[X]_E = \{Y\in P: E(X,Y)\}$ as an abbreviation for the $E$-equivalence classes of an element~$X$ of $P$. Further, we use $\nicefrac{P}{E} = \{[X]_E: X\in P\}$ for the set of all equivalence classes. Finally, representatives for the equivalence classes will be given by any injection $\iota: \nicefrac{P}{E}\rightarrow P$ such that $E(X,\iota([X]_E))$. More generally, often in what follows we shall be interested in the related situation of injections $\iota: \nicefrac{P(M)}{E}\rightarrow M$. As we'll see at the outset of the next section, this is sometimes useful for construction models of abstraction principles.
\section{The Natural Bijection}\label{sec02.5}
With these preliminary definitions pertaining to the background second-order logic in place, we can now proceed to define what a model of an abstraction principle is. Suppose that~$E(X,Y)$ is an~$L_0$-formula with exactly two free concept variables. Let~$L_0[\partial]$ be the expansion of~$L_0$ by a function symbol~$\partial$ which takes unary concepts as inputs and outputs objects. Then the \emph{abstraction principle~$A[E]$ associated to~$E$} is as in equation~(\ref{eqn:AE}) from the previous section. By abuse of notation, we also use $A[E]$ to refer to the theory consisting of this abstraction principle, the full comprehension schema~(\ref{eqn:fullcomp}), the axiom of choice ${\tt AC}$~(\ref{eqn:AC}), and the global choice schema ${\tt GC}$~(\ref{eqn:gcschema}). Then in contrast to equation~(\ref{eqn:defn:models2}), models of~$A[E]$ have the form:
\begin{myequation}\label{eqn:ohsaycanyouseee}
\mathcal{M}=(M,S_1[M], S_2[M], \ldots, <,\partial)
\end{myequation}
wherein~$\partial:S_1[M]\rightarrow M$ and wherein~$\mathcal{M}$ models the full comprehension schema~(\ref{eqn:fullcomp}), the axiom of choice~(\ref{eqn:AC}), and the global choice schema~${\tt GC}$~(\ref{eqn:gcschema}). In the case where the structure~$\mathcal{M}$ from~(\ref{eqn:defn:models2}) is standard, if there is an injection $\iota:\nicefrac{P(M)}{E}\rightarrow M$, then one can build a model as in equation~(\ref{eqn:ohsaycanyouseee}) by setting $\partial(X)=\iota([X]_E)$. Of course, there is such an injection if and only if $\left|\nicefrac{P(M)}{E}\right|\leq \left|M\right|$, which is a non-trivial assumption.
Now consider the case in which there are, within a single model, two abstraction operators which satisfy a given abstraction principle. Again suppose that~$E(X,Y)$ is an~$L_0$-formula with exactly two free concept variables. Let~$L_0[\partial_1, \partial_2]$ be the expansion of~$L_0$ by two function symbols~$\partial_1, \partial_2$ which takes unary concepts as inputs and outputs objects. Then the theory $A^2[E]$ consists of the axiom~(\ref{eqn:AE2}) from \S\ref{sec01},
as well as the the full comprehension schema~(\ref{eqn:fullcomp}), the axiom of choice~${\tt AC}$~(\ref{eqn:AC}), and the global choice schema~${\tt GC}$~(\ref{eqn:gcschema}). So models of~$A^2[E]$ have the following form:
\begin{myequation}\label{eqn:1}
\mathcal{M}=(M, S_1[M], S_2[M], \ldots,<, \partial_1, \partial_2)
\end{myequation}
wherein~$\partial_i:S_1[M]\rightarrow M$ and $\mathcal{M}$ models the full comprehension schema~(\ref{eqn:fullcomp}), the axiom of choice~${\tt AC}$~(\ref{eqn:AC}), and the global choice schema~${\tt GC}$~(\ref{eqn:gcschema}).
In the description of natural relative categoricity from the earlier section, one of the key ideas is that we restrict down to the ranges of the individual abstraction operators. Formally, we make this precise by taking a model~$\mathcal{M}$ of~$A^2[E]$ as in equation~(\ref{eqn:1}), and defining the following induced~$L_0[\partial_i]$-structure for $i=1,2$:
\begin{myequation}\label{eqn:induced}
\mathcal{M}_i = (\mathrm{rng}(\partial_i), S_1[M]\cap P(\mathrm{rng}(\partial_i)), S_2[M]\cap P(\mathrm{rng}(\partial_i)^2), \ldots, \partial_i\upharpoonright (S_1[M]\cap P(\mathrm{rng}(\partial_i))))
\end{myequation}
Hence $\mathcal{M}\mapsto \mathcal{M}_1$ and $\mathcal{M}\mapsto \mathcal{M}_2$ are maps from an $L_0[\partial_1, \partial_2]$-structure $\mathcal{M}$ to an $L_0[\partial_i]$-structure $\mathcal{M}_i$. So notationally, $\mathcal{M}_i$ is a structure induced from $\mathcal{M}$, and not simply yet another structure indexed by a subscript. Note that we do \emph{not} include the global-well order $<$ in the signature of the induced structures $\mathcal{M}_i$. This is because our natural relative categoricity concerns isomorphisms between these structures, and we do not want to insist that isomorphisms preserve this global well-order. This
is because the global well-order is an artifact employed to make various second-order notions like cardinality more like classical metatheoretic notions. But of course since we're reasoning about the induced structures $\mathcal{M}_i$ as defined within the larger structure $\mathcal{M}$, we can use global choice in that setting to reason about the induced structures if we like. This disparity between the induced structures $\mathcal{M}_i$ and the structure $\mathcal{M}$ as regards global choice does not extend to the issue of comprehension. For, the induced structures $\mathcal{M}_i$ models the full comprehension schema~(\ref{eqn:fullcomp}) in its signature simply because they are definable within the structure $\mathcal{M}$ which is assumed to satisfy comprehension in its signature. However, note that in general there is no reason that the induced structure~$\mathcal{M}_i$ need model the abstraction principle~$A[E]$.
The notion of natural relative categoricity was defined in \S\ref{sec01} by the condition that the map $\Gamma(\partial_1(X))=\partial_2(X)$ was an isomorphism. Before further examining the condition that this map is an isomorphism, let us take a first and preliminary step of examining the properties of the map itself, which we call the natural bijection. So given any model~$\mathcal{M}$ of~$A^2[E]$ as in equation~(\ref{eqn:1}), \emph{the natural bijection} $\Gamma$ is the map $\Gamma:\mathrm{rng}(\partial_1)\rightarrow \mathrm{rng}(\partial_2)$ defined by
\begin{myequation}\label{eqn:defn}
\Gamma(\partial_1(X))=\partial_2(X)
\end{myequation}
wherein~$X$ ranges over elements of~$S_1[M]$. It then follows from the axiom~(\ref{eqn:AE2}) of~$A^2[E]$ that this map is well-defined and injective:
\begin{myequation}
\partial_1(X)=\partial_1(Y) \Longleftrightarrow E(X,Y) \Longleftrightarrow \partial_2(X)=\partial_2(Y)
\end{myequation}
Trivially, by definition,~$\Gamma: \mathrm{rng}(\partial_1)\rightarrow \mathrm{rng}(\partial_2)$ is surjective and so it is indeed a bijection. Further, the natural bijection is definable in~$\mathcal{M}$ by the following formula:
\begin{myequation}\label{eqn:defn:natret}
\Gamma(x)=y \Longleftrightarrow \mathcal{M}\models [\exists \; X \; (\partial_1(X)=x \; \& \; \partial_2(X)=y)]
\end{myequation}
So by full comprehension~(\ref{eqn:fullcomp}), the graph of the natural bijection~$\Gamma$ is a member of~$S_2[M]$. Likewise, by full comprehension~(\ref{eqn:fullcomp}), if~$X\in S_1[M]\cap P(\mathrm{rng}(\partial_1))$ then the following is an element of $S_1[M]\cap P(\mathrm{rng}(\partial_2))$:
\begin{myequation}\label{eqn:dafasdfsd}
\overline{\Gamma}(X)=\{\Gamma(x): x\in X\}
\end{myequation}
and similarly for~$n$-ary relations. By abuse of notation, we also use the symbol $\overline{\Gamma}$ to refer to the map~$\overline{\Gamma}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ given by~$\Gamma$ on the objects and~$\overline{\Gamma}$ as in equation~(\ref{eqn:dafasdfsd}) on the~$n$-ary relations for all~$n\geq 1$; and we sometimes also refer to the map $\overline{\Gamma}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ as the natural bijection. This map~$\overline{\Gamma}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is also trivially an injection since~$\Gamma$ is. As is easily verified, it is a surjection as well.
So, indeed ~$\overline{\Gamma}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is also a bijection. For ease of future reference, let's record this in the following definition:
\begin{defn}\label{defn:nat:bijection}
Suppose that $\mathcal{M}$ is a model of $A^2[E]$ as in equation~(\ref{eqn:1}), and that $\mathcal{M}_1, \mathcal{M}_2$ are the induced structures as in equation~(\ref{eqn:induced}). Then the \emph{natural bijection} $\overline{\Gamma}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is given by the bijection $\Gamma:\mathrm{rng}(\partial_1)\rightarrow \mathrm{rng}(\partial_2)$ defined by $\Gamma(\partial_1(X))=\partial_2(X)$ for each concept $X$ from the ambient structure~$\mathcal{M}$. Further, $\overline{\Gamma}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is defined on concepts $X\subseteq \mathrm{rng}(\partial_1)$ from the ambient structure by $\overline{\Gamma}(X)=\{\Gamma(x):x\in X\}$, and similarly for $n$-ary relations.
\end{defn}
\noindent The various appeals to the full comprehension schema~(\ref{eqn:fullcomp}) that we made in the previous paragraph underscore the apparent necessity of the adoption of this schema in the context of the present discussion. For instance, to show that the graph of $\Gamma$ exists as a binary concept, we appealed to its definition in equation~(\ref{eqn:defn:natret}), which is $\Sigma^1_1$. This is precisely the amount of comprehension that one needs to show that Basic Law~V, the abstraction principle of Frege's \emph{Grundgesetze}, is inconsistent (cf. \cite{Walsh2012aa} Proposition 4 p. 1682, Proposition 29 p. 1692). Hence, it seems that studying natural relative categoricity in the context of limited comprehension would not be feasible. Before moving on, it's worth recording one final point in regards to the natural bijection: namely, that a routine argument establishes the following.
\begin{prop}\label{prop:inverse}
If~$\overline{\Gamma}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is the natural bijection, then its inverse $\Delta=\Gamma^{-1}$ is the natural bijection~$\overline{\Delta}:\mathcal{M}_2\rightarrow \mathcal{M}_1$.
\end{prop}
So having defined the natural bijection $\overline{\Gamma}:\mathcal{M}_1\rightarrow \mathcal{M}_2$, let's now examine carefully what it would mean for this to be a isomorphism between the induced structures $\mathcal{M}_1$ and $\mathcal{M}_2$. Recall that if~$L$ is an arbitrary signature, then two~$L$-structures~$\mathcal{N}_1$ and~$\mathcal{N}_2$ are \emph{isomorphic} if there is a bijection~$\gamma:\mathcal{N}_1\rightarrow \mathcal{N}_2$ such that for all~$L$-formulas~$\theta(x_1, \ldots, x_n)$ and~$a_1, \ldots, a_n$ from~$\mathcal{N}_1$, it is the case that
\begin{myequation}\label{eqn:Iso}
\mathcal{N}_1 \models \theta(a_1, \ldots, a_n) \Longleftrightarrow \mathcal{N}_2 \models \theta(\gamma(a_1), \ldots, \gamma(a_n))
\end{myequation}
Of course, this condition is difficult to verify directly, so one usually works with the equivalent condition that equation~(\ref{eqn:Iso}) holds in the case of atomic formulas (cf. \cite{Marker2002} Definition~1.1.3 pp.~8-9 and the proof of Theorem~1.1.10 p. 13, or \cite{Enderton2001} p.~94 and the Homomorphism Theorem part~(c) p.~96). For instance, consider the atomic formula $\theta(x_1, \ldots, x_n,y)\equiv F(x_1, \ldots, x_n)=y$. Suppose that $a_1, \ldots, a_n, b$ are from $\mathcal{N}_1$ and that $F^{\mathcal{N}_1}(a_1, \ldots, a_n)=b$, so that $\mathcal{N}_1\models \theta(a_1, \ldots, a_n,b)$. Then equation~(\ref{eqn:Iso}) implies that $\mathcal{N}_2\models \theta(\gamma(a_1), \ldots, \gamma(a_n),\gamma(b))$, or that $F^{\mathcal{N}_2}(\gamma(a_1), \ldots, \gamma(a_n))=\gamma(b)$, which of course implies that $F^{\mathcal{N}_2}(\gamma(a_1), \ldots, \gamma(a_n))=\gamma(F^{\mathcal{N}_1}(a_1, \ldots, a_n))$. Elementary considerations such as these show that $\gamma:\mathcal{N}_1\rightarrow \mathcal{N}_2$ is an isomorphism if and only if for all relations symbols $R$, constant symbols $c$, and function symbols $F$ in the signature of the structures, and all $a_1, \ldots, a_n$ from $\mathcal{N}_1$, one has
\begin{myeqnarray}
R^{\mathcal{N}_1}(a_1, \ldots, a_n) & \Longleftrightarrow & R^{\mathcal{N}_2}(\gamma(a_1), \ldots, \gamma(a_n)) \label{eqn:defn:iso:rel} \\
\gamma(c^{\mathcal{N}_1})& = & c^{\mathcal{N}_2} \label{eqn:defn:iso:con} \\
\gamma(F^{\mathcal{N}_1}(a_1, \ldots, a_n)) & = & F^{\mathcal{N}_2}(\gamma(a_1), \ldots, \gamma(a_n)) \label{eqn:defn:iso:func}
\end{myeqnarray}
\noindent While these considerations are admittedly elementary, it's worth underscoring them since they help to motivate the definition of natural relative categoricity (Definition~\ref{eqn:defn:NRC}), which we now build towards.
Now consider the natural bijection~$\overline{\Gamma}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ and what it would mean for it to be an isomorphism. Since $\overline{\Gamma}(X)=\{\Gamma(x): x\in X\}$, clearly one has that equation~(\ref{eqn:defn:iso:rel}) always holds in the case of the predication relations, which per the definition of $L_0$ in Definition~\ref{defn:L000} are the \emph{only} relations in the signature of $L_0$. So $\overline{\Gamma}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is an isomorphism of~$L_0[\partial]$-structures if and only if equation~(\ref{eqn:defn:iso:func}) holds with respect to the operator~$\partial$. That is, the natural bijection ~$\overline{\Gamma}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is an isomorphism of~$L_0[\partial]$-structures if and only if
\begin{myequation}
X\in (S_1[M]\cap P(\mathrm{rng}(\partial_1))\Longrightarrow \Gamma(\partial_1(X))=\partial_2(\overline{\Gamma}(X))
\end{myequation}
Given the way that the natural bijection~$\Gamma$ was defined in equation~(\ref{eqn:defn}), this happens if and only if
\begin{myequation}
X\in (S_1[M]\cap P(\mathrm{rng}(\partial_1))\Longrightarrow \partial_2(X)=\partial_2(\overline{\Gamma}(X))
\end{myequation}
which, by the fact that the model~$\mathcal{M}$ from equation~(\ref{eqn:1}) satisfies~$A^2[E]$, holds if and only if
\begin{myequation}\label{eqn:final}
\mathcal{M} \models [\forall \; X \; (X\subseteq \mathrm{rng}(\partial_1)) \rightarrow E(X, \overline{\Gamma}(X))]
\end{myequation}
Now, the natural bijection $\overline{\Gamma}: \mathcal{M}_1\rightarrow \mathcal{M}_2$ is an isomorphism if and only if its inverse $\Delta=\Gamma^{-1}$ is an isomorphism, and by Proposition~\ref{prop:inverse} its inverse is the natural bijection $\overline{\Delta}:\mathcal{M}_2\rightarrow \mathcal{M}_1$. Hence, by parity of reasoning and the fact that $E$ is an equivalence relation, one has that $\overline{\Gamma}: \mathcal{M}_1\rightarrow \mathcal{M}_2$ is an isomorphism if and only if
\begin{myequation}\label{eqn:final2}
\mathcal{M} \models [\forall \; Y \; (Y\subseteq \mathrm{rng}(\partial_2)) \rightarrow E(Y, \overline{\Gamma}^{-1}(Y))]
\end{myequation}
For ease of future reference, let us summarize these results as follows. First let's record our official definition of natural relative categoricity:
\begin{defn}\label{eqn:defn:NRC}
An abstraction principle $A[E]$ is \emph{naturally relatively categorical} if all models~$\mathcal{M}$ of~$A^2[E]$ from equation~(\ref{eqn:1}), the natural bijection $\overline{\Gamma}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ from Definition~\ref{defn:nat:bijection} is an isomorphism of the induced structures $\mathcal{M}_1, \mathcal{M}_2$ from equation~(\ref{eqn:induced}).
\end{defn}
\noindent The only way in which this formalization of the notion is more precise than the descriptions of this notion given in \S\ref{sec01} is that now we have formally defined the particulars of our background second-order logic and have likewise defined the natural bijection and indicated precisely what it takes for it to be a isomorphism.
The elementary considerations from the previous paragraphs give us a simple equivalent characterization of natural relative categoricity. In particular, we have:
\begin{prop}\label{prop:simpleequivalent} An abstraction principle $A[E]$ is naturally relatively categorical if and only if all models~$\mathcal{M}$ of~$A^2[E]$ from equation~(\ref{eqn:1}) satisfy one of the two following equivalent conditions:
\begin{myequation}
\mathcal{M} \models [\forall \; X \; (X\subseteq \mathrm{rng}(\partial_1)) \rightarrow E(X, \overline{\Gamma}(X))] \tag{\ref{eqn:final}}
\end{myequation}\vspace{-10mm}
\begin{myequation}
\mathcal{M} \models [\forall \; Y \; (Y\subseteq \mathrm{rng}(\partial_2)) \rightarrow E(Y, \overline{\Gamma}^{-1}(Y))]\tag{\ref{eqn:final2}}
\end{myequation}
wherein $\Gamma$ is the natural bijection (cf. Definition~\ref{defn:nat:bijection}).
\end{prop}
\noindent Expressed in these terms, natural relative categoricity is patently a deductive property of the theory~$A^2[E]$.
In the next section we'll prove Theorem~\ref{thm:ncr=iia=cca} which gives a characterization of natural relative categoricity in terms of cardinality coarsening on abstracts~(\ref{eqn:defn:CC}) and injection invariance on abstracts~(\ref{eqn:defn:II}). In the previous section we've formally defined our background second-order logic and so we can be a bit more precise now about the content of these conditions. Recall that $A[E]$ may be used as the abbreviation for the theory consisting of the abstraction principle~(\ref{eqn:AE}) in addition to the full comprehension schema~(\ref{eqn:fullcomp}), the axiom of choice~(\ref{eqn:AC}), and the global choice schema~(\ref{eqn:gcschema}). Then officially, we say that $A[E]$ is \emph{cardinality coarsening on abstracts} if the following is a theorem of $A[E]$:
\begin{myequation}
\forall \; X, Y\; ((Y\approx X \; \& \; X\subseteq \mathrm{rng}(\partial)) \rightarrow E(X,Y))]\tag{\ref{eqn:defn:CC}}
\end{myequation}
Likewise, officially $A[E]$ is \emph{injection invariant on abstracts} if the following is a theorem of $A[E]$:
\begin{myequation}
\forall \; \mbox{ injection } \iota:V\hspace{-1mm}\rightarrow\hspace{-1mm}V \; \forall \; X\subseteq \mathrm{rng}(\partial) \;E(X,\overline{\iota}(X))\tag{\ref{eqn:defn:II}}
\end{myequation}
So both cardinality coarsening on abstracts and injection invariance on abstracts are, by definition, deductive properties of the theory $A[E]$. By contrast, as was made clear by Proposition~\ref{prop:simpleequivalent} of the previous paragraph, natural relative categoricity is a deductive property of the theory $A^2[E]$. So one of the implications of Theorem~\ref{thm:ncr=iia=cca}, which establishes the equivalence of these notions, is that we're able to further reduce natural relative categoricity to a deductive property of the theory $A[E]$ as opposed to $A^2[E]$.
Before setting up the particulars of our second main theorem, let's record for reference when an isomorphism $\overline{H}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is equal to the natural bijection $\overline{\Gamma}: \mathcal{M}_1\rightarrow \mathcal{M}_2$. It's natural to focus attention on those isomorphisms $\overline{H}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ whose restriction $H\upharpoonright \mathrm{rng}(\partial_1)$ is an element of $S_2[M]$, since it is only with respect to these that we can define further elements of $\mathcal{M}$ in terms of $\overline{H}$ and $H$ by recourse to the comprehension schema~(\ref{eqn:fullcomp}). By a routine argument, we can establish the following:
\begin{prop}\label{prop:whenarbirisnat}
Suppose that $\mathcal{M}$ is a model of $A^2[E]$ with induced structures $\mathcal{M}_1$ and $\mathcal{M}_2$. Suppose that $\overline{H}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is a map whose restriction $H\upharpoonright \mathrm{rng}(\partial_1)$ to $\mathrm{rng}(\partial_1)$ is an element of $S_2[M]$. Then $\overline{H}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is isomorphism if and only if one has $\mathcal{M}\models [\forall \; X \; (X\subseteq \mathrm{rng}(\partial_1)\rightarrow E(X, \overline{H}(X))]$.
\end{prop}
\noindent As a corollary to Theorem~\ref{thm:ncr=iia=cca}, we will establish in the next section that such isomorphisms are \emph{always} equal to the natural bijection in the setting of natural relative categoricity (cf. Corollary~\ref{cor:whenarbirisnat}).
Finally, let's briefly say something about the content of our second main Theorem~\ref{thm:coverthm}. For ease of future reference, let's record the official notion in the following definition:
\begin{defn}\label{eqn:defn:NRC:covered}
An abstraction principle $A[E]$ is \emph{surjectively relatively categorical} if all models~$\mathcal{M}$ of~$A^2[E]$ from~(\ref{eqn:1}) wherein the abstraction operators $\partial_i:S_1[M]\rightarrow M$ are surjective, the natural bijection $\overline{\Gamma}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ from Definition~\ref{defn:nat:bijection} is an isomorpism of the induced structures $\mathcal{M}_1, \mathcal{M}_2$ from equation~(\ref{eqn:induced}).
\end{defn}
\noindent So clearly natural relative categoricity implies surjective relative categoricity. For an example of an abstraction principle which is surjectively relatively categorical but not naturally relatively categorical, see the example of the Bicardinality Principle in \S\ref{sec:bicardinality}. In the statement of Theorem~\ref{thm:coverthm}, the key notions were that of permutation invariance~(\ref{eqn:defn:piI}) and bicardinality coarsening~(\ref{eqn:defn:biC}). In the context of Theorem~\ref{thm:coverthm}, it is understood that to say an abstraction principle $A[E]$ has one of these properties is to say that these properties are deducible from the supposition that (i) the abstraction operator is a surjection as well as from (ii) the abstraction principle itself, the full comprehension schema~(\ref{eqn:fullcomp}), the axiom of choice~(\ref{eqn:AC}), and the global choice schema~${\tt GC}$~(\ref{eqn:gcschema}).
\section{The Equivalent Characterizations}\label{sec03}
The goal of this section is to establish Theorem~\ref{thm:ncr=iia=cca} and Theorem~\ref{thm:coverthm}. The first provides an equivalent characterization of natural relative categoricity in terms of cardinality coarsening on abstracts~(\ref{eqn:defn:CC}) and injective invariance on abstracts~(\ref{eqn:defn:II}). The second provides an equivalent characterization of surjectively relatively categoricity in terms of bicardinality coarsening~(\ref{eqn:defn:biC}) and permutation invariance~(\ref{eqn:defn:piI}). These theorems gives us two qualitatively distinct means by which to identify and recognize our versions of relative categoricity. For, in and of themselves, natural relative categoricity and surjective relative categoricity (Definition~\ref{eqn:defn:NRC} and Definition~\ref{eqn:defn:NRC:covered}) are claims about determining a single structure. But the notions of injection invariance on abstracts~(\ref{eqn:defn:II}) and permutation invariance~(\ref{eqn:defn:piI}) deal in a different currency: these conditions say say that a certain second-order relation should be invariant under certain mappings of the entire domain. Cardinality coarsening on abstracts~(\ref{eqn:defn:CC}) and bicardinality coarsening~(\ref{eqn:defn:biC}) are different still: they are more local in character and concern the comparative sizes of a concept (and its relative complement).
Here is then the proof of Theorem~\ref{thm:ncr=iia=cca}:
\begin{proof}
First suppose that $A[E]$ is naturally relatively categorical. Suppose that~$\mathcal{M}^{\ast}=(M, S_1[M], S_2[M], \ldots, <, \partial_1)$ is an arbitrary model of~$A[E]$. Note that~$V=\{x:x=x\}$~(\ref{eqn:defnV}) as interpreted on~$\mathcal{M}^{\ast}$ is exactly~$M$. So with an eye towards showing injection invariance on abstracts, suppose that~$\iota:M\rightarrow M$ is an injection whose graph is in~$S_2[M]$. Then define~$\partial_2:S_1[M]\rightarrow M$ by~$\partial_2=\iota\circ \partial_1$. Note that since~$\iota:M\rightarrow M$ is an injection, we have that the following holds in $\mathcal{M}$:
\begin{myequation}\label{eqn:iamanaequationinaproof}
\partial_2(X)=\partial_2(Y) \Longleftrightarrow \partial_1(X)=\partial_1(Y) \Longleftrightarrow E(X,Y)
\end{myequation}
Hence, since~$\partial_2$ is~$\mathcal{M}^{\ast}$-definable, the following structure is a model of~$A^2[E]$:
\begin{myequation}
\mathcal{M}=(M, S_1[M], S_2[M], \ldots, <,\partial_1, \partial_2)
\end{myequation}
Since by hypothesis~$A[E]$ is naturally relatively categorical, we have that the natural bijection~$\overline{\Gamma}: \mathcal{M}_1\rightarrow \mathcal{M}_2$ is an isomorphism. Then by definition of~$\Gamma$ in equation~(\ref{eqn:defn}), we have that $X\in S_1[M]$ implies $\Gamma(\partial_1(X)) = \partial_2(X) = \iota (\partial_1(X))$. Hence~$\Gamma=\iota \upharpoonright (\mathrm{rng}(\partial_1))$. Now we may finally finish verifying injection invariance on abstracts. Suppose that~$X\in S_1[M]\cap P(\mathrm{rng}(\partial_1))$. Then~$\overline{\Gamma}(X)=\overline{\iota}(X)$. Hence from Proposition~\ref{prop:simpleequivalent} (and in particular equation~(\ref{eqn:final})) we may infer that~$E(X,\overline{\Gamma}(X))$ and hence~$E(X,\overline{\iota}(X))$.
Second suppose~$A[E]$ is injection invariant on abstracts. To show that~$A[E]$ is naturally relatively categorical, suppose that
\begin{myequation}
\mathcal{M} = (M, S_1[M], S_2[M], \ldots, <,\partial_1, \partial_2)
\end{myequation}
is a model of~$A^2[E]$. So we must show that the natural bijection~$\Gamma:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is an isomorphism. By Cardinal Comparability~(\ref{eqn:CC}),
\begin{myequation}\label{eqn:choice}
\left|M\setminus \mathrm{rng}(\partial_1)\right|\leq \left| M\setminus \mathrm{rng}(\partial_2)\right| \hspace{5mm} \mbox{or} \hspace{5mm} \left| M\setminus \mathrm{rng}(\partial_2)\right| \leq \left| M\setminus \mathrm{rng}(\partial_1)\right|
\end{myequation}
First suppose that $\left|M\setminus \mathrm{rng}(\partial_1)\right|\leq \left| M\setminus \mathrm{rng}(\partial_2)\right|$. Then let~$\Delta:M\setminus \mathrm{rng}(\partial_1) \rightarrow M\setminus \mathrm{rng}(\partial_2)$ be a witnessing injection. Define an injection~$\iota:M\rightarrow M$ by
\begin{myequation}
\iota \upharpoonright \mathrm{rng}(\partial_1) = \Gamma, \hspace{10mm}\iota \upharpoonright (M\setminus \mathrm{rng}(\partial_1))=\Delta
\end{myequation}
Since~$\Gamma$ has range~$\mathrm{rng}(\partial_2)$ and~$\Delta$ has range~$M\setminus \mathrm{rng}(\partial_2)$, the map~$\iota:M\rightarrow M$ is indeed an injection. Now, we verify natural relative categoricity by verifying equation~(\ref{eqn:final}). So suppose that~$X\in (S_1[M]\cap P(\mathrm{rng}(\partial_1))$. Then by injection invariance on abstracts applied to~$\iota$, we have that~$\mathcal{M}\models E(X,\overline{\iota}(X))$. But since~$X\subseteq \mathrm{rng}(\partial_1)$, we have that~$\overline{\iota}(X)=\overline{\Gamma}(X)$, so that~$\mathcal{M}\models E(X,\overline{\Gamma}(X))$. Hence, we have finished verifying natural relative categoricity via equation~(\ref{eqn:final}).
Conversely, suppose that~$\left|M\setminus \mathrm{rng}(\partial_2)\right|\leq \left|M\setminus \mathrm{rng}(\partial_1)\right|$ with witnessing injection~$\Delta:M\setminus \mathrm{rng}(\partial_2) \rightarrow M\setminus \mathrm{rng}(\partial_1)$. Define an injection~$\iota:M\rightarrow M$ by
\begin{myequation}
\iota \upharpoonright \mathrm{rng}(\partial_2) = \Gamma^{-1}, \hspace{10mm}\iota \upharpoonright (M\setminus \mathrm{rng}(\partial_2))=\Delta
\end{myequation}
Since~$\Gamma^{-1}$ has range~$\mathrm{rng}(\partial_1)$ and~$\Delta$ has range~$M\setminus \mathrm{rng}(\partial_1)$, the map~$\iota:M\rightarrow M$ is indeed an injection. Now, we verify natural relative categoricity by verifying equation~(\ref{eqn:final2}). So suppose that~$Y\in (S_1[M]\cap P(\mathrm{rng}(\partial_2))$. Then by injection invariance on abstracts applied to~$\iota$, we have that~$\mathcal{M}\models E(Y,\overline{\iota}(Y))$. But since~$Y\subseteq \mathrm{rng}(\partial_2)$, we have that~$\overline{\iota}(Y)=\overline{\Gamma}^{-1}(Y)$, so that~$\mathcal{M}\models E(Y,\overline{\Gamma}^{-1}(Y))$. Hence, we have finished verifying natural relative categoricity via equation~(\ref{eqn:final2}).
Having shown the equivalence of natural relative categoricity and injection invariance on abstracts, we now show that these are equivalent to cardinality coarsening on abstracts. First, note that
cardinality coarsening on abstracts trivially implies injection invariance on abstracts. For, suppose that we're working in a model of~$A[E]$ and there's an injection~$\iota:V\rightarrow V$ and~$X\subseteq \mathrm{rng}(\partial_1)$. Then let~$Y=\overline{\iota}(X)$, so that~$Y\approx X$ and $X \subseteq \mathrm{rng}(\partial_1)$. Then by cardinality coarsening on abstracts, we have~$E(X,Y)$, which is just to say~$E(X,\overline{\iota}(X))$, so that we have verified injection invariance on abstracts.
Now assume that~$A[E]$ is injection invariant on abstracts. Consider a model~$\mathcal{M}^{\ast}=(M, S_1[M], S_2[M], \ldots,<, \partial_1)$ of~$A[E]$, and suppose that~$X_0,Y_0$ are members of~$S_1[M]$ with~$Y_0\approx X_0$ and $X_0\subseteq \mathrm{rng}(\partial_1)$. We must show that~$E(X_0,Y_0)$. There are several cases to consider, which for the sake of readability, we enumerate separately. For the abbreviations of cardinality notions which we employ here, see in particular (\ref{eqn:cardinalityabb:1})-(\ref{eqn:cardinalityabb:3}) from \S\ref{sec02}.
Case I:~$\left| Y_0\right| = \left| X_0\right| =\left| V\right|$. Then~$V\approx X_0\subseteq \mathrm{rng}(\partial_1)\subseteq V$ implies that~$\left|\mathrm{rng}(\partial_1)\right| = \left|V\right|$. Choose a bijection~$\pi: \mathrm{rng}(\partial_1)\rightarrow V$ and define a map~$\partial_2:S_1[M]\rightarrow M$ by~$\partial_2(X)=\pi(\partial_1(X))$, so that since~$\pi: \mathrm{rng}(\partial_1)\rightarrow V$ is a surjection, we have that~$\mathrm{rng}(\partial_2)=V$. Then observe that for any~$X,Y$ we have the following in $\mathcal{M}^{\ast}$ since~$\pi$ is an injection:
\begin{myequation}\label{eqn:iamausualmove0}
\partial_2(X)=\partial_2(Y) \Longleftrightarrow \partial_1(X)=\partial_1(Y) \Longleftrightarrow E(X,Y)
\end{myequation}
Hence, the structure~$\mathcal{M}^{\dagger}=(M, S_1[M], S_2[M], \ldots, <,\partial_2)$ is likewise a model of~$A[E]$, and so by injection invariance on abstracts we have
\begin{myequation}
\mathcal{M}^{\dagger}\models [ \forall \; \mbox{ injection } \iota:V\hspace{-1mm}\rightarrow\hspace{-1mm}V \; \forall \; X\subseteq \mathrm{rng}(\partial_2) \;E(X,\overline{\iota}(X))]
\end{myequation}
But since~$\mathrm{rng}(\partial_2)=V$, this can be simplified to:
\begin{myequation}
\mathcal{M}^{\dagger}\models [ \forall \; \mbox{ injection }\iota:V\hspace{-1mm}\rightarrow\hspace{-1mm}V \; \forall \; X \;E(X,\overline{\iota}(X))]
\end{myequation}
Now, since~$Y_0\approx X_0\approx V$, choose bijections~$j_1:V\rightarrow X_0$ and~$j_2:V\rightarrow Y_0$. Then by the previous equation, we have~$E(V,\overline{j_1}(V))$ and~$E(V,\overline{j_2}(V))$, or what is the same~$E(V,X_0)$ and~$E(V,Y_0)$. Since $E$ is an equivalence relation, we have that~$E(X_0,Y_0)$, which was to be demonstrated.
Case II:~$\left|Y_0\right|= \left|X_0\right| <\left|V\right| \; \& \: \left|V\right|<\omega$. By Cardinal Comparability~(\ref{eqn:CC}),
\begin{myequation}
\left|V\setminus X_0 \right|\leq \left|V\setminus Y_0 \right|\hspace{5mm} \mbox{or} \hspace{5mm} \left|V\setminus Y_0 \right|\leq \left|V\setminus X_0 \right|
\end{myequation}
First suppose that~$\left|V\setminus X_0 \right|\leq \left|V\setminus Y_0 \right|$. Choose injection~$\iota:V\rightarrow V$ such that~$\iota\upharpoonright X_0: X_0\rightarrow Y_0$ is a bijection and~$\iota \upharpoonright (V\setminus X_0): V\setminus X_0 \rightarrow V\setminus Y_0$ is an injection. Then since~$A[E]$ is injection invariant on abstracts, we have that~$E(X_0,\overline{\iota}(X_0))$, which is the same as~$E(X_0,Y_0)$. Second suppose that~$\left|V\setminus Y_0 \right|\leq \left|V\setminus X_0 \right|$. Choose injection~$j:V\rightarrow V$ such that~$j\upharpoonright Y_0: Y_0\rightarrow X_0$ is a bijection and~$j \upharpoonright (V\setminus Y_0): V\setminus Y_0 \rightarrow V\setminus X_0$ is an injection. Since~$\left|V\right|<\omega$, we have that the injection ~$j:V\rightarrow V$ is actually a bijection. Let~$\iota = j^{-1}$, so that~$\iota:V\rightarrow V$ is a bijection and~$\overline{\iota}(X_0)=Y_0$. Then by injection invariance on abstracts, we again have~$E(X_0, \overline{\iota}(X_0))$ or~$E(X_0, Y_0)$.
Case III:~$\left|Y_0\right|= \left|X_0\right| <\left|V\right| \; \& \: \left|V\right|\geq \omega$. Then by Infinite Sums are Maxs~(\ref{eqn:InfSumMax}), our case assumptions imply that $\left|V\right| = \max\{\left|V\setminus X_0\right|, \left|X_0\right|\} = \left|V\setminus X_0\right|$ and $\left|V\right| = \max\{\left|V\setminus Y_0\right|, \left|Y_0\right|\} = \left|V\setminus Y_0\right|$.
Hence, trivially one has that~$ \left|V\setminus X_0\right|\leq \left|V\setminus Y_0\right|$. Choose injection~$\iota:V\rightarrow V$ such that~$\iota\upharpoonright X_0: X_0\rightarrow Y_0$ is a bijection and~$\iota \upharpoonright (V\setminus X_0): V\setminus X_0 \rightarrow V\setminus Y_0$ is an injection. Then since~$A[E]$ is injection invariant on abstracts, we have that~$E(X_0,\overline{\iota}(X_0))$, which is the same as~$E(X_0,Y_0)$.
\end{proof}
Finally, let's note an instructive corollary to Theorem~\ref{thm:ncr=iia=cca}. This corollary tells us that in the context of natural relative categoricity, the only definable isomorphisms between the induced structures are identical to the natural bijection:
\begin{cor}\label{cor:whenarbirisnat}
Suppose that $A[E]$ is naturally relatively categorical. Suppose that $\mathcal{M}$ is a model of $A^2[E]$ with induced structures $\mathcal{M}_1$ and $\mathcal{M}_2$. Suppose that $\overline{H}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is a map whose restriction $H\upharpoonright \mathrm{rng}(\partial_1)$ to $\mathrm{rng}(\partial_1)$ is an element of $S_2[M]$. If $\overline{H}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is an isomorphism, then it is equal to the natural bijection $\overline{\Gamma}: \mathcal{M}_1\rightarrow \mathcal{M}_2$.
\end{cor}
\begin{proof}
So suppose that $\overline{H}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is an isomorphism. To show that $\overline{H}$ is equal to the natural bijection $\overline{\Gamma}: \mathcal{M}_1\rightarrow \mathcal{M}_2$, it suffices by Proposition~\ref{prop:whenarbirisnat} to show that
\begin{myequation}
\mathcal{M}\models [\forall \; X \; (X\subseteq \mathrm{rng}(\partial_1)\rightarrow E(X, \overline{H}(X))]
\end{myequation}
Suppose that $X\subseteq \mathrm{rng}(\partial_1)$, and let $Y=\overline{H}(X)$, so that $Y\approx X$ and $X\subseteq \mathrm{rng}(\partial_1)$. Since $A[E]$ is naturally relatively categorical, by Theorem~\ref{thm:ncr=iia=cca} it is cardinality coarsening on abstracts~(\ref{eqn:defn:CC}), from which we can infer $E(X,Y)$, which is the same as $E(X,\overline{H}(X))$, so that indeed the previous equation is satisfied.
\end{proof}
Let's turn now to the proof of our other main theorem, namely, Theorem~\ref{thm:coverthm}:
\begin{proof}
First suppose that $A[E]$ is surjectively relatively categorical (cf. Definition~\ref{eqn:defn:NRC:covered}). Suppose that $(M, S_1[M], S_2[M], \ldots, <,\partial_1)$ is a model of $A[E]$ where $\partial_1:S_1[M]\rightarrow M$ is a surjection, and suppose that $\pi:M\rightarrow M$ is a bijection. Let $\partial_2:S_1[M]\rightarrow M$ be defined by $\partial_2=\pi\circ \partial_1$. Then since $\pi:M\rightarrow M$ is an injection, we have that the following holds in our model:
\begin{myequation}\label{eqn:iamausualmove}
\partial_2(X)=\partial_2(Y) \Longleftrightarrow \partial_1(X)=\partial_1(Y) \Longleftrightarrow E(X,Y)
\end{myequation}
Hence $\mathcal{M}=(M, S_1[M], S_2[M], \ldots, <,\partial_1, \partial_2)$ is a model of $A^2[E]$. Further, since $\pi:M\rightarrow M$ is an surjection, we have that $\partial_2:S_1[M]\rightarrow M$ is a surjection. Then since by the hypothesis of $A[E]$ being surjectively relatively categorical, we have that the natural bijection $\overline{\Gamma}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is an isomorphism of the induced structures (cf. equation~(\ref{eqn:induced})). Then by surjective relative categoricity (cf. equation~(\ref{eqn:final})), we have that $\mathcal{M}$ models $E(X,\overline{\Gamma}(X))$ for any $X\in S_1[M]$. But for any $X\in S_1[M]$, one may use the surjectivity of the operators to check that $\overline{\pi}(X)=\overline{\Gamma}(X)$, which of course implies that $E(X,\overline{\pi}(X))$, so that we are done.
Now suppose that $A[E]$ plus the surjectivity of the abstraction operator proves permutation invariance~(\ref{eqn:defn:piI}). Then we show that $A[E]$ is surjectively relatively categorical. So suppose that $\mathcal{M}$ is a model of $A^2[E]$ wherein $\partial_1, \partial_2$ are surjective. Then the natural bijection is a bijection $\Gamma:V\rightarrow V$. Then by permutation invariance~(\ref{eqn:defn:piI}), we have that $E(X,\overline{\Gamma}(X))$ for all~$X$. Then by equation~(\ref{eqn:final}), we have that $\overline{\Gamma}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is an isomorphism.
So we've shown that surjective relative categoricity is equivalent to permutation invariance, assuming that the abstraction operator is surjective. Now we show that these two conditions are equivalent to the condition of bicardinality coarsening, under the hypothesis that the abstraction operator is surjective. First suppose that that $A[E]$ plus the surjectivity of the abstraction operator proves permutation invariance~(\ref{eqn:defn:piI}). Then suppose that $X, Y$ such that $\left|X\right|=\left|Y\right|$ and $\left|V\setminus X\right|=\left|V\setminus Y\right|$. Any two witnessing bijections can be conjoined into a bijection $\pi:V\rightarrow V$ such that $\overline{\pi}(X)=Y$ and $\overline{\pi}(V\setminus X)=V\setminus Y$. Then by permutation invariance~(\ref{eqn:defn:piI}), we have that $E(X,\overline{\pi}(X))$ or $E(X,Y)$, which is what we wanted to establish. Finally, suppose that $A[E]$ plus the surjectivity of the abstraction operator proves bicardinality coarsening~(\ref{eqn:defn:biC}). Suppose that $\pi:V\rightarrow V$ is a bijection. Let $X$ be a concept and let $Y=\overline{\pi}(X)$. Then since $\pi$ is a bijection, we have that $\left|X\right|=\left|Y\right|$ and $\left|V\setminus X\right|=\left|V\setminus Y\right|$. So by bicardinality coarsening~(\ref{eqn:defn:biC}), it follows that $E(X,Y)$ or $E(X,\overline{\pi}(X))$.
\end{proof}
In analogue to Corollary~\ref{cor:whenarbirisnat}, we have the following result showing that the only isomorphism is the natural bijection in the setting of surjective relative categoricity. We omit the proof since it is entirely analogous to the proof of the this earlier corollary.
\begin{cor}\label{cor:whenarbirisnat2}
Suppose that $A[E]$ is surjectively relatively categorical. Suppose that $\mathcal{M}$ is a model of $A^2[E]$, where the abstraction operators are surjective, with induced structures $\mathcal{M}_1$ and $\mathcal{M}_2$. Suppose that $\overline{H}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is a map whose restriction $\overline{H}\upharpoonright \mathrm{rng}(\partial_1)$ to $\mathrm{rng}(\partial_1)$ is an element of $S_2[M]$. If $\overline{H}:\mathcal{M}_1\rightarrow \mathcal{M}_2$ is an isomorphism, then it is equal to the natural bijection $\overline{\Gamma}: \mathcal{M}_1\rightarrow \mathcal{M}_2$.
\end{cor}
So the equivalent characterizations featuring in Theorem~\ref{thm:ncr=iia=cca} and Theorem~\ref{thm:coverthm} concern the abstraction principle $A[E]$. It will be useful to have analogues of these for the underlying equivalence relations $E$ as well. So we define:
\begin{myenumerate}
\item \emph{Injection Invariant}:~$\models [ \forall \; \mbox{ injection } \iota:V\hspace{-1mm}\rightarrow\hspace{-1mm}V \; \forall \; X \;E(X,\overline{\iota}(X))]$\label{eqn:RC2xsemi}
\item \emph{Permutation Invariant}:~$\models [ \forall \; \mbox{ bijection } \pi:V\hspace{-1mm}\rightarrow\hspace{-1mm}V \; \forall \; X \;E(X,\overline{\pi}(X))]$\label{eqn:RC2xsemi:permu}
\item \emph{Cardinality Coarsening}:~$\models [ \forall \; X, Y\; (\left|X\right|=\left|Y\right|\rightarrow E(X,Y))]$\label{eqn:RC3xsemi}
\item \emph{Bicardinality Coarsening}:~$\models [ \forall \; X, Y\; ((\left|X\right|=\left|Y\right| \; \& \; \left|V\setminus X\right|=\left|V\setminus Y\right|)\rightarrow E(X,Y))]$\label{eqn:RC3xsemi:bicardinality}
\item \emph{Injection Invariant on Small Concepts}: \label{eqn:RC2xsmall}
\item[] \hspace{30mm}~$\models [ \forall \; \mbox{ injection }\iota:V\hspace{-1mm}\rightarrow\hspace{-1mm}V \; \forall \; X \; (\left|X\right|\leq \left|\nicefrac{P(V)}{E}\right| \;\rightarrow E(X,\overline{\iota}(X)))]$
\item \emph{Cardinality Coarsening on Small Concepts}: \label{eqn:RC3xsmall}
\item[] \hspace{30mm}~$\models [ \forall \; X, Y\; (\left|Y\right|=\left|X\right|\leq \left|\nicefrac{P(V)}{E}\right| \rightarrow E(X,Y))]$
\end{myenumerate}
In the statements of these notions, the~$\models$ relation is the deduction relation from the deduction system of second-order logic which is the background of all our theories. In the final two conditions~(\ref{eqn:RC2xsmall})-(\ref{eqn:RC3xsmall}), the clause~$\left|X\right|\leq \left|\nicefrac{P(V)}{E}\right|$ just means that there's an injection from~$X$ to the~$E$-equivalence classes of second-order objects. This can be written in second-order logic as follows:
\begin{myequation}\label{eqn:whatimeans}
\exists \; R \; \forall \; x,y\in X \; (x\neq y \rightarrow \neg E(R[x], R[y]))
\end{myequation}
wherein~$R$ is a binary relation and where~$R[x]=\{z: Rxz\}$. These conditions~(\ref{eqn:RC2xsemi})-(\ref{eqn:RC3xsmall}) are all conditions on an arbitrary formula~$E(X,Y)$, which we assume to be an $L_0$-formula (cf. Definition~\ref{defn:L000}) which is provably an equivalence relation in our background second-order logic.
In diagrammatic form, the relationship between these notions are displayed in Figure~\ref{diagram1}. In the figure, the arrows going in both directions-- i.e. ``$\leftrightarrow$''-- indicate a provable equivalence, while the double-lined arrows that go in only one direction-- i.e. ``$\Rightarrow$''-- indicate that the implication cannot be reversed. The implications between e.g. injection
invariance and cardinality coarsening follows automatically from the analogous part of the proof of Theorem~\ref{thm:ncr=iia=cca}. The only implications in Figure~\ref{diagram1} that are less immediate are the implications from the conditions in the middle column to the conditions in the far-right column. So let's show that if $E$ is cardinality coarsening on small concepts then $A[E]$ is cardinality coarsening on abstracts. To see this, it suffices to note that the Axiom of Choice~${\tt AC}$~(\ref{eqn:AC}) implies that
\begin{myequation}\label{eqn:niceappchoice}
\left|\mathrm{rng}(\partial)\right|\leq \left|\nicefrac{P(V)}{E}\right|
\end{myequation}
For, for each $x$ from $\mathrm{rng}(\partial)$ there is $X$ such that $\partial(X)=x$. Then by ${\tt AC}$~(\ref{eqn:AC}), there is $R$ such that for all $x$ from $\mathrm{rng}(\partial)$ one has that $\partial(R[x])=x$, where $R[x]=\{y: Rxy\}$ which exists by comprehension. Then suppose that $x\neq y$ are both from $\mathrm{rng}(\partial)$ but $E(R[x], R[y])$. Then by $A[E]$ we have $x=\partial(R[x])=\partial(R[y])=y$, a contradiction. So indeed we have~(\ref{eqn:niceappchoice}).
Let us end this section by discussing the witnessing counterexamples featuring in Figure~\ref{diagram1}. For an example of an $E$ which is bicardinality coarsening but not cardinality coarsening, see the discussion of the Bicardinality Principle in \S\ref{sec:bicardinality}. There are different kinds of witnessing counterexamples which show that the conditions on $A[E]$ don't imply the analogous conditions on $E$. One way to see this is to consider~$A[E]$ which are inconsistent. For instance, take~$E_0(X,Y)\equiv X=Y$. Then $A[E_0]$ is just the abstraction principle Basic Law~V from Frege's \emph{Grundgesetze}, and as we noted earlier this is inconsistent with full comprehension (which we are assuming in this paper). Since the conditions on~$A[E]$ are conditions on derivability in~$A[E]$, trivially the inconsistent~$A[E_0]$ satisfies all of these. One might hope that the right-most arrows could be reversed with the additional assumption of the consistency of~$A[E]$. But this is not the case. For consider
\begin{myequation}\label{eqn:noreverseconst}
E(X,Y) \equiv (|V|<\omega \; \&\; X = Y) \vee (|V|\geq \omega\; \&\; X \approx Y)
\end{myequation}
Again, for our abbreviations of cardinality-related notions, see (\ref{eqn:cardinalityabb:1})-(\ref{eqn:cardinalityabb:3}) from \S\ref{sec02}. So on finite domains,~$E$ acts like~$E_0$. But for~$|V|\geq \omega$,~$E$ is just equinumerosity.
The principle~$A[E]$ is also naturally relatively categorical, since~$A[E]$ only has models with infinite first-order domains, and in those models,~$E$ acts exactly like equinumerosity, which we showed to be naturally relatively categorical in the earlier paper (\cite{Walsh2012aa} Proposition 14 p. 1687; see also \S\ref{sec04}). However,~$E$ is not cardinality coarsening on small concepts (or bicardinality coarsening), since if~$1<|V|<\omega$ and~$a\neq b$ are distinct objects then one has that~$\neg E(\{a\}, \{b\})$.
Second, let's show that cardinality coarsening on small concepts does not imply cardinality coarsening. First define the auxiliary formula:
\begin{myequation}
\theta(X,Y)\equiv \left|X\right|=\left|Y\right| \wedge [(X\neq V \; \& \; Y\neq V) \vee (X=V \; \& \; Y=V)]
\end{myequation}
Consider then the following equivalence relation~$E$:
\begin{myeqnarray}\label{eqn:iamanequivalencerelation}
E(X,Y) & \equiv & \left|V\right|=\omega_1 \rightarrow [(\left|X\right|=\left|V\right| \vee \left|Y\right|=\left|V\right|)\rightarrow \theta(X,Y)] \notag \\
& \wedge & \left|V\right|=\omega_1 \rightarrow [(\left|X\right|<\left|V\right| \vee \left|Y\right|<\left|V\right|)\rightarrow \left|X\right|=\left|Y\right|] \notag\\
& \wedge & \left|V\right|\neq \omega_1 \rightarrow \left|X\right|=\left|Y\right|
\end{myeqnarray}
Intuitively, this says that if the domain~$V$ is the first uncountable cardinal, then~$V$ is the only member of its own equivalence class, while all the other concepts of the same cardinality as~$V$ form an equivalence class, and then properly smaller concepts are separated into equivalence classes according to cardinality; while if the domain~$V$ is any other size, then all the concepts are separated into equivalence classes according to cardinality. Note that~$\left|V\right|=\omega_1$ can be written in second-order logic in a standard way: for, since we have global choice in the background, it simply consists in the claim that the global well-order of~$V$ has a limit point, and that any initial segment of the global well-order is bijective with the initial segment corresponding to the first limit point, but that~$V$ itself is not bijective with this initial segment.
Let's verify that this $E$ from~(\ref{eqn:iamanequivalencerelation}) is cardinality coarsening on small concepts but not cardinality coarsening. For the former, there are two cases to consider. First suppose that the domain~$V$ has cardinality~$\omega_1$. Then by construction~$\left|\nicefrac{P(V)}{E}\right|= \omega$. Suppose that~$\left|Y\right|=\left|X\right|\leq \omega$. Then by definition~$E(X,Y)$ since~$E$ is sameness of cardinality on smaller concepts. Second suppose that the domain of~$V$ is any other cardinality. Then by construction~$E$ is just sameness of cardinality and so we are done. Now, let us note that~$E$ is not cardinality coarsening. For, consider a model where the domain~$V$ has size~$\omega_1$. Consider~$Y_0=V$ and~$X_0=Y_0\setminus\{y_0\}$, where~$y_0$ is any element of~$Y_0=V$. Then by construction we have that~$\neg E(X_0,Y_0)$, while they of course have the same cardinality.
\begin{figure}
\begin{center}
\includegraphics[width=7.5cm]{rel-cat-diagram}
\end{center}
\caption{Provability Relation Among Conditions on $E$ and $A[E]$}\label{diagram1}
\end{figure}
\FloatBarrier
\section{Some Examples and Non-Examples}\label{sec04}
In this section, we give some examples and non-examples of naturally relatively categorical abstraction principles. In the case of abstraction principles which are not naturally relatively categorical, we have always been able to find a single sentence which illustrates this. So we define:
\begin{defn}\label{eqn:nateleequiv}
The abstraction principle $A[E]$ is \emph{relatively elementary equivalent} if whenever $\mathcal{M}$ is a model of $A^2[E]$ as in equation~(\ref{eqn:1}), then for any sentence $\varphi$ in the signature $L_0[\partial]$ of the induced structures $\mathcal{M}_i$ from equation~(\ref{eqn:induced}) one has that $\mathcal{M}_1\models \varphi$ if and only if $\mathcal{M}_2\models \varphi$. If $A[E]$ is not relatively elementarily equivalent, then a sentence $\varphi$ of $L_0[\partial]$ such that there is a model $\mathcal{M}$ of $A^2[E]$ with $\mathcal{M}_1\models \varphi$ and $\mathcal{M}_2\models \neg \varphi$ (or vice-versa) is called a \emph{witness} to the failure of relative elementary equivalence.
\end{defn}
\noindent Further, note that natural relative categoricity trivially implies relative elementary equivalence. Prior to stepping into the examples, let us mention that there's an obvious sense in which relative elementarily equivalence is a more apposite formalization of determinacy of truth-value ideas than natural relative categoricity itself. However, it seems difficult to study relative elementarily equivalence directly, and so we study natural relative categoricity instead, since it is the obvious sufficient condition for relative elementarily equivalence in this setting. It is not even obvious to us whether these notions are distinct in the setting of abstraction principles:
\begin{Q}\label{eqn:Q1}
Suppose that $E(X,Y)$ is an $L_0$-formula which is provably an equivalence relation in our background second-order logic and such that $A[E]$ is consistent. Suppose further that $A[E]$ is relatively elementarily equivalent. Is it necessarily the case that $A[E]$ is naturally relatively categorical?
\end{Q}
\noindent One suspects that the answer to this question is `no,' but we have been unable to produce a counterexample.
\subsection{Hume's Principle}
Recall that Hume's Principle is the abstraction principle associated to the equivalence relation of equinumerosity.
In \cite{Walsh2012aa} Proposition 14 p. 1687, it was shown that Hume's Principle is naturally relatively categorical. In that paper, the result was established by hand. But with our main Theorem~\ref{thm:ncr=iia=cca} now in place, we can reduce this to the one-line observation that equinumerosity is trivially cardinality coarsening on abstracts.
\subsection{Boolos' New V}\label{sec:NewV}
In his \cite{Boolos1989aa}, Boolos drew attention to the following equivalence relation:
\begin{myequation}
E(X,Y)\equiv (\left|X\right|<\left|V\right| \vee \left|Y\right|<\left|V\right|)\rightarrow X=Y
\end{myequation}
Intuitively, this equivalence identifies all the concepts bijective with the universe~$V$, but acts like Basic Law~V on small concepts. By Theorem~\ref{thm:ncr=iia=cca}, it's easy to see that this equivalence relation is not naturally relatively categorical. For, it is trivially not cardinality coarsening on abstracts. Indeed, any two distinct small concepts which are equinumerous will not be equivalent under this equivalence relation. Further, it turns out that New~V is not relatively elementarily equivalent~(\ref{eqn:nateleequiv}), and that the witnessing sentence was previously studied by Jan\'e and Uzquiano \cite{Jane2004aa}. For, they noted that some models of New~V generated membership relations which were well-founded while others did not.
To see this, enumerate the finite subsets of~$\omega$ as~$X_1, X_2, X_3, \ldots$, and without loss of generality, suppose that~$1\in X_1$. Then let~$\partial_1:P(\omega)\rightarrow \omega$ be any surjection that sends all the infinite subsets of~$\omega$ to~$0$, and sends~$X_1$ to~$1$. Further, let~$\partial_2:P(\omega)\rightarrow \omega$ be the surjective map that sends all the infinite subsets of~$\omega$ to~$0$, and acts on the finite subsets of~$\omega$ as follows:
\begin{myequation}
\partial_2(X_i) = \min(\omega\setminus (X_i \cup \{0,\partial(X_1), \ldots, \partial(X_{i\mbox{-}1})\}))
\end{myequation}
Then~$\mathcal{M}=(\omega, P(\omega), P(\omega\times \omega), \ldots, \partial_1, \partial_2)$ is model of~$A^2[E]$~(\ref{eqn:AE2}). Since both maps are surjective, we have that the induced structures~$\mathcal{M}_i$ from equation~(\ref{eqn:induced}) will satisfy $\mathcal{M}_i=(\omega, P(\omega), P(\omega\times\omega), \ldots, \partial_i)$.
If~$A[E]$ were naturally relatively categorical, then $A[E]$ would be relatively elementarily equivalent. But let $\varphi$ be the following sentence in the signature of $L_0[\partial]$:
\begin{myequation}\label{eqn:witnsessnewv}
\varphi\equiv \exists \; X \; \exists \; b \; (\left|X\right|<\left|V\right| \; \& \; b=\partial(X) \; \& \; Xb)
\end{myequation}
Then it's easy to see that $\mathcal{M}_1\models \varphi$ since $b=\partial_1(X_1)$ is a witness. However, by construction, $\mathcal{M}_2\models \neg \varphi$. So $\varphi$ is a witness to the failure of relative elementarily equivalence of New~V, so that New~V is not naturally relatively categorical. Boolos was interested in New~V because it allowed one to define an ersatz membership relation:
\begin{myequation}\label{eqn:membership}
a\eta b \Longleftrightarrow \exists \; X \; (\left|X\right|<\left|V\right| \; \& \; \partial(X)=b \; \& \; Xa)
\end{myequation}
Expressed in these terms, $\varphi$ from (\ref{eqn:witnsessnewv}) says that there's a $b$ with $b\eta b$, which intuitively says that the membership relation from~(\ref{eqn:membership}) is not well-founded.
\subsection{Bicardinality}\label{sec:bicardinality}
Consider the equivalence relation:
\begin{myequation}\label{eqn:bicard}
E(X,Y)\equiv \left|X\right|=\left|Y\right| \wedge \left|V\setminus X\right|=\left|V\setminus Y\right|
\end{myequation}
It's easy to see that this is provably an equivalence relation in our background second-order logic. Further, this equivalence relation is trivially an example of an equivalence relation which is bicardinality coarsening but not cardinality coarsening, since for instance in infinite structures $V$ and $V\setminus\{a\}$ will have the same cardinality but will not be $E$-equivalent. Let's call the associated principle~$A[E]$ the \emph{Bicardinality Principle}. By Theorem~\ref{thm:coverthm}, we have that the Bicardinality Principle is surjectively relatively categorical. However, it turns out that the Bicardinality Principle is not relatively elementarily equivalent, and hence not naturally relatively categorical.
The non-relative elementary equivalence of the Bicardinality Principle is related to the different ways this principle can interpret the natural numbers. Just as with Hume's Principle, the Bicardinality Principle allows one to build a copy of the natural numbers $\{\overline{0}, \overline{1}, \ldots, \overline{n}, \overline{n\mbox{+}1}\,\ldots\}$ by setting $\overline{0}=\partial(\emptyset)$ and $\overline{n\mbox{+}1} = \partial(\{\overline{0}, \ldots, \overline{n}\})$. But the Bicardinality principle allows one to build a second copy $\{\widehat{0}, \widehat{1}, \ldots, \widehat{n}, \widehat{n\mbox{+}1}\,\ldots\}$ of the natural numbers by setting $\widehat{0}=\partial(V)$ and $\widehat{n\mbox{+}1} = \partial(V\setminus \{\widehat{0}, \ldots, \widehat{n}\})$. Then we can define the following sentences for each $n>0$:
\begin{myequation}
\varphi_{n} \equiv \bigwedge_{m=0}^{n-1} \overline{m}\neq \overline{n}, \hspace{10mm} \widehat{\varphi}_{n} \equiv \bigwedge_{m=0}^{n-1} \widehat{m}\neq \widehat{n},
\end{myequation}
Then one has that the Bicardinality Principle proves each $\varphi_n$ and each $\widehat{\varphi}_n$. The proof is very similar to the proof that Hume's Principle proves the variant $\psi_n$ of $\varphi_n$ wherein $\overline{n}$ is defined in terms of~$\#$ instead of~$\partial$ (where again, $\#$ is the symbol reserved for the abstraction operator featuring in Hume's Principle). Indeed, the sentences $\psi_n$ are part of the means by which one establishes the principle~Nq mentioned in the introduction \S\ref{sec01} (cf. \cite{Walsh2014aa} equation~(34) p. 111).
However, we have that $\widehat{\varphi}_n$ for each $n>0$ is a witness to the Bicardinality Principle being not relatively elementarily equivalent. Consider a model of the Bicardinality Principle of the form
\begin{myequation}\label{eqn:anotherequation}
\mathcal{M}^{\ast} = (\omega, P(\omega), P(\omega^2), \ldots, \partial_1)
\end{myequation}
wherein~$\partial_1:P(\omega)\rightarrow \omega$ is a surjection (cf. Proposition~\ref{prop:existencesurject}). Define the injection $\iota:\omega\rightarrow \omega$ by $\iota(n)=2n$, and define $\partial_2=\iota\circ \partial_1$. Then by an argument with which we are now familiar (cf. equations~(\ref{eqn:iamausualmove0}) and (\ref{eqn:iamausualmove})), we have that the following is also a model of $A^2[E]$:
\begin{myequation}
\mathcal{M} = (\omega, P(\omega), P(\omega^2), \ldots, \partial_1, \partial_2)
\end{myequation}
Since $\partial_1$ is surjective, we have that the induced structure~$\mathcal{M}_1$ from equation~(\ref{eqn:induced}) is identical to the structure $\mathcal{M}^{\ast}$ from~(\ref{eqn:anotherequation}), and so $\mathcal{M}_1$ models $\widehat{\varphi}_1$ since it is a model of the Bicardinality Principle. However, if $\mathcal{E}$ denotes the evens, then we have that the induced structure $\mathcal{M}_2$ is equal to the following structure
\begin{myequation}
\mathcal{M}_2 = (\mathcal{E}, P(\mathcal{E}), P(\mathcal{E}^2), \ldots, \partial_2\upharpoonright P(\mathcal{E}))
\end{myequation}
Then let $D=\mathcal{E}\setminus \{\partial_2(\mathcal{E})\}$. Then $D,\mathcal{E}$ have cardinality $\omega$, as do the their relative complements $\omega\setminus D, \omega\setminus \mathcal{E}$ in $\omega$. Hence since $\mathcal{M}$ models the Bicardinality Principle, we have that $\partial_2(\mathcal{E})=\partial_2(D)$. But this implies that on $\mathcal{M}_2$, we have that $\widehat{0}=\widehat{1}$, so that $\mathcal{M}_2$ does not model $\widehat{\varphi}_1$. The same argument works for $\widehat{\varphi}_n$ for all $n\geq 1$.
\subsection{The Nuisance Principle}\label{sec:nuisances}
Consider the equivalence relation $E(X,Y) \equiv \left|X\triangle Y\right| < \omega$ wherein $X\triangle Y$ denotes the symmetric difference $X\triangle Y = (X\setminus Y)\cup (Y\setminus X)$. In this, recall that the notion of $\left|Z\right|<\omega$ is that of Dedekind-finiteness~(\ref{eqn:cardinalityabb:3}), so that $E$ is $L_0$-definable. But per Proposition~\ref{eqn:equivchardedfin}, this aligns with the notion of being finite in the sense of being bijective with the initial segments $I_a=\{x: x<a\}$ from our global well-order where $a$ is finite, i.e. is less than the first limit point. So while $E$ is expressible purely in terms of the signature of the background second-order logic $L_0$ (cf. Definition~\ref{defn:L000}), we can use the global well-order to show that it is an equivalence relation. For, using the global well-order we can show that the union of any two finite sets is finite, and so the transitivity of $E$ follows from $
X\triangle Z \subseteq (X\triangle Y)\cup (Y\triangle Z)$.
The abstraction principle $A[E]$ has been called the ``Nuisance Principle'' following Wright's identification of its abstracts as ``nuisances'' \cite{Wright1997aa}, and is related to an earlier principle presented by Boolos \cite{Boolos1990}. Let's show that $A[E]$ is naturally relatively categorical, and let's begin with the following proposition. This proposition is well-known if one assumes the standard semantics, but we know of no extant proof for the Henkin semantics with choice principles. In the statement of this theorem, the notion of finiteness is Dedekind-finiteness~(\ref{eqn:cardinalityabb:3}) or the aforementioned equivalent characterization (cf. again Proposition \ref{eqn:equivchardedfin}).
\begin{prop}\label{prop:nufinite}
$A[E]$ implies that $V$ is finite.
\end{prop}
\begin{proof}
So suppose not. Then let's work deductively in the theory $A[E]$ under the assumption that the universe $V$ is infinite. Let $\omega$ denote the least limit point in the global well-order. First let's establish that there's a way to enumerate all finite concepts:
\begin{claim}\label{nu:claim0}
There is a ternary relation $R$ such that for all $X$, $\left|X\right|<\omega$ if and only if there is $a<\omega$ and $b$ such that $R[a,b]=X$, where again $R[a,b]=\{c: R(a,b,c)\}$.
\end{claim}
\noindent This claim follows trivially by comprehension from the following claim:
\begin{claim}\label{nu:claim1}
There is a ternary relation $R$ such that for all $a<\omega$, and all $X$ with $\left|X\right|\leq \left|I_a\right|$ there is $b$ with $R[a,b]=X$, where again $R[a,b]=\{c: R(a,b,c)\}$.
\end{claim}
\noindent This claim of course follows from the following claim by a single application of ${\tt AC}$~(\ref{eqn:AC}):
\begin{claim}\label{nu:claim2}
For all $a<\omega$ there is binary relation $R_a$ such that for all $X$ with $\left|X\right|\leq \left|I_a\right|$ there is $b$ with $R_a[b]=X$.
\end{claim}
\noindent We argue for this latter claim by induction on $a$. For $a=0$, it holds trivially since we may choose $R_a$ equal to the empty binary concept. Now suppose it holds for $a_0$ with witness $R_{a_0}$, and suppose $a=s(a_0)$, where this is the partial successor operation from~(\ref{eqn:defnsucconord}). By Infinite Products are Maxs~(\ref{eqn:InfProdMax}), there is a bijection $\langle \cdot, \cdot\rangle: V\times V\rightarrow V$. Then we define the binary relation $R_{a}$ as follows:
\begin{myequation}
R_{a}[b]=\{z: \exists \; b_0,c_0 \; b=\langle b_0,c_0\rangle \; \& \; (z=c_0 \vee R_{a_0}[b_0](z)) \}
\end{myequation}
So this finishes the proof of Claim~\ref{nu:claim2} and with it the proof of Claim~\ref{nu:claim0}.
Using this enumeration of the finite concepts, let's define a partial injective map from finite concepts to objects. For this, let us fix a ternary relation $R$ as in Claim~\ref{nu:claim0}. Then consider the following partial map from concepts to objects:
\begin{myequation}
\nabla(X)=c \Longleftrightarrow \left|X\right|<\omega \; \& \; c=\min_{<}\{\langle a,b\rangle: a<\omega \; \& \; R[a,b]=X\}
\end{myequation}
Then this map is defined on all finite concepts, and on these, it is an injection. For, supposing that $\nabla(X)=\langle a,b\rangle=\nabla(Y)$, we have $X=R[a,b]=Y$. Hence, indeed $\nabla$ is a partial map from concepts to objects which is defined and injective on finite concepts.
So now consider $\mathrm{rng}(\partial)$, where $\partial$ as usual is the abstraction operator associated to $A[E]$. As in the argument for (\ref{eqn:niceappchoice}) in the previous section, we may use ${\tt AC}$~(\ref{eqn:AC}) to show that there is a binary relation $S$ such that for all $x$ from $\mathrm{rng}(\partial)$ one has that $\partial(S[x])=x$. Then for all concepts $X$, there is unique $x$ from $\mathrm{rng}(\partial)$ such that $E(X,S[x])$. Hence there are finite concepts $F_X, G_X$ such that $X=(S[x]\cup F_X)\setminus G_X$. Then define a map $\partial^{\prime}$ from concepts to objects by $\partial^{\prime}(X)=\langle x,\langle a,b\rangle \rangle$ iff $x$ is from $\mathrm{rng}(\partial)$ and $E(X,S[x])$ and
\begin{myequation}\label{eqn:nurussell}
\langle a,b\rangle = \min_<\{\langle c,d\rangle: \exists \; F_X, G_X \; X=(S[x]\cup F_X)\setminus G_X \; \& \; \nabla(F_X)=c \; \& \; \nabla(G_X)=d\}
\end{myequation}
Then by construction $\partial^{\prime}$ is an injection from concepts to objects, and so using the full comprehension schema, we may again replicate the Russell paradox to derive a contradiction.
\end{proof}
\noindent Using this result, we can now deduce:
\begin{prop}
$A[E]$ is naturally relatively categorical.
\end{prop}
\begin{proof}
Let's work within $A[E]$. By the above result, $V$ is finite. Hence, since $\left|X \triangle Y \right|<\omega$ for all finite $X$ and $Y$, we have that $E(X,Y)$ for all $X,Y$. And then trivially $A[E]$ is cardinality coarsening on abstracts. Hence by Theorem~\ref{thm:ncr=iia=cca}, $A[E]$ is naturally relatively categorical.
\end{proof}\noindent So this proof shows us that naturally relatively categorical abstraction principles are not pairwise consistent. For, as noted earlier, Hume's Principle is naturally relatively categorical and yet it implies that $V$ is infinite, since for instance when one defines the natural numbers using the resources of Hume's Principle, they will be Dedekind-infinite. But of course one would not have expected relatively categorical concepts to be pairwise consistent. For instance, the standard relative categoricity argument for set theory can be deployed to show that the standard axioms plus ``there are no inaccessibles'', as well as the standard axioms plus ``there are inaccessibles,'' are both relatively categorical, at least assuming (as we are here) that the domain of the model is the entire universe. In \S\ref{sec05stable}, we'll note by contrast that equivalence relations which are cardinality coarsening on small concepts are pairwise consistent. So this is another way of seeing that the conditions on $A[E]$ in Figure~\ref{diagram1} don't have implications for the analogous conditions on $E$: while the Nuisance Principle is naturally relatively categorical and hence cardinality coarsening on abstracts, it is not the case that the underlying equivalence relation is cardinality coarsening on small concepts.
\subsection{The Complementation Principle}
Let's say that a concept $X$ is a \emph{complement}, abbreviated $\mathrm{Cmp}(X)$ if there is $Y\approx X$ such that~$X\sqcup Y = V$. Then we define:
\begin{myequation}
E(X,Y)\equiv (\mathrm{Cmp}(X) \vee \mathrm{Cmp}(Y))\rightarrow (X=Y \vee (X\approx Y \; \& \; X\sqcup Y =V))
\end{myequation}
\noindent This equivalence relation sorts out concepts as follows: each pair of equinumerous complementary sets constitute a separate equivalence class, everything else occupies a single ``junk'' equivalence class.
This abstraction principle has finite models only for odd domains, and domains of sizes 2 and 4. For, in the case of odd domains, there are no complements and so there is only one equivalence class. In the case of even domains of size $2n$, the number of $E$-equivalence classes is exactly $f(n)=\frac{1}{2}\binom{2n}{n}+1$, and one has that $f(1)=2, f(2)= 4$ and $f(n)\geq 2n+1$ for $n\geq 3$, as one can establish by induction on $n$.
Unlike the Nuisance Principle, this $A[E]$ is not naturally relatively categorical and indeed not relatively elementary equivalent. For, consider the domain $M=\{a,b,c,d\}$ of size $4$, where there are exactly 4 equivalence classes. Define two abstraction operators by \begin{myequation}\label{eqn:comp-counter}
\begin{array}{cccc}
\partial_1(\{a,b\}) = a, & \partial_1(\{a,c\})= b, & \partial_1(\{a,d\})= c, & \partial_1(\emptyset) = d, \\
\partial_2(\{a,b\}) = c, & \partial_2(\{a,c\})= b, & \partial_2(\{a,d\})= a, & \partial_2(\emptyset) = d
\end{array}
\end{myequation}
This determines a model $\mathcal{M}$ of $A^2[E]$ with first-order part $M$. Then consider the sentence:
\begin{myequation}\label{eqn:CP-witness}
\forall X\; [|X|=2 \rightarrow \exists Y (E(X,Y) \wedge Y(\partial_i(X))\wedge Y(\partial_i(\emptyset))]
\end{myequation}
This sentence fails in $\mathcal{M}_1$ with witness $X=\{a,b\}$ but holds in $\mathcal{M}_2$. Hence $A[E]$ is not relatively elementary equivalent and hence not naturally relatively categorical. But like with the Nuisance Principle, $A[E]$
proves $V$ is finite.
Hence, it is not this feature alone which permitted the Nuisance Principle to be naturally relatively categorical.
\section{Stability Criteria and the Bad Company Problem}\label{sec05stable}
One of locus of activity on abstraction principles in recent years has been stability criteria (cf. Cook~\cite{Cook2012aa}). Some of the key stepping stones in this hierarchy are the following:
\begin{myenumerate}
\item The abstraction principle $A[E]$ is \emph{stable} if there is some cardinal~$\lambda$ such that, for all~$\kappa\geq \lambda$,~$A[E]$ has a standard model of size~$\kappa$.\label{eqn:defn:stable}
\item The abstraction principle $A[E]$ is \emph{strongly stable} if there is some cardinal~$\lambda$ such that, for all cardinals~$\kappa$,~$A[E]$ has a standard model of size~$\kappa$ if and only if~$\kappa\geq\lambda$.\label{eqn:defn:superstable}
\end{myenumerate}
\noindent As above, a structure~$\mathcal{M}=(M, S_1[M], S_2[M], \ldots)$ is said to be \emph{standard} if~$S_n[M]=P(M^n)$ for each~$n\geq 1$ (cf. \S~\ref{sec02}). Further, here one identifies the \emph{cardinality of~$\mathcal{M}$} as~$\left|M\right|$, i.e. the cardinality of its first-order part. So this convention on the cardinality of the many-sorted structure $\mathcal{M}$ differs from other settings in which it would be more natural to define its cardinality as the cardinality of the union of its various domains (cf. \cite{Walsh2014aa} \S{6.1} p. 107 equation (18), \cite{Manzano1996} p. 231 and \cite{Ebbinghaus1985aa} pp. 32, 64).
These criteria have been proposed as solutions to the so-called \emph{Bad Company Problem}, namely the problem of identifying criteria on abstraction principles which would ensure consistency of $A[E]$; perhaps also joint consistency with like abstraction principles and the ability to interpret mathematics of various sorts. Of course, the relative categoricity notions studied here are not candidates for a solution to the Bad Company Problem since they do not ensure consistency. However, the sufficient conditions on the equivalence relations themselves that we have identified for relative categoricity \emph{do} ensure consistency, and indeed stability and joint consistency. In particular, we have the following results:
\begin{prop}\label{prop:stabileforcc} Suppose that $E(X,Y) $ is an $L_0$-formula and suppose that~$E$ is cardinality coarsening on small concepts. Then for all infinite cardinals~$\kappa$ there is a standard model of~$A[E]$ of cardinality~$\kappa$.
\end{prop}
\begin{prop}\label{prop:stableforbcc} Suppose that $E(X,Y) $ is an $L_0$-formula and suppose that $E$ is bicardinality coarsening. Then for all infinite cardinals $\kappa$ there is a standard model of $A[E]$ of cardinality $\kappa$.
\end{prop}
These two propositions imply that the equivalence relations satisfying these constraints are stable~(\ref{eqn:defn:stable}). However, this cannot be improved to strong stability~(\ref{eqn:defn:superstable}). For, consider the following equivalence relation:
\begin{myequation}\label{eqn:SEDcounter}
E(X,Y) \equiv[\left|V\right|<\omega \; \& \; \textrm{$|V|$ is even}\rightarrow X\approx Y] \wedge [\neg(\left|V\right|<\omega \; \& \; \textrm{$|V|$ is even})\rightarrow X=X]
\end{myequation}
This equivalence relation is cardinality coarsening on small concepts. In the case where $\left|V\right|<\omega$ is even, we have that $E$ is equinumerosity, so that $\left|\nicefrac{P(V)}{E}\right|\geq \left|V\right|+1$, all concepts are small, and thus trivially $X\approx Y $ implies $E(X,Y)$. But in the other case, $E$ says that all concepts are equivalent, so that again we trivially have that $X\approx Y $ implies $E(X,Y)$. So this $E$ is cardinality coarsening on small concepts, but $A[E]$ is not strongly stable~(\ref{eqn:defn:superstable}). For $A[E]$ is satisfiable on all finite odd domains but no finite even domains.
Cook~\cite{Cook2012aa} recommends strong stability as the appropriate solution to the Bad Company Problem, and so the previous examples indicate that the solution offered by cardinality coarsening on small concepts and bicardinality coarsening will be extensionally distinct from Cook's solution. However, it is worth noting that
Propositions~\ref{prop:stabileforcc} and~\ref{prop:stableforbcc} imply that if $E$ is cardinality coarsening on small concepts (respectively, bicardinality coarsening), all structures witnessing that $E$ is not strongly stable will be finite.
But cardinality coarsening on small concepts and bicardinality coarsening have a more mixed scorecard on other desiderata taken to be relevant to judging the success of proposed solutions to the Bad Company problem. On the one hand, Proposition~\ref{prop:stabileforcc} and Proposition~\ref{prop:stableforbcc} imply that all these abstraction principles are jointly consistent since they all have models of any infinite cardinality. But by the same token, our conditions on $E$ restrict the mathematics that can be recovered in the theory $A[E]$. Inspection of the below proof of these
propositions show that the joint theory of all these abstraction principles will be interpretable in second-order Peano arithmetic ${\tt PA}^2$ (cf. \cite{Simpson1999} pp. 4 ff for the definition of ${\tt PA}^2$ and cf. \cite{Walsh2014aa} \S{2} for the definition of interpretation). This is of course because a standard model of cardinality~$\omega$ is the underlying first-order domain of the standard model of ${\tt PA}^2$, and the proofs of the propositions for the case $\kappa=\omega$ are formalizable in ${\tt PA}^2$. Hence, there will be no hope of interpreting, e.g., standard ${\tt ZFC}$-set theory by restricting attention to such abstraction principles, because ${\tt ZFC}$ proves the consistency of ${\tt PA}^2$ and so ${\tt PA}^2$ cannot interpret ${\tt ZFC}$.
But it's difficult to compare this directly to the situation of stability or strong stability. For, suppose that $\Phi$ is a sentence of second-order logic that is true on all and only standard models of cardinality $\geq \lambda$. Then $A[E]$ will be strongly stable for $E(X,Y)\equiv (X=Y) \vee \Phi$ (disjunctive abstraction principles like this are due to Heck~\cite{Heck-Jr.1992aa}). So such $A[E]$ will be able to encode a good deal of interpretability strength, at least when interpretability with parameters is allowed (cf. \cite{Walsh2014aa} \S{2} for the definition of interpretations with parameters). For instance, $\Phi$ could say that there is a model of ${\tt ZFC}^2$. It's unknown to us whether the interpretability strength-- where the interpretation is \emph{without} parameters-- of the theories associated to all stable or strongly stable abstraction principles is strictly above ${\tt PA}^2$. This might be related to the fact that stability conditions often depend on undecidable questions in set theory. For instance, the claim that the abstraction principle New V is strongly stable is equivalent to the generalized continuum hypothesis (cf. \cite{Shapiro1999ac} p. 315, \cite{Cook2007aa} p. 297). Our conditions, by contrast, concern only what is demonstrable in a sound and complete deductive system.
So let's proceed to the proofs of Proposition~\ref{prop:stabileforcc} and Proposition~\ref{prop:stableforbcc}. In these proofs, we employ the notion on equivalence classes from the close of \S\ref{sec02}. We begin with a helpful lemma:
\begin{lem}\label{lem:dichtomylem}
(\emph{Coarsening Dichotomy}) Suppose that~$E$ is cardinality coarsening on small concepts. Then for all infinite~$\kappa$ we have $\left| \nicefrac{P(\kappa)}{E}\right| <\kappa$ or $\left| \nicefrac{P(\kappa)}{E}\right|=\left| \nicefrac{P(\kappa)}{\approx}\right|=\kappa$,
and hence in either case we have~$\left|\nicefrac{P(\kappa)}{E}\right|\leq \kappa$.
\end{lem}
\begin{proof}
So suppose that~$\left| \nicefrac{P(\kappa)}{E}\right| \geq \kappa$. We must show that~$ \left| \nicefrac{P(\kappa)}{E}\right|=\left| \nicefrac{P(\kappa)}{\approx}\right|=\kappa$. Since~$\left|\nicefrac{P(\kappa)}{E}\right| \geq \kappa$, we of course have that $X\subseteq \kappa$ implies $\left|X\right|\leq \left|\nicefrac{P(\kappa)}{E}\right|$.
Then we have:
\begin{myequation}
[X,Y\subseteq \kappa \; \& \; \left|Y\right|= \left|X\right|] \Longrightarrow [\left|Y\right|=\left|X\right|\leq \left|\nicefrac{P(\kappa)}{E}\right|]
\end{myequation}
and the consequent of this conditional clearly implies $E(X,Y)$ since~$E$ is cardinality coarsening on small concepts. In terms of the equivalence classes, this says that the partition of~$P(\kappa)$ by~$E$ is coarser than the partition of~$P(\kappa)$ by equinumerosity. Then choose representatives~$X_0, X_1, \ldots$ for the~$E$-equivalence classes, so that~$\nicefrac{P(\kappa)}{E}=\bigsqcup_{i\in I} [X_i]_{E}$. Then define~$I:\nicefrac{P(\kappa)}{E}\rightarrow \nicefrac{P(\kappa)}{\approx}$ by~$I([X_i]_E)=[X_i]_{\approx}$. Then we claim that~$I$ is an injection. For, suppose that~$I([X_i]_E)=I([X_j]_E)$ so that~$[X_i]_{\approx}=[X_j]_{\approx}$. Then~$\left|X_i\right|=\left|X_j\right|$ and so by the previous equation we have~$E(X_i,X_j)$ and hence~$[X_i]_E=[X_j]_E$ and so~$i=j$ since the~$X_i,X_j$ are representatives of the~$E$-equivalence classes. Since~$I:\nicefrac{P(\kappa)}{E}\rightarrow \nicefrac{P(\kappa)}{\approx}$ is indeed injective, we then have the following, where the last inequality appeals to the infinitude of~$\kappa$: $\left| \nicefrac{P(\kappa)}{E}\right| \leq \left| \nicefrac{P(\kappa)}{\approx}\right| \leq \kappa$. Since we're assuming~$\kappa\leq \left| \nicefrac{P(\kappa)}{E}\right|$, we are done.
\end{proof}
So we can now prove Proposition~\ref{prop:stabileforcc}:
\begin{proof}
Let~$\kappa$ be an infinite cardinal, and consider the standard structure, where $<$ is the natural well-ordering on the cardinal: $
\mathcal{M}_0=(\kappa, P(\kappa), P(\kappa\times \kappa), \ldots, <)$.
By the Coarsening Dichotomy, we have that~$\left|\nicefrac{P(\kappa)}{E}\right| \leq \kappa$. Choose an injection~$\widehat{\partial}: \nicefrac{P(\kappa)}{E}\rightarrow \kappa$. Then we may define the map~$\partial:P(\kappa)\rightarrow \kappa$ by~$\partial(X)=\widehat{\partial}([X]_E)$. Then by construction we have that~$\mathcal{M}=(\kappa, P(\kappa), P(\kappa\times \kappa), \ldots, <, \partial)$ is a model of~$A[E]$ of cardinality~$\kappa$.
\end{proof}
Similarly, we can prove Proposition~\ref{prop:stableforbcc}:
\begin{proof}
Let's use $E_0$ as an abbreviation for the equivalence relation of bicardinality. So since $E$ is bicardinality coarsening, by definition we have that $
E_0(X,Y)$ implies $E(X,Y)$.
So as in the proof of the Coarsening Dichotomy, this implies that $\left|\nicefrac{P(\kappa)}{E}\right|\leq \left|\nicefrac{P(\kappa)}{E_0}\right|$. Then one may argue that $
\left|\nicefrac{P(\kappa)}{E}\right|\leq \left|\nicefrac{P(\kappa)}{E_0}\right| \leq \kappa \cdot \kappa \leq \kappa$.
Since~$\kappa$ is infinite, the only non-trivial inequality is the second. For this, consider the map $[X]_{E_0} \mapsto \langle \left|X\right|, \left|\kappa\setminus X\right|\rangle$. This is an injection because we have by definition of~$E_0$ that $E_0(X,Y)$ iff $ \langle \left|X\right|, \left|\kappa\setminus X\right|\rangle=\langle \left|Y\right|, \left|\kappa\setminus Y\right|\rangle$. From $\left|\nicefrac{P(\kappa)}{E}\right|\leq \kappa$, we can use the same construction as employed in the proof of the above proposition to build models of $A[E]$.
\end{proof}
Since $E$ being bicardinality coarsening is a sufficient condition for $A[E]$ being surjectively relatively categorical, it's natural to ask about when there are standard models of $A[E]$ on which the abstraction operator is surjective.
\begin{prop}\label{prop:existencesurject}
Suppose that $E$ is bicardinality coarsening. Then for all infinite cardinals $\kappa$, there is a standard model of $A[E]$ of cardinality $\kappa$ wherein the abstraction operator is surjective if and only if $\left|\nicefrac{P(\kappa)}{E}\right|=\left|\{\lambda: \lambda<\kappa\}\right| = \kappa$.
\end{prop}
\begin{proof}
First suppose that there is a standard model of $A[E]$ of cardinality $\kappa$ where the abstraction operator is surjective. Then surjectivity implies that $\kappa= \left|\nicefrac{P(\kappa)}{E}\right|$. Then as in the proof of the Proposition~\ref{prop:stabileforcc}, we may argue that $\kappa= \left|\nicefrac{P(\kappa)}{E}\right|\leq \left|\nicefrac{P(\kappa)}{E_0}\right| \leq \kappa$, so that in fact we have an equality. Since $\kappa$ is infinite, one further has that $\left|\nicefrac{P(\kappa)}{E_0}\right|=\left|\nicefrac{P(\kappa)}{\approx}\right|$. But trivially one has that $\left|\nicefrac{P(\kappa)}{\approx}\right|=\left|\{\lambda: \lambda<\kappa\}\right|$. For the converse, suppose that $\left|\nicefrac{P(\kappa)}{E}\right|=\left|\{\lambda: \lambda<\kappa\}\right| = \kappa$, so that trivially $\left|\nicefrac{P(\kappa)}{E}\right|= \kappa$. Then the model construction from the previous proposition yields a model of $A[E]$ in which the abstraction operator is surjective.
\end{proof}
\section{Antonelli and Fine on Logicality and Invariance}\label{sec05:aldo}
The famous Tarski-Sher thesis on logicality (\cite{Tarski1986aa}, \cite{Sher1991aa}) suggests that logical notions are those that are invariant under all permutations of the domain. This can be made precise as follows. If~$\pi:M\rightarrow M$ is a permutation, then~$\pi$ induces permutations~$\overline{\pi}:M^n\rightarrow M^n$ and~$\overline{\pi}:P(M)\rightarrow P(M)$. By iterating, a permutation~$\pi: M\rightarrow M$ induces a permutation of any sort of~$\omega$-th order higher-order structure with first-order domain~$M$. Then one says:
\begin{myenumerate}
\item A subset~$X$ of any sort of this structure is \emph{permutation-invariant} if~$\overline{\pi}(X)=X$ holds for all permutations~$\pi:M\rightarrow M$.\label{eqn:defn:permTS}
\end{myenumerate}
So part of what we want to do in this section is to carefully distinguish this notion coming from Tarski-Sher from our notion of permutation invariance for abstraction principles~(\ref{eqn:defn:piI}). To illustrate the Tarski-Sher notion, consider~$X=\{(A,B,C)\in (P(M))^3: A\cap B=C\}$. Then for any permutation~$\pi:M\rightarrow M$, we have
\begin{myequation}
A\cap B=C \Longleftrightarrow \overline{\pi}(A\cap B)=\overline{\pi}(C) \Longleftrightarrow \overline{\pi}(A)\cap \overline{\pi}(B)=\overline{\pi}(C)
\end{myequation}
So intersection comes out logical in this sense, and similarly for all the other boolean operations.
Antonelli (\cite{Antonelli2010aa}) distinguishes several ways that abstraction principles and their associated equivalence relations can be invariant. One way is in terms of the abstraction operator itself. Since the abstraction operator is a function from concepts to objects, its graph is a certain collection of ordered pairs of concepts and objects. Hence an abstraction principle will be logical in the sense of Tarski-Sher just if this collection of ordered pairs is closed under the taking of permutations. This of course happens if and only if $\partial(X)=a$ implies $\partial(\overline{\pi}(X))=\pi(a)$ and vice-versa for all permutations $\pi:V\rightarrow V$. And this is equivalent to the requirement that $\partial(\overline{\pi}(X))=\pi(\partial(X))$ for all permutations $\pi:V\rightarrow V$. Antonelli calls abstraction principles which satisfy this condition \emph{objectually invariant} (\cite{Antonelli2010aa} p. 286). However, objectually invariant abstraction operators are rare. For instance, Hume's Principle is not objectually invariant, nor is the Bicardinality Principle. Hence, if one insisted upon the logicality of abstraction \emph{operators} in the sense of Tarski-Sher, then as Antonelli notes this would rule out most interesting examples (cf. \cite{Antonelli2010aa} p. 286).
The notion which we are calling permutation invariance~(\ref{eqn:defn:piI}) is called \emph{simple invariance} by Antonelli (\cite{Antonelli2010aa} p. 286). This notion was studied earlier in Burgess' discussion of Fine's work on abstraction principles (\cite{Burgess2005} p. 171). However, the notion which Fine himself was primarily interested in was the permutation invariance of the equivalence relation itself (cf. \cite{Fine2002} p. 111):
\begin{myequation}\label{eqn:finevinara}
\forall \; \mbox{ bijection } \pi:V\hspace{-1mm}\rightarrow\hspace{-1mm}V \; (E(X,Y)\rightarrow E(\pi(\overline{X}), \pi(\overline{Y}))
\end{myequation}
This of course is just the logicality of the equivalence relation~$E$ in the sense of Tarski-Sher. However, Fine rather motivates this constraint on equivalence relations by reference to Frege's ideas about the generality of logic (\cite{Fine2002} p. 109, cf. \cite{MacFarlane2002aa} p. 34), and does not at all invoke the Tarski-Sher thesis. But whatever its motivation, all the equivalence relations $E$ studied here will satisfy this constraint since they are assumed to be formulas in the background signature $L_0$ (cf. Definition~\ref{defn:L000}), and so will all be invariant under permutations in the sense of~(\ref{eqn:finevinara}).
Antonelli's work on abstraction principles and notions of permutation invariance (\cite{Antonelli2010aa}) complements his work on abstraction principles and generalized quantifiers (\cite{Antonelli2010ac,Antonelli2010ab}). In this work, the idea was to think about the equivalence relations featuring in abstraction principles as examples of generalized quantifiers. For instance, the truth-condition of the sentence ``Just as many students [A] as teachers [B] are hockey fans [C],'' is given by the generalized quantifier $Q(A,B,C)\equiv \left|A\cap C\right|=\left|B\cap C\right|$. So one could then view Hume's Principle as yielding a way to provide generalized quantifiers with first-order truth-conditions. The connection to permutation invariance in the sense of (\ref{eqn:defn:permTS}) and (\ref{eqn:finevinara}) is that this is one condition among many that have been developed for assaying which generalized quantifiers actually occur in natural language (cf. \cite{Peters2008aa} pp. 157, 330, \cite{Keenan1985aa} p. 77).
However, neither Antonelli nor Burgess is committed to there being any positive reason for insisting on the constraint of permutation invariance in the sense of~(\ref{eqn:defn:piI}). It clearly does not follow from the Tarski-Sher logicality constraint on the abstraction operator or on the underlying equivalence relation. Further, it's not obviously required by the generality of logic since there are many equivalence relations which are expressible purely in the language~$L_0$ of our background second-order logic which are not permutation invariant in the sense of~(\ref{eqn:defn:piI}). However, our Theorem~\ref{thm:coverthm} suggests an instrumental reason to be interested in equivalence relations which are permutation invariant in the sense of~(\ref{eqn:defn:piI}). For, it indicates that its a necessary and sufficient condition for a type of relative categoricity. So if one was interested in determinacy of truth-value in the sense of natural relative categoricity, this result would give one a reason to be interested in permutation invariance in the sense of~(\ref{eqn:defn:piI}).
Fine was himself interested in determinacy and established several categoricity results. His first result concerns what we called cardinality coarsening~(\ref{eqn:RC3xsemi}), a notion which Fine calls \emph{numericality} (\cite{Fine2002} p. 126). This first categoricity theorem of Fine's can be stated in our terminology as follows:
\begin{thm}\label{thm:finethm} (\cite{Fine2002} p. 126) Suppose that $\mathcal{M}$ is a model of $A^2[E]$ as in equation~(\ref{eqn:1}) where $E$ is cardinality coarsening, and suppose that $\mathcal{M}$ models $\left|M\setminus \mathrm{rng}(\partial_1)\right|=\left|M\setminus \mathrm{rng}(\partial_2)\right|$. For each $i\in \{1,2\}$, consider the following induced models
\begin{myequation}\label{eqn:fineinduced}
\mathcal{N}_i=(M, S_1[M], S_2[M], \ldots, \partial_i)
\end{myequation}
Then $\mathcal{N}_1$ is isomorphic to $\mathcal{N}_2$.
\end{thm}
\noindent This theorem of Fine's occurs far within his book \cite{Fine2002} which treats a great variety of topics and issues. In our view, this result deserves to be better known-- for instance, it is not discussed in the \emph{Philosophical Studies} book symposium on Fine's book (cf. \cite{Fine2005ac}), nor is it treated in Burgess' discussion of Fine (\cite{Burgess2005} Chapter~3). For this reason and for the sake of completeness, let us record its proof:
\begin{proof}
By the hypothesis, there is a bijection from $M\setminus \mathrm{rng}(\partial_1)$ to $M\setminus \mathrm{rng}(\partial_2)$. But the natural bijection $\Gamma$ is a bijection from $\mathrm{rng}(\partial_1)$ to $\mathrm{rng}(\partial_2)$. By joining these two bijections, we may obtain a bijection~$\Delta:M\rightarrow M$ such that $\Delta \upharpoonright \mathrm{rng}(\partial_1)$ is the natural bijection~$\Gamma:\mathrm{rng}(\partial_1)\rightarrow \mathrm{rng}(\partial_2)$. Extend to~$\overline{\Delta}:\mathcal{N}_1\rightarrow \mathcal{N}_2$ by setting~$\overline{\Delta}(X)=\{\Delta(x): x\in X\}$. Then we claim that~$\overline{\Delta}:\mathcal{N}_1\rightarrow \mathcal{N}_2$ is an isomorphism. Let~$X\in S_1[M]$. We must show that $\overline{\Delta}(\partial_1(X)) = \partial_2(\overline{\Delta}(X))$.
Since~$\Delta$ extends the natural bijection, this is equivalent to $ \partial_2(X) = \partial_2(\overline{\Delta}(X))$.
And since~$\mathcal{M}\models A^2[E]$, this is equivalent to~$E(X, \overline{\Delta}(X))$. But since~$E$ is cardinality coarsening, of course $E(X, \overline{\Delta}(X))$ follows from~$\overline{\Delta}(X)\approx X$.
\end{proof}
Some special cases of Fine's Theorem can be viewed as a combination of certain parts of our results. For instance, if $E$ is cardinality coarsening, then $E$ is bicardinality coarsening (cf. Figure~\ref{diagram1}) and hence $A[E]$ is surjectively relatively categorical by one direction of Theorem~\ref{thm:coverthm}. This same result follows from the special case of Fine's theorem wherein one assumes that $M\setminus \mathrm{rng}(\partial_1)$ and $M\setminus \mathrm{rng}(\partial_2)$ are both empty. However, nothing in Fine's Theorem concerns the other direction of our results, namely that certain conditions like cardinality coarsening on small concepts and bicardinality coarsening are necessary for various forms of relative categoricity. Another difference between our work and Fine's work is with the precise induced models which figure in the statement of the results. In particular, the induced structures~$\mathcal{N}_i$ in (\ref{eqn:fineinduced}) are different from the induced structures~$\mathcal{M}_i$ from (\ref{eqn:induced}) with which we have been working in that the structures~$\mathcal{M}_i$ restrict their first-order domain down to the range of the abstraction operator~$\partial_i$. Of course, these two types of induced models will align in the case where the abstraction operators are surjective. So while Fine's theorem predicts that Hume's Principle is, in our terminology, surjectively relatively categorical, it does not obviously have any implications for the natural relative categoricity of Hume's Principle.
Fine's second categoricity theorem concerns a general theory of abstraction which he terms~${\tt GA}^{+}$. Roughly, this theory is the amalgamation of abstraction principles $A[E]$ which satisfy a combination of Tarski-Sher permutation invariance conditions~(\ref{eqn:defn:permTS}) and varieties of stability-like conditions as discussed in \S\ref{sec05stable}. For the sake of simplicity, let's consider the case of a single such abstraction principle~$A[E]$. Fine's second theorem then indicates that any model $\mathcal{M}$ of $A^2[E]$ which satisfies the constraint that $M\setminus \mathrm{rng}(\partial_1)$ and $M\setminus \mathrm{rng}(\partial_2)$ have the same cardinality will be such that the induced structures $\mathcal{N}_i$ in (\ref{eqn:fineinduced}) are isomorphic. The official statement of Fine's second theorem is more complicated since one must precisely define the analogue $A^2[E_1, E_2, \ldots]$ of $A^2[E]$ in the case where abstraction principles associated to $E_1, E_2, \ldots$ are present. See Fine~\cite{Fine2002} p.~189 for the precise statement of this result, and see Fine~\cite{Fine2002} p.~170 for the precise statement of the theory~${\tt GA}^{+}$.
In the subsequent section of his book (\cite{Fine2002} pp.~189~ff), Fine proceeds to examine the interpretability strength of~${\tt GA}^{+}$ and related theories. It is in the context of surveying these results (cf. \cite{Burgess2005} p. 171) that Burgess introduces the notion what we have called permutation invariance~(\ref{eqn:defn:piI}), which does not occur in Fine's own work. In particular, Burgess introduces a theory (cf. \cite{Burgess2005} p. 173) in which one assumes that the equivalence relations~$E$ are permutation invariant in our sense~(\ref{eqn:defn:piI}) and further that there are at most two equivalence classes:
\begin{myequation}
\exists \; X,Y \; \forall \; Z \; (E(Z,X) \vee E(Z,Y))
\end{myequation}
This last condition is less restrictive than one might initially expect, since Burgess is working in a setting where one can consider equivalence relations not only on second-order objects, but on third order-objects, fourth-order objects, etc. However, Burgess uses this theory merely to motivate elements of Fine's theory, so that neither Fine nor Burgess suggest restricting attention to theories which satisfy these specific conditions.
As to its broader philosophical significance, Fine notes that one path to determinacy of truth-value would proceed through categoricity results like Theorem~\ref{thm:finethm}. For instance, discussing the specialization of this result to the ``number~of'' abstraction operator, Fine writes: ``Thus once we know the cardinality of the non-numbers, we are in a position to specify the truth of every arithmetical statement in purely logical terms'' (\cite{Fine2002} p. 86, cf. p. 93). But ultimately Fine rejected this path to determinacy of truth-value, due to concerns about one's access to claims about the cardinality of parts of the domain. He writes: ``The difficulty with this approach is to see how someone could grasp what these truth-conditions are without already having access to an infinite domain of abstract objects'' (\cite{Fine2002} p. 94). This was one reason among many that led Fine to develop an alternative approach on which one postulates ``a procedure for the construction of the domain'' (\cite{Fine2006ab} p. 90). This ``procedural postulationism'' is designed to secure not only determinacy of truth-value but also determinacy of reference (\cite{Fine2006ab} p. 89, \cite{Fine2002} p. 100). While this is no place to discuss Fine's later procedural postulationism, it's worth underscoring that the specific worry which Fine cites with respect to categoricity results does not seem so damaging to one who would insist on the requirement of natural relative categoricity. For, unlike the hypotheses of Fine's Theorem (Theorem~\ref{thm:finethm}), there are no assumptions in natural relative categoricity about the cardinality of the non-abstracts.
However, Fine's concern might worry someone who insisted on the requirement of surjective relative categoricity as it is unclear
how someone could have advance assurance that every object is an abstract
\section{Hodes and Supervaluationism}\label{sec05:hodes}
The work of Hodes (\cite{Hodes1984}, \cite{Hodes1990aa}, \cite{Hodes1991}) constitutes a sustained attempt to forge techniques and ideas from Frege's \emph{Grundlagen} into a viable version of fictionalism. Hodes writes: ``[\ldots] mathematical discourse, when carried on within the mathematical object-picture, [is] a special sort of fictional discourse: numbers are fictions `created' with a special purpose, to encode numerical object-quantifiers and thereby enable us to `pull down' a fragment of third-order logic, dressing it in first-order clothing'' ( \cite{Hodes1984} p. 144). Hodes differs from other fictionalists in his invocation of supervaluationist semantics, by which Hodes can say with fictionalists that mathematical language doesn't refer, but also affirm that certain sentences containing mathematical vocabulary are true in a very demanding sense.
One can implement Hodes-style supervaluationism with respect to an arbitrary equivalence relation. Hodes does this only with respect to equivalence relations associated to cardinality and sets, in \cite{Hodes1990aa} and \cite{Hodes1991} respectively. But it seems to us that the definitions offered in \cite{Hodes1990aa} pp.~364-365, \cite{Hodes1991} p.~158 naturally generalize as follows:
\begin{defn}\label{defn:bivalence}
Suppose that $E(X,Y)$ is an $L_0$-formula and $\kappa$ is a cardinal, and suppose further that $\varphi$ is an $L_0[\partial]$-sentence. Then $\varphi$ is said to be \emph{${\kappa}$-supertrue relative to $A[E]$} (resp. \emph{${\kappa}$-superfalse relative to $A[E]$}) if for all standard models $\mathcal{M}$ of $A[E]$ of cardinality $\kappa$, it is also the case that $\mathcal{M}\models \varphi$ (resp. $\mathcal{M}\models \neg \varphi$). Further, $\varphi$ is said to be \emph{$\kappa$-bivalent relative to $A[E]$} if $\varphi$ is $\kappa$-supertrue or $\kappa$-superfalse.
\end{defn}
\noindent In this definition, we are, as in the previous sections, identifying the cardinality of the model $\mathcal{M}$ of $A[E]$ with the cardinality of its first-order part.
As this definition makes clear, Hodes' approach was focused on the standard semantics for second-order logic. Moreover, there's a reason for this: if one instead used the Henkin semantics, then the analogue of supertruth would reduce to provability, at least in the case where $A[E]$ has only infinite models. This is the content of the following elementary proposition, whose proof we omit since it is a simple application of the L\"owenheim-Skolem theorems.
\begin{prop}
Suppose that $E(X,Y)$ is an $L_0$-formula and $A[E]$ is consistent but has only infinite models. Suppose further that $\varphi$ is an $L_0[\partial]$-sentence and $\kappa$ is an infinite cardinal. If all models $\mathcal{M}$ of $A[E]$ of cardinality $\kappa$ satisfy $\varphi$, then $A[E]$ proves $\varphi$.
\end{prop}
\noindent So this proposition indicates that something is gained by Hodes' invocation of standard models, namely, the idea of supertruth does not reduce to that of deduction.
Hodes' fictionalism suggests the idea of maximizing bivalence, and so Hodes himself established various results indicating that ``[\ldots] our actual mathematical reasoning makes no use of sentences parsed by non-bivalent sentences [\ldots]'' (\cite{Hodes1990aa} p. 370, cf. Observations 4-5 pp. 367-368). With an eye towards maximizing bivalence, we introduce the following definition of bivalence-compatibility:
\begin{defn}\label{defn:bivalenceompat}
The abstraction principle $A[E]$ is \emph{bivalence-compatible} if there is an infinite cardinal $\kappa$ such that $\varphi$ is $\kappa$-bivalent relative to $A[E]$ for each $L_0[\partial]$-sentence $\varphi$.
\end{defn}
\noindent There might be other ways of maximizing bivalence, but this at least seems like a natural enough route: the idea is that there's some size such that all standard models of that size must agree on the truth-value of sentences expressible using the abstraction operator.
It's then natural to ask which abstraction principles are bivalence compatible. By using Fine's Theorem~\ref{thm:finethm} and the Coarsening Dichotomy (Lemma~\ref{lem:dichtomylem}), one can easily show:
\begin{prop}\label{prop:iamaprop}
If~$E$ is cardinality coarsening then~$A[E]$ is bivalence compatible, and indeed $A[E]$ is $\omega_1$-bivalent.
\end{prop}
\begin{proof}
Letting $\kappa=\omega_1$, let's note that the Coarsening Dichotomy Lemma implies that $\left|\nicefrac{P(\kappa)}{E}\right|<\kappa$. Since $\left|\nicefrac{P(\kappa)}{E}\right|<\kappa$, it follows that for any model $\mathcal{M}$ of $A^2[E]$~(\ref{eqn:AE2}) with cardinality $\kappa$, we have that $\left|\mathrm{rng}(\partial_i)\right|<\kappa$. By Infinite Sums are Maxs~(\ref{eqn:InfSumMax}), we have that $\left|M\setminus \mathrm{rng}(\partial_1)\right|=\kappa=\left|M\setminus \mathrm{rng}(\partial_2)\right|$. Then by Fine's Theorem~\ref{thm:finethm}, we have $\mathcal{N}_1$ and $\mathcal{N}_2$ as defined in equation~(\ref{eqn:fineinduced}) are isomorphic. So for any sentence $\varphi$ of $L_0[\partial]$, we have that $\mathcal{N}_1\models \varphi$ iff $\mathcal{N}_2\models \varphi$.
\end{proof}
The situation with respect to bicardinality coarsening and cardinality coarsening on small concepts is slightly more subtle. As for bicardinality coarsening, since it was introduced in connection with surjective relative categoricity, it's natural to modify the definition of $\kappa$-bivalence (Definition~\ref{defn:bivalence}) so that attention is restricted to models of $A[E]$ where the abstraction operator is surjective. Now it's not necessarily the case that every bicardinality coarsening equivalence relation will have such a model for a given $\kappa$. For instance, the Bicardinality Principle from \S\ref{sec04} won't have such a model for $\kappa=\omega_1$, as one can easily check by reference to Proposition~\ref{prop:existencesurject}. However, for those cardinals $\kappa$ for which there are such models, Theorem~\ref{thm:coverthm} trivially implies that bicardinality coarsening suffices for $\kappa$-bivalence in the modified sense, since again isomorphism suffices for elementary equivalence.
As for cardinality coarsening on small concepts, it is simply unknown to us whether this implies bivalence compatibility. So we record the following question:
\begin{Q}\label{eqn:Q2}
Suppose that $E(X,Y)$ is an $L_0$-formula which is provably an equivalence relation in our background second-order logic and which is cardinality coarsening on small concepts. Is it necessarily the case that $A[E]$ is bivalence compatible?
\end{Q}
\noindent If this question is answered in the negative, then it would indicate that the way in which natural relative categoricity captures the idea of determinacy of truth-value is distinct from the way in which Hodes' supervaluationism captures this idea. Of course, these two notions are extensionally distinct since an equivalence relation can be bivalence compatible simply by mimicking Hume's Principle on domains of cardinality $\omega_1$ and appealing to Proposition~\ref{prop:iamaprop}, while violating cardinality coarsening on small concepts on domains of other sizes. So the interesting direction is that which is at issue in the above question, since a negative answer would indicate that these two determinacy of truth-value ideas studied in our work and Hodes work are orthogonal to one another.
\section{Conclusions}\label{sec07}
Our goal has been to articulate various notions of relative categoricity for abstraction principles and to study which abstraction principles are accordingly relative categorical. The import of our Theorem~\ref{thm:ncr=iia=cca} and Theorem~\ref{thm:coverthm} is that such relatively categorical abstraction principles qualitatively look like Hume's Principle. Our results contravene the general experience we have with relative categoricity. For, this notion is highly non-domain-specific in that one has relatively categorical axiomatizations of number, set, the reals, etc. But when we restrict attention down to abstraction principles, our Theorem~\ref{thm:ncr=iia=cca} and Theorem~\ref{thm:coverthm} show that relative categoricity is tied to cardinality coarsening notions.
Finally, it's worth emphasizing the limited scope of our study. First, we have focused exclusively on abstraction principles formed from equivalence relations on unary concepts, and many natural abstraction principles like that associated to the Burali-Forti paradox concern abstraction principles on binary concepts. Antonelli (\cite{Antonelli2010ac} pp. 10-11) notes that the equivalence relation associated to the Burali-Forti paradox is permutation invariant in the sense of~(\ref{eqn:defn:piI}) once one extends this notion naturally from equivalence relations on unary concepts to binary concepts, and similarly it will be injection invariant. So this indicates that the study of relative categoricity concepts will be quite different when one goes from equivalence relations on unary concepts to those on binary concepts. For instance, this example indicates that in this more general setting we can't have that injection invariance suffices for having standard models of infinite cardinality (cf. Proposition~\ref{prop:stabileforcc}). So it's hard to predict \emph{apriori} how much of the present study holds when we pass from equivalence relations on unary concepts to those on binary concepts or $n$-ary concepts.
A similar limitation that should be emphasized is that we have focused on some specific notions of relative categoricity, namely natural relative categoricity and surjective relative categoricity. It would of course be ideal to have analogues of Theorem~\ref{thm:ncr=iia=cca} and Theorem~\ref{thm:coverthm} for the notion of relative elementary equivalence and bivalence compatibility (Definition~\ref{eqn:nateleequiv} and Definition~\ref{defn:bivalenceompat}), but we have been unable to obtain any such characterizations. Further, as indicated in Question~\ref{eqn:Q1} and Question~\ref{eqn:Q2}, even the relationships between these notions and our notions is not yet resolved. As a final note, it should be underscored that natural relative categoricity concerns a specific bijection (namely, the natural bijection) being an isomorphism. In Corollary~\ref{cor:whenarbirisnat}, we noted that this is the only isomorphism when natural relative categoricity does obtain. But it would be important to study the more general notion of relative categoricity which did not restrict attention to the natural bijection. We have been unable to establish analogues of Theorem~\ref{thm:ncr=iia=cca} and Theorem~\ref{thm:coverthm} for this more general notion. Our motivation for considering the natural bijection $\Gamma(\partial_1(X))=\partial_2(X)$ is that this seemed like a natural enough way for agents to exchange information about their abstraction operators, broadly similar in character to Parsons' agents translating their interlocutor's arithmetical vocabulary by their own arithmetical vocabulary.
\section*{Acknowledgments}
Parts of this material were presented on March 27, 2012 at the workshop on the Mathematics of Abstraction at Birkbeck, University of London; at May 23, 2014 at the workshop Abstraction: Philosophy and Mathematics at the University of Oslo; and on January 7, 2015 at the logic seminar in the department of Logic and Philosophy of Science at the University of California, Irvine. Thanks to the organizers and participants of these events and seminars, as well as to the many others who provided valuable feedback on this work. In particular, thanks to: Aldo Antonelli, Kyle Banick, Roy Cook, Samuel Eklund, Salvatore Florio, J.~Ethan Galebach, Jeremy Heis, Graham Leach-Krouse, Greg Lauro, Sarah Lawsky, {\O}ystein Linnebo, Richard Mendelsohn, Christopher Mitsch, Alexander C.~R. Oldemeier, Markus Pantsar, Jonathan Payne, Terence Parsons, Agust\'in Rayo, Sam Roberts, Marian Rogers, J.~Schatz, Gabriel Uzquiano, and Kai Wehmeier. Thanks also to the anonymous referees for many helpful comments. Walsh would also like to acknowledge the support of {\O}ystein Linnebo's European Research Council-funded project ``Plurals, Predicates, and Paradox'' and a Kurt G\"odel Research Prize Fellowship.
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\section{Introduction}
Glassy polymeric fluids have complicated shear-dependent dynamic rheology.
In steady shear flows, glassy fluids are highly viscous, and shear thinning occurs at sufficiently large shear rates due to chain elongations.\cite{book:92M, book:96S}
In unsteady flows, glassy fluids exhibit elastic behaviors if the characteristic time scale of polymer dynamics is comparable to or larger than that in the flow system.
The viscoelastic property can be measured by the shear moduli, i.e., the storage modulus $G'$ for the elasticity and the loss modulus $G''$ for the viscosity.
The shear moduli can be measured under uniform oscillatory shear flow with a finite shear strain, both experimentally or numerically.
In general non-uniform flows, however, the local rheological properties become heterogeneous depending on the local flow variables.
Thus, the rheological behaviors of glassy polymeric fluids in highly non-uniform flows are so complicated that the theoretical or experimental approaches to this problem are very difficult.
It is also difficult to predict the flow behaviors of such fluids because the reliable constitutive equations are not known in general, although there is an important accumulation of both experimental and theoretical works to construct them.\cite{book:87BAH,book:88L}
In the present paper, we investigate the dynamic rheology of a model polymer melt composed of short chains between rapidly oscillating plates by using the hybrid simulation of molecular dynamics (MD) and computational fluid dynamics (CFD).
The temperature of the melt is so low that the glassy behavior is observed in the stress relaxation function in the quiescent state.
Non-uniform oscillatory shear flows are generated over the oscillating plate at sufficiently large oscillation frequencies due to inertia of the fluid via the term $\rho\partial {\bm v}/\partial t$, which is sometimes called the transient force.
Thus, heterogeneous rheological behaviors arise according to local flow variables.
Oscillatory shear flows under the transient force for the viscoelastic fluid have been investigated by several researchers so far.
Scharg analytically solved the flows of a linear viscoelastic fluid\cite{art:77S}. Dunwoody investigated the inertia effect for a weak non-linear viscoelastic fluid with the K-BKZ model by using a perturbation analysis\cite{art:96D}. Yosick {\it et al}. performed
numerical analysis for a non-linear viscoelastic fluid with the Berkeley model.
Ding {\it et al}. investigated the viscous dissipation under the transient force in the temperature field for linear viscoelastic fluids\cite{art:99DGBK}.
In previous works, some constitutive model equations have been used to calculate flow profiles.
In the present hybrid simulation, no constitutive model is required to obtain a local stress.
The local stress is generated by a local MD simulation according to the local flow variables.
In the hybrid simulation method, the macroscopic flows of the melt are calculated by using the CFD scheme; however, instead of using any constitutive equations, the local stresses of the melt are calculated by using molecular dynamic simulations of polymer chains according to the local strain rates.\cite{art:08YY, art:09YY, art:10YY}
The basic idea of the present hybrid simulation method was first proposed by E and Engquist\cite{art:03EE, art:07EELRV}, where the heterogeneous multiscale method (HMM) is presented as a general methodology for the efficient numerical computation of problems with multiscale characteristics.
The HMM has also been applied to the simulation of complex fluids.\cite{art:05RE}
Equation-free multiscale computation was also proposed by Kevrekidis {\it et al}. on the basis of a similar idea and has been applied to various problems.\cite{art:03KGHKRT, art:09KS}
De {\it et al}. have developed a hybrid method, called the scale bridging method, which can correctly reproduce the memory effect of a polymeric liquid and demonstrated non-linear viscoelastic behavior of a polymeric liquid between oscillating plates.\cite{art:06DFSKK}
The multiscale simulation based on a similar idea has been also applied to rarefied gas flows, recently.\cite{art:10KOK}
In what follows, we characterize the linear dynamic rheology of a model polymer melt by using the MD simulation in Sec. II.
Then, we investigate the dynamic rheology of the melt in non-uniform oscillatory shear flows under the transient force between rapidly oscillating plates in Sec. III, where the simulation method, velocity profiles, shear moduli, and LAOS analysis are introduced.
Finally, we summarize the results in Sec. IV.
\section{Linear dynamic rheology of a model polymer melt}
We consider a model polymer melt composed of short chains with ten beads of a uniform density $\rho_0$ and a uniform temperature $T_0$.
The number of bead particles on each chain is represented by $N_{\rm b}$.
Thus, $N_{\rm b}=10$.
All of the bead particles interact with a truncated Lennard-Jones potential defined by\cite{art:90KG},
\begin{equation}\label{eq1}
U_{\rm LJ}(r)=
\left\{
\begin{array}{c c}
4\epsilon\left[
({\sigma}/{r})^{12}
-({\sigma}/{r})^{6}
\right]
+\epsilon & (r\le 2^{1/6}\sigma),\\
0 & ( r> 2^{1/6}\sigma).
\end{array}
\right .
\end{equation}
By using only the repulsive part of the Lennard-Jones potential, we may prevent spatial overlap of the particles.
Consecutive beads on each chain are connected by an anharmonic spring potential,
\begin{equation}\label{eq2}
U_{\rm F}(r)=-\frac{1}{2}k_c R_0^2 \ln
\left[
1-({r}/{R_0})^2
\right],
\end{equation}
where $k_c$=30$\epsilon/\sigma^2$ and $R_0$=$1.5\sigma$.
The temperature of the melt is $k_B T_0/\epsilon$=0.2, where $k_B$ is the Boltzmann constant.
The number density of the bead particles is $\rho_0/m$=1/$\sigma^3$, where $m$ is the mass of the bead particle.
With this number density and temperature, the configuration of the bead particles becomes severely jammed, resulting in a complicated non-Newtonian viscosity and long-time relaxation phenomena characteristic of glassy polymers.\cite{book:92M, art:02YO}
Hereafter, unless otherwise stated, we measure the physical quantities with units of length $\sigma$, time $\sqrt{m\sigma^2/\epsilon}$, and temperature $\epsilon/k_B$.
In this section, we clarify the linear viscoelastic properties of the model polymer melt.
Figure \ref{fig_geq} shows the stress relaxation function $G(t)$ in the quiescent state.
The stress relaxation function $G(t)$ of the model polymer melt was obtained in Ref. \onlinecite{art:02YO} (although we recomputed $G(t)$ in the present study in order to calculate the accurate linear complex moduli as seen below).
The details of the molecular dynamic simulation can be found in Ref. \onlinecite{art:02YO}.
The stress relaxation function $G(t)$ is calculated as
\begin{equation}\label{eq_gt}
G(t)=<\Pi_{xy}(t+t_0)\Pi_{xy}(t_0)>/k_B T V,
\end{equation}
where $\Pi_{xy}$ is the space integral of the microscopic stress tensor in the volume $V$.
In the figure, the $\alpha$ relaxation time $\tau_\alpha$ and the Rouse relaxation time $\tau_R$ in the quiescent state, where $\tau_\alpha$=310 and $\tau_R$=$6\times 10^4$, are also plotted.
The $\alpha$ relaxation time $\tau_\alpha$ represents the characteristic time of the structural relaxation of bead particles and is calculated from the van Hove self-correlation function, and the Rouse relaxation time $\tau_R$ represents the characteristic time of the conformational relaxation of polymer chains and is calculated from the time-correlation function of the end-to-end vector of each polymer chain.
After the early oscillating behavior for $t \lesssim 10$, which corresponds to the vibrations of the bonds of bead particles on each chain, $G(t)$ exhibits the stretched exponential relaxation of the Kohlrausch-Williams-Watts (KWW) form $G_s(t)$,
\begin{equation}\label{eq_gs}
G_s(t)=G_0\exp[-(t/\tau_s)^c].
\end{equation}
$G(t)$ can be nicely fitted to Eq. (\ref{eq_gs}) with $G_0$=5, $c$=0.5, and $\tau_s=90$ ($\simeq 0.33\tau_\alpha$) for 1$\lesssim t \lesssim 10^3$.
Ultimately, $G(t)$ follows the Rouse dynamics characterized by the Rouse relaxation time $\tau_R$.
The Rouse relaxation function $G_R(t)$ is written as
\begin{equation}\label{eq_gr}
G_R(t)=\frac{\rho_0 T}{N_{\rm b}}\sum_{p=1}^{N_{\rm b}-1}\exp(-2t/\tau_p),
\end{equation}
where $\tau_p/\tau_R=\sin^2(\pi/2N_{\rm b})/\sin^2(\pi p/2N_{\rm b})$ for $p=1,\cdots,N_{\rm b}$.
Thus, in the quiescent state, the stress relaxation function $G(t)$ can be approximately described by the sum of the stretched relaxation function $G_s$ in Eq. (\ref{eq_gs}) and the Rouse relaxation function $G_R(t)$ in Eq. (\ref{eq_gr}), i.e., $G(t)\simeq G_s(t) + G_R(t)$, except the period of initial oscillating modes, and decreases so rapidly that it becomes negligible in the late stage, while $G_R(t)$ is so small as to be negligible in the early stage but can describe the late stage of $G(t)$.
The frequency-dependent shear moduli, i.e., the storage modulus $G'(\omega)$ and the loss modulus $G''(\omega)$, in the linear response regime are obtained by the Fourier transform of the stress relaxation function $G(t)$ in the quiescent state as
\begin{subequations}\label{eq8}
\begin{align}
G'(\omega)&=\omega\int_0^\infty G(t) \sin\omega t \,dt,
\\
G''(\omega)&=\omega\int_0^\infty G(t) \cos\omega t \,dt.
\end{align}
\end{subequations}
$G'(\omega)$ and $G''(\omega)$ represent the elasticity and viscosity of the melt, respectively.
Figure \ref{fig_gpgpp} shows the linear storage modulus $G'(\omega)$ and loss modulus $G''(\omega)$ versus the frequency $\omega$.
The crossover of $G'(\omega)$ and $G''(\omega)$ is observed at $\omega\simeq\tau_\alpha^{-1}$.
The model polymer melt is rather elastic ($ G' > G''$) for $\omega > \tau_\alpha^{-1}$, while it is rather viscous ($G''>G'$) for $\omega< \tau_\alpha^{-1}$.
At the low frequency, i.e., $\omega \lesssim \tau_R^{-1}$, the loss modulus $G''$ is quite dominant and almost proportional to $\omega$.
This indicates that, as the frequency $\omega$ is smaller than $\tau_R^{-1}$, the dynamic viscosity $\eta'$ defined as $\eta'=G''/\omega$ is approximately constant so as to be a simple viscous fluid with a constant viscosity $\eta'$.
The shear moduli calculated from the sum of the stretched exponential form $G_s(t)$ and the Rouse relaxation function $G_R(t)$ are also plotted in the figure.
It is seen that, in the linear response regime, the moduli of the model polymer melt can be well described by those calculated from the sum of $G_s(t)$ and $G_R(t)$, except for the high frequency regime as $\omega \gg \tau_\alpha^{-1}$, which corresponds to the oscillation mode of $G(t)$ in the early stage (See Fig. \ref{fig_geq}).
\section{The effect of inertia of the fluid}
\subsection{Problem and simulation method}
In the rapidly oscillating plates, the oscillatory shear flow becomes non-uniform due to inertia of the fluid via the term $\rho\partial v_x/\partial t$, say the transient force, such that the local rheological property spatially varies according to the local velocity field.
In this section, we investigate the dynamic rheology of the melt in the non-uniform oscillatory shear flow between rapidly oscillating plates (see Fig. \ref{pic_problem}(a)).
The upper- and lower- plate start to oscillate in the $x$-direction at a time $t$=0 as, respectively,
\begin{equation}\label{eq_vw}
v_w(t)=\mp \Gamma_0 H \omega_0 \cos(\omega_0 t),
\end{equation}
where $\Gamma_0$ is the amplitude of the strain of the system and $H$ is the half of width between the upper- and lower- plate.
We assume that the macroscopic quantities are uniform in the $x$- and $z$-directions, $\partial/\partial x$=$\partial/\partial z$=0.
The macroscopic velocity $v_\alpha$ is described by the following equations,
\begin{equation}\label{eq_mac}
\rho_0\frac{\partial v_x}{\partial t} =
\frac{\partial \sigma_{xy}}{\partial y},
\end{equation}
and $v_y$=$v_z$=0, where $t$ is the time and $\sigma_{xy}$ is the shear stress.
We also assume a non-slip boundary condition on each plate.
In the present study, we fix the width between the plates at $2H$=5000.
For the strain amplitude of the system $G_0$, $\Gamma_0$=0.5 is the value that is mainly utilized, while $G_0$=0.02 is a subsidiary used for the comparison.
However, the oscillation frequency of the plate $\omega_0$ is
widely varied in order to investigate the effect of the changing oscillation
frequency on the rheological property of the melt.
The oscillation frequencies $\omega_0$ used in the present simulations are shown by diamonds $\Diamond$ on the upper-axis around $\omega_0\sim\tau_\alpha^{-1}$ in Fig. \ref{fig_gpgpp}.
We solve this problem by using a hybrid simulation of the molecular dynamics (MD) and computational fluid dynamics (CFD).
The details of the method can be found in Ref. \onlinecite{art:10YY}.
Here, we briefly explain the hybrid simulation method.
We calculate the macroscopic velocity in Eq. (\ref{eq_mac}) by using a usual finite volume scheme with a uniform mesh system (see Fig. \ref{pic_problem}(b) ).
However, instead of using any constitutive equation for $\sigma_{xy}$, we calculate the local stresses in small MD cells associated with each mesh interval according to the local strain rates, which are calculated at the CFD level, at each time step of the CFD simulation.\cite{book:89AT, book:08EM}
The MD simulations are performed in each MD cell for the duration of the time-step size of the CFD calculation, and the molecular configurations obtained in each MD cell after one MD run are memorized as the initial configurations of molecules for the next MD run in each MD cell
(see Fig. \ref{pic_problem}(c) ).
By using this method, one can reproduce the memory effect caused by the slow dynamics of the molecular conformation correctly.
In the present study, we divide the lower half between the plates into 128 mesh intervals with a mesh size of $\Delta x$=19.5 and use the symmetric condition at the middle between the plates for the CFD calculation.
For the MD simulation, we use a cubic MD cell with a side length $l_{\rm MD}$=10 so that each MD cell contains 1000 bead particles.
The ratio of the mesh size of CFD $\Delta x$ to the side length of the MD cell $l_{\rm MD}$, which represents the efficiency of the hybrid simulation compared to the full MD simulation, is $\Delta x/l_{\rm MD}$=1.95.
The time-step size of the CFD calculation $\Delta t$ and that of the MD calculation$\Delta \tau$ are fixed at $\Delta t$=1 and $\Delta \tau$=0.001, respectively. Thus, one thousand time steps are carried out in each MD run at each time step of the CFD simulation ($M=1000$ in Fig. \ref{pic_problem} (c)).
\subsection{Velocity profile}
Figure \ref{fig_vx} (a) shows snapshots of the velocity profile of the melt for $\omega_0$=0.0015 and $\Gamma_0$=0.5.
Due to the transient force, the amplitude of the oscillatory velocity rapidly decreases with distance from the oscillating plate, and a thin boundary layer forms over the oscillating plate.
The thickness of the boundary layer $l_b$, which is defined as $v_x(y=l_b)/v_0=e^{-1}$, is also shown at different oscillation frequencies $\omega_0$ for $\Gamma_0$=0.02 and 0.5 in Fig. \ref{fig_vx} (b).
The solid line shows the thickness of the boundary layer for the linear viscoelastic fluid with a linear storage and loss modulus shown in Fig. \ref{fig_gpgpp}.
As is seen in Fig. \ref{fig_gpgpp}, at the low frequency (i.e., $\omega \lesssim \tau_R^{-1}$), the storage modulus $G'$ is much smaller than the loss modulus $G''$ and the dynamic viscosity $\eta'$, which is calculated as $G''/\omega$, becomes almost constant.
Thus, the slope of $\omega^{-1/2}$ for the Newtonian fluid arises at the low frequency in Fig. \ref{fig_vx} (b).
The thickness of the boundary layer of the present polymer melt is close to that of the linear viscoelastic fluid at low oscillation frequencies for the small strain amplitude of the system, $\Gamma_0=0.02$; however, as the oscillation frequency increases, the boundary layer of the melt becomes much thinner than that of the viscoelastic fluid.
The thickness of boundary layer for the large strain amplitude,
$\Gamma_0=0.5$, is thinner than that for the small strain amplitude,
$\Gamma_0=0.02$ at any of the oscillation frequencies.
These features are caused by the shear thinning of the melt because the local strain becomes larger near the oscillating plate as the oscillation frequency $\omega_0$ and
the strain amplitude of the system $\Gamma_0$ increase.
Due to the emergence of the boundary layer, the rheological properties of the melt become more complex in nature, as we see below.
\subsection{Storage and loss modulus}
In this subsection, we investigate the ``local'' rheological properties of the melt in the slab in terms of the storage modulus $G'$ and loss modulus $G''$.
The local moduli are calculated from the first harmonics of the Fourier series of the time evolutions of the local shear stress and strain.
By using the Fourier transform of the time evolution of the local strain $\gamma(y,t)$ and selecting the mode of the oscillation frequency of the plate $\omega_0$, we can approximate the time evolution of the local strain $\gamma$ in the form of $\gamma=\gamma_0(y)\cos(\omega_0t+\psi(y))$.
Here, $\gamma_0(y)$ is the strain amplitude, and $\psi(y)$ is the phase retardation.
In the same way, the local shear stress can also be written as
$\sigma_{xy}=\sigma'(y)\cos(\omega_0t+\psi)-\sigma''\sin(\omega_0t+\psi)$.
The local storage modulus and loss modulus are obtained as
$G'(y)=\sigma'(y)/\gamma_0(y)$ and $G''(y)=\sigma''(y)/\gamma_0(y)$, respectively.
We note that the contribution of the higher harmonics is also important
in the large amplitude oscillatory shear (LAOS) regime and is actually
detected in the present simulations.
However, the amplitude of the higher harmonics is smaller than that of the first harmonics; the fractional power spectrum of the higher harmonics of the local shear stress is at most 2.8\% in the present simulations.
Thus, the storage and loss modulus represent the basic viscoelastic properties of the melt in the slab.
(The non-linear effect of higher harmonics is investigated in the next subsection.)
In the present subsection, we fix the strain amplitude of the system as $\Gamma_0=0.5$ and change the oscillation frequency of the plate $\omega_0$ variously in order to investigate the dependency of the local rheological property on the oscillation frequency of the plate.
Figure \ref{fig_gpgpp_gmgmd_omw} shows the dependency of the storage and loss modulus on the oscillation frequency, $G'$ and $G''$ vs. $\omega_0$ and that of the strain and strain rate amplitudes on the oscillation frequency, $\gamma_0$ and $\dot\gamma_0$ vs. $\omega_0$, at a fixed position.
Figure \ref{fig_gpgpp_gmgmd_omw} (a) shows the storage and loss modulus versus oscillation frequency and the strain and strain rate amplitudes versus oscillation frequency at far distances from the plate and (b) those at the near distances from the plate.
It can be seen that, at the high oscillation frequency, say $\omega_0=0.01$, the storage modulus $G'$ is larger than the loss modulus $G''$ at large distances from the plate, e.g., $y=1309$ (Blue) and 771 (Green) in Fig. \ref{fig_gpgpp_gmgmd_omw} (a), while $G'$ is smaller than $G''$ as the distance decreases, e.g., $y=381$ (Red) in Fig. \ref{fig_gpgpp_gmgmd_omw} (a) and at smaller distances in Fig. \ref{fig_gpgpp_gmgmd_omw} (b).
In close vicinity to the plate, e.g., $y=10$ in Fig. \ref{fig_gpgpp_gmgmd_omw} (b), the viscosity is quite dominant, $G''\gg G'$.
Thus, the local rheological properties of the melt vary considerably according to the local flow fields such that three different rheological regimes, i.e., the viscous fluid regime, the liquid-like viscoelastic regime, and the solid-like viscoelastic regime, are formed over the rapidly oscillating plate.
On the contrary, at a low oscillation frequency, say $\omega_0=0.001$, the differences of the storage modulus $G'$ and loss modulus $G''$ are not as large as those at a high oscillation frequency at any distance, and the loss modulus $G''$ is larger than the storage modulus $G'$.
The differences of local modulus between the different distances are also not as large as those at a high oscillation frequency.
Thus, the local rheological properties of the melt vary moderately between the plates, and the melt has liquid-like viscoelastic behaviors throughout the slab.
At large distances from the plate [Fig. \ref{fig_gpgpp_gmgmd_omw} (a)], the local strain $\gamma_0$ monotonically decreases as the oscillation frequency $\omega_0$ increases because, as we have seen in Fig. \ref{fig_vx}, a thin boundary layer forms over the rapidly oscillating plate, and the thickness of the boundary layer becomes thinner as the oscillation frequency $\omega_0$ increases.
Thus, the local moduli deviate from the linear moduli more at the lower oscillation frequencies due to the shear thinning, while they are rather close to the linear values at the high oscillation frequencies.
The shear thinning behaviors of the local moduli to the local strain amplitude $\gamma_0$ are shown in Fig. \ref{fig_gpep_gm}.
It is seen that the storage modulus $G'$ decreases when the local strain $\gamma_0$ is larger than about 2\%, while the loss modulus $G''$ starts to decrease at a larger strain amplitude ($\gamma_0>2\%$).
The non-monotonic behavior of the loss modulus $G''$ on the strain amplitude
$\gamma_0$ is also observed at a high oscillation frequency [Fig. \ref{fig_gpep_gm} (c)]; the weak shear thickening occurs at a small strain amplitude $\gamma_0\lesssim 0.1$, and then, the shear thinning occurs at a large strain amplitude $\gamma_0>0.1$.
The storage modulus $G'$ decreases more rapidly than the loss modulus $G''$.
These features of the shear thinning behaviors can explain the crossover behavior of the local storage modulus and loss modulus shown in Fig. \ref{fig_gpgpp_gmgmd_omw} (a).
At the high oscillation frequencies, both local moduli are close to the linear moduli because the local strain amplitude is smaller than about 2 \%.
In the linear regime, the storage modulus $G'$ is larger than the loss modulus $G''$ at high oscillation frequencies.
The local storage modulus $G'$ deviates from the linear modulus as the oscillation frequency $\omega_0$ decreases, and the local strain $\gamma_0$ exceeds about 2\%, while the local loss modulus $G''$ remains close to the linear modulus at $\gamma_0\sim 2\%$.
Thus, the storage modulus $G'$ crosses over the loss modulus $G''$ at a certain oscillation frequency, say a crossover frequency $\omega_0^c$.
The loss modulus $G''$ also starts to decrease as the oscillation frequency $\omega_0$ is smaller than the crossover frequency $\omega_0^c$.
However, because the storage modulus $G'$ decreases more rapidly than the loss modulus $G''$ as the strain amplitude $\gamma_0$ increases, the storage modulus $G'$ is smaller than the loss modulus $G''$ for oscillation frequencies smaller than the crossover frequency, $\omega_0<\omega_0^c$.
Figure \ref{fig_deb_omw} shows the local Deborah numbers, $De^\alpha$ and $De^R$, versus the oscillation frequency $\omega_0$.
The local Deborah numbers, $De^\alpha$ and $De^R$, are defined by the products of the oscillation frequency $\omega_0$ and the shear-dependent $\alpha$ relaxation time $\tau_\alpha(\dot\gamma_0)$, $De^\alpha=\omega_0\tau_\alpha(\dot\gamma_0)$, and the shear-dependent Rouse relaxation time $\tau_R(\dot\gamma_0)$, $De^R=\omega_0\tau_R(\dot\gamma_0)$, respectively.
Here, we use the fitting functions for the relaxation times $\tau_\alpha$ and $\tau_R$ for the simple shear flows obtained in Ref. \onlinecite{art:02YO}.
It is seen that the local Deborah numbers $De^\alpha$ are equal to unity around the crossover frequencies for each local moduli $\omega_0^c$.
In the lower figure in Fig. \ref{fig_gpgpp_gmgmd_omw} (a), the local strain rate $\dot\gamma_0$ increases as the distance from the plate $y$ decreases, while it does not so much depend on the oscillation frequency $\omega_0$ but only slightly decreases as the oscillation frequency $\omega_0$ increases.
The $\alpha$ relaxation time $\tau_\alpha(\dot\gamma)$ is the monotonically decreasing function on the strain rate $\dot\gamma$.
Hence, in Fig. \ref{fig_deb_omw} (a), the local Deborah number $De^\alpha$ decreases as the distance from the plate $y$ decreases but does not alter the shape of the curve very much, such that the oscillation frequency
at which the local Deborah number $De^\alpha$ is equal to unity, i.e., the crossover frequency $\omega_0^c$, shifts to a higher value as the distance $y$ decreases.
As the local Deborah number $De^\alpha$ is less than unity, the loss modulus $G''$ also decreases as the oscillation frequency $\omega_0$ decreases as is seen in Fig. \ref{fig_gpgpp} for the linear moduli.
The behaviors of the storage modulus and loss modulus and the amplitude of the local strain and strain rate versus oscillation frequency near the plate are shown in Fig. \ref{fig_gpgpp_gmgmd_omw} (b).
The dependency of the local strain and strain rate, $\gamma_0$ and $\dot\gamma_0$, on the oscillation frequency $\omega_0$ near the plate is quite different from those far from the plate.
The local strains $\gamma_0$ at $y$=88 and 185 slightly increase with the oscillation frequency in the low oscillation frequencies, e.g., $\omega_0\lesssim 0.002$, but decrease as the oscillation frequency increases in $\omega_0\gtrsim 0.002$, while the local strain at $y$=10 monotonically increases with the oscillation frequency.
The local strain rates $\dot\gamma_0$ monotonically increases with the oscillation frequency in the close vicinity of the plate, i.e, $y$=88 and 10, while the strain rate at $y$=185 shows the non-monotonic dependency on the oscillation frequency.
The spatial variations of local strains and local strain rates are small at low oscillation frequencies and are large at high oscillation frequencies.
This feature also holds for the local moduli.
In Fig. \ref{fig_deb_omw} (b), we show the local Deborah numbers near the plate.
The non-monotonic dependency of the local storage modulus $G'$ on the oscillation frequency $\omega_0$, which can be seen in Fig. \ref{fig_gpgpp_gmgmd_omw} (b), e.g., $G'$ at $y$=88 and 185, might be related to the local Deborah number $De^R$ in Fig. \ref{fig_deb_omw} (b).
As can be seen in Fig. \ref{fig_gpgpp_gmgmd_omw} (b), the local strain rate
$\dot\gamma_0$ rapidly increases as the oscillation frequency $\omega_0$ increases at low oscillation frequencies; however, at high oscillation frequencies, it shows a different dependency on the oscillation frequency $\omega_0$. The local strain rate slightly decreases at $y$=185, does not change much at $y$=88, and monotonically increases at $y$=10, as the oscillation frequency $\omega_0$ increases.
The Rouse relaxation time $\tau_R$ monotonically decreases as the strain rate $\dot\gamma_0$ increases.
Hence, the local Deborah number $De^R$, $De^R=\omega_0\tau_R(\dot\gamma_0)$, decreases even if the oscillation frequency $\omega_0$ increases at low oscillation frequencies because the Rouse relaxation time $\tau_R$ rapidly decreases.
On the contrary, at high oscillation frequencies, $De^R$ increases at $y$=88 and 185 as the oscillation frequency $\omega_0$ increases because $\tau_R$ dose not change much or rather increases slightly.
The elasticity grows as the local Deborah number $De^R$, but it becomes negligible as $De^R$ is less than unity.
Thus, the local storage modulus $G'$ at $y$=88 and 185 in Fig. \ref{fig_gpgpp_gmgmd_omw} (b) varies according to the local Deborah number $De^R$, but the local storage modulus $G'$ at $y$=10 becomes negligibly small except at low oscillation frequencies.
In Fig. \ref{fig_etap_gmd}, we also show shear thinning behavior of the local dynamic viscosity $\eta'$(=$G''/\omega_0$) to the local strain rate $\dot\gamma_0$ for various oscillation frequencies, i.e., $\omega_0$=$1.5\times 10^{-3}$, $6.1\times 10^{-3}$, $1.2\times 10^{-2}$, and $2.5\times 10^{-2}$.
It is seen that, at large strain rates, e.g., $\dot\gamma_0 \gtrsim 0.01$, the dependence of the dynamic viscosity $\eta'$ on the oscillation frequency $\omega_0$ is weakened due to which the results for different oscillation frequencies coincide with each other for $\dot \gamma_0\gtrsim$ 0.1.
A second Newtonian regime is also observed at very large strain rates, e.g., $\dot\gamma_0 > 0.4$.
We also find that the slope of the shear thinning is similar to that observed in steady shear flows, in which the slope is about -0.7\cite{art:02YO}.
Thus, the shear thinning behavior similar to that of the steady shear flows is observed in the vicinity of the plate at high oscillation frequencies.
We also show a diagram of the loss tangent $\tan\delta$, which is defined as the ratio of the viscosity to the elasticity, $\tan\delta=G''/G'$, for different oscillation frequencies and local strain rates in Fig. \ref{fig_losstan_omw_gmd}.
In the diagram, the dashed and dotted lines show that the inverses of the shear-dependent $\alpha$ and Rouse relaxation times, $\tau_\alpha(\dot\gamma)^{-1}$ and $\tau_R(\dot\gamma)^{-1}$, equal the oscillation frequency $\omega_0$; i.e., on the dashed and dotted lines, the local Deborah numbers $De^\alpha$ and $De^R$ are equal to unity, respectively.
The upper side of the diagram indicates the smaller distance from the plate while the lower side the larger distance because the local strain rate decreases as the distance from the plate increases.
No symbols are plotted for large and small strain rates at low oscillation frequencies because no data are available given that the spatial variations of local strain rates are small at low oscillation frequencies as we have seen in Fig. \ref{fig_gpgpp_gmgmd_omw}.
Below the dashed line, the loss tangent is less than unity, while above the dashed line, the loss tangent is larger than unity.
Thus, the crossover of the storage modulus and loss modulus takes place at the dashed line.
Near or above the dotted line, the loss tangent is quite large, and the elasticity may be negligible.
Hence, the melt behaves as a viscous fluid provided that the value of the local strain rate is larger than or close to values that lie on the dotted line.
Thus, the melt forms three different rheological regimes, i.e., the solid-like viscoelastic, liquid-like viscoelastic, and viscous fluid regimes, according to the local strain rates and oscillation frequencies.
\subsection{LAOS analysis}
As the local strain increases near the oscillating plate, the amplitude of higher harmonics of the local macroscopic quantities becomes large, and thus, the time evolution of the local quantities deforms evidently from that of pure sinusoidal curves.
In the present subsection, we carry out LAOS analysis\cite{art:02HKAL,art:05CHAL,art:08EHM} to examine the non-linear effects of higher harmonics on the local macroscopic quantities.
Figure \ref{fig_powspec} shows the power spectra of the local shear stress and strain rate, $|\tilde \sigma_{xy}(\omega)|^2$ and $|\tilde{\dot\gamma}(\omega)|^2$, in the rapidly oscillating plates with an oscillation frequency $\omega_0=0.025$.
Here, $\tilde \sigma_{xy}(\omega)$ and $\tilde {\dot\gamma}(\omega)$ represent the Fourier coefficients of the shear stress and strain rates, respectively.
The peaks of the higher harmonics are detected in the odd harmonics, $3\omega_0$, $5\omega_0$, $\cdots$, near the oscillating plate but disappear far from the plate.
The higher harmonics arise both in the local stress and strain rate because the higher harmonics of the local strain rate is induced by the local stress with the higher harmonic contribution and the higher harmonics of the local stress is also induced by that local strain rate.
Figure \ref{fig_ylb_powspec} shows the spatial variation of the fractional amplitude of the third harmonics to the basic oscillation for various oscillation frequencies $\omega_0$ at $\Gamma_0=0.5$.
The horizontal axis is the normalized distance with respect to the thickness of boundary layer shown in Fig. \ref{fig_vx}.
Even though the local strain monotonically increases while approaching the oscillating plate, the fractional amplitude of the third harmonics rather decreases rapidly in the boundary layer, i.e., $y\lesssim l_b$.
This is caused by the boundary effect because the velocity at the oscillating plate is purely sinusoidal, and higher harmonics are not allowed in the local strain rate on the oscillating plate.
Thus, the contribution of the higher harmonics for the local stress is depressed in the boundary layer.
The fractional amplitude of the third harmonics takes the maximum value at the outside of the boundary layer for each oscillation frequency, $y>l_b$, and then decreases as the normalized distance increases.
We also show the fractional amplitude of the third harmonics versus local strain amplitude at different strain amplitudes of the system, $\Gamma_0$=0.5 and 0.02, for various oscillation frequencies $\omega_0$ in Fig. \ref{fig_gm_powspec}.
For a large strain amplitude of the system, $\Gamma_0=0.5$, the fractional amplitude of the third harmonics has a maximum value around the position where the local strain amplitude is unity, $\gamma_0\simeq 1$, and rapidly decreases in the thickness of boundary layer, $y\lesssim l_b$.
On the contrary, for a small strain amplitude of the system $\Gamma_0=0.02$, the maximum occurs not at $\gamma_0\simeq 1$ but around the position that the value of the distance from the plate coincides with the value of the thickness of boundary layer, $y\simeq l_b$.
For $\Gamma_0=0.02$, the position at which the local strain amplitude is unity lies at the inside of the boundary layer.
Thus, the intrinsic maximum of the fractional amplitude of the third harmonics for $\gamma_0\simeq 1$ is suppressed inside the thickness of boundary layer, $y \lesssim l_b$.
Figure \ref{fig_gm_pxy} shows the Lissajous-Bowditch curves of local shear stress $\sigma_{xy}$ versus local strain $\gamma$ at different oscillation frequencies of the plate $\omega_0$ with $\Gamma_0=0.5$.
The dotted line (green) indicates a perfect ellipse drawn by the storage and loss modulus calculated from the Fourier coefficients of the first harmonics.
Thus, the deviation of the Lissajous-Bowditch curve from the pure ellipse represents the contribution of the higher harmonics in each figure.
At each oscillation frequency, the deviation is more evident at some distance away from the plate than in close vicinity to the plate.
This agrees with the fact that the contribution of the higher harmonics is depressed inside the boundary layer and that the fractional amplitude of the third harmonics assumes a maximum at the outside of boundary layer.
In Fig. \ref{fig_gm_pxy}, the thicknesses of the boundary layer $l_b$ are $l_b$=223, 45, and 20 for $\omega_0$=$1.5\times 10^{-3}$, $6.1\times 10^{-3}$, and 0.025, respectively.
We also show the minimum-strain modulus $G'_M$ and large-strain modulus $G'_L$ defined as $G'_M=d \sigma_{xy}/d \gamma |_{\gamma=0}$ and $G'_L=\sigma_{xy}/\gamma|_{\gamma=\gamma_0}$,\cite{art:08EHM} respectively.
The minimum-strain modulus $G'_M$ yields the elasticity at the point where the change of strain rate is zero, $d\dot \gamma/dt=0$, and the large-strain modulus $G'_L$ yields the elasticity at the point where the instantaneous strain rate is zero, $\dot \gamma=0$.
Both the minimum-strain $G'_M$ and large-strain moduli $G'_L$ coincide with the elastic modulus $G'$ in the linear regime, $G'_M, G'_L \rightarrow G'$ for small $\gamma_0$.
It is seen that the large-strain modulus $G'_L$ is larger than the minimum-strain modulus $G'_M$ within a cycle of Lissajous-Bowditch curves at the close vicinity of the plate, e.g., $y=10$.
Thus, intra-cycle stiffening occurs in close vicinity of the plate, although the storage modulus $G'$ exhibits shear-thinning behavior for the local strain amplitude $\gamma_0$, i.e., inter-cycle softening (see also Fig. \ref{fig_gpep_gm}).
Finally, we show the 3D Lissajous-Bowditch curve of the local shear stress $\sigma_{xy}$, local strain $\gamma$, and local strain rate $\dot\gamma$ near the rapidly oscillating plate.
The 2D projections on each plane are also shown.
The cycle of $\dot\gamma$-- $\sigma_{xy}$ curve is very narrow, and a secondary loop\cite{art:10EM} is observed at a large instantaneous strain rate.
The $\gamma$--$\dot\gamma$ curve also deviates from conforming to a perfect ellipse because the higher harmonics are also involved in the local strain and strain rate.
\section{summary}
We investigated the dynamic rheology of a model polymer melt in non-uniform oscillatory shear flows under the transient force between rapidly oscillating plates by using a hybrid simulation of the molecular dynamics and computational fluid dynamics.
In the quiescent state, the melt is in a supercooled state, where the stress relaxation function exhibits a stretched exponential form on the time scale of the $\alpha$ relaxation time $\tau_\alpha$ and then follows the Rouse relaxation function characterized by the Rouse relaxation time $\tau_R$. [See Fig. \ref{fig_geq}.]
In the rapidly oscillating plates, the melt forms a thin boundary layer over the plates due to the transient force [See Fig. \ref{fig_vx}] such that the dynamic rheology of the melt spatially varies considerably according to the local flow field.
At a high oscillation frequency, the melt forms three different rheological regimes, i.e., the viscous fluid regime ($G'\ll G''$), the liquid-like viscoelastic regime ($G'<G''$), and the solid-like viscoelastic regime ($G'>G''$), over the oscillating plates according to the local Deborah number, while, at a low oscillation frequency, the spatial variation of the storage modulus and loss modulus is rather small, and the loss modulus is larger than the storage modulus, $G'<G''$, at any distance from the plate.
The dependency of the local moduli on the oscillation frequency, $G'$ and $G''$ vs. $\omega_0$ at a fixed position changes according to the distance from the plate.
Far from the plate [Fig. \ref{fig_gpgpp_gmgmd_omw} (a)], the local strain $\gamma_0$ decreases as the oscillation frequency $\omega_0$ increases such that the local moduli deviate from the linear moduli larger at a low frequency than at a high oscillation frequency.
Near the plate [Fig. \ref{fig_gpgpp_gmgmd_omw} (b)], the dependency of the local strain and strain rate on the oscillation frequency is quite different from that far from the plate, e.g., in close vicinity to the plate, the local strain and strain rate monotonically increase as the oscillation frequency.
As the local strain rate becomes larger than about 0.01 near the plate, the shear thinning of the dynamic viscosity is increased, and the shear thinning behavior becomes similar to that observed in steady shear flows [see Fig. \ref{fig_etap_gmd}.]
The diagram of the loss tangent of the melt for different oscillation frequencies and local strain rates is also shown in Fig. \ref{fig_losstan_omw_gmd}.
It is seen in the diagram that the melt generates different rheological regimes according to the oscillation frequency and local strain rates.
We also investigate the non-linear rheological properties in the LAOS regime in the vicinity to the oscillating plate.
The odd higher harmonics, $3\omega_0$, $5\omega_0$, $\cdots$, are detected in the power spectra of the local macroscopic quantities near the oscillating plate [see Fig. \ref{fig_powspec}.]
The fractional amplitude of the higher harmonics rapidly decreases inside the boundary layer while approaching the oscillating plate, although the local strain increases monotonically. [See Fig. \ref{fig_ylb_powspec}.]
This is because higher harmonics are not allowed in the velocity on the oscillating plate due to a non-slip boundary, and thus, the higher harmonics of local quantities are suppressed within the boundary layer.
The Lissajous-Bowditch curve of the local shear stress versus local strain changes the shape due to the contribution of the higher harmonics depending on the distance from the plate.
The elastic modulus exhibits shear-thinning behavior between the different positions (inter-thinning) [see Fig. \ref{fig_gpep_gm}], but shear-thickening behavior is observed in a cycle of the Lissajous-Bowditch curve at a fixed position in the vicinity of the plate (intra-thickening) [see Fig. \ref{fig_gm_pxy}].
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 795
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Q: How to stop all threads on KeyboardInterupt with Python's workerpool This is my Job class:
class QueryJob(workerpool.Job):
"Job for downloading a given URL."
def __init__(self, query):
self.query = query # The query we'll need to download when the job runs
def run(self):
try:
// Query something...
except (Exception, KeyboardInterrupt, SystemExit):
# TODO: The KeyboardInterrupt does not seem to work...
print '*** shutting down ***'
pool.shutdown()
pool.wait()
This is how I start it:
# Initialize a pool, 12 threads in this case
pool = workerpool.WorkerPool(size=12)
# Loop over input file and create a job to download the URL on each line
for query in open(options.file):
job = QueryJob(query)
pool.put(job)
If I'd like it to stop before it's finished, I hit Ctrl-C, but nothing happens. I then try Ctrl-C repeatedly also to no avail. Finally, I'll do Ctrl-Z and then find the process id and do a kill -9 to stop all the threads.
Is this the only want to do it? Is there no way to actually catch the KeyboardInterrupt like I'm trying to do above?
Note, I've tried other things in the except like sys.exit() and raise. But it seems like it's not even reaching that point and Ctrl-C has no affect at all once the threads are executing.
Is there something trivial that I'm missing?
Thanks.
A: I found this:
http://code.activestate.com/recipes/577187-python-thread-pool/
It seems to function just as workerpool does, but actually will listen to the KeyboardInterrupt and halt the script.
This works for me, so I'm answering my own question with it. I'm still up for finding a way to use workerpool, but for anybody else with this same situation - in the meantime I recommend using the Python thread module as is done in the above recipe.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,566
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\section{Introduction}\label{sec:intro}
A translation surface can be defined as an assembling of Euclidean polygons with appropriate identifications of sides or, in an equivalent manner, as a pair $(X,\omega)$ where $X$ is a compact Riemann surface and $\omega$ a holomorphic $1$-form on $X$.
Such a pair can be considered as an element of a rank $g$ vector bundle $\Omega\mathcal{T}_g\to\mathcal{T}_g$ over the Teichm\"uller space $\mathcal{T}_g$ of genus $g$ Riemann surfaces.
The moduli space of holomorphic $1$-forms with a unique (double) zero on a genus $2$ Riemann surface is denoted by $\mathcal{H}(2)$.
There exists a natural action of the group $\GL_2^+(\R)$ on translation surfaces.
The projections of the $\SL_2(\R)$-orbits into the Riemann moduli space $\mathcal{M}_g$ are called Teichm\"uller disks.
It may happen that the stabilizer of a translation surface under the $\SL_2(\R)$-action is a lattice.
Passing to the quotient, it gives rise to a Teichm\"uller curve, that is, an algebraic curve in the Riemann moduli space, isometrically immersed for the Teichm\"uller metric.
To date very few is known about how one passes explicitly from one description of a complex structure to another under the $\GL_2^+(\R)$ action.
For example, how does the period matrix of a Riemann surface vary under this action? What about the equations defining the corresponding algebraic curve?
Note that after this paper was written, M.~M\"oller wrote an important result on a closely related family of examples, see \cite[Theorem~0.1]{moeller11}.\\
In this paper we study the family of Riemann surfaces defined by the $\SL_2(\R)$-orbit of the L-shaped translation surface tiled by three squares (see Figure \ref{fig:3-square-tiled_surface}).
\begin{figure}[!h]
\centering \input{fig-3squares.tex}
\caption{The L-shaped translation surface tiled by three squares}\label{fig:3-square-tiled_surface}
\end{figure}
According to \cite[Example in \S6]{mcmullen05a}, this family is the Teichm\"uller curve of discriminant $9$ and, following McMullen's notation, will be denoted by $W_9$ (comprehensive overviews on Teichm\"uller curves can be found {\it e.g.} in \cite{mcmullen03a} and \cite{lochak05}).
We will sometimes denote by $W_9^{\mathrm{M}}$ the Teichm\"uller geodesic generated by the $3$-square-tiled surface, that is, its orbit under the diagonal subgroup \footnote{Note that the usual parametrization of a Teichm\"uller geodesic is $(\begin{smallmatrix}e^t&0\\0&e^{-t}\end{smallmatrix})$ for $t\in\R$.} $\{(\begin{smallmatrix}t&0\\0&t^{-1}\end{smallmatrix})\}_{t>0}$.
The $3$-square-tiled surface admits an order $4$ automorphism; period matrices of Riemann surfaces defined by such translation surfaces in $\mathcal{H}(2)$ were computed by R.~Silhol in \cite[\S3]{silhol06}.
We will first show the following.
\begin{proposition}\label{prop:autos_w9m}
The only Riemann surface in the family $W_9^{\mathrm{M}}$ admitting a non-hyperelliptic automorphism is the one defined by the L-shaped translation surface tiled by three squares.
\end{proposition}
As automorphisms provide precious informations in order to compute the period matrix of a Riemann surface, that prevents to compute an exact expression for period matrices of these surfaces by the classical method described, for instance, in \cite[\S11.7]{birkenhake&lange04} (see Remark \ref{rema:periods_usual_computation} below).
Nevertheless, we consider a certain family of double covers of those surfaces (whose construction will be described in detail) admitting many automorphisms, for which we obtain the following characterization of their period matrices.
\begin{mytheorem}\label{theo:double_cover_thetanull}
Let $(X,\omega)$ be a translation surface in $\mathcal{H}(2)$, then $X$ is in the family $W_9$ if and only if a certain explicit double cover $\hat{X}$ admits a period matrix $\hat{Z}$ of the form
\[
\hat{Z}=
\begin{pmatrix}
z_1 & \frac12z_1 & z_{13}\\
\frac12z_1 & \frac12+\frac34z_1-\frac12z_{13} & \frac12z_1\\
z_{13} & \frac12z_1 & z_1
\end{pmatrix}
\]
for which $\thetasc{1&1&1\\1&0&1}(\hat{Z})=0$.
\end{mytheorem}
\noindent Recall that for all $m,n\in(\rquotient{\Z}{2\Z})^g$, the theta characteristic $\thetasc{m\\n}$ is defined by
\[
\thetabc{m\\n}(Z)=\sum_{k\in\Z^g} \exp\pi i\left[\T{\left(k+\frac12m\right)}Z\left(k+\frac12m\right)+\T{\left(k+\frac12m\right)}n\right]
\]
for all $Z\in\M_g(\C)$ such that $\T{Z}=Z$ and $\IM(Z)>0$.
Riemann surfaces in the Teichm\"uller geodesic generated by the 3-square-tiled surface correspond to real algebraic curves defined by polynomials with real roots.
The situation being more rigid in this case, this allows us to establish a form for their period matrices and deduce necessary and sufficient conditions for a Riemann surface to be in the family $W_9^{\mathrm{M}}$.
\begin{mytheorem}\label{theo:w9m_periods}
Let $(X_1,\omega_1)$ be the L-shaped translation surface tiled by three squares.
For any real number $t\geq1$, let $(X_t,\omega_t)=\left(\begin{smallmatrix}1&0\\ 0&t\end{smallmatrix}\right)\cdot(X_1,\omega_1)$.
Then $Z_t$ is a period matrix of $X_t$ associated to a certain explicit homology basis if, and only if there exists a unique real number $y_t>2t/3$ such that
\[
Z_t=
\begin{pmatrix}
1+i(2y_t-t) & iy_t\\
iy_t & i(y_t/2+t)
\end{pmatrix}
\]
and satisfying
\begin{multline}\label{eq:main_equation}
\sum_{(k_1,k_2,k_3)\in\Z^3}\exp\pi\Biggl[\\
\left(\frac{t}{2}-y_t+\frac{1}{2}i\right)\sum_{\l=1}^3 k_\ell^2+\left(y_t-t+i\right)\sum_{1\leq\ell<m\leq3}k_\ell k_m+\left(\frac{3}{2}i-\frac{t}{2}\right)\sum_{\ell=1}^3 k_\ell\Biggr]=0.
\end{multline}
\end{mytheorem}
\noindent The construction of the homology basis will be described in detail.
\begin{acknowledgements}
I would like to express my gratitude toward my Ph.D. advisor Robert Silhol for helpful conjectures as well as fulfilling discussions.
I also wish to thank Emmanuel Royer, Pascal Hubert and Guillaume Bulteau for various advices and useful discussions and comments.
\end{acknowledgements}
\section{Preliminaries}\label{sec:preliminaries}
\subsection{Translation surfaces}\label{subsec:translation_surfaces}
A \emph{translation surface} is a finite collection of Euclidean polygons in the complex plane such that\begin{itemize}
\item the boundary of each polygon is oriented counterclockwise;
\item for every side of a polygon, there exists another side (possibly of the same polygon) parallel and of the same length: both sides are then identified by translation.
\end{itemize}
Such a collection of polygons defines a topological surface admitting a \emph{translation structure}, that is, away from a finite set of points, a maximal atlas whose transition functions are translations.
As a non-trivial example consider a compact Riemann surface equipped with a holomorphic $1$-form.
Integrating the form yields, away from its zeros, an atlas with polygonal charts and transition functions that are translations.
Conversely, a translation structure defines a complex structure since translations are biholomorphic.
Pulling back the $1$-form $dz$ on the complex plane by the charts gives a holomorphic $1$-form on the surface.
As a consequence, we can define in an equivalent manner a translation surface as a pair $(X,\omega)$ where $X$ is a compact Riemann surface and $\omega$ a holomorphic $1$-form on $X$.
At a regular point, in the local coordinate defined by integrating the form, we have $\omega=dz$.
At an order $k$ zero of $\omega$, we have
\[
\omega=z^kdz=d\left(\frac{z^{k+1}}{k+1}\right)
\]
so that the Riemann surface $X$ is locally a ($k+1$)-fold cover over the complex plane.
This means that an order $k$ zero corresponds to a cone-type singularity of angle $2\pi(k+1)$ for the locally Euclidean metric $|\omega|$.
More details can be found in \cite[\S1]{masur06} concerning the equivalence of these definitions.
See also \cite{zorich06} for a general survey on translation surfaces.
We will use the notation $(X,\omega)=(\rquotient{\mathcal{P}}{\sim},dz)$ where the quotient $\rquotient{\mathcal{P}}{\sim}$ designates an assembling of Euclidean polygons with appropriate identifications of sides by translation and $dz$ is the holomorphic $1$-form on $\C$.
\begin{example}[Translation surface tiled by three squares]\label{exam:3-square-tiled_surface}
Consider the L-shaped polygon obtained by assembling three copies of the Euclidean unit square equipped with the glueings specified in Figure \ref{fig:3-square-tiled_surface}.
The black dots are identified to the cone-type singularity of angle $6\pi$, hence defining a translation surface $(X,\omega)$ in $\mathcal{H}(2)$.
Rotation by angle $\pi/2$ around the center of the bottom left square induces an order $4$ automorphism on the Riemann surface $X$: the corresponding algebraic curve then admits an equation of the form
\[
y^2=x(x^2-1)(x-a)(x-1/a)
\]
and the order $4$ automorphism is
\[
(x,y)\mapsto\left(\frac1x, \frac{iy}{x^3}\right).
\]
Following \cite[\S3\&4]{silhol06}, in this example we have $a=7+4\sqrt3$ and the holomorphic $1$-form $\omega$ is
\[
\omega=\mu\left(\frac{dx}{y}-\frac{xdx}{y}\right)
\]
with $\mu\in\C^*$.
\end{example}
\begin{remark}\label{rema:half-translation_surface}
From a more general point of view, translation surfaces are a specific case of half-translation surfaces, for which the transition functions are of the form $z\mapsto\pm z+c$ for $c\in\C$.
Such a surface can be defined as a pair $(X,q)$ where $q$ is a holomorphic quadratic differential on $X$.
If $(X,\omega)$ is a translation surface, then the quadratic differential defining the complex structure is $\omega^2$.
\end{remark}
\subsection{$\GL_2^+(\R)$-action}\label{subsec:GL(2,R)-action}
There exists a natural action of the linear group on translation structures.
An element $M=(\begin{smallmatrix}a&b\\c&d\end{smallmatrix})\in\GL_2^+(\R)$ acts on $z\in\C$ by
\[
M\cdot z=ax+by+i(cx+dy).
\]
This is just the affine action on the complex plane identified to $\R^2$.
When a translation surface is defined by a collection of polygons $(\rquotient{\mathcal{P}}{\sim},dz)$, then the group $\GL_2^+(\R)$ operates naturally on the polygons, giving a new translation surface.
The action is well defined since linear applications transform parallelograms into parallelograms.
On a form $(X,\omega)$, the action of $M$ is defined as follows: let
\[
\eta:=a\RE(\omega)+b\IM(\omega)+i\big(c\RE(\omega)+d\IM(\omega)\big),
\]
then $\eta$ is a harmonic form on $X$.
There exists a unique complex structure on the underlying topological surface for which $\omega$ is holomorphic, so that we obtain a new Riemann surface $Y$ and we set
\[
M\cdot(X,\omega)=(Y,\eta).
\]
\begin{remark}\label{rema:stable_under_SO(2,R)}
For every translation surface $(X,\omega)$, the complex structure defined by $(X, \omega)$ is stable under the action of the subgroup $\R_+^*\cdot\SO_2(\R$), since this action corresponds to multiplying $\omega$ by a non zero scalar complex.
\end{remark}
\subsubsection*{Teichm\"uller geodesics}\label{paragraph:teichmueller_geodesics}
Let $t$ be a real number such that $t>1$ and consider the $\R$-linear application $M_t:\C\to\C$ defined by
\[
z\mapsto\frac12(1+t)z+\frac12(1-t)\bar{z}.
\]
Let $(X,\omega)$ be a translation surface and $(X_t,\omega_t)=M_t\cdot(X,\omega)$.
The change of complex structure yields a natural application $f_t:X\to X_t$ verifying $df_t=M_t$ and having constant complex dilatation:
\[
\forall P\in X,\quad\mu_{f_t}(P):=\frac{\bar{\partial}f_t(P)}{\partial f_t(P)}=\frac{1-t}{1+t}.
\]
The maximal dilatation is then
\[
K(f_t):=\sup_{P\in X}\frac{1+|\mu_{f_t}(P)|}{1-|\mu_{f_t}(P)|}=t.
\]
The homeomorphism $f_t:X\to X_t$ is then a Teichm\"uller extremal map.
We call the Riemann surface $X_t$ the \emph{Teichm\"uller deformation of $X$ of dilatation $t$ with respect to $\omega$} and the family $\{X_t\}_{t\geq1}$ a \emph{Teichm\"uller geodesic} (see {\it e.g.} \cite[chap.~1]{abikoff80} for more details).
\begin{remark}\label{rema:isomorphic_surfaces}
Let $(X,\omega)$ be a L-shaped translation surface of the form indicated in Figure \ref{fig:L-shaped_surface}.
Then $X$ admits an order $4$ automorphism induced by rotation of angle $\pi/2$ around $0$.
\begin{figure}[!h]
\centering \input{fig-l-shaped.tex}
\caption{An L-shaped translation surface with an order $4$ automorphism}\label{fig:L-shaped_surface}
\end{figure}
Let $t$ be a real number such that $t>0$, we define the translation surfaces
\begin{align*}
(X_{g_t},\omega_{g_t})&=(\begin{smallmatrix}t&0\\0&t^{-1}\end{smallmatrix})\cdot(X,\omega),\\
(X_{h_t},\omega_{h_t})&=(\begin{smallmatrix}t&0\\0&1\end{smallmatrix})\cdot(X,\omega),\\
\text{and }(X_{v_t},\omega_{v_t})&=(\begin{smallmatrix}1&0\\0&t\end{smallmatrix})\cdot(X,\omega).
\end{align*}
Then by Remark \ref{rema:stable_under_SO(2,R)} it is readily checked that
\begin{enumerate}[(1)]
\item the Riemann surfaces $X_{h_t}$ and $X_{v_t}$ are isomorphic;
\item $X_{g_t}$ and $X_{h_{t^2}}$ (resp. $X_{g_{t^{-1}}}$ and $X_{v_{t^2}}$) are isomorphic;
\item $X_{h_t}$ and $X_{h_{t^{-1}}}$ (resp. $X_{v_t}$ and $X_{v_{t^{-1}}}$) are isomorphic.
\end{enumerate}
\end{remark}
\subsection{Period matrix}\label{subsec:period_matrix}
Let $X$ be a compact Riemann surface of genus $g$ and let $\mathcal{B}=(\alpha_1,\ldots,\alpha_g,\beta_1,\ldots,\beta_g)$ be a symplectic basis for $\HH_1(X,\Z)$, that is, such that the matrix of the intersection product is
\[
\begin{pmatrix}0&-\I_g\\ \I_g&0\end{pmatrix}
\]
Let $(\omega_1,\ldots,\omega_g)$ be a basis of holomorphic $1$-forms on $X$, we define
\[
A=\left(\int_{\alpha_j}\omega_k\right)_{j,k}\text{ and }B=\left(\int_{\beta_j}\omega_k\right)_{j,k}.
\]
Then $Z=AB^{-1}$ is \emph{the period matrix associated to $\mathcal{B}$}.
Note that $Z$ does not depend on the choice of the basis $(\omega_1,\ldots,\omega_g$).
It is well known that $Z$ verifies the Riemann bilinear relations, that is, $Z$ is symmetric and $\IM(Z)$ is positive definite.
The Siegel upper half-space is defined by
\[
\mathfrak{S}_g=\{Z\in\M_g:\T{Z}=Z\text{ and }\IM(Z)>0\}.
\]
Let $\alpha,\beta,\gamma,\delta\in\M_g(\R)$, an element $M=(\begin{smallmatrix}\alpha&\beta\\ \gamma&\delta\end{smallmatrix})$ of the symplectic group
\[
\SP_{2g}(\R)=\left\{M\in\M_{2g}(\R):\T{M}
\begin{pmatrix}0&-\I_g\\ \I_g&0\end{pmatrix}
M=
\begin{pmatrix}0&-\I_g\\ \I_g&0\end{pmatrix}\right\}
\]
acts on an element $Z\in\frak{S}_g$ as follows:
\[
M(Z)=(\alpha Z+\beta)(\gamma Z+\delta)^{-1}.
\]
If $\mathcal{B}'$ is another symplectic basis for $\HH_1(X,\Z)$ and $Z'$ the period matrix associated to $\mathcal{B}'$, let $M$ be the base change matrix from $\mathcal{B}'$ to $\mathcal{B}$; then $M$ is a symplectic matrix with integer entries and $Z$ and $Z'$ are related by
\[
Z'=\T{M}(Z).
\]
Recall that if $M$ is symplectic, then $\T{M}$ is also symplectic.
Moreover, by the Torelli theorem, the period matrix characterizes the complex structure: if $X$ and $X'$ are compact Riemann surfaces with period matrices $Z$ and $Z'$ respectively, then $X$ and $X'$ are isomorphic if, and only if there exists $M\in\SP_{2g}(\Z)$ such that $M(Z)=Z'$ (see \cite[Theorem~11.1.7]{birkenhake&lange04}).
\begin{example}[Translation surface with an order $4$ automorphism]\label{exam:order4_automorphism}
Let $(X,\omega)$ be the L-shaped translation surface defined in Figure \ref{fig:L-shaped_surface}.
The rotation by angle $\pi/2$ around $0$ induces an order $4$ automorphism on the Riemann surface $X$.
Then following \cite[\S3]{silhol06},
\[
Z=i\begin{pmatrix}\frac{2\lambda^2-2\lambda+1}{2\lambda-1}&\frac{-2\lambda(\lambda-1)}{2\lambda-1}\\ \frac{-2\lambda(\lambda-1)}{2\lambda-1}&\frac{2\lambda^2-2\lambda+1}{2\lambda-1}\end{pmatrix}
\]
is the period matrix of $X$ associated to $\{\alpha_1,\alpha_2,\beta_1,\beta_2\}$.
\end{example}
\begin{remark}\label{rema:periods_usual_computation}
The main tool in Silhol's calculation is the existence of a non-hyperelliptic involution whose action permutes $\omega$ with another linearly independent holomorphic $1$-form that can be explicitly described (enabling to compute the whole period matrix, following \cite[\S11.7]{birkenhake&lange04} for example).
However, on the one hand, generic algebraic curves have no non-trivial automorphisms, and on the other hand it is not known in general how to provide a description of another holomorphic $1$-form.
\end{remark}
\subsubsection*{Hyperelliptic Riemann surfaces}\label{paragraph:hyperelliptic_homology_basis}
Here we describe a construction of a period matrix of a hyperelliptic Riemann surface.
If $X$ is hyperelliptic, then the associated algebraic curve is defined by an equation of the form
\[
y^2=\prod_{j=1}^m(x-x_j)
\]
where the $x_j$ are distinct complex numbers and $m=2g+1$ or $2g+2$.
If $m=2g+1$, then let $x_{2g+2}=\infty$
Let $\varepsilon_1$ be a simple arc in $\mathbb{P}^1(\C)$ joining $x_1$ to $x_2$ and not passing through any of the other $x_j$ for $j\geq3$.
Let $\varepsilon_2$ a second simple arc joining $x_2$ to $x_3$ and not passing through $x_1$ nor any of the other $x_j$'s for $j\geq4$, and such that $\varepsilon_2$ only intersects $\varepsilon_1$ in $x_2$.
In the same way, we construct simple arcs $\varepsilon_3,\ldots,\varepsilon_{2g+1},\varepsilon_{2g+2}$ joining respectively $x_3$ to $x_4$, \ldots, $x_{2g+1}$ to $x_{2g+2}$ and $x_{2g+2}$ to $x_1$, so that $\varepsilon_j$ only intersects $\varepsilon_{j+1}$ in one point ($j\mod{2g+2}$).
Let $\pi:X\to\mathbb{P}^1(\C)$ denote the projection $(x,y)\mapsto x$ and, for $j=1,\ldots,2g+2$, let $\delta_j:=\pi^{-1}(\varepsilon_j)$: this is a simple closed curve in $X$.
We choose on each $\varepsilon_j$ a holomorphic determination of $\sqrt{P}$ so that the induced orientation on $\delta_j$ is such that $(\delta_j\cdot\delta_{j+1})=1$ ($j\mod2g+2)$, all other intersection numbers being zero.
With this convention, up to homology, we thus have $\sum_{j=1}^g\delta_{2j}=-\delta_{2g+2}$ and $\sum_{j=1}^g\delta_{2j-1}=-\delta_{2g+1}$ (this is a readily checked by a topological sketch of the situation, the reader may also refer to \cite[\S VII.1.1]{farkas&kra92} where this construction is described).
For $j=1,\ldots,g$, we define
\begin{align*}
\alpha_j &=-\sum_{\ell=1}^{j-1}\delta_{2\ell}-\delta_{2g+2},\\
\beta_j &=\delta_{2j-1}.
\end{align*}
It is readily checked that $\mathcal{B}:=(\alpha_1,\ldots,\alpha_g,\beta_1,\ldots,\beta_g)$ is a symplectic basis for $\HH_1(X,\Z)$.
Moreover, as $X$ is a hyperelliptic Riemann surface,
\[
\frac{dx}{y},\frac{xdx}{y},\ldots,\frac{x^{g-1}dx}{y}
\]
is a basis of holomorphic $1$-form on $X$ (see \cite[\S III.7.5, Corollary~1]{farkas&kra92}).
Let
\begin{align*}
A&=\left(-\sum_{\ell=1}^{j-1}\int_{\varepsilon_{2\ell}}\frac{x^{k-1}dx}{\sqrt{P(x)}}-\int_{\varepsilon_{2g+2}}\frac{x^{k-1}dx}{\sqrt{P(x)}}\right)_{j,k}\\
B&=\left(\int_{\varepsilon_{2j-1}}\frac{x^{k-1}dx}{\sqrt{P(x)}}\right)_{j,k}
\end{align*}
then $Z=AB^{-1}$ is the period matrix associated to $\mathcal{B}$.
\subsection{Real algebraic curves}\label{subsec:real_alg_curves}
\subsubsection*{Definitions}\label{paragraph:real_alg_curves_defs}
F.~Klein observed that a complex algebraic curve $X$ is defined by real polynomial equations if, and only if $X$ admits an anti-holomorphic involution $\sigma$ (see \cite[\S21]{klein63}), called a \emph{real structure}.
Moreover, these polynomials can always be chosen so that $\sigma$ is induced by complex conjugation.
A \emph{real algebraic curve} is a couple $(X,\sigma)$.
When it is clear from the context, we omit $\sigma$ and simply say that $X$ is a real curve, in particular when $X$ is defined by a real polynomial equation and $\sigma$ is the complex conjugation.
If $X$ is of genus $g$, then the connected components of the fixed point set of $\sigma$ are said to be real.
We say that $X$ is an M-curve if it admits the maximum number of real components, which is $g+1$ (see \cite[Proposition~3.1]{gross&harris81}).
\subsubsection*{Real hyperelliptic M-curves}\label{paragraph:real_hyperelliptic_mcurves}
Suppose that $X$ is a hyperelliptic curve defined by a polynomial equation $y^2=P(x)$ with $\deg P=2g+1$ or $2g+2$, and such that $\sigma$ is induced by complex conjugation.
Then $(X,\sigma)$ is a real M-curve if, and only if all roots of $P$ are real.
Composing $\sigma$ with the hyperelliptic involution $h_X$ yields a second real structure denoted by $-\sigma$.
The connected components of the fixed point set of $-\sigma$ are said to be pure imaginary and the Weierstrass points of $X$ are exactly the intersection points of the real and pure imaginary components.
\begin{example}[M-curve defined by a translation surface]\label{exam:mcurve_from_translation_surface}
Let $(X,\omega)=(\rquotient{\mathcal{P}}{\sim},dz)$ be a translation surface in $\mathcal{H}(2)$ obtained from four mirror images of a L-shaped polygon (see Figure \ref{fig:mcurve}).
We can always assume that the polygon $\mathcal{P}$ admits $0$ as a center of symmetry and is stable by complex conjugation.
The latter defines an anti-holomorphic involution $\sigma$ on $X$ that fixes pointwise the three simple closed curves coming from the horizontal axis of symmetry of $\mathcal{P}$ and its horizontal sides: we thus obtain a real M-curve $(X,\sigma)$.
The Weierstrass points are represented by black dots (identified to the double zero of $\omega$) and small circles in Figure \ref{fig:mcurve}.
Cutting and reassembling the cross-shaped polygon in the left part of Figure \ref{fig:mcurve} gives the L-shaped polygon in the right part of Figure \ref{fig:mcurve}, where the segments corresponding to the simple closed curves fixed by $\sigma$ are the horizontal and vertical segments that join the black dots and those passing through the circles.
\begin{figure}[!ht]
\centering \input{fig-mcurve.tex}
\caption{A L-shaped translation surface defines a real M-curve}\label{fig:mcurve}
\end{figure}
\end{example}
\begin{remark}\label{rema:mcurves_are_teich_def}
In what follows, if $(X,\sigma)$ is a real M-curve defined by a translation surface $(X,\omega)$, then the real structure $\sigma$ will always be the one defined by complex conjugation as in Example \ref{exam:mcurve_from_translation_surface}.
If $(X_1,\omega_1)$ denotes the L-shaped translation surface tiled by three squares, then it corresponds to the unique, so-called \emph{splitting prototype} in \cite[\S3]{mcmullen05a} and by \cite[\S6]{mcmullen05a}, this translation surface generates the whole Teichm\"uller curve $W_9$.
The above convention on the definition of the real structure fixes the orientation of the L-shaped polygon, then by Remark \ref{rema:isomorphic_surfaces} the set of M-curves in the family $W_9$ thus coincides with the Teichm\"uller deformations of $X_1$ with respect to $\omega_1$.
\end{remark}
\subsubsection*{Automorphisms of genus $2$ real M-curves}\label{paragraph:genus2_real_mcurves_autos}
If $(X,\sigma)$ is a real algebraic curve, we denote by $\AUT(X,\sigma)$ the group of its \emph{real automorphisms}, that is, biholomorphic applications $\phi:X\to X$ such that $\phi\circ\sigma=\sigma\circ\phi$.
The group $\AUT X$ is sometimes called the group of \emph{complex automorphisms} of $(X,\sigma)$.
F.-J.~Cirre computed the groups of real and complex automorphisms of a real M-curve as stated below, where $D_n$ denote the dihedral group of order $2n$.
\begin{theorem}[Cirre]\label{theo:cirre}
Let $a$, $b$, $c$ be three real numbers such that $0<a<b<c<1$ and let $(X,\sigma)$ be the real M-curve defined by the equation
\[
y^2=P(x)=x(x-a)(x-b)(x-c)(x-1)
\]
Then $\AUT(X,\sigma)=\AUT X$ if, and only if $a\neq b(c-1)/(b-1)$.
Moreover, we have the following two cases:
\begin{enumerate}[(1)]
\item Suppose that $\AUT(X,\sigma)=\AUT X$:
\begin{enumerate}[(a)]
\item if we have $a=bc$ or $a=(b-c)/(c-1)$ or $a=1+c-c/b$, then $\AUT X\simeq D_2$;
\item if we have $bc=a=(b-c)/(c-1)$ or $bc=a=1+c-c/b$ or $(b-c)/(c-1)=a=1+c-c/b$, then $\AUT X\simeq D_6$;
\item else, $\AUT X\simeq\Z/2\Z$.
\end{enumerate}
\item Suppose that $\AUT(X,\sigma)\neq\AUT X$:
\begin{enumerate}[(a)]
\item if we have $a=bc$ or $a=(b-c)/(c-1)$ or $a=1+c-c/b$, then $\AUT(X,\sigma)\simeq D_2$ and $\AUT X\simeq D_4$;
\item if we have $bc=a=(b-c)/(c-1)$ or $bc=a=1+c-c/b$ or $(b-c)/(c-1)=a=1+c-c/b$, then
\[
(a,b,c)=\left(\frac{1}{3},\frac{1}{2},\frac{2}{3}\right),
\]
$\AUT(X,\sigma)\simeq D_6$ and $\AUT X$ is isomorphic to the group $G_{24}$ of order $24$ admitting the following presentation:
\begin{equation}\label{eq:group_G24}
G_{24}=\langle r,s | r^4,s^6, (rs)^2, (r^{-1}s)^2\rangle;
\end{equation}
\item else, $\AUT(X,\sigma)\simeq\Z/2\Z$ and $\AUT X\simeq D_2$.
\end{enumerate}
\end{enumerate}
\end{theorem}
The details of the proof can be found in \cite[Theorem~4.2]{cirre01} and \cite[Proposition~3.5]{cirre03}.\\
This classification can also be translated in terms of the period matrices and of the hyperbolic structure of the algebraic curve.
See \cite[chap.~3]{rodriguez10} for more details, see also \cite{natanson78}.
\section{Real M-curves with automorphisms in $W_9$}
\subsection{Description of the family $W_9$}\label{subsec:description_of_w9}
The $\SL_2(\R)$-orbit of the L-shaped translation surface tiled by three squares is denoted by $\Omega W_9$.
It projects into the Riemann moduli space $\mathcal{M}_2$ as an irreducible algebraic curve, which is denoted by $W_9$.
According to \cite[Remark, p.~3]{hubert&lelievre05}, the latter is the modular curve defined by the quotient $\lquotient{\Gamma}{\mathbb{H}}$ where $\Gamma$ is the level $2$ congruence subgroup generated by
\[
\begin{pmatrix}1&2\\0&1\end{pmatrix}
\text{ and }
\begin{pmatrix}0&-1\\1&0\end{pmatrix}.
\]
In \cite[\S4]{moeller05}, M.~M\"oller provides equations for the family $W_9$.
R.~Silhol gives in \cite[Theorem~A]{silhol07} a description of the algebraic curves in this family and shows that a translation surface $(X,\omega)$ is an element of $\Omega W_9$ if, and only if the curve $X$ admits an equation of the form
\begin{align}
y^2&=P_u(x)=x(x-1)\left(x^3+ux^2-\frac{8}{3}ux+\frac{16}{9}u\right)\label{eq:w9_magic_form}\\
\text{with }\omega&=\lambda\frac{xdx}{y}\nonumber
\end{align}
for $u\in\C\setminus\{-9,0\}$ and for some constant $\lambda\in\C^*$.
The degree $3$ polynomial
\[
x^3+ux^2-\frac83ux+\frac{16}{9}u
\]
admits exactly three real distinct roots if, and only if its discriminant is positive, that is, if, and only if $u$ is a real number such that $u<-9$.
Thus, a genus $2$ curve $X=X_u$ defined by an equation of the form \eqref{eq:w9_magic_form} is a real M-curve if, and only if $u<-9$.
The following fact was observed in \cite{silhol07} but not stated.
\begin{proposition}
There exists a bijection between the set of real automorphism classes of real M-curves in $W_9$ and the interval $[-18;-9[$.
\end{proposition}
\begin{proof}
In \cite[Proposition~4.1]{silhol07}, the author considers a certain family whose image in moduli space is shown to be the quotient of $\mathbb{P}^1(\mathbb{\C})\setminus\{-9,0,\infty\}$ under $u\mapsto -9u/(u+9)$ (see also \cite[Remarks~4.11]{silhol07}).
In particular, there is a bijection between this image and $\mathbb{P}^1(\mathbb{\C)}$ minus two points and a cone point of order $2$, namely the one corresponding to $u=-18$.
Is is then shown in \cite[Lemma~5.4]{silhol07} that the aforementioned family is $W_9$.
If we now consider the case of real M-curves, then by the above discussions there is a bijection between $W_9^{\mathrm{M}}$ and $[-18;-9[$ on the one hand, and between $W_9^{\mathrm{M}}$ and $]-\infty; -18]$ on the other hand.
Furthermore, it results from \cite[Proposition~4.1 and Lemma~5.4]{silhol07} that if $X_u$ is a real M-curve defined by an equation $y^2=P_u(x)$ as in Equation \eqref{eq:w9_magic_form}, then the transformation $x\mapsto x/(x-1)$ induces a (complex, but non-real) isomorphism between $X_u$ and $X_{u'}$ with $u'=-9u/(u+9)$.
\end{proof}
Defining
\[
f_3:x\mapsto\frac{x+\sqrt{3}}{-\sqrt{3}x+1},
\]
we note that the M\"obius transformation $f_3$ is of order $3$ and fixes the points $i$ and $-i$.
The orbits of $0$ and $\infty$ under $f_3$ are respectively
\[
\{\sqrt3,-\sqrt3,0\}\text{ and }\{-\sqrt3/3,\sqrt3/3,\infty\}.
\]
We consider a genus $2$ algebraic curve defined by an equation of the form
\[
y^2=Q_s(x)=x(x+1)(x-s^2)\big(x-f_3(s)^2\big)\Big(x-f_3\big(f_3(s)\big)^2\Big).
\]
If we apply the transformation $x\mapsto x+1$ to the roots of $Q_s(x)$, then a direct calculation shows that this curve also admits an equation of the form \eqref{eq:w9_magic_form} with
\[
u=\frac{-81(s^2+1)^3}{(3s+\sqrt{3})^2(3s-\sqrt{3})^2}.
\]
We note that the function
\[
s\mapsto g(s)=\frac{-81(s^2+1)^3}{(3s+\sqrt3)^2(3s-\sqrt3)^2}
\]
is even and invariant under $f_3$.
This leads to the following:
\begin{proposition}\label{prop:description_of_w9}
Let $(X,\omega)$ be a translation surface in $\mathcal{H}(2)$.
Then $(X,\omega)$ is an element of $\Omega W_9$ if, and only if the algebraic curve $X$ admits an equation of the form
\begin{align}
y^2&=Q_s(x)=x(x+1)(x-s^2)\Big(x-f_3\big(f_3(s)\big)^2\Big)\big(x-f_3(s)^2\big)\label{eq:w9_order3_auto_form}\\
\text{with }\omega&=\lambda\left(\frac{dx}{y}+\frac{xdx}{y}\right)\nonumber
\end{align}
with $s\in\C\setminus\{-\sqrt{3},-\sqrt3/3,-1,0,\sqrt3/3,\sqrt{3},-i,i\}$ and for some constant $\lambda\in\C^*$.
\end{proposition}
\begin{proof}
According to \cite[Theorem~A]{silhol07}, a translation surface $(X,\omega)$ in $\mathcal{H}(2)$ is an element of $\Omega W_9$ if, and only if $X$ admits an equation of the form $y^2=P_u(x)$ as defined by \eqref{eq:w9_magic_form} with $u\in\C\setminus\{-9,0\}$ and $\omega$ admitting a double zero at $0$.
The condition in the statement is already proven to be sufficient by the discussion above.
Conversely, let $(X,\omega)$ be an element of $\Omega W_9$, then $X$ is defined by an equation of the form $y^2=P_u(x)$ with $u\in\C\setminus\{-9,0\}$. From the study of the function $g$ we can take $u=g(s)$ for some $s\in\C\setminus\{-\sqrt{3},-\sqrt3/{3},-1,0,\sqrt3/3,\sqrt{3},-i,i\}$.
Applying the transformation $x\mapsto x-1$ to the roots of the equation $y^2=P_u(x)$ then leads to the announced form \eqref{eq:w9_order3_auto_form} of the equation $y^2=Q_s(x)$.
Moreover, up to a non-zero, complex scalar multiple, $dx/y+xdx/y$ is the only holomorphic $1$-form on $X$ admitting a double zero at $(-1,0)$.
\end{proof}
Noting that we have $g(s)\leq-9$ for every $s\in\R$ and that
\[
\forall s\in]0;\sqrt3/3[,\quad s^2<f_3\big(f_3(s)\big)^2<f_3(s)^2,
\]
we obtain another description of this set.
\begin{lemma}\label{lemm:description_of_w9m}
Let $s$ be a real number such that $0<s<\sqrt3/3$, implying
\[
\frac{\sqrt3}{3}<\left|f_3\big(f_3(s)\big)\right|<\sqrt3<|f_3(s)|.
\]
Let $X$ be the real M-curve defined by the equation
\[
y^2=Q_s(x)=x(x+1)\big(x-a(s)\big)\big(x-b(s)\big)\big(x-c(s)\big),
\]
with $a(s)=s^2$, $b(s)=f_3\big(f_3(s)\big)^2$ and $c(s)=f_3(s)^2$.
Then $X$ is in the family $W_9$.
Conversely, every real M-curve in the family $W_9$ admits such a description.
\end{lemma}
As a consequence, we have the following:
\begin{proposition}
There exists a bijection between the set of real automorphism classes of real M-curves in $W_9$ and the interval $]0;\sqrt{3}/{3}[$.
\end{proposition}
\subsection{Automorphisms}\label{subsec:proof_autos_w9m}
The preceding discussion encourages to consider the curve defined by an equation of the form \eqref{eq:w9_magic_form} with $u=-18$, that is
\[
y^2=P_u(x)=x(x-1)(x-8+4\sqrt3)(x-2)(x-8-4\sqrt3).
\]
This curve admits an order $4$ automorphism induced by the M\"obius transformation $x\mapsto x/(x-1)$.
Applying the transformation $x\mapsto x-1$ to the set of the roots of the polynomial $P_u$, we then get the equation
\[
y^2=x(x^2-1)(x-a)(x-1/a)\text{ with }a=7-4\sqrt3.
\]
By Example \ref{exam:3-square-tiled_surface} this curve is defined by the $3$-square-tiled translation surface.
We note that $7-4\sqrt3=(2-\sqrt3)^2$ with $0<2-\sqrt3<\sqrt3/3$, and that
\[
f_3(2-\sqrt3)^2=7+4\sqrt3=\frac1a\text{ and }f_3\big(f_3(2-\sqrt3)\big)^2=1,
\]
hence this curve is defined by an equation of the form \eqref{eq:w9_order3_auto_form} with $s=2-\sqrt3$.
By Example \ref{exam:order4_automorphism}, the Riemann surface defined by the $3$-square-tiled translation surface admits an order $4$ automorphism induced by an affine transformation.
In order to weaken this condition, we could consider lower order automorphisms of the Riemann surface, for example non-hyperelliptic holomorphic involutions.
However, we observe that in genus $2$ such automorphisms can not be induced by affine transformations:
\begin{lemma}
Let $(X,\omega)$ be a translation surface in $\mathcal{H}(2)$ and $\varphi$ be an order $2$ automorphism defined by an order $2$ automorphism affine with respect to $\omega$.
Then $\varphi$ is the hyperelliptic involution $h_X$.
\end{lemma}
\begin{proof}
Let $\varphi$ be such an automorphism: since $X$ is hyperelliptic, then following \cite[Theorem~V.2.13]{farkas&kra92}, $\varphi$ must satisfy one of the following:
\begin{enumerate}[(a)]
\item $\varphi$ has no fixed point;
\item $\varphi$ only fixes non-Weierstrass points;
\item $\varphi$ is the hyperelliptic involution.
\end{enumerate}
Now $\varphi$ must fix the double zero of $\omega$, which is necessarily a Weierstrass point, hence the conclusion.
\end{proof}
We now prove Proposition \ref{prop:autos_w9m} restated as follows.
\begin{proposition}
Let $s$ be a real number such that $0<s<\sqrt3/3$ and let $X$ be the real M-curve defined by the equation
\[
y^2=Q_s(x)=x(x+1)(x-s^2)\Big(x-f_3\big(f_3(s)\big)^2\Big)\big(x-f_3(s)^2\big)
\]
Then $\AUT X\neq\langle h_X\rangle$ if, and only if $s=2-\sqrt3$.
\end{proposition}
\begin{proof}
Considering Theorem \ref{theo:cirre}, it is sufficient to consider M\"obius transformations that could give an order $2$ automorphism.
By applying a suitable M\"obius transformation to the roots of $Q_s$, we can easily adapt the conditions ensuring the existence of non-trivial automorphisms stated in the theorem to equations of the form \eqref{eq:w9_order3_auto_form} with $0<a(s)<b(s)<c(s)$ for all $s\in]0;\sqrt3/3[$.
The possibilities are the following:
\begin{enumerate}[(a)]
\item the M\"obius transformation
\[
x\mapsto\frac{c(s)-b(s)}{b(s)-a(s)}\frac{x-a(s)}{x-c(s)},
\]
maps $(a,b,c)$ to $(0,-1,\infty)$ and induces a holomorphic involution on $X$ if, and only if we have
\[
a(s)=b(s)-1+\frac{b(s)}{c(s)}.
\]
Calculations lead to
\[
\frac{b(s)}{c(s)}=-\frac{16\sqrt3x(x^2+1)}{(x+\sqrt3)^2(\sqrt3x+1)^2}
\]
then to
\[
b(s)-1+\frac{b(s)}{c(s)}-a(s)=-\frac{(x^2+1)(3x^4+8\sqrt3x^3+18x^2+16\sqrt3x-9)}{(x+\sqrt3)^2(\sqrt3x+1)^2}.
\]
The degree $4$ polynomial in the numerator admits two real roots, namely $-2-\sqrt3$ and $2-\sqrt3$, the latter being the only one in the interval $]0;\sqrt3/3[$.
According to the above discussion at the beginning of this section, this curve has an order $4$ automorphism;
\item the M\"obius transformation
\[
x\mapsto a(s)\frac{x+1}{x-a(s)}
\]
induces an automorphism on $X$ if, and only if
\[
a(s)=\frac{b(s)c(s)}{1+b(s)+c(s)}.
\]
The only real solutions lead to the singular curve of equation
\[
y^2=x(x+1)(x-\sqrt3/3)(x+\sqrt3/3)
\]
corresponding to $s=\sqrt3/3$;
\item the M\"obius transformation
\[
x\mapsto\frac{c(s)-x}{x+1}
\]
induces an automorphism if, and only if
\[
a(s)=\frac{c(s)-b(s)}{1+b(s)},
\]
which gives the singular curve defined by the equation
\[
y^2=x^2(x+1)(x-\sqrt{3})(x+\sqrt{3})\]
corresponding to $s=0$.
Note that the M\"obius transformation $x\mapsto1/x$ induces an automorphism between the two curves defined by $s=0$ and $s=\sqrt3/3$;
\item lastly, the curve $X$ has a holomorphic involution induced by
\[
x\mapsto\frac{a(s)-b(s)}{b(s)-c(s)}\frac{x-c(s)}{x-a(s)}
\]
if, and only if
\[
a(s)=\frac{b(s)}{1-b(s)+c(s)},
\]
which also gives the solution $s=2-\sqrt{3}$.
\end{enumerate}
Calculations are tedious, but routine.
\end{proof}
\section{Periods of real M-curves in $W_9$}\label{sec:periods_of_real_mcurves_in_w9}
\subsection{Theta characteristics}\label{subsec:theta-characteristics}
\subsubsection*{Definitions and elementary properties}\label{paragraph:definitions_and_properties}
Let $z\in\C^g$ and $Z\in\frak{S}_g$, the Riemann $\vartheta$ function is defined by
\begin{equation}\label{eq:theta}
\vartheta(z,Z)=\sum_{k\in\Z^g} \exp(\pi i\T{k}Zk+2\pi i\T{k}z).
\end{equation}
One shows that the above series defines a holomorphic function on $\C^g\times\frak{S}_g$ (see \cite[chap.~II, Proposition~1.1]{mumford_tata1}).
Let $m,n\in\frac12\Z^g$, we define order $2$ theta characteristics by
\begin{align*}
\thetabc{2m\\2n}(z,Z) &= \sum_{k\in\Z^g} \exp\big(\pi i\T{(k+m)}Z(k+m)+2\pi i\T{(k+m)}(z+n)\big)\\
&= \exp\big(\pi i\T{m}Zm+2\pi i\T{m}(z+n)\big)\vartheta(z+Zm+n,Z),
\end{align*}
which, by the above identity, are also holomorphic functions on $\C^g\times\frak{S}_g$.
The following proposition points out well known properties of the function $z\mapsto\thetasc{2m\\2n}(z,Z)$.
\begin{proposition}\label{prop:theta-properties}
Let $Z\in\frak{S}_g$, $m,n\in\frac12\Z^g$ and $p,q\in\Z^g$, then for every $z\in\C^g$, the functions $\thetasc{2m\\2n}$ satisfy:
\begin{equation}\label{eq:theta-quasi_periodicity}
\thetabc{2m\\ 2n}(z,Z) = \exp\big(\pi i\T{p}Zp+2\pi i\T{p}(z+n)-2\pi i \T{m}q\big) \thetabc{2m\\ 2n}(z+Zp+q,Z)
\end{equation}
and
\begin{equation}\label{eq:theta-mod2}
\thetabc{2m+2p\\ 2n+2q}(z,Z) = \exp(2\pi i\T{m}q) \thetabc{2m\\ 2n}(z,Z).
\end{equation}
One also has:
\begin{equation}\label{eq:theta-even_odd}
\thetabc{2m\\ 2n}(-z,Z) = \exp(4\pi i\T{m}n)\thetabc{2m\\ 2n}(z,Z).
\end{equation}
\end{proposition}
\noindent See for example \cite[p.~123]{mumford_tata1} for \eqref{eq:theta-quasi_periodicity} and \eqref{eq:theta-mod2}, and \cite[\S II.3, Proposition 3.14]{mumford_tata1} for \eqref{eq:theta-even_odd}.
\begin{remark}\label{rema:theta-characteristics_mod2}
According to identity \eqref{eq:theta-even_odd}, for all $m,n\in\frac12\Z^g$, the function $z\mapsto\thetasc{2m\\2n}(z,Z)$ is even (resp. odd) if and only if $4\T{m}n\equiv0\mod2$ (resp. $4\T{m}n\equiv1\mod2$).
There are exactly $2^{2g}$ order $2$ theta characteristics, among which $2^{g-1}(2^g+1)$ are even and $2^{g-1}(2^g-1)$ are odd functions (see \cite[Corollary~VI.1.5]{farkas&kra92}).
\end{remark}
\subsubsection*{Modular transformation formula}\label{paragraph:modular_formula}
The following describes how $Z\mapsto\thetasc{2m\\2n}(z,Z)$ transforms under the action of the symplectic group.
\begin{theorem}\label{theo:theta_modular_formula}
Let $m,n\in\frac12\Z^g$ and $M=(\begin{smallmatrix}\alpha&\beta\\ \gamma&\delta\end{smallmatrix})\in\SP(2g,\Z)$.
For every $(z,Z)\in\C^g\times\frak{S}_g$ we define
\[
M(z,Z)=\left(\T{(\gamma Z+\delta)}^{-1}z,(\alpha Z+\beta)(\gamma Z+\delta)^{-1}\right).
\]
Then the following transformation formula holds:
\[\thetabc{2m'\\2n'}\big(M(z,Z)\big)=\zeta_M\exp\left(\pi i\T{z}(\gamma Z+\delta)^{-1}\gamma z\right)\det(\gamma Z+\delta)^{\frac{1}{2}}\thetabc{2m\\2n}(z,Z)
\]
with
\[
\begin{pmatrix}m'\\ n'\end{pmatrix}
=
\begin{pmatrix}\delta m-\gamma n\\ -\beta m+\alpha n\end{pmatrix}
+\frac12
\begin{pmatrix}\DIAG(\gamma\T{\delta})\\ \DIAG(\alpha\T{\beta})\end{pmatrix},
\]
where $\DIAG(N)=(N_{11},\ldots,N_{gg})$ for $N\in\M_g(\C)$, and where $\zeta_M\in\C^*$ is a eighth root of the unity only depending on $M$.
\end{theorem}
\noindent See \cite[\S II.5, pp.~189-197]{mumford_tata1} for a proof.
\subsubsection*{Theta characteristics and hyperelliptic curves}\label{paragraph:theta-characteristics_and_hyperelliptic}
Let $X$ be a genus $g$ curve and $Z\in\frak{S}_g$ a period matrix of $X$.
Let $m,n\in(\rquotient{\Z}{2\Z})^g$, from now on we will denote
\[
\thetabc{m\\ n}(Z)=\thetabc{m\\ n}(0,Z).
\]
The \emph{theta characteristics of $Z$} are the values $\thetasc{m\\ n}(Z)$.
A theta characteristic is said to be even (resp. odd) if $\T{m}n$ is even (resp. odd).
In particular, every odd theta characteristic is zero.
\begin{remark}\label{rema:theta-mod2}
If $\thetasc{m\\ n}(Z)$ is zero, then by \eqref{eq:theta-mod2}, for all $p,q\in(\Z/2\Z)^g$ such that $p,q\equiv0\mod2$, the theta characteristic $\thetasc{m+p\\ n+q}(Z)$ is also zero.
\end{remark}
The important role played by theta characteristics in the theory of hyperelliptic curves is illustrated by the following result, stated here in the specific case of genus $3$.
\begin{theorem}\label{theo:hyperelliptic_genus3_thetanull}
Let $Z$ be a period matrix of a genus $3$ curve $X$.
If $X$ is not hyperelliptic, then no even theta characteristic of $Z$ is zero, and $X$ is hyperelliptic if, and only if exactly one even theta characteristic of $Z$ is zero.
\end{theorem}
\noindent The reader may refer to \cite[\S IIIa.9, Theorem~9.1]{mumford_tata2}.
\subsection{Double cover associated to a curve in $W_9$}\label{subsec:double_cover}
In this section we describe the construction of a non ramified double cover of a translation surface in $\mathcal{H}(2)$ tiled by three parallelograms.
\subsubsection*{Construction}\label{paragraph:construction_of_double_covers}
Let $(X,\omega)$ be a translation surface in the $\SL_2(\R)$-orbit of the L-shaped surface tiled by three squares.
Such a surface is geometrically defined by the quotient $(\rquotient{\mathcal{P}}{\sim},dz)$ where $\mathcal{P}$ is the Euclidean hexagon obtained by assembling three copies of a parallelogram of unit area, as decribed in Figure \ref{fig:double_cover}.
\begin{figure}[!ht]
\centering \input{fig-double-cover.tex}
\caption{Double cover: identifications and Weierstrass points}\label{fig:double_cover}
\end{figure}
In this representation, the six Weierstrass points of $X$ correspond to:
\begin{itemize}
\item the cone-type singularity of angle $6\pi$, represented by black dots in Figure \ref{fig:double_cover};
\item the center of the parallelograms and the middle points of the two horizontal and vertical sides, pairwise identified, of the two non-adjacent parallelograms, all represented by small circles in Figure \ref{fig:double_cover}.
\end{itemize}
We construct the non-ramified double cover $p:(\hat{X},\hat{\omega})\to(X,\omega)$ by assembling $(X,\omega)$ with its image by the symmetry whose center is one of the two Weierstrass points that is neither the singularity, nor the center of a parallelogram.
More precisely, we can suppose that, up to a translation, the point denoted by $P_1$ in Figure \ref{fig:double_cover} is $0$ and we denote by $-\mathcal{P}$ the image of the polygon $\mathcal{P}$ by $z\mapsto-z$.
Note that the choice of one or another of the two Weierstrass points $P_1$ or $P_2$ has no incidence on the construction, as is readily checked by reassembling the parallelograms.
Then $\mathcal{P}\cup(-\mathcal{P})$ is an Euclidean dodecagon and we consider the identifications by translation specified in Figure \ref{fig:double_cover}.
The quotient $\big(\rquotient{\mathcal{P}\cup(-\mathcal{P})}{\sim},dz\big)$ defines a staircase-shaped translation surface tiled by six squares, whose vertices are identified to two cone-type singularities of angle $6\pi$, marked by black disks and squares in Figure \ref{fig:double_cover}.
We thus obtain a genus $3$ translation surface $(\hat{X},\hat{\omega})$ such that $\hat{\omega}$ has two double zeros on $\hat{X}$.
\subsubsection*{Automorphisms}\label{subs:autos-revt-3c}
By a classical result of algebraic geometry, the algebraic curve $\hat{X}$ defined above is hyperelliptic, as a non-ramified cover of a genus $2$ curve; its eight Weierstrass points are
\begin{itemize}
\item the two cone-type singularities;
\item the centers of the parallelograms, represented by small circles in Figure \ref{fig:double_cover}.
\end{itemize}
The central symmetry defines an involution that fixes exactly four points. These points are represented by small crosses in Figure \ref{fig:double_cover} and correspond to:
\begin{itemize}
\item the center of symmetry of the assembling of parallelograms;
\item the middle points of the two horizontal sides of the two central parallelograms;
\item the middle points of the four vertical sides of the two parallelograms located at the extremities.
\end{itemize}
\noindent The central symmetry then induces a non-hyperelliptic order $2$ automorphism on $\hat{X}$, which will be denoted by $\psi_2$.
The curve $\hat{X}$ then admits an equation of the form
\begin{align*}
w^2&=\hat{P}(z)=(z^2+1)(z^2-a^2)(z^2-b^2)(z^2-c^2)\\
\text{with }\hat{\omega}&=\frac{dz}{w}+\frac{z^2dz}{w},
\end{align*}
for which $\psi_2$ is defined by $(z,w)\mapsto(-z,w)$.
Composing $\psi_2$ with the hyperelliptic involution $h_{\hat{X}}:(z,w)\mapsto(z,-w)$ yields an extra involution $\tau:(z,w)\mapsto(-z,-w)$, that is fixed point free and such that $X=\hat{X}/\langle\tau\rangle$; the covering map $p:\hat{X}\to X$ is then given by $(z,w)\mapsto(z^2,zw)$.
The algebraic curve $X$ then admits the equation
\begin{align*}
y^2&=P(x)=x(x+1)(x-a^2)(x-b^2)(x-c^2)\\
\text{with }\omega&=\frac12\left(\frac{dx}{y}+\frac{xdx}{y}\right).
\end{align*}
Furthermore, the curve $\hat{X}$ admits an order $3$ automorphism defined as follows.
Consider the affine transformation induced by rotation of angle $\pi$ around each of the two cone-type singularities, operating by circular permutation of the three parallelograms belonging to a same diagonal row.
Letting this transformation act three times is equivalent to replace $\hat{\omega}$ by $-\hat{\omega}$.
Now this operation leaves invariant the quadratic differential $\hat{\omega}^2$ that induces the complex structure on $\hat{X}$ (see Remark \ref{rema:half-translation_surface}).
The automorphism thus defined on $\hat{X}$ is of order $3$ and will be denoted by $\psi_3$.
\subsubsection*{Homology basis and periods}\label{paragraph:curve_and_cover_homology_bases}
Let $X$ be a genus $2$ algebraic curve defined by
\[
y^2=P(x)=x(x+1)(x-a^2)(x-b^2)(x-c^2).
\]
Let $\pi:X\to\mathbb{P}_{\C}^1$ be the projection $(x,y)\mapsto x$.
Using the construction presented in p.~\pageref{paragraph:hyperelliptic_homology_basis} applied to
\[
x_1=-1,\ x_2=0,\ x_3=a^2,\ x_4=b^2\ \text{and}\ x_ 5=c^2,
\]
we obtain simple closed curves $\delta_1,\ldots,\delta_6$ in $X$, oriented such that the intersection numbers are $(\delta_j\cdot\delta_{j+1})=1$ ($j\mod6$), all others being zero, and such that $\sum_{j=1}^3\delta_{2j}=0$ and $\sum_{j=1}^3\delta_{2j-1}=0$.
Let $\hat{X}$ be the genus $3$ hyperelliptic curve defined by
\begin{equation}\label{eq:double_cover}
w^2=\hat{P}(z)=(z^2+1)(z^2-a^2)(z^2-b^2)(z^2-c^2)
\end{equation}
and let $\hat{\pi}:\hat{X}\to\mathbb{P}_{\C}^1$ be the projection $(z,w)\mapsto z$.
We proceed the same way by applying the construction in p.~\pageref{paragraph:hyperelliptic_homology_basis} to
\[
x_1=-c,\ x_2=-b,\ x_3=-a,\ x_4=i,\ x_ 5=-i,\ x_6=a,\ x_7=b\ \text{and}\ x_8=c.
\]
We denote by $\gamma_1,\ldots,\gamma_8$ the obtained cycles, satisfying $(\gamma_j\cdot\gamma_{j+1})=1$ ($j\mod8$), all others being zero, such that $\sum_{j=1}^4\gamma_{2j}=0$ and $\sum_{j=1}^4\gamma_{2j-1}=0$.
\begin{figure}[!ht]
\centering \input{fig-homology_bases.tex}
\caption{Homology bases for $X$ and $\hat{X}$}\label{fig:homology_bases}
\end{figure}
Now let
\begin{equation}\label{eq:double_cover_homology_basis}
\begin{array}{ll}
\hat{\alpha}_1=\gamma_1, &\hat{\beta}_1=-\gamma_2,\\
\hat{\alpha}_2=\gamma_1+\gamma_3+\gamma_4, &\hat{\beta}_2=-\gamma_4,\\
\hat{\alpha}_3=\gamma_7, &\hat{\beta}_3=\gamma_6
\end{array}
\end{equation}
and
\begin{equation}\label{eq:curve_homology_basis}
\begin{array}{ll}
\alpha_1=\delta_1-\delta_6, &\beta_1=\delta_1,\\
\alpha_2=\delta_4, &\beta_2=\delta_3.
\end{array}
\end{equation}
Then $\hat{\mathcal{B}}=(\hat{\alpha}_1,\hat{\alpha}_2,\hat{\alpha}_3,\hat{\beta}_1,\hat{\beta}_2,\hat{\beta}_3)$ and $\mathcal{B}=(\alpha_1,\alpha_2,\beta_1,\beta_2)$ are symplectic bases for $\HH_1(\hat{X},\Z)$ and $\HH_1(X,\Z)$ respectively, represented in Figure \ref{fig:homology_bases}.
\begin{remark}\label{rema:hyperelliptic_M-curve_homology_basis}
If $a^2$, $b^2$ and $c^2$ are positive real numbers, then $X$ is a real genus $2$ M-curve and $\hat{X}$ is a real genus $3$ curve with three real components: this case corresponds to the situation where the translation surfaces $(X,\omega)$ and $(\hat{X},\hat{\omega})$ are tiled by rectangles.
We can then specialize the above construction: we call $\delta_1$ the pullback of $[-1;0]$ to $X$ by $\pi$, $\delta_2$ the pullback of $[0;a^2]$ and so on.
Since $P$ is non-zero in the upper half-plane $\mathbb{H}$ that is simply connected, we can choose on $\mathbb{H}$ the determination of $\sqrt{P}$ that is real and positive on $[-1;0]$.
This determination can be extended to $\R$ and even to the strips below the open intervals bounded by the roots of $P(x)$.
Note that it will then be pure imaginary with positive imaginary part on $]-\infty;-1]$, pure imaginary with negative imaginary part on $[0;a]$, real and negative on $[a;b]$, and so on (see also \cite[Lemma~2.4]{silhol01b}).
We construct in the same way the cycles $\gamma_j$'s on $\hat{X}$ for $j=1,\ldots,8$: the paths $\varepsilon_i$ are chosen as intervals in $\R\cup\{\infty\}$ for $i\notin\{3,4,5\}$, $\varepsilon_4$ as the interval from $i$ to $-i$ contained in the imaginary axis and $\varepsilon_3$ and $\varepsilon_5$ symmetric to the origin.
The orientation is defined by the choice of a determination of $\sqrt{\hat{P}}$ that is real and positive on $[-b;-a]$.
\end{remark}
The above construction allows to give an expression of the periods of $X$ in terms of the periods of its double cover $\hat{X}$.
\begin{lemma}\label{lemm:double_cover_periods_auto2}
Let $X$ be a genus $2$ algebraic curve defined by an equation of the form
\[
y^2=P(x)=x(x+1)(x-a^2)(x-b^2)(x-c^2)
\]
where $a$, $b$ and $c$ are complex numbers such that $a^2$, $b^2$ and $c^2$ are distinct and different from $0$ and $-1$, and $\hat{X}$ the double cover defined by
\[
w^2=\hat{P}(z)=(z^2+1)(z^2-a^2)(z^2-b^2)(z^2-c^2).
\]
Then the period matrix $\hat{Z}$ of $\hat{X}$ associated to the basis $\hat{\mathcal{B}}$ of $\HH_1(\hat{X},\Z)$ has the form
\[
\hat{Z}=
\begin{pmatrix}
z_1&z_{12}&z_{13}\\
z_{12}&z_2&z_{12}\\
z_{13}&z_{12}&z_1
\end{pmatrix}
\]
and the period matrix $Z$ of $X$ associated to the basis $\mathcal{B}$ of $\HH_1(X,\Z)$ is given by
\[
Z=
\begin{pmatrix}
2z_{2}&2z_{12}\\
2z_{12}&z_1+z_{13}
\end{pmatrix}.
\]
\end{lemma}
\begin{proof}
In order to make the calculation clear, the reader can consider the specialization of the construction of the homology basis $\hat{\mathcal{B}}$ to the case where $a$, $b$ and $c$ are real numbers such that $0<a<b<c$, see Remark \ref{rema:hyperelliptic_M-curve_homology_basis} above.
The curve $\hat{X}$ admits the non-hyperelliptic order $2$ automorphism defined by
\[
\psi_2:(z,w)\mapsto(-z,w).
\]
We note that ${\psi_2}_*(\gamma_1)=-\gamma_7$ as $\gamma_1$ and $\gamma_7$ have the same orientation, and that ${\psi_2}_*(\gamma_2)=\gamma_6$ since $\gamma_2$ and $\gamma_6$ have opposite orientations.
Moreover, we have ${\psi_2}_*(\gamma_3)=-\gamma_5$ and ${\psi_2}_*(\gamma_4)=-\gamma_4$.
That yields to ${\psi_2}_*(\hat{\alpha}_1)=-\hat{\alpha}_3$, ${\psi_2}_*(\hat{\alpha}_2)=-\hat{\alpha}_2$ and ${\psi_2}_*(\hat{\alpha}_3)=-\hat{\alpha}_1$ and the same holds for the $\hat{\beta}_j$'s.
We thus obtain the rational representation of $\psi_2$ in the symplectic basis $\hat{\mathcal{B}}$:
\[
\T{M_2}=
\begin{pmatrix}
0&0&-1&0&0&0\\
0&-1&0&0&0&0\\
-1&0&0&0&0&0\\
0&0&0&0&0&-1\\
0&0&0&0&-1&0\\
0&0&0&-1&0&0
\end{pmatrix}
=\rho_\Q(\psi_2).
\]
Then the matrix $\hat{Z}$ is stable under the action of the symplectic matrix $M_2$, hence the expression for $\hat{Z}$.
We denote by
\[
(\hat{\omega}_1,\hat{\omega}_2,\hat{\omega}_3)=\left(\frac{dz}{w},\frac{zdz}{w},\frac{z^2dz}{w}\right)
\]
the usual basis for the holomorphic $1$-forms on $\hat{X}$, and we introduce the matrices
\[
\hat{A}=\left(\int_{\hat{\alpha}_j}\hat{\omega}_k\right)_{j,k}\text{ and }\hat{B}=\left(\int_{\hat{\beta}_j}\hat{\omega}_k\right)_{j,k}.
\]
Noting that ${\psi_2}^*(\hat{\omega}_k)=-\hat{\omega}_k$ for $k=1$ and $3$, we deduce from the above calculation of $M_2$ that $\hat{A}_{11}=\hat{A}_{31}$ and $\hat{A}_{13}=\hat{A}_{33}$.
Also, since ${\psi_2}^*(\hat{\omega}_2)=\hat{\omega}_2$ then we have $\hat{A}_{12}=-\hat{A}_{32}$ and $\hat{A}_{22}=0$.
We obtain identical relations for $\hat{B}$, thus we have:
\[
\hat{A}=
\begin{pmatrix}
a_1&a_2&a_3\\
a_{21}&0&a_{23}\\
a_1&-a_2&a_3
\end{pmatrix}
\text{ and }
\hat{B}=\begin{pmatrix}
b_1&b_2&b_3\\
b_{21}&0&b_{23}\\
b_1&-b_2&b_3
\end{pmatrix}.
\]
Then we get $\hat{Z}=\hat{A}\hat{B}^{-1}$ under the announced form, with
\begin{align*}
z_1&=\frac{1}{2}\frac{a_2}{b_2}+\frac{1}{2}\frac{a_1b_{23}-a_3b_{21}}{b_1b_{23}-a_3b_{21}},\\
z_{12}&=\frac{a_3b_1-a_1b_3}{b_1b_{23}-b_3b_{21}}=\frac{1}{2}\frac{a_{21}b_{23}-a_{23}b_{21}}{b_1b_{23}-b_3b_{21}},\\
z_{13}&=\frac{1}{2}\frac{a_1b_{23}-a_3b_{21}}{b_1b_{23}-b_3b_{21}}-\frac{1}{2}\frac{a_2}{b_2},\\
z_2&=\frac{a_{23}b_1-a_{21}b_3}{b_1b_{23}-b_3b_{21}}.
\end{align*}
The curve $X$ is the quotient of $\hat{X}$ by the fixed point free involution $\tau:(z,w)\mapsto(-z,-w)$, which leaves invariant $\hat{\omega}_1$ and $\hat{\omega}_3$ on $\hat{X}$.
These differentials then induce holomorphic forms on $X$, which will be denoted by $\omega_1$ and $\omega_2$ respectively.
Let
\[
A=\left(\int_{\alpha_j}\omega_k\right)_{j,k}\text{ and }B=\left(\int_{\beta_j}\omega_k\right)_{j,k}.
\]
Let $p:\hat{X}\to X$ be the quotient map, then $p$ sends $\hat{\alpha}_1$ and $\hat{\alpha}_3$ onto $\alpha_2$, and $\hat{\alpha}_2$ onto $\alpha_1$, whereas $\hat{\beta}_1$ and $\hat{\beta}_3$ are sent onto $\beta_2$, and $\hat{\beta}_2$ onto $\beta_1$.
Furthermore, the restriction of $p$ is of degree $2$ on $\hat{\beta}_2$ and bijective on each $\hat{\alpha}_j$, $\hat{\beta}_j$ for $j\neq 2$.
We then have
\[
A=
\begin{pmatrix}
a_{21}&a_{23}\\
a_1&a_3
\end{pmatrix}
\text{ and }
B=
\begin{pmatrix}
\frac12b_{21}&\frac12b_{23}\\
b_1&b_3
\end{pmatrix},
\]
and a direct calculation yields the expression of the period matrix $Z=AB^{-1}$ of the curve $X$.
\end{proof}
\subsection{Characterization of the cover in terms of the periods}\label{subsec:characterization_of_cover}
This section is devoted to the proof of Theorem \ref{theo:double_cover_thetanull}.
In the following, we deal with real M-curves in $W_9$.
This is only to fix ideas because the arguments used here work verbatim for the non-real case: the only difficulty lies in expressing the choice of arcs in $\mathbb{P}^1(\mathbb{C})$ whose pullbacks will provide suitable cycles for the construction of the symplectic bases $\hat{\mathcal{B}}$ and $\mathcal{B}$.
The method employed to exhibit the form of the period matrix and identify the corresponding theta characteristic is inspired from \cite[Theorem~5.5]{silhol01b}.
We first establish the expression of a period matrix of $\hat{X}$ when $X$ is a real M-curve in $W_9$.
\begin{proposition}\label{prop:double_cover_periods_auto3}
Let $X$ be a real M-curve in the family $W_9$.
Let $\hat{Z}$ be the period matrix of its double cover $\hat{X}$ associated to the symplectic basis $\hat{\mathcal{B}}$ of $\HH_1(\hat{X},\Z)$ described above.
Then $\hat{Z}$ has the form
\begin{equation} \label{eq:genus3_auto3_periods}
\hat{Z}=
\begin{pmatrix}
iy_1 & \frac12iy_1 & iy_{13}\\
\frac12iy_1 & \frac12+\frac34iy_1-\frac12iy_{13} & \frac12iy_1\\
iy_{13} & \frac12iy_1 & iy_1
\end{pmatrix}
\end{equation}
with $y_1,y_{13}\in\mathbb{R}$.
\end{proposition}
\begin{proof}
Let $f_3$ be the M\"obius transformation defined in \S\ref{subsec:description_of_w9}, then $X$ admits the equation
\[
y^2=x(x+1)(x-a^2)(x-b^2)(x-c^2)
\]
where $a$, $b$ and $c$ are real numbers satisfying the conditions of Lemma \ref{lemm:description_of_w9m}.
The double cover $\hat{X}$ is defined by
\[
w^2=(z^2+1)(z^2-a^2)(z^2-b^2)(z^2-c^2),
\]
and $f_3$ induces an order $3$ automorphism on $\hat{X}$, denoted by $\psi_3$, defined by
\[
\psi_3:(z,w)\mapsto\left(\frac{z+\sqrt{3}}{-\sqrt{3}z+1},\frac{16w}{(1-\sqrt{3}z)^4}\right).
\]
Let $(\hat{\alpha}_j,\hat{\beta}_j)$ ($j=1,2,3$), $(\hat{\omega}_1,\hat{\omega}_2,\hat{\omega}_3)$ and $\hat{A}$, $\hat{B}$ be as in p.~\pageref{paragraph:curve_and_cover_homology_bases}.
From the proof of Lemma \ref{lemm:double_cover_periods_auto2}, we know that
$\hat{A}_{11}=\hat{A}_{31}$, $\hat{A}_{13}=\hat{A}_{33}$, $\hat{A}_{12}=-\hat{A}_{32}$ and $\hat{A}_{22}=0$ on the one side, and $\hat{B}_{11}=\hat{B}_{31}$, $\hat{B}_{13}=\hat{B}_{33}$, $\hat{B}_{12}=-\hat{B}_{32}$ and $\hat{B}_{22}=0$ on the other side.
A direct calculation gives
\[
{\psi_3}^*(\hat{\omega}_1)=\frac14\hat{\omega}_1-\frac{\sqrt3}{2}\hat{\omega}_2+\frac34\hat{\omega}_3
\]
and, noting that ${\psi_3}_*(\hat{\alpha}_3)=\hat{\alpha}_1$, we get $\hat{A}_{12}=\frac{\sqrt3}{2}(\hat{A}_{11}-\hat{A}_{13})$.
Since ${\psi_3}_*(\hat{\beta}_1)=\hat{\beta}_3$, we also have $\hat{B}_{12}=\frac{\sqrt3}{2}(\hat{B}_{13}-\hat{B}_{11})$.
As ${\psi_3}_*(\hat{\alpha}_1)=\hat{\alpha}_1-2\hat{\alpha}_2+\hat{\alpha}_3+\hat{\beta}_2$, we have
\begin{align*}
\int_{{\psi_3}_*(\hat{\alpha}_1)}\hat{\omega}_1 &= \hat{A}_{11}-2\hat{A}_{21}+\hat{A}_{31}+\hat{B}_{21}\\
=\int_{\hat{\alpha}_1}{\psi_3}^*(\hat{\omega}_1) &= \frac14\hat{A}_{11}-\frac{\sqrt3}{2}\hat{A}_{12}+\frac34\hat{A}_{13},
\end{align*}
hence $\hat{A}_{21}=\frac54\hat{A}_{11}-\frac34\hat{A}_{13}+\frac12\hat{B}_{21}$.
Noting that ${\psi_3}_*(\hat{\beta}_3)=\hat{\beta}_1+\hat{\beta}_2+\hat{\beta}_3$, the same arguments yield $\hat{B}_{21}=\frac32\hat{B}_{13}-\frac52\hat{B}_{11}$.
Considering $\int_{{\psi_3}_*(\hat{\alpha}_1)}\hat{\omega}_3=\int_{\hat{\alpha}_1}{\psi_3}^*(\hat{\omega}_3)$ with
\[
{\psi_3}^*(\hat{\omega}_3)=\frac34\hat{\omega}_1+\frac{\sqrt3}{2}\hat{\omega}_2+\frac14\hat{\omega}_3,
\]
we find $\hat{A}_{23}=\frac54\hat{A}_{13}-\frac34\hat{A}_{11}+\frac12\hat{B}_{23}$ and in a similar way, we finally obtain $\hat{B}_{23}=\frac32\hat{B}_{11}-\frac52\hat{B}_{13}$.
We have shown that $\hat{A}$ and $\hat{B}$ have the form
\begin{align*}
\hat{A} &=
\begin{pmatrix}
a_1 & \frac{\sqrt{3}}{2}(a_1-a_3) & a_3\\
\frac{5}{4}(a_1-b_1)+\frac{3}{4}(b_3-a_3) & 0 & \frac{3}{4}(b_1-a_1)+\frac{5}{4}(a_3-b_3)\\
a_1 & \frac{\sqrt{3}}{{2}}(a_3-a_1) & a_3
\end{pmatrix}\\
\hat{B} &= \begin{pmatrix}
b_1 & \frac{\sqrt{3}}{{2}}(b_3-b_1) & b_3\\
\frac{3}{2}b_3-\frac{5}{2}b_1 & 0 & \frac{3}{2}b_1-\frac{5}{2}b_3\\
b_1 & \frac{\sqrt{3}}{{2}}(b_1-b_3) & b_3
\end{pmatrix}
\end{align*}
with $a_1$, $a_3\in i\R$ and $b_1$, $b_3\in\R$ (by definition of the $\alpha_j$'s and $\beta_j$'s for $j=1,3$ and Remark \ref{rema:hyperelliptic_M-curve_homology_basis}).
Then the period matrix of $\hat{X}$ associated to the symplectic basis $\hat{\mathcal{B}}$ for $\HH_1(\hat{X},\Z)$ is
\begin{equation}
\hat{A}\hat{B}^{-1}=
\begin{pmatrix}
z_1 & \frac{1}{2}z_1 & z_{13}\\
\frac{1}{2}z_1 & \frac{1}{2}+\frac{3}{4}z_1-\frac{1}{2}z_{13} & \frac{1}{2}z_1\\
z_{13} & \frac{1}{2}z_1 & z_1
\end{pmatrix}
\end{equation}
where $z_1,z_{13}\in i\R$ are defined by
\begin{align*}
z_1 &= \frac{4}{3}\frac{a_3b_1-a_1b_3}{b_1^2-b_3^2}\\
z_{13} &= \frac{1}{3}\frac{a_3b_1-a_1b_3+3(a_1b_1-a_3b_3)}{b_1^2-b_3^2}
\end{align*}
hence the expression for $\hat{Z}$.
\end{proof}
We now compute the period matrix of the double cover of one particular real M-curve in the family $W_9$.
The natural choice consists in considering the curve defined by the translation surface tiled by three squares: by Proposition \ref{prop:autos_w9m} this is the only non-singular curve in this family admitting a non-hyperelliptic automorphism.
An equation of this curve was given in \S\ref{subsec:proof_autos_w9m}.
\begin{lemma}\label{lemm:3-square-tiled_periods}
Let $X_1$ be the real M-curve defined by the $3$-square-tiled translation surface, defined by the equation
\[
y^2=P(x)=x(x^2-1)(x-a^2)\left(x-\frac{1}{a^2}\right)\text{ with }a=2-\sqrt{3}
\]
and let $\hat{X}_1$ be its double cover.
Then the period matrix $\hat{Z}_1$ of $\hat{X}_1$ associated to $\hat{\mathcal{B}}$ is
\[
\hat{Z}_1=
\begin{pmatrix}
\frac43i&\frac23i&\frac13i\\
\frac23i&\frac12+\frac56i&\frac23i\\
\frac13i&\frac23i&\frac43i
\end{pmatrix}.
\]
\end{lemma}
\begin{proof}
The curve $X_1$ admits an order $4$ automorphism induced by $x\mapsto 1/x$.
Its double cover $\hat{X}_1$ is defined by the equation
\[
w^2=\hat{P}(z)=(z^4-1)(z^2-a^2)\left(z^2-\frac{1}{a^2}\right)
\]
and $\varphi$ lifts to an order $4$ automorphism of $\hat{X}_1$, denoted by $\psi_4$ and defined by
\[
\psi_4:(z,w)\mapsto\left(\frac{1}{z},\frac{iw}{z^4}\right).
\]
It is readily checked that
\[
{\psi_4}^*\left(\frac{dz}{w}\right)=i\frac{z^2dz}{w}\text{ and }{\psi_4}^*\left(\frac{z^2dz}{w}\right)=i\frac{dz}{w}.
\]
We also note that ${\psi_4}_*(\hat{\alpha}_1)=-\hat{\beta}_1$ hence, with the notations defined in the proof of Proposition \ref{prop:double_cover_periods_auto3}, we get $\hat{B}_{11}=-i\hat{A}_{13}$ and $\hat{B}_{13}=-i\hat{A}_{11}$.
A direct calculation then gives the period matrix $\hat{Z}_1$.
\end{proof}
\begin{remark}\label{rema:3-square-tiled_surface_period_matrix}
By Lemma \ref{lemm:double_cover_periods_auto2}, the period matrix of $X_1$ associated to the basis $\mathcal{B}$ is
\[
Z_1=
\begin{pmatrix}
1+\frac53i&\frac43i\\
\frac43i&\frac53i
\end{pmatrix}.
\]
\end{remark}
As the hyperelliptic curve $\hat{X}_1$ has many automorphisms, the modular transformation formula will enable us to identify the only even theta characteristic that vanishes for the period matrix $\hat{Z}_1$.
\begin{proposition}\label{prop:3-square-tiled_thetanull}
Let $X_1$ be the real M-curve defined by the $3$-square-tiled translation surface, let $\hat{Z}_1$ be the period matrix of its double cover $\hat{X_1}$ associated to $\hat{\mathcal{B}}$.
Then
\[
\thetasc{1&1&1\\ 1&0&1}(\hat{Z}_1)=0.
\]
\end{proposition}
\begin{proof}
Let $M=(\begin{smallmatrix}\alpha&\beta\\ \gamma&\delta\end{smallmatrix})\in\SP_6(\R)$ and
\[
p=\DIAG(\gamma\T{\delta})\text{ and }q=\DIAG(\alpha\T{\beta}).
\]
Then, following Theorem \ref{theo:theta_modular_formula}, we have the following transformation formula for theta characteristics:
\begin{equation} \label{eq:theta_modular_transformation}
\thetabc{2m\\2n}\big(M(Z)\big)=\phi(M,m,n,Z)\thetabc{2m'\\2n'}(Z),
\end{equation}
with
\begin{equation} \label{eq:characteristics_modular_transformation}
\begin{bmatrix}m'\\ n'\end{bmatrix}=\begin{bmatrix}
\T{\alpha}\left(m-\frac12p\right) +\T{\gamma}\left(n-\frac12q\right)\\
\T{\beta}\left(m-\frac12p\right) +\T{\delta}\left(n-\frac12q\right)
\end{bmatrix}=:M\scar{m\\ n}
\end{equation}
and where $\phi$ is a function, depending only on $M$, on $m,n\in(\rquotient{\mathbb{Z}}{2\mathbb{Z}})^3$ and on $Z\in\frak{S}_3$, that never vanishes.
By construction, $\hat{X}_1$ is a genus $3$ hyperelliptic curve, hence by Theorem \ref{theo:hyperelliptic_genus3_thetanull}, there exists a unique even theta characteristic $\scar{m\\ n}=\scar{m_1&m_2&m_3\\ n_1&n_2&n_3}$ for which $\thetasc{m\\ n}(\hat{Z}_1)=0$.
Period matrices of the form \eqref{eq:genus3_auto3_periods} are stable under the action of the two symplectic matrices
\begin{align*}
M_2&=
\begin{pmatrix}
0&0&-1&0&0&0\\
0&-1&0&0&0&0\\
-1&0&0&0&0&0\\
0&0&0&0&0&-1\\
0&0&0&0&-1&0\\
0&0&0&-1&0&0
\end{pmatrix}
=\T{\rho_\Q(\psi_2)}\\
\text{and }
M_3&=\begin{pmatrix}
1&-2&1&0&1&0\\
1&-1&0&0&0&-1\\
1&0&0&0&0&0\\
0&0&0&0&0&1\\
0&0&0&0&-1&-2\\
0&0&0&1&1&1
\end{pmatrix}
=\T{\rho_\Q(\psi_3)},
\end{align*}
then by equation \eqref{eq:theta_modular_transformation} and Remark \ref{rema:theta-characteristics_mod2}, we must have $M_k\scar{m\\ n}\equiv\scar{m\\ n}\MOD2$ for $k=2$ and $3$.
As a consequence, we obtain
\[
\begin{cases}
m_1\equiv m_2\equiv m_3\MOD2\\
n_1\equiv m_2\equiv n_3\MOD2
\end{cases}
\]
which, among the even theta characteristics, reduces the possibilities to the following three:
\[
\thetasc{0&0&0\\0&1&0},\thetasc{1&1&1\\1&0&1}\text{ and }\thetasc{0&0&0\\0&0&0}
\]
the latter never being zero by Riemann theorem on theta divisor (for instance, see \cite[Theorem~VI.2.4]{farkas&kra92}).
Furthermore, the period matrix $\hat{Z}_1$ is stable under the action of
\[
M_4=
\begin{pmatrix}
0&0&0&1&0&0\\
0&1&0&0&-1&0\\
0&0&0&0&0&1\\
-1&0&0&0&0&0\\
0&2&0&0&-1&0\\
0&0&-1&0&0&0
\end{pmatrix}
=\T{\rho_\Q(\psi_4)},
\]
hence $M_4\scar{m\\ n}\equiv\scar{m\\ n}\MOD2$, which provides the extra condition
\[
m_2\equiv1\MOD2,
\]
hence the conclusion.
\end{proof}
Now we can prove the theorem:
\begin{proof}[Proof of Theorem \ref{theo:double_cover_thetanull}]
From now on we assume that the period matrices of the double covers are associated to the same symplectic basis $\hat{\mathcal{B}}$ for $\HH_1(\hat{X},\Z)$, such as these matrices have the form presented in the theorem.
The set of isomorphism classes of genus $2$ curves defined by an equation of the form
\begin{equation} \label{eq:genus2_order3_auto}
y^2=Q_s(x)=x(x+1)(x-s^2)\big(x-f_3(s)^2\big)\Big(x-f_3\big(f_3(s)\big)^2\Big).
\end{equation}
is connected, hence the associated family of curves also form a connected subset in the moduli space of genus $3$ hyperelliptic curves.
The map associating to the equation of such a double cover its period matrix is continuous, then the set of these matrices is connected.
By Theorem \ref{theo:hyperelliptic_genus3_thetanull}, exactly one even theta characteristic $\thetasc{m\\ n}$vanishes for these period matrices.
As the set of these period matrices is connected and the set of order $2$ theta characteristics is discrete, the same theta characteristic will vanish for the whole family.
Since by Proposition \ref{prop:3-square-tiled_thetanull}, the theta characteristic $\thetasc{1&1&1\\1&0&1}$ is zero for one member of this family, then it also vanishes for the period matrix of any double cover of a curve in the family defined by equation \eqref{eq:genus2_order3_auto}.
\end{proof}
\subsection{Periods of real M-curves from periods of double covers}
\label{subsec:period_of_curves_in_w9}
We now proceed to the proof of the main theorem.
\begin{proof}[Proof of Theorem \ref{theo:w9m_periods}]
Let $(X_1,\omega_1)$ be the L-shaped translation surface tiled by three squares; if $t$ is a real number such that $t>1$, then let $(X_t,\omega_t)=\left(\begin{smallmatrix}1&0\\0&t\end{smallmatrix}\right)\cdot(X_1,\omega_1)$.
By Remark \ref{rema:mcurves_are_teich_def}, Proposition \ref{prop:description_of_w9} and Lemma \ref{lemm:description_of_w9m}, every $(X_t,\omega_t)$ is defined by an equation of the form
\begin{align}
y^2&=Q_s(x)=x(x+1)(x-s^2)\Big(x-f_3\big(f_3(s)\big)^2\Big)\big(x-f_3(s)^2\big)\label{eq:3-square-tiled_surface_final}\\
\text{with }\omega_t&=\lambda_s\left(\frac{dx}{y}+\frac{xdx}{y}\right)\nonumber
\end{align}
for some real number $s$ such that $0<s<\sqrt3/3$ and some constant $\lambda_s\in\C^*$.
We construct from equation \eqref{eq:3-square-tiled_surface_final} a symplectic basis $\tilde{\mathcal{B}}=(\tilde{\alpha}_1,\tilde{\alpha}_2,\tilde{\beta}_1,\tilde{\beta}_2)$ for $\HH_1(X_t,\Z)$ as described in p.~\pageref{paragraph:hyperelliptic_homology_basis}: with the notations defined in Figure \ref{fig:3-square-tiled_deformation}, the point $P_1$ corresponds to $(-1,0)$, $P_2$ to $(0,0)$, $P_3$ to $\left(s^2,0\right)$, $P_4$ to $\left(f_3\big(f_3(s)\big)^2,0\right)$, $P_5$ to $\left(f_3(s)^2,0\right)$ and $P_6$ to the point at infinity.
For all $t\geq1$, we choose the constant $\lambda_s$ such that $\int_{\tilde{\beta}_1}\omega_t=1$.
\begin{figure}[!ht]
\centering \input{fig-3squares-stretched.tex}
\caption{Stretching the $3$-square-tiled surface} \label{fig:3-square-tiled_deformation}
\end{figure}
For $t$ being fixed, let $\eta_1=\omega_t$ and let $\eta_2$ be the unique holomorphic $1$-form on $X_t$ such that $\int_{\tilde{\beta}_1}\eta_2=0$ and $\int_{\tilde{\beta}_2}\eta_2=1$.
As $X_t$ is a real M-curve, and by construction of the homology basis $\tilde{\mathcal{B}}$, the period matrix $A_tB^{-1}$ must satisfy $\RE{(A_tB^{-1})}=0$.
A direct calculation then shows that there exist two unique real numbers $y_t$ and $y'_t$ such that
\[
A_t:=\left(\int_{\tilde{\alpha}_j}\eta_k\right)_{j,k}=\begin{pmatrix}-it & iy_t\\ -2it & iy'_t\end{pmatrix}\text{ and }B:=\left(\int_{\tilde{\beta}_j}\eta_k\right)_{j,k}=\begin{pmatrix}1&0\\-2&1\end{pmatrix},
\]
The basis $\mathcal{B}=(\alpha_1,\alpha_2,\beta_1,\beta_2)$ for $\HH_1(X_t,\Z)$ defined in p.~\pageref{paragraph:curve_and_cover_homology_bases} is obtained from $\tilde{\mathcal{B}}$ by the change of basis given by the symplectic matrix
\[
N=
\begin{pmatrix}
1&0&0&0\\
0&1&0&0\\
1&0&1&0\\
0&0&0&1
\end{pmatrix}
\in\SP_4(\Z).
\]
Then the period matrix of $X_t$ associated to $\mathcal{B}$ is
\[
Z_t=\T{N}(A_tB^{-1})=
\begin{pmatrix}
1+i(2y_t-t) & iy_t\\
iy_t & i(y_t/2+t)
\end{pmatrix}
\]
whose imaginary part is positive definite if, and only if $y_t>2t/3$.
Hence, following the notations of Theorem \ref{theo:double_cover_thetanull}, we have
\begin{align*}
z_1 &= iy_t\\
z_{13} &= i(t-y_t/2)
\end{align*}
from which we deduce the expression of the period matrix associated to the basis $\mathcal{B}$ of the double cover $\hat{X}_t$:
\[
\hat{Z}_t=\begin{pmatrix}iy_t&iy_t/2&i(t-y_t/2)\\ iy_t/2&\frac12+i(y_t-t/2)&iy_t/2\\ i(t-y_t/2)&iy_t/2&iy_t\end{pmatrix}.
\]
Consider the symplectic basis obtained from $\mathcal{B}$ by the change of basis given by
\[
M=
\begin{pmatrix}
0&0&1&0&0&0\\
-1&1&-1&0&0&0\\
1&0&0&0&0&0\\
1&1&1&0&1&1\\
1&0&1&0&1&0\\
1&1&1&1&1&0
\end{pmatrix}
\in\SP_6(\Z),
\]
then the period matrix associated to this new basis is
\[
\hat{Z}_t'=\T{M}(\hat{Z}_t)=
\begin{pmatrix}
\frac12+i\left(y_t-\frac12t\right)&\frac12-\frac12i(y_t-t)&\frac12-\frac12i(y_t-t)\\
\frac12-\frac12i(y_t-t)&\frac12+i\left(y_t-\frac12t\right)&\frac12-\frac12i(y_t-t)\\
\frac12-\frac12i(y_t-t)&\frac12-\frac12i(y_t-t)&\frac12+i\left(y_t-\frac12t\right)
\end{pmatrix},
\]
fo which we can prove, by the same arguments as those used in the proof of Theorem \ref{theo:double_cover_thetanull}, that the corresponding vanishing even theta characteristic is $\thetasc{1&1&1\\0&0&0}$.
Developping, we get
\begin{multline*}
\thetasc{1&1&1\\0&0&0}(\hat{Z}_t')=
\sum_{(k_1,k_2,k_3)\in\Z^3}\exp\pi\Biggl[y_t\Big(k_1k_2+k_2k_3+k_3k_1-(k_1^2+k_2^2+k_3^2)\Big)\\
+t\left(\frac12(k_1^2+k_2^2+k_3^2)-(k_1k_2+k_2k_3+k_3k_1)-\frac12(k_1+k_2+k_3)-\frac38\right)\\
+i\left(\frac12(k_1^2+k_2^2+k_3^2)+k_1k_2+k_2k_3+k_3k_1+\frac32(k_1+k_2+k_3)+\frac98\right)\Biggr],
\end{multline*}
hence equation \eqref{eq:main_equation}.
\end{proof}
\bibliographystyle{amsalpha}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 6,567
|
Tonight, I spend most of my time hunting a pesky bug related to using class attributes instead of instance attributes in my classes. Since I am fairly new to python the distinction wasn't clear to me. It was hard to track down since everything was working beautifully until I made the slightest of change.
As for progress, the gameplay is inching its way forward little by little. I am going to hold off on any screen shots until I can replace the graphics (scheduled to be done Friday).
Today was a good day for the design of the game. The first few days the design was kinda of nebulous. I had a ruff idea of elements I wanted to include, but the game as a cohesive whole was not yet formed in my mind. That all changed today with hopefully enough time to code it all by the end of the pyweek.
Not the most productive day since I had to work for most of it, but I did get some features half implemented like the forecast and rain effect. I found a quick and easy particle system in Ian Mallett's PAdLib which I'll use for the rain effect.
I am really resisting the urge to redo all the crappy looking graphics, but without the gameplay being fun yet I will have to stick with them.
The graphics are just place holders. The ugly looking circles and rectangles are flowers which will hopefully be replaced with pixel art once the gameplay is hammered out. This is more of just a test of the flower DNA mutations.
The idea behind "Mutate!" is that the player can mutate the nucleotides in the DNA of flowers on a distant planet each generation (this game is by no means scientifically correct). The DNA is made up of the color elements RGB that change the flowers color, size and shape. The challenge will be in mutating the DNA of the flower to survive the changing environmental conditions on the planet. These conditions are also based on color so different color suns or rains will have different effects. There will be a seven day forecast of the conditions of the planet so that the player can strategize and prepare for the coming days. The end goal is to have a certain number of plants surviving or take up the majority of the land, but I will need to playtest to make sure this is actually fun.
I am calling it a night. I have to work in the morning.
Using Pygame, Humerus, and Albow I was able to quickly (~3hrs) get some of the ground work for the mutation game mechanic coded. There is not much on the screen except some debug text and buttons, but I hope to have a screenshot of a ruff version of Mutate! up tomorrow.
So far I am having a blast with pyweek!
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 6,226
|
FROM python:3.7.0-slim
ENV PYTHONUNBUFFERED 1
RUN apt-get update && apt-get install -y --no-install-recommends \
gdal-bin \
&& rm -rf /var/lib/apt/lists/*
WORKDIR /app
COPY src /app/
RUN pip3 install -r requirements.txt && pip3 install gunicorn
EXPOSE 8000
CMD ["python", "manage.py", "runserver", "0.0.0.0:8000"]
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,683
|
{"url":"http:\/\/www.geomagsphere.org\/index.php\/adiabatic-invariants","text":"The first kind of motion that a charged particle has in a magnetic field is a gyration around the field\u00a0lines. If the magnetic field is $$\\overrightarrow{B}$$ the frequency of gyration is $$\\omega_{B}=\\frac{eB}{m}$$ and the\u00a0gyroradius is $$r_{B}=\\frac{mv_{\\perp}}{Be}$$ where $$v_{\\perp}$$ is the component of the velocity\u00a0perpendicular to the magnetic field and $$v_{\\Vert}$$ is parallel.\u00a0If the only force acting on the particle is the magnetic one, no work is done on the particle and the\nmagnetic flux $$\\phi_{m}$$ is constant, so:\n\n\\label{eq:fluxmag}\n\\phi_{m}=B \\pi r^{2}_{B}=\\frac{2\\pi m E^{\\perp}_{k}}{e^{2}B}\n\nwhere\u00a0$$E^{\\perp}_{k}$$ is the kinetic energy associated with the transverse motion and so is\u00a0$$\\frac{mv^{2}_{\\perp}}{2}$$.\u00a0From eq. \\ref{eq:fluxmag} we have $$\\frac{E^{\\perp}_{k}}{B}=constant$$ so the magnetic\u00a0moment of the current\u00a0loop $$\\mu$$ given by:\n\n\\label{eq:mu}\n\\mu = i\\times A = \\frac{ev_{\\perp}}{2 \\pi r_{B}}\\pi r^{2}_{B} = \\frac{E^{\\perp}_{k}}{B}\n\nis constant too (and is called {\\it first adiabatic invariant}). This invariant is related to the bounce motion\u00a0(motion parallel to the field lines).\u00a0We have calling {\\it pitch angle} $$\\alpha$$ the angle bewtween perpendicular and parallel velocity component\u00a0(so $$\\tan \\alpha = \\frac{v_{\\perp}}{v_{\\Vert}}$$)\u00a0\u00a0$$\\frac{E_{k}\\sin ^{2} \\alpha}{B}=constant$$.\u00a0Because the ratio\u00a0$$\\frac{E^{\\perp}_{k}}{B}$$ is constant, when a particle moves toward the Earth magnetic pole,\u00a0$$v_{\\perp}$$ and $$\\sin^{2}\\alpha$$ must\u00a0increase (the magnetic field $$B$$ increases), eventually reaching the value $$\\alpha=90^{o}$$. In this point the\u00a0particle motion is reversed and this is called the {\\it mirror point} (that correspond to a value $$B_{m}$$ or\u00a0mirror field).\u00a0This mechanisn approximate the {\\it magnetic bottle} mechanism in a non-uniform field.\u00a0The total energy of the particle is not changing, so $$v$$ is constant and\u00a0calling $$B_{0}$$ and $$\\alpha_{0}$$\u00a0the values of the magnetic field and the pitch angle at the geomagnetic equator,\u00a0we can write the relation\n\n\\label{eq:alpha}\n\\frac{B_{0}}{B_{m}}=\\frac{\\sin^{2} \\alpha_{0} }{\\sin^{2} 90^{o} }=\\sin^{2} \\alpha_{0}\n\nIf particles encounter the atmosphere before they bounce back they will be lost by absorption (interaction)\u00a0with it, this happens for all particles that in any location $$X$$ have a picth angle $$\\alpha _{LC}$$ that is\u00a0$$\\alpha < \\alpha_{LC}$$, where\n\n\\label{eq:loss}\n\\sin^{2} \\alpha_{LC}= \\frac{B_{X}}{B_{a}}\n\nwhere $$B_{X}$$ is the intensity in $$X$$ and $$B_{a}$$ is the intensity at the intersection of the field line with\u00a0the atmosphere.\u00a0There are two more adiabatic invariants, the first (namely the {\\it second adiabatic invariant})\u00a0one is related to the effect called the {\\it curvature-gradient drift}. This effect is due to both the gradient of the field approaching the Earth and the curvature\u00a0of the field lines that both produce a drift motion in the plane perpendicular to the dipole axis.\u00a0So electrons are driven eastward and protons westwards.\u00a0The second adiabatic invariant is\u00a0expressed as:\n\n\\label{eq:second}\nJ_{2} = p \\int^{A}_{A'} \\sqrt{1-\\frac{B}{B_{m}} dl_{b}}\n\nor better $$I_{}=\\frac{J_{2}}{2p} \\simeq constant$$.\n\nThe {\\it third adiabatic invariant} is related to a slowly changing magnetic field, where first and second\u00a0adiabatic invariants (usually conserved in a static magnetic field) are still conserved, the particle\u00a0momentum may change, but the magnetic flux in a drift path is conserved. This is:\n\n\\label{eq:third}\nJ_{3} = \\int (q \\overrightarrow{A}+ \\overrightarrow{p})d\\overrightarrow{l}_{d} \\simeq q\\phi \\simeq constant\n\nwhere $$\\phi$$ is the magnetic flux enclosed in the drift path.\u00a0The invariance is violated if changes occur in a time $$t< \\tau_{d}$$, where $$\\tau_{d}$$ is the drift period.\nMagnetic trapping occurs if the respective periods have a strict jerarchy, so\u00a0$$\\tau_{g} < \\tau_{b}< \\tau_{d}$$, where $$\\tau_{g}$$ is gyration period and $$\\tau_{b}$$\u00a0is the bouncing period.","date":"2019-01-20 05:32:37","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9814618229866028, \"perplexity\": 890.2070034086349}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-04\/segments\/1547583700012.70\/warc\/CC-MAIN-20190120042010-20190120064010-00609.warc.gz\"}"}
| null | null |
Q: Haskell addition with custom data type Just need the basic syntax of Haskell explained here, because I'm apparently missing something and I can't find anything explaining how to properly do this.
Given:
data Year = Year Integer
How do I allow for addition, such as (Year 2000) + 10 which would return Year 2010
I tried
instance Num Year where
(Year a) + (b) = Year (a + b)
But that didn't work. Tried a few others, but I thought this was the most obvious solution.
Thanks for any help.
A: Num defines + like this:
(+) :: a -> a -> a
So both the left and right sides of + have to be the same type. You're trying to define a Num instance where that isn't the case. If you wanted to, you could make + work on two Years:
Year a + Year b = Year (a + b)
But if you want to be able to add, say, a Year and an Integer, you'd need to use a different operator name, e.g.:
Year a +++ b = Year (a + b)
(If you went this route, you might then want to define a precedence for this new operator.)
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 2,691
|
Last year was quite exceptional as far as the smartphone's design is a concern. The Chinese smartphone manufacturer Xiaomi started the trend of the bezel-less device back in 2016 and the idea was well appreciated not only in China but also across the globe in 2017. The success of the device prompted other smartphone manufacturers to unveil smartphones with minimal bezels. With each passing day, the demand for bezel-less smartphones is increasing. Almost all OEMs brought at least one bezel-less smartphone in the market.
Last year all the latest iPhones have the bezel-less design like the 10th anniversary iPhone X. So if you liked the last year's design you can purchase any one of the three latest iPhones. Apart from traditional notch design, we have seen smartphone manufacturers also introduced dewdrop notch which slims the top bezel even further.
We are doing buying guides for quite some time to facilitate our readers regarding the best choices available in the market. We recently summed up the best smartphones available in the Indian market below 1500. Thanks to a number of options, the price tag of bezel-less display smartphones dropped significantly and now buyers can even purchase an affordable bezel-less smartphone. Well if you are amongst those who are keen to grab a bezel-less smartphone, In today's roundup, we will take a look at top 5 best bezel-less display smartphones up for sale in the market. During December we had seen new punch-hole design phones from Samsung and Huawei as Galaxy A8s and Nova 4 respectively.
Recently the Chinese giant Xiaomi took the stage to announce their flagship Mi Mix 3. It is Xiaomi's latest offering in the bezel-less arena. Since the original Mi Mix phone, Xiaomi didn't bring any significant upgrade in the design with the Mi Mix 2 and Mi Mix 2S.
However, with the Mi Mix 3, the company stepped up their design game by introducing the ultimate full-screen display with almost none bezel on the top and bottom of the display. According to Xiaomi, the Mi Mix 3 screen-to-body is 93.4% which is certainly worth appreciating. The company further claims the new Mi Mix 3 has 4.46mm thinner chin than the predecessor. Xiaomi didn't opt notch instead the company opted the magnetic slider for the selfie cameras.
In terms of specs, the Mi Mix 3 is featuring a 6.39-inches display with Full HD+ screen resolution of 1080 x 2340 pixels. The Qualcomm's Octa-core Snapdragon 845 chipset is powering the device. It is available in three configurations with either 6GB, 8GB or even whopping 10GB RAM. The base model has 128GB storage whereas the top of the line model has 256GB storage. The built-in storage isn't further expandable via MicroSD.
The dual rear cameras are of 12MP, the primary sensor is a normal lens with f/.1.8 aperture whereas the secondary sensor is a telephoto sensor with f/2.0 aperture. Up front, it has dual cameras of 24MP+2MP. It lacks the traditional 3.5mm headphone jack instead rely on the USB-C port for connectivity and charging. A 3,200mAh battery is on board to keep its lights on. As OS it is pre-installed with Android Pie with MIUI 10 skin over it.
Back in December 2018, the Chinese giant Huawei wraps off the cover from the Nova 4 as the company's first phone with the punch-hole design. So far the Nova 4 is exclusive for the Chinese market only. Later on, in January Huawei's subsidiary Honor unveiled View 20 in Europe for global customers. The Honor View 20 is not only special due to punch-hole design but also due to 48MP snapper on the rear.
With the punch-hole design, Honor tries to opt a new way to enhance the screen-to-body ratio. The Honor View 20 chassis is made up of metal with glass covering the rear side. On the rear side, it has dual cameras placed horizontally on the top left corner.
As far as the hardware specs are a concern the Honor View 20 is featuring a 6.4-inches IPS display with Full HD+ screen resolution of 1080 x 2310 pixels. The device is powered up by the company's latest 7nm Kirin 980 SoC. The base model has 6GB RAM with 128GB native storage whereas the top-tier model has 8GB RAM with 256GB storage. As OS the device is pre-installed with Android Pie based EMUI 9.
In terms of hardware specs, the Vivo Nex S sports a 6.59-inches display with Full HD+ screen resolution of 1080 x 2316 pixels. Under the hood, the Qualcomm's Snapdragon 845 chipset is on board with 8GB RAM with either 128GB or 256GB non-expandable memory. The rear side has dual cameras of 12MP+5MP. The front-facing selfie camera is 8MP.
As OS the device is pre-installed with Android Oreo 8.1. Apart from having the pop-up camera, the device has an in-glass fingerprint scanner. A 4,000mAh battery cell is on board to keep its on.
This year Huawei announced four variants of Mate 20 series. Surprisingly the best screen-to-body ratio is of Mate 20 instead of the Pro model. The Mate 20 comes with an ultra-thin water drop notch whereas the Mate 20 Pro has a thin bezel at the top of the display. The Mate 20 is not only great due to its design but also it packs with one of the best hardware. The chassis is made up of aluminum with glass covering the rear side.
The P20 Pro was the company's first flagship with triple rear cameras, now they brought triple rear cameras on the Mate 20 series with a new square box design. The triple sensors are accompanied with a LED flashlight.
The Mate 20 features a 6.53-inches display with Full HD+ screen resolution of 1080 x 2244 pixels. Under the hood the company's latest Octa-core Kirin 980 SoC is powering the device with a dual Neural processing unit. The Octa-core chipset is accompanied with 4GB RAM and 128GB native storage.
The primary rear snapper is 20MP with f/1.8 aperture whereas the secondary sensor is an ultra-wide 12MP module with f/2.4 aperture and the last sensor is a telephoto sensor with optical zoom up to 2x. The front-facing selfie snapper is 24MP. A 4,000mAh battery is on board to keep its lights on.
This year once again Honor was amongst the last to introduce their flagship for the last half of the year. The latest Magic 2 is bringing a lot of goodies on board to attract buyers. Apart from having the top of the line hardware, it comes with six cameras setup. Not just that Honor also reduces the top bezels to the minimal level by introducing a slider mechanism for selfie cameras.
So if you are amongst those who are looking for a true bezel-less phone the Honor Magic 2 is certainly a pretty great option with 91% screen-to-body ratio. Other goodies include the company's own YOYO digital Assistant, 108% DCI-P3 color gamut and dual neural processing units to better handle AI tasks efficiently and under-glass fingerprint scanner.
As far as the hardware specs are a concern the Honor Magic 2 is featuring a 6.39-inches AMOLED display with Full HD+ screen resolution of 1080 x 2340 pixels. The Kirin 980 chipset is powering the phone with up to 8GB RAM and 256GB storage. The primary rear snapper is 16MP with f/1.8 aperture, the secondary sensor is a 24MP monochrome module with f/1.8 aperture. Last but not the least the third sensor is a 16MP super wide-angle module with f/2.2 aperture.
Up front, you will get triple cameras in the slider mechanism which pop-up when the camera app is open. The front-facing cameras are of 16MP with f/2.2 aperture and dual 2MP sensors with f/2.4 aperture. A 3,500mAh battery is on board to keep its lights on. It supports 40W super fast charging which means it can be charged completely in just 5 minutes.
The Huawei Mate 20 isn't still available online. To be notified when it becomse available click here.
The vivo NEX S isn't still available online. To be notified when it becomse available click here.
I've had my Note 9 now for 3 weeks and a few of my friends have other flagships and the Note can do everything their devices can but vice versa is not true . So right now the Note is just far an away the best SP right now. Battery, SPen, Screen quality, Storage, Bixby if you like it or not. It's glass over alum and glass design is gorgeous. Yes others are beautiful. But when you weigh it all it's just not close to me.
As of now, the best choice looks to be the Galaxy Note 9 followed by the Oppo Find X.
But the iPhone X looks the odd man out here. All other phones are Android phones. And it's the only one on iOS.
Are there any deals or discounts going on around at the moment so I can grab any of these?
That's a lovely thought, James. The screen-to-size ratio automatically comes in the picture when we talk about bezel-less phones.
And that also brings in the picture pop up camera too!
I heard that Micromax is also going to bring out a bezel-less phone on the Indian market. Is that true?
bcoz megapixel is not important to give image quality like dslr camera ,which apature ratio is good to give image quality like dslr in smartphone..can u suggest me?
I guess around 1.5 to 2.0 would work great. Though it matters on what the MPs are too.
what is main advantages of dual lens camera?
Actually, the dual lens means the two human eyes. This allows the camera to focus on the subject better than a single lense camera. Obviously, you get better output.
does note8 gives image quality like dslr camera?
I don't think it'd be right to expect DSLR quality from a smartphone camera.
I have been using the Redmi Note 4 for a few days now. It's not really a bezel-less phone. But what I realized is that my fingers touch the screen from the side when I hold it straight. Icons get tapped unintentionlly.
Hahaha... Yes, this does happen with me a lot of times and it does get a bit frustrating at times. I have to fix it every time it happens.
The image of the Lenovo Zuk Edge is the apt example of that. Just see the little and ring finger. How much care may you take, it does touch the screen. No one has highlighted this downside, I guess.
Though the Ulefone Future is a good phone in this category, it has been kind of overshadowed by the other big names in the industry like Mi MIX and Honor Magic. But yes, we have to agree that even the Future has well trimmed bezels capable of taking on the other biggies in the industry.
For me, nothing can beat the ZUK Edge. The full HD display having the curved feature makes the phone look more attractive. And I think they have christened the phone with the right word - Edge.
I guess the Xiaomi Mi MIX is the most prominent of these bezel-less phones. Though it might not be the first - maybe it even can be, because I don't know the chronology - it has always been at the forefront of bezel-less phones. And it's my top favorite in this category.
The black-colored Honor Magic looks really cool. Though it's nowhere near the Mi MIX, it still looks okay. But doesn't match the looks of the Xiaomi Mi MIX. On the contrary the magic has been created by the Mi MIX....!!!!
I agree. It's actually a phablet with 6.4-inch screen. And I also like the fact that it has a stupendous 90% of body ratio. So, no wonder, it's the apple of our eyes.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 3,286
|
\subsection{Graphs with bounded degree and planar graphs}
\label{degree-section}
In this subsection, we will prove the following theorem:
\begin{theorem}
\label{degree-lower-bound}
For each $\Delta \geq 4$ and odd $d \geq 1$,
there exists a graph with maximum degree bounded by $\Delta$
containing a distance-$d$ half graph of order $\left\lfloor \frac{\Delta}{2}\right\rfloor^{
\left\lceil \frac{d}{2} \right\rceil}$.
\end{theorem}
We fix two integer variables, $k \geq 2$ and $h \geq 1$.
We will construct an undirected graph $H_{k,h}$ with the following properties:
\begin{itemize}
\item The degree of each vertex in the graph is bounded by $2k$.
\item The graph contains vertices $a_1, b_1, a_2, b_2, \dots, a_{k^h}, b_{k^h}$
forming a distance-$(2h-1)$ half graph of order~$k^h$.
\end{itemize}
In the construction of $H_{k,h}$, we will create two isomorphic rooted trees
$\mathcal{A}$ and $\mathcal{B}$, each having $k^h$ leaves, and connect pairs of vertices of
these trees using paths of small, positive length.
We fix an alphabet $\Sigma = \{1, 2, \dots, k\}$ with the natural ordering of its elements.
This allows us to introduce a lexicographical ordering of all words in $\Sigma^*$,
denoted $\preccurlyeq$.
For a word $s \in \Sigma^*$, by $|s|$ we mean the length of $s$.
And for a pair of words $x, y \in \Sigma^*$, by $x \cdot y$ we mean the concatenation of
$x$ and $y$.
For each word $s \in \Sigma^*$, $|s| \in [0, h]$, we create two vertices: $a_s \in V(\mathcal{A})$
and $b_s \in V(\mathcal{B})$.
The edges in both trees are constructed in the following way:
for each word $s \in \Sigma^*$, $|s| \leq h-1$, and each character $c \in \Sigma$,
we add an edge between vertices $a_s$ and $a_{s \cdot c}$ in $\mathcal{A}$, and between
the vertices $b_s$ and $b_{s \cdot c}$ in $\mathcal{B}$.
We also connect the trees in the following way:
for each word $s \in \Sigma^*$, $|s| \leq h-1$, and each pair of characters $c, d \in \Sigma$
such that $c < d$, we connect the vertices $a_{s \cdot d} \in V(\mathcal{A})$ and $b_{s \cdot c} \in V(\mathcal{B})$ by
a path of length $2|s| + 1$.
This finishes the construction of $H_{k,h}$.
Examples of such graphs can be found in Figure~\ref{degree-examples-fig}.
\begin{figure}[h]
\centering
\begin{minipage}[b]{0.185\textwidth}
\centering
\input{figures/degree-a.tex}
(a)
\end{minipage}\begin{minipage}[b]{0.285\textwidth}
\centering
\input{figures/degree-b.tex}
(b)
\end{minipage}\begin{minipage}[b]{0.53\textwidth}
\centering
\input{figures/degree-c.tex}
(c)
\end{minipage}
\caption{Graphs: (a) --- $H_{2,1}$, (b) --- $H_{4,1}$, (c) --- $H_{2,3}$. $\varepsilon$
denotes an empty word.}
\label{degree-examples-fig}
\end{figure}
\vspace{0.5em}
We now need to prove the required properties of $H_{k, h}$.
Firstly, we prove that each vertex has at most $2k$ neighbors in the graph.
Vertices belonging to neither $\mathcal{A}$ nor $\mathcal{B}$ lie on the paths connecting $\mathcal{A}$ with $\mathcal{B}$,
so their degrees are equal to $2$.
Let us now fix a vertex belonging to $\mathcal{A}$ or $\mathcal{B}$.
In its own tree, this vertex has at most $k$ children and one parent.
This vertex is also an endpoint of at most $k-1$ paths connecting $\mathcal{A}$ with $\mathcal{B}$;
the bound is satisfied with equality for vertices $a_{s \cdot k}$ and $b_{s \cdot 1}$
($1, k \in \Sigma$, $s \in \Sigma^*$, $|s| \leq h-1$).
Hence, the total number of neighbors of each vertex of $\mathcal{A}$ and $\mathcal{B}$ is bounded by $2k$.
Secondly, each tree obviously has $k^h$ leaves, since the leaves are parameterized by a word
of length $h$ over an alphabet of size $k$.
Finally, we need to find a half graph in this graph. Let $(t_1, t_2, \dots, t_{k^h})$ be the sequence
of all words of length $h$ over $\Sigma$, ordered lexicographically.
The following lemma proves that the lexicographical ordering of the leaves of $\mathcal{A}$ and $\mathcal{B}$
produces a half graph:
\begin{lemma}
\label{lemma-degree-distance}
Fix two indices $i, j \in [1, k^h]$.
The distance between $b_{t_i}$ and $a_{t_j}$ is equal to $2h-1$ if $i < j$, and is greater
than $2h - 1$ if $i \geq j$.
\begin{proof}
For simplicity, we can assume that each path of length $\ell$ ($\ell \geq 1$)
connecting a vertex of $\mathcal{A}$ with a vertex of $\mathcal{B}$ is, in fact, a weighted edge of length
$\ell$ connecting these two vertices.
We introduce the \textbf{level function} $\xi\,:\,V(\mathcal{A}) \cup V(\mathcal{B}) \to \mathbb{N}$,
defined in the following way:
$$ \xi(v) = \begin{cases}
h - |s| & \text{if }v = a_s\text{ for }s \in \Sigma^*, \\
h + |s| - 1 & \text{if }v = b_s\text{ for }s \in \Sigma^*.
\end{cases} $$
For a vertex $v$, we say that the value $\xi(v)$ is the \textbf{level} of vertex $v$.
We see that the levels of the vertices of $\mathcal{A}$ range between
$0$ and $h$, while the levels of the vertices of $\mathcal{B}$ range between $h-1$ and $2h - 1$
(Figure \ref{degree-levels-fig}).
\begin{figure}[h]
\centering
\input{figures/degree-levels.tex}
\label{degree-levels-fig}
\caption{The levels of vertices of $H_{2,3}$. Each weighted edge resulting from
a contracted path is colored violet and is labeled by its length.}
\end{figure}
We can now observe that:
\begin{itemize}
\item For every two vertices of $\mathcal{A}$ connected by an edge --- $a_s$ and $a_{s \cdot c}$
for some $s \in \Sigma^*$, $c \in \Sigma$ --- we have that $\xi(a_{s}) = \xi(a_{s \cdot c}) + 1$.
\item For every two vertices of $\mathcal{B}$ connected by an edge --- $b_s$ and $b_{s \cdot c}$ ---
we have that $\xi(b_{s \cdot c}) = \xi(b_s) + 1$.
\item For every two vertices $a_{s \cdot d} \in V(\mathcal{A})$, $b_{s \cdot c} \in V(\mathcal{B})$
($s \in \Sigma^*, c, d \in \Sigma, c < d$), connected by a weighted edge of length
$2|s| + 1$, we have
$$\xi(b_{s \cdot c}) - \xi(a_{s \cdot d}) = (h + |s|) - (h - |s| - 1) = 2|s| + 1.$$
\end{itemize}
Hence, for each edge of weight $x$ connecting two vertices $u, v$, we have that
$x = |\xi(u) - \xi(v)|$.
Therefore, for all pairs of vertices $u, v$, the distance between these vertices
is bounded from below by $|\xi(u) - \xi(v)|$, and the bound is satisfied with equality only if
there exists a path between $u$ and $v$ on which the values of $\xi$ change
monotonically.
We will call such paths \textbf{monotonous}.
Fix $i, j \in [1, k^h]$, and consider the vertices $b_{t_i}$ and $a_{t_j}$.
By the definition of $\xi$, we know that $\xi(a_{t_j}) = 0$ and $\xi(b_{t_i}) = 2h - 1$,
hence the distance between these two vertices is at least $2h - 1$.
We will now analyze when this distance is equal to $2h - 1$.
We see that the value of $\xi$ only increases when: going up the tree $\mathcal{A}$ (in the direction
of the root of $\mathcal{A}$), taking a weighted edge from a vertex of $\mathcal{A}$ to a vertex of
$\mathcal{B}$ (but not the other way around), and going down the tree $\mathcal{B}$ (away from the root
of $\mathcal{B}$).
Hence, each path between $b_{t_i}$ and $a_{t_j}$
of length $2h-1$ can only have such three segments, in this exact order, as it needs to
be monotonous.
If $i < j$, then $t_i \prec t_j$, so the words
$t_i$ and $t_j$ admit the following factorization:
$$ t_i = p \cdot c \cdot s_i, \qquad t_j = p \cdot d \cdot s_j $$
for $p, s_i, s_j \in \Sigma^*$, $c, d \in \Sigma$ and $c < d$.
Therefore, the path originating at $a_{t_j}$, going up $\mathcal{A}$ to the vertex $a_{p \cdot d}$, taking
the weighted edge to $b_{p \cdot c}$ connecting both trees (this is possible since $c < d$),
and then going down $\mathcal{B}$ to the destination $b_{t_i}$, is monotonous.
Hence, $\mathrm{dist}(b_{t_i}, a_{t_j}) = 2h - 1$.
Conversely, if a path from $a_{t_j}$ to $b_{t_i}$ has length $2h - 1$, then it is monotonous.
Therefore, it must follow from $a_{t_j}$ to an ancestor of $a_{t_j}$ (we will name it
$a_x$ where $x$ is a prefix of $t_j$), then take a weighted
edge to an ancestor of $b_{t_i}$ (we will call it $a_y$ where $y$ is a prefix of $t_i$),
and then walk down the tree $\mathcal{B}$ to $b_{t_i}$.
By the construction of the tree, $x$ and $y$ must be both of the form
$x = p \cdot d$, $y = p \cdot c$ where $p \in \Sigma^*$, $c, d \in \Sigma$, $d > c$.
Since $x$ and $y$ are prefixes of $t_j$ and $t_i$, respectively, this means
that $t_j \succ t_i$.
Hence, $j > i$.
Therefore, the path of length $2h - 1$ exists between $a_{t_j}$ and $b_{t_i}$ if and only if
$i < j$; otherwise the shortest path between these vertices is longer.
\end{proof}
\end{lemma}
Lemma \ref{lemma-degree-distance} proves that the graph $H_{k, h}$ contains
a half graph of order $k^h$.
Since $k \geq 2$ and $h \geq 1$ were two arbitrary variables, this statement is satisfied
for each choice of these variable.
\vspace{0.5em}
Let us now finish the proof of Theorem \ref{degree-lower-bound}.
For each $\Delta \geq 4$ and odd $d \geq 1$ we can see that the graph
$H_{\left\lfloor\frac{\Delta}{2}\right\rfloor, \frac{d+1}{2}}$ has its maximum degree
bounded by $2\left\lfloor\frac{\Delta}{2}\right\rfloor \leq \Delta$,
and contains a distance-$d$ half graph of order $\left\lfloor\frac{\Delta}{2}\right\rfloor^{
\left\lceil\frac{d}{2}\right\rceil}$.
Hence, the proof of the theorem is complete.
\medskip
We note the following immediate conclusion from Theorem \ref{degree-lower-bound}:
\begin{corollary}
\label{degree-lower-bound-asym}
Let $\mathcal{C}_\Delta$ be the class of graphs with maximum degree bounded by $\Delta \geq 4$.
Then the maximum order of a distance-$d$ half graph ($d \geq 1$) in $\mathcal{C}_\Delta$ is bounded
from below by $\Delta^{\Omega(d)}$.
\end{corollary}
It turns out that the presented family of examples also witness as an exponential lower
bound on the maximum order of a distance-$d$ half graph in the class of planar graphs.
This is proved explained by following lemma:
\begin{lemma}
\label{degree-four-is-planar-lemma}
For each $h \geq 1$, the graph $H_{2, h}$ is planar.
\begin{proof}
For each $h \geq 1$, let $H'_{2, h}$ be the graph obtained from $H_{2, h}$ by contracting
each path connecting two trees to a single edge.
Obviously, $H'_{2, h}$ is planar if and only if $H_{2, h}$ is planar.
Then, for $h \geq 2$, the graph $H'_{2, h}$ can be created from two copies of the graph
$H'_{2, h-1}$ in the following way:
\begin{enumerate}
\item In the $i$-th copy of the graph ($i \in \{1, 2\}$), replace each vertex $a_s$
($s \in \{1, 2\}^*$) by $a_{i \cdot s}$, and analogously each vertex $b_s$ by $b_{i \cdot s}$.
\item Create new roots of $\mathcal{A}$ and $\mathcal{B}$ --- $a_\varepsilon$ and $b_\varepsilon$,
respectively.
\item Add the following edges: $a_\varepsilon a_1$, $a_\varepsilon a_2$,
$b_\varepsilon b_1$, $b_\varepsilon b_2$, $b_1 a_2$.
\end{enumerate}
\begin{figure}[h]
\centering
\begin{minipage}[b]{0.35\textwidth}
\centering
\input{figures/planar-conn-a.tex}
$H'_{2,2}$
\end{minipage}\begin{minipage}[b]{0.63\textwidth}
\centering
\input{figures/planar-conn-b.tex}
$H'_{2,3}$
\end{minipage}
\caption{A step in the inductive process of creating $H'_{2,h}$ for each $h \geq 2$.
Two copies of $H'_{2,2}$ (left; its roots are marked green and yellow) are put side by side,
two new vertices are added, and five new edges (blue) are drawn, resulting in the graph
$H'_{2,3}$ (right).}
\label{planar-conn-fig}
\end{figure}
Note that $H'_{2, 1} = H_{2, 1}$ is planar (Figure \ref{degree-examples-fig}(a)), and moreover,
in the presented embedding, its vertices $a_\varepsilon$ and $b_\varepsilon$ lie on the
outer face of the graph.
These two properties can be maintained inductively:
for $h \geq 2$, we take the embeddings of two copies of $H'_{2, h-1}$ satisfying these
properties, put them side by side,
and add the required edges, making sure that the graph remains planar and
that the new roots of the trees are on the outer face of the graph (Figure \ref{planar-conn-fig}).
\end{proof}
\end{lemma}
We immediately infer the following:
\begin{corollary}
\label{planar-lower-bound}
For every $d \geq 1$, the maximum order of a distance-$d$ half graph ($d \geq 1$)
in the class of planar graphs is bounded from below by $2^{\left\lceil \frac{d}{2} \right\rceil}$.
\begin{proof}
Assume $d$ is odd.
Then, by Lemma \ref{degree-four-is-planar-lemma}, the graph $H_{2, \frac{d+1}{2}}$ is planar.
Also, it contains a distance-$d$ half graph of order
$2^{\frac{d+1}{2}} = 2^{\left\lceil \frac{d}{2} \right\rceil}$.
For even $d$, we construct a planar graph containing a distance-$(d-1)$ half graph
of order $2^{\frac{d}{2}} = 2^{\left\lceil \frac{d}{2} \right\rceil}$, and then for
each vertex $a_i$ in this graph ($1 \leq i \leq 2^{\frac{d}{2}}$), we add an edge whose
one endpoint is $a_i$, and another is a new vertex $a'_i$.
We now can see that the vertices $a'_1, b_1, a'_2, b_2, \dots, a'_{2^{\frac{d}{2}}},
b_{2^{\frac{d}{2}}}$ form a distance-$d$ half graph of required order.
\end{proof}
\end{corollary}
\subsection{Graphs with bounded pathwidth}
\label{pw-section}
In this section, we will find large half graphs in the class of graphs with bounded pathwidth.
Specifically, we will prove the following theorem:
\begin{theorem}
\label{pw-lower-bound}
For each $d \geq 1$ and $p \geq 0$, there exists a graph $P_{p,d}$ with pathwidth
at most $p + 2$ which contains a distance-$(4d-1)$ half graph of order
$(2d+1)^p$.
\begin{proof}
Let $\ell_{p,d} := (2d+1)^p$.
We define a slightly broader class of graphs $\{P_{p,d,k}\,\mid\,d \geq 1,\,
p \geq 0,\,k\geq0\}$
where $P_{p,d,k}$ has the following properties:
\begin{itemize}
\item The graph has pathwidth at most $p + 2$.
\item The graph contains a distance-$(4d-1)$ half graph
$a_1, a_2, \dots, a_{\ell_{p,d}}$, $b_1, b_2,
\dots, b_{\ell_{p, d}}$ in which every two vertices are at distance
$2d$ or more from each other.
\item Each of the vertices of the half graph
has $k$ vertex disjoint paths of length $3d$ attached to it (called
\emph{appendices});
in other words, after removing any of these vertices, there are at least $k$
connected components which are paths with $3d$ vertices.
\end{itemize}
Thanks to the first two conditions, the graph $P_{p, d} := P_{p, d, 0}$ will satisfy
Theorem~\ref{pw-lower-bound}.
The final condition is purely technical and will help us argue that pathwidths
of the graphs constructed in the process described below do not grow too large.
\medskip
The construction will be inductive over $p$.
First, for $d \geq 1$, $k \geq 0$, we choose the graph $P_{0, d, k}$
to be the $3d$-subdivision of two disjoint stars with $k$ edges, with the
distance-$(4d-1)$ half graph of order $\ell_{0,d} = 1$ given by the centers of both stars.
It can be easily verified that this graph satisfies the requirements; in particular,
$\pw{P_{0,d,k}} \leq 2$.
\medskip
We shall now describe how to construct $P_{p, d, k}$ for $p, d \geq 1$ and $k \geq 0$:
\begin{enumerate}
\item Take $2d+1$ disjoint copies of $P_{p-1, d, k+1}$, and renumber the vertices
of the half graph in each of the copies, ordering all $2d+1$ half graphs one after another.
Formally, the labels of the vertices
$a_i$ and $b_i$ of the half graph in the $j$-th disjoint copy of the graph are changed to
$a_{(j-1)\ell_{p-1,d} + i}$ and $b_{(j-1)\ell_{p-1,d} + i}$, respectively.
Since $\ell_{p,d} = (2d+1)\ell_{p-1,d}$,
the graph contains vertices $a_i$, $b_i$ for each $i \in [1, \ell_{p, d}]$.
The following steps of the construction will ensure that these vertices form
a distance-$(4d-1)$ half graph, provided that $P_{p-1,d,k+1}$ satisfies the required properties.
\item Add a new vertex $r$ to the graph.
\item For each vertex $b_i$ in the $j$-th disjoint copy of the graph, $j \in [1, 2d+1]$,
we connect $b_i$ with $r$ with a~path of length $d + (j - 1)$.
In order to do that, we use up one of $k+1$ appendices attached to $b_i$
by connecting $r$ with the $(d+j-2)$-nd vertex of the appendix with an edge
(Figure \ref{pw-appendix-join});
the part of the appendix after this vertex can then be safely discarded.
\item We apply a similar procedure to the vertices $a_i$ of the half graph, only that
the vertex of the half graph in the $j$-th disjoint copy of the graph is connected
with $r$ with a~path of length $3d - (j - 1)$.
This finishes the construction of $P_{p, d, k}$.
\end{enumerate}
\begin{figure}[h]
\centering
\begin{minipage}[b]{0.33\textwidth}
\centering
\input{figures/pw-appendix-join-a.tex}
\end{minipage}\begin{minipage}[b]{0.33\textwidth}
\centering
\input{figures/pw-appendix-join-b.tex}
\end{minipage}\begin{minipage}[b]{0.33\textwidth}
\centering
\input{figures/pw-appendix-join-c.tex}
\end{minipage}
\caption{The process of turning an appendix attached to $b_i$
into a path of length $5$ connecting $b_i$ with $r$.}
\label{pw-appendix-join}
\end{figure}
Obviously, each vertex $a_i$ and $b_j$ in $P_{p,d,k}$
has $k$ remaining appendices.
We also note that $P_{p, d, k} \setminus \{r\}$ is a subgraph of a graph formed
from $2d+1$ disjoint copies of $P_{p-1, d, k+1}$. Hence,
$$ \pw{P_{p, d, k}} \leq \pw{P_{p,d,k} \setminus \{r\}} + 1 \leq
\pw{P_{p-1, d, k+1}} + 1 \leq p + 2. $$
We also argue that $a_1, a_2, \dots, a_{\ell_{p,d}}$, $b_1, b_2, \dots,
b_{\ell_{p,d}}$ is a distance-$(4d-1)$ half graph satisfying the distance requirements
of $P_{p,d,k}$.
In the construction, multiple disjoint copies of $P_{p-1,d,k+1}$ were connected
by vertex disjoint paths to a new vertex $r$, where each path has length at least
$d$ and at most $3d$.
Hence, the shortest path between any two vertices of the new half graph is either fully
contained in a copy of $P_{p-1,d,k+1}$ (and it must not be shorter than $2d$
by the inductive assumption), or it passes through $r$ and thus it follows two
paths of length at least $d$, so its length is at least $2d$ as well.
From this property,
we infer that if the shortest path between any two vertices of the half graph has length
at most $4d - 1$, then this path must avoid all other vertices of the half graph.
Let us now consider whether there exists a path between two vertices $a_i$ and $b_j$
of the half graph of length $4d - 1$.
Again, this path must either be fully contained in a single copy of
$P_{p-1,d,k+1}$ (and this condition is only satisfied if $i > j$), or it passes through $r$.
In the latter case, this path must consist of a direct connection from $a_i$ to $r$,
and then a direct connection from $r$ to $b_j$.
Assuming that $a_i$ is in the $x$-th disjoint copy of $P_{p-1,d,k+1}$, and $b_j$ is
in the $y$-th copy of the graph ($x, y \in [1, 2d+1]$), we infer that the length of that path
is exactly
$$[d + (y - 1)] + [3d - (x - 1)] = 4d + (y - x).$$
Hence, such a path exists if and only if $x > y$; that is, only if $i > j$ and both
$a_i$ and $b_j$ come from the different copies of $P_{p-1,d,k+1}$.
We conclude that $\mathrm{dist}(a_i, b_j) \leq 4d-1$ if and only if $i > j$.
Therefore, all the required conditions are satisfied, so $P_{p,d,k}$ is defined correctly.
This finishes the proof of the lower bound.
\end{proof}
\end{theorem}
On an end note, we remark the following asymptotic version of Theorem \ref{pw-lower-bound}:
\begin{corollary}
\label{pw-lower-bound-asym}
For each pair of integers $p \geq 2$, $d \geq 4$, the maximum order of a distance-$d$
half graph in the class of graphs with pathwidth bounded by $p$ is bounded from below
by $\Theta(d)^{p - O(1)}$.
\end{corollary}
\subsection{Graphs with bounded treewidth and minor-free graphs}
\label{tw-section}
In this section, we will construct a family of graphs with small treewidth containing large
half graphs.
Since the graphs with bounded treewidth also avoid large cliques as minors, this
family will also serve as examples of graphs avoiding relatively small cliques as minors,
but still containing large half graphs.
To start with, we shall introduce a variant of a tree decomposition of a graph $G$
containing a distance-$2d$ half graph.
\begin{definition}
\label{pairing-td-def}
A rooted tree decomposition $\mathcal{T}$ of a graph $G$ is
a~\textbf{distance-$d$ pairing decomposition} if all the following conditions hold:
\begin{itemize}
\item The root of $\mathcal{T}$ is a bag containing exactly two elements, called $A$ and
$B$.
\item Each leaf of $\mathcal{T}$ is a bag containing exactly two elements, called $a_i$ and
$b_i$, where $i \in \{1, 2, \dots, \ell\}$ and $\ell$ is the number of leaves in $\mathcal{T}$.
\item All vertices $A, B, a_1, b_1, a_2, b_2, \dots, a_\ell, b_\ell$ are pairwise different.
\item For each pair of integers $i, j$ such that $1 \leq i < j \leq \ell$, we have that
$\mathrm{dist}(b_i, a_j) = 2d$.
\item For each pair of integers $i, j$ such that $1 \leq j \leq i \leq \ell$, we have that
$\mathrm{dist}(b_i, a_j) = 2d + 1$.
\end{itemize}
For such a tree decomposition, we define two objects: its root
$\mathsf{Root}(\mathcal{T}) = (A, B)$ and the sequence of vertices in its leaves
$\mathsf{Leaves}(\mathcal{T}) = (a_1, b_1, a_2, b_2, \dots, a_\ell, b_\ell)$.
We will refer to the value $\ell$ as the \textbf{order} of $\mathcal{T}$.
We also define the \textbf{width} of the tree decomposition in the standard way.
\end{definition}
We remark that Definition \ref{pairing-td-def} implies that
the set of vertices $a_1, a_2, \dots, a_\ell, b_1, b_2, \dots, b_\ell$ forms
a distance-$2d$ half graph of order $\ell$ in $G$.
However, the conditions required here are even stronger
as the definition of a half graph only requires that $\mathrm{dist}(b_i, a_j) \leq 2d$ for each pair of integers
$i < j$, and $\mathrm{dist}(b_i, a_j) > 2d$ for $i > j$.
This strengthening will be essential in the proof of the correctness
of the construction.
We also note that $\mathcal{T}$ --- in some way ---
``exposes'' the vertices of the underlying half graph
in the form of the leaf bags of the tree decomposition ($\mathsf{Leaves}(\mathcal{T})$),
and two other vertices in the form of the root bag of the decomposition ($\mathsf{Root}(\mathcal{T})$).
These outer bags of the tree decomposition are ``sockets'' which
can connect to the ``sockets'' of pairing decompositions of other graphs, allowing
a~recursive construction of large graphs.
\begin{example}
\label{pairing-td-example}
We consider the graph $G$ presented in Figure \ref{pairing-td-fig}(a)
with the tree decomposition $\mathcal{T}$ depicted in Figure \ref{pairing-td-fig}(b).
This decomposition is distance-$1$ pairing and has order~$2$ and width~$3$.
The table in Figure \ref{pairing-td-fig}(c) shows the distances between
$a_i$ and $b_j$ for each pair of indices $i, j$.
We can see that $\mathrm{dist}(b_1, a_2) = 2$ and all the remaining distances are equal to~$3$.
Moreover, $\mathsf{Root}(\mathcal{T}) = (A, B)$ and $\mathsf{Leaves}(\mathcal{T}) = (a_1, b_1, a_2, b_2)$.
\begin{figure}[h]
\centering
\begin{minipage}[b]{0.37\textwidth}
\centering
\input{figures/tw-basic-a.tex}
(a)
\end{minipage}\begin{minipage}[b]{0.37\textwidth}
\centering
\input{figures/tw-basic-b.tex}
(b)
\end{minipage}\begin{minipage}[b]{0.26\textwidth}
\centering
\begin{tabular}{c|c|c}
$\mathrm{dist}(\cdot, \cdot)$ & $a_1$ & $a_2$ \\ \hline
$b_1$ & $3$ & $2$ \\ \hline
$b_2$ & $3$ & $3$
\end{tabular}
\vspace{1em}
(c)
\end{minipage}
\caption{(a) --- the graph $G$ in Example \ref{pairing-td-example};
(b) --- its tree decomposition; (c) --- its distance matrix.}
\label{pairing-td-fig}
\end{figure}
\end{example}
In the construction of our family of graphs, we will need to use a refinement
of Definition~\ref{pairing-td-def}.
Intuitively, we want to expose the root vertices of the decomposition in an efficient way.
We will do it by creating a stronger variant of the pairing decomposition in which
one of the root vertices is adjacent to all the vertices on one side of the half graph, while
the other root vertex is adjacent to the other side.
\begin{definition}
Consider an arbitrary undirected graph $G$ with a distance-$d$ pairing decomposition
$\mathcal{T}$ where $\mathsf{Root}(\mathcal{T}) = (A, B)$ and $\mathsf{Leaves}(\mathcal{T}) = (a_1, b_1, \dots, a_\ell, b_\ell)$.
We will say that $\mathcal{T}$ is \textbf{neighboring} if for each $i \in \{1, 2, \dots, \ell\}$, we have that:
$$ \mathrm{dist}(a_i, A) = \mathrm{dist}(b_i, B) = 1, \quad\ \ \mathrm{dist}(a_i, B) \geq 2d + 1, \quad\ \
\mathrm{dist}(b_i, A) \geq 2d + 1. $$
Moreover, $A$ must be adjacent only
to vertices $a_1, \dots, a_\ell$, and $B$ must be adjacent only to vertices
$b_1, \dots, b_\ell$.
\end{definition}
\vspace{0.5em}
We can verify that the decomposition from Example \ref{pairing-td-example} is not neighboring
since the vertices $A$ and $B$ are connected by an edge.
\vspace{0.5em}
We will now present a few lemmas.
Lemma \ref{make-neighboring-lemma} will allow us to turn an arbitrary decomposition into
a neighboring decomposition by incurring a small cost on the width of the decomposition.
Lemma \ref{tw-combine-lemma} will be a method of combining two pairing decompositions ---
a neighboring decomposition of width $t$ and order $\ell_1$, and a pairing decomposition
of width $t-2$ and order $\ell_2$, into a pairing decomposition of order $\ell_1\ell_2$.
Then, the combination of these two lemmas (Lemma \ref{combine-any-tw}) will provide us
with a procedure, which we will use to create graphs with enormous pairing decompositions.
\begin{lemma}
\label{make-neighboring-lemma}
There exists a procedure which takes an arbitrary undirected graph $G$ with
a distance-$d$ pairing decomposition $\mathcal{T}$ of width $t$ and order $\ell$,
and produces a graph $G'$ with a neighboring distance-$d$
pairing decomposition $\mathcal{T}'$ of width $t+2$ and order $\ell$.
\begin{proof}
Let $\mathsf{Leaves}(\mathcal{T}) = (a_1, b_1, \dots, a_\ell, b_\ell)$.
We construct $G'$ from $G$ by creating two new vertices $A_{\mathrm{new}}$ and
$B_{\mathrm{new}}$, connecting $A_{\mathrm{new}}$ directly by an edge
to each of the vertices $a_i$ for $i \in [1, \ell]$, and analogously connecting
$B_{\mathrm{new}}$ to each of the vertices $b_i$.
We will now construct a rooted tree decomposition $\mathcal{T}'$ from $\mathcal{T}$ in the following way
\begin{enumerate}
\item For each leaf bag $L_i \in V(\mathcal{T})$ containing vertices $a_i$ and $b_i$,
we clone it (without cloning the vertices in the bag), and connect it with $L_i$ in $\mathcal{T}$.
This way, the clone becomes a leaf in the new decomposition instead of $L_i$.
\item We create a new bag $(A_{\mathrm{new}}, B_{\mathrm{new}})$, which we directly
connect to the root of $\mathcal{T}$.
\item To each bag of $\mathcal{T}$ which is neither the root nor a leaf of the new tree decomposition,
we add both $A_{\mathrm{new}}$ and $B_{\mathrm{new}}$.
\end{enumerate}
We can easily see that $\mathcal{T}'$ is a tree decomposition of $G'$ of width $t + 2$.
We will now show that $(G', \mathcal{L}')$ is a neighboring decomposition
by deducing all the required equalities and inequalities between the distances.
Obviously, $\mathrm{dist}(a_i, A_{\mathrm{new}}) = \mathrm{dist}(b_i, B_{\mathrm{new}}) = 1$ for each
$i \in [1, \ell]$.
Furthermore, by considering all neighbors of $B_{\mathrm{new}}$, we can see
that for each $i \in [1, \ell]$, we have that
$$ \mathrm{dist}(a_i, B_{\mathrm{new}}) = \min_{j \in \{1, \dots, \ell\}} \left(
\mathrm{dist}(a_i, b_j) + 1\right) \geq 2d + 1. $$
Analogously, $\mathrm{dist}(b_i, A_{\mathrm{new}}) \geq 2d+1$ for every $i \in [1, \ell]$.
We can now prove that no path connecting $b_i$ and $a_j$ which has length $2d$ or less,
for any choice of indices $i, j \in [1, \ell]$, can pass through $A_{\mathrm{new}}$:
$$ \mathrm{dist}(b_i, A_{\mathrm{new}}) \geq 2d + 1 \qquad\Rightarrow\qquad
\mathrm{dist}(b_i, A_{\mathrm{new}}) + \mathrm{dist}(A_{\mathrm{new}}, a_j) > 2d + 1. $$
Analogously, no such path can pass through $B_{\mathrm{new}}$.
If $i < j$, then $\mathrm{dist}_G(b_i, a_j) = 2d$ holds in $G$.
Since $A_{\mathrm{new}}$ and $B_{\mathrm{new}}$ were the only vertices added to
$G$ in the construction of $G'$, and no path with length $2d$ or less can pass through
these vertices, it means that we also have $\mathrm{dist}_{G'}(b_i, a_j) = 2d$.
Analogously, if $i \geq j$, then $\mathrm{dist}_G(b_i, a_j) = 2d+1$ in also implies
$\mathrm{dist}_{G'}(b_i, a_j) = 2d+1$.
\end{proof}
\end{lemma}
Let the procedure introduced in the statement of Lemma \ref{make-neighboring-lemma}
be named $\mathsf{MakeNeighboring}$.
The procedure takes a graph $G$ together with its pairing distance-$d$ tree
decomposition $\mathcal{T}$, and produces a modified graph $G'$ together with its
neighboring pairing distance-$d$ decomposition $\mathcal{T}'$ of width larger by $2$ than that
of $\mathcal{T}$:
$$ (G', \mathcal{T}') = \mathsf{MakeNeighboring}(G, \mathcal{T}).$$
\begin{lemma}
\label{tw-combine-lemma}
For every $d \geq 2$, $t \geq 1$ and $\ell_1, \ell_2 \geq 2$, there exists a procedure which takes:
\begin{itemize}
\item a graph $G$ with a distance-$(d-1)$ pairing decomposition $\mathcal{T}_G$
of order $\ell_1$ and width $t$,
\item a graph $H$ with a neighboring distance-$d$ pairing decomposition $\mathcal{T}_H$
of order $\ell_2$ and width $t$,
\end{itemize}
and produces a graph with a distance-$d$ pairing decomposition of order $\ell_1\ell_2$
and width $t$.
\begin{proof}
We fix the graph $G$ with its pairing decomposition $\mathcal{T}_G$, and let
$\mathsf{Root}(\mathcal{T}_G) = (A, B)$, $\mathsf{Leaves}(\mathcal{T}_G) = (A_1, B_1, A_2, B_2, \dots,
A_{\ell_1}, B_{\ell_1})$.
We also create $\ell_1$ disjoint copies of the graph $H$ together with its tree decomposition
$\mathcal{T}_H$.
For each $i \in [1, \ell_1]$, we define the graph $H_i$ as the $i$-th copy of $H$.
In its tree decomposition $\mathcal{T}_{H_i}$, we name the vertices of the root bag and the leaf bags:
\begin{equation*}
\begin{split}
\mathsf{Root}(\mathcal{T}_{H_i}) &= (\alpha_i, \beta_i), \\
\quad \mathsf{Leaves}(\mathcal{T}_{H_i}) &= (a_{(i-1)\ell_2 + 1},
b_{(i-1)\ell_2 + 1}, a_{(i-1)\ell_2 + 2}, b_{(i-1)\ell_2 + 2}, \dots, a_{i\ell_2}, b_{i\ell_2}).
\end{split}
\end{equation*}
We remark that the vertices $A_1, B_1, A_2, B_2, \dots, A_{\ell_1}, B_{\ell_1}$ form a half graph
in $G$.
Moreover, for each $i \in [1, \ell_1]$, the set of vertices $a_j, b_j$ for all $j \in [(i-1)\ell_2+1,
i\ell_2]$ forms a half graph in $H_i$.
We also note that in the sequence
$(a_1, b_1, a_2, b_2, \dots, a_{\ell_1\ell_2}, b_{\ell_1\ell_2})$, the vertices of $H_1$ form a prefix,
followed by the vertices of $H_2$, then $H_3$, and so on,
and a suffix of this sequence is the vertices of $H_{\ell_1}$.
We create a new undirected graph $U$, together with its tree decomposition $\mathcal{T}_U$,
in the following way (Figure \ref{combine-tw-algo-fig}):
\begin{enumerate}
\item We take the disjoint union of the graphs $G, H_1, \dots, H_{\ell_1}$, together with
the forest created by the disjoint union of the corresponding tree decompositions
$\mathcal{T}_G, \mathcal{T}_{H_1}, \mathcal{T}_{H_2}, \dots, \mathcal{T}_{H_{\ell_1}}$.
\item For each $i \in \{1, 2, \dots, \ell_1\}$, we fuse the vertices $A_i$ and $\alpha_i$, and
the vertices $B_i$ and $\beta_i$.
\item In the forest of tree decompositions,
for each $i \in \{1, 2, \dots, \ell_1\}$, we fuse the $i$-th leaf bag of $\mathcal{T}_G$
(containing vertices $A_i$ and $B_i$) with the root bag of $\mathcal{T}_{H_i}$ (containing
$\alpha_i$ and $\beta_i$).
This step is possible since $A_i = \alpha_i$ and $B_i = \beta_i$.
We call the resulting tree $\mathcal{T}_U$.
\end{enumerate}
\begin{figure}[h]
\centering
\begin{minipage}[b]{0.5\textwidth}
\centering
\input{figures/tw-combine-a.tex}
(a)
\end{minipage}\begin{minipage}[b]{0.5\textwidth}
\centering
\input{figures/tw-combine-b.tex}
(b)
\end{minipage}
\caption{(a) --- tree decompositions after Step 1 of the algorithm;
all the bags apart from the root and leaves have been omitted. \\
(b) --- the resulting tree decomposition $\mathcal{T}_U$.}
\label{combine-tw-algo-fig}
\end{figure}
It is straightforward to see that $\mathcal{T}_U$ is a tree decomposition of $U$,
and that its width remains equal to $t$.
In $U$, we can identify the subgraphs $G, H_1, \dots, H_{\ell_1}$, originating from the disjoint
union in Step 1.
We stress that for each $i \in [1, \ell_1]$, subgraphs $G$ and $H_i$ share two vertices ---
$A_i$ and $B_i$.
These two vertices form a bag separating $\mathcal{T}_G$ from $\mathcal{T}_{H_i}$.
This has a couple of consequences, directly implied by the properties of tree decompositions:
\begin{itemize}
\item If a simple path $P$ connects a vertex from $H_i$ with a vertex outside of $H_i$,
then $P$ must pass through one of the vertices $A_i$, $B_i$ (possibly both);
\item If a simple path $P$ has both endpoints in $H_i$, but contains a vertex outside of $H_i$,
then $P$ must pass through both $A_i$ and $B_i$.
\end{itemize}
We now proceed to proving all the distance equalities and inequalities required by the
definition of a distance-$d$ pairing decomposition.
\begin{claim}
\label{tw-claim-bottom-long-path}
For each $k \in [1, \ell_1]$, the vertices $A_k$ and $B_k$ are at distance $2d+2$
in $H_k$.
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
The set of neighbors of $A_k$ in $H_k$ is exactly
$\{a_j\,\mid\, j \in [(k-1)\ell_2+1,\,k\ell_2]\}$, while
the set of neighbors of $B_k$ in $H_k$ is
$\{b_i\,\mid\, i \in [(k-1)\ell_2+1,\,k\ell_2]\}$.
Hence, the second vertex on the shortest path from $A_k$ to $B_k$ in $H_k$
is $a_j$ for some $j \in [(k-1)\ell_2+1,\,k\ell_2]$,
while the penultimate vertex on this path is $b_i$
for some $i \in [(k-1)\ell_2+1,\,k\ell_2]$.
Since the vertices $a_i, b_i$ for $i \in [(k-1)\ell_2+1,\,k\ell_2]$ are in the distance-$d$ pairing
decomposition $\mathcal{T}_{H_k}$, we get that $\mathrm{dist}_{H_k}(b_i, a_j) = 2d$
if $i < j$; otherwise, this distance is larger than $2d$.
As $\ell_2 \geq 2$, the vertices $b_{k\ell_2-1}$ and $a_{k\ell_2}$ both belong to
$H_k$, and the distance between them is equal to $2d$.
Hence,
\[ \mathrm{dist}_{H_k}(A_k, B_k) = 2 + \min_{i, j \in [(k-1)\ell_2+1,\,k\ell_2]} \mathrm{dist}_{H_k} (b_i, a_j) = 2 +
\mathrm{dist}_{H_k}(b_{k\ell_2 - 1}, a_{k\ell_2}) = 2d + 2. \]
\end{claimproof}
\end{claim}
\begin{claim}
\label{tw-claim-top-same-dists}
For each pair of vertices $u, v \in V(G)$, we have that $\mathrm{dist}_U(u, v) = \mathrm{dist}_G(u, v)$.
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
We first note that for each $k \in [1, \ell_1]$, the vertices $A_k$ and $B_k$ are at distance
$2d - 1$ in $G$; this is because $\mathcal{T}_G$ is a distance-$(d-1)$ pairing decomposition
of $G$.
Let us fix two vertices $u, v \in V(G)$ and assume that the shortest path in $U$
between them passes through a vertex $x \not\in V(G)$.
Then, $x \in V(H_k)$ for some $k \in [1, \ell_1]$.
Hence, the path enters the subgraph $H_k$ through one of the vertices $A_k, B_k$,
passes through $x$, and then leaves this subgraph through the other of these vertices.
It means that this shortest path contains a subpath connecting $A_k$ and $B_k$ which
is fully contained within $H_k$.
By Claim \ref{tw-claim-bottom-long-path}, this subpath has length at least $2d + 2$,
and therefore it can be replaced by the shortest path in $G$ connecting $A_k$ and $B_k$,
which has length $2d - 1$.
Therefore, the considered path was not a shortest path in the first place --- a contradiction.
Hence, the shortest path between $u$ and $v$ lies fully within $G$ and thus
$\mathrm{dist}_U(u, v) = \mathrm{dist}_G(u, v)$.
\end{claimproof}
\end{claim}
Claim \ref{tw-claim-top-same-dists} significantly simplifies the structure of the distances
between the vertices of $U$;
no shortest path between a pair of vertices in $U$ can enter a subgraph $H_k$ for some
$k \in [1, \ell_1]$ and then leave it, since there exists a strictly shorter path between
these two vertices omitting this subgraph.
Also, as a corollary of Claim \ref{tw-claim-top-same-dists}, we note the following:
for each $k \in [1, \ell_1]$, we have that $\mathrm{dist}_U(A_k, B_k) = \mathrm{dist}_G(A_k, B_k) = 2d - 1$.
We will now prove a claim that will directly imply that $\mathcal{T}_U$ is a distance-$d$
pairing decomposition of $U$.
\begin{claim}
\label{tw-combined-distances}
For each pair of indices $i, j \in [1, \ell_1\ell_2]$, we have that
$$ \mathrm{dist}_U(b_i, a_j) = \begin{cases}
2d & \text{if }i < j, \\
2d+1 & \text{if }i \geq j.
\end{cases} $$
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
Firstly, let us assume that $b_i$ and $a_j$
are located in the same subgraph $H_k$ of $U$ for some $k \in [1, \ell_1]$;
that is, $i, j \in [(k-1)\ell_2 + 1, k\ell_2]$.
The shortest path in $U$ between these two vertices will have one of the following shapes:
\begin{itemize}
\item The path is fully contained within $H_k$. In this case,
$$ \mathrm{dist}_U(b_i, a_j) = \mathrm{dist}_{H_k}(b_i, a_j) = \begin{cases}
2d & \text{if }i < j, \\
2d+1 & \text{if }i \geq j,
\end{cases} $$
as required.
\item The path leaves $H_k$ and then reenters this subgraph.
This would, however, require the path to contain a path between $A_k$ and $B_k$
as a subpath.
Since $\mathrm{dist}_U(A_k, B_k) = 2d - 1$, and neither $A_k$ nor $B_k$ can be an endpoint
of the considered path, we get that
$$ \mathrm{dist}_U(b_i, a_j) \geq 2 + \mathrm{dist}_U(A_k, B_k) \geq 2d + 1. $$
However, there exists a path of equal or shorter length contained within $H_k$.
\end{itemize}
Therefore, there is a shortest path between $b_i$ and $a_j$ that is fully contained
within $H_k$, which completes the proof in this case.
\vspace{0.5em}
Let us now assume that $a_i, b_i \in V(H_s)$ and $a_j, b_j \in V(H_t)$ for some
$s, t \in [1, \ell_1]$,
$s < t$, and let us compute the distances $\mathrm{dist}_U(b_i, a_j)$ and $\mathrm{dist}_U(b_j, a_i)$.
By the construction of $U$, we infer that $i < j$.
By our considerations above, we deduce that the shortest path from $b_i$ to $a_j$
originates in $H_s$, then enters $G$ through either of the vertices $A_s$, $B_s$,
then enters $H_t$ through either of the vertices $A_t$, $B_t$, and eventually
terminates in $H_t$ (Figure \ref{tw-shortest-paths-fig}).
The same applies to the shortest path from $b_j$ to $a_i$.
We will split this shortest path into three parts: the first part, terminating at either of
the vertices $A_s, B_s$; the second part, taking off from where the first path finished,
and continuing to either of the vertices $A_t, B_t$; and the final part, continuing until
the reaching $a_j$ or $b_j$.
If there are multiple possible partitions, we pick the split minimizing the length of the first
and the third part.
This ensures us that the first path is fully contained within $H_s$, and the final part is
fully contained within $H_t$.
Since $A_s, B_s, A_t, B_t \in V(G)$, Claim \ref{tw-claim-top-same-dists} asserts that
the second part of the path is also fully contained within $G$.
\begin{figure}[h]
\centering
\input{figures/tw-distances.tex}
\caption{The important vertices on the shortest path from $b_i$ to $a_j$, and
on the shortest path from $b_j$ to $a_j$.
The edges are labeled by the length of the shortest path between the connected vertices
or the lower bound on this length.}
\label{tw-shortest-paths-fig}
\end{figure}
Since $\mathcal{T}_{H_s}$ is a neighboring tree decomposition of $H_s$, we figure that
$$ \mathrm{dist}_{H_s}(a_i, A_s) = \mathrm{dist}_{H_s}(b_i, B_s) = 1, \quad \mathrm{dist}_{H_s}(a_i, B_s) \geq 2d+1, \quad
\mathrm{dist}_{H_s}(b_i, A_s) \geq 2d + 1. $$
Analogously, in $H_t$:
$$ \mathrm{dist}_{H_t}(a_j, A_t) = \mathrm{dist}_{H_t}(b_j, B_t) = 1, \quad \mathrm{dist}_{H_t}(a_j, B_t) \geq 2d+1, \quad
\mathrm{dist}_{H_t}(b_j, A_t) \geq 2d + 1. $$
Finally, in $G$, since $A_s \neq A_t$, we get that $\mathrm{dist}_G(A_s, A_t) \geq 1$; similarly,
$\mathrm{dist}_G(B_s, B_t) \geq 1$.
By the definition of $G$ (which has a distance-$(d-1)$ pairing decomposition)
and the fact that $s < t$, we infer that $\mathrm{dist}_G(B_s, A_t) = 2d - 2$
and $\mathrm{dist}_G(B_t, A_s) = 2d - 1$.
By verifying all possibilities, we can now conclude that (Figure \ref{tw-shortest-paths-fig}):
\begin{equation*}
\begin{split}
\mathrm{dist}_U(b_i, a_j) &= \min_{X_s \in \{A_s, B_s\}} \min_{X_t \in \{A_t, B_t\}}
\left[ \mathrm{dist}_{H_s}(b_i, X_s) + \mathrm{dist}_G(X_s, X_t) + \mathrm{dist}_{H_t}(X_t, a_j) \right] = \\
& = \mathrm{dist}_{H_s}(b_i, B_s) + \mathrm{dist}_G(B_s, A_t) + \mathrm{dist}_{H_t}(A_t, a_j) = 2d
\end{split}
\end{equation*}
and
\begin{equation*}
\begin{split}
\mathrm{dist}_U(a_i, b_j) &= \min_{X_s \in \{A_s, B_s\}} \min_{X_t \in \{A_t, B_t\}}
\left[ \mathrm{dist}_{H_s}(a_i, X_s) + \mathrm{dist}_G(X_s, X_t) + \mathrm{dist}_{H_t}(X_t, b_j) \right] = \\
& = \mathrm{dist}_{H_s}(a_i, A_s) + \mathrm{dist}_G(A_s, B_t) + \mathrm{dist}_{H_t}(B_t, b_j) = 2d + 1.
\end{split}
\end{equation*}
Hence, in this case, $i < j$ implies $\mathrm{dist}(b_i, a_j) = 2d$ and $\mathrm{dist}(b_j, a_i) = 2d+1$.
Therefore, the statement of the claim holds in this case as well.
\vspace{0.5em}
Since the statement of the claim is true for each choice of a pair of indices $i, j$ ---
no matter whether $b_i$ and $a_j$ are in the same subgraph $H_k$ for some $k$
or not --- the proof is complete.
\end{claimproof}
\end{claim}
Claim \ref{tw-combined-distances} directly proves the lemma.
Therefore, there exists a procedure constructing a distance-$d$ pairing decomposition
of $U$ of width $t$ and order $\ell_1\ell_2$.
\end{proof}
\end{lemma}
We will name the procedure described in Lemma \ref{tw-combine-lemma} as
$\mathsf{CombineNeighboring}$.
This procedure:
\begin{itemize}
\item takes a graph $G$, together with its distance-$(d-1)$ pairing decomposition $\mathcal{T}_G$
of order $\ell_1$ and width $t$;
\item and a graph $H$, together with its neighboring distance-$d$
pairing decomposition $\mathcal{T}_H$ of order $\ell_2$ and width $t$;
\item and produces a graph $U$ and its distance-$d$ decomposition $\mathcal{T}_U$
of order $\ell_1\ell_2$ and width $t$.
\end{itemize}
We apply this procedure in the following way:
$$ (U, \mathcal{T}_U) = \textsf{CombineNeighboring}((G, \mathcal{T}_G), (H, \mathcal{T}_H)). $$
We can now combine Lemmas \ref{make-neighboring-lemma} and \ref{tw-combine-lemma}
in order to produce an even stronger procedure combining two pairing decompositions:
\begin{corollary}
\label{combine-any-tw}
There exists a procedure $\sf{Combine}$, which for $d \geq 2$, $t \geq 3$,
$\ell_1, \ell_2 \geq 2$ takes:
\begin{itemize}
\item a graph $G$ with a distance-$(d-1)$ pairing decomposition $\mathcal{T}_G$
of order $\ell_1$ and width $t$, and
\item a graph $H$ with a distance-$d$ pairing decomposition $\mathcal{T}_H$
of order $\ell_2$ and width $t - 2$,
\end{itemize}
and constructs a graph with a distance-$d$ pairing decomposition
of order $\ell_1\ell_2$ and width $t$.
\begin{proof}
We set
$$ \mathsf{Combine}((G, \mathcal{T}_G), (H, \mathcal{T}_H)) = \mathsf{CombineNeighboring}(
(G, \mathcal{T}_G), \mathsf{MakeNeighboring}(H, \mathcal{T}_H)). $$
By Lemma \ref{make-neighboring-lemma}, $\mathsf{MakeNeighboring}(H, \mathcal{T}_H)$
is a graph with a distance-$d$ neighboring pairing decomposition of order
$\ell_2$ and width $t$.
By applying Lemma \ref{tw-combine-lemma} on $G$ and the newly produced graph,
we create a graph with a distance-$d$ pairing decomposition of
order $\ell_1\ell_2$ and width~$t$.
\end{proof}
\end{corollary}
Using this corollary, we will now produce huge pairing decompositions.
Precisely, for each pair of integers $d \geq 1$, $k \geq 1$, we will define
an undirected graph $G_{d,k}$, together with its distance-$d$ pairing decomposition
$\mathcal{T}_{d,k}$ of width $2k+1$.
Since the tree decomposition of the graph in Example \ref{pairing-td-example}
is distance-$1$ pairing and has width $3$, we shall take it as $\mathcal{T}_{1, 1}$, and the corresponding
graph as $G_{1,1}$.
The decomposition $\mathcal{T}_{1, 1}$ has order $2$.
For $d \geq 2$, we create the graph $G_{d, 1}$ and its distance-$d$ decomposition
$\mathcal{T}_{d, 1}$ from $G_{1,1}$ and $\mathcal{T}_{1,1}$ in the
following way: for each vertex $v \in \{a_1, b_1, a_2, b_2\}$, we append to the graph
a path of length $d - 1$ whose one endpoint is $v$, and the other endpoint is a new vertex
$v' \in \{a'_1, b'_1, a'_2, b'_2\}$.
We can easily create a distance-$d$ pairing
decomposition $\mathcal{T}_{d, 1}$ of $G_{d, 1}$ of width $3$ (Figure \ref{tw-longer-fig}).
We remark that $\mathcal{T}_{d, 1}$ also has order $2$.
\begin{figure}[h]
\centering
\begin{minipage}[b]{0.5\textwidth}
\centering
\input{figures/tw-longer-a.tex}
(a)
\end{minipage}\begin{minipage}[b]{0.5\textwidth}
\centering
\input{figures/tw-longer-b.tex}
(b)
\end{minipage}
\caption{(a) --- the graph $G_{3, 1}$; (b) --- an example tree decomposition $T_{3, 1}$.}
\label{tw-longer-fig}
\end{figure}
Also, for $k \geq 2$, we create the graph $G_{1, k}$ and its distance-$1$ pairing
decomposition $\mathcal{T}_{1, k}$ from $G_{1,1}$ and $\mathcal{T}_{1,1}$ by adding $2(k-1)$
isolated vertices to $G_{1, 1}$, and appending each new vertex
to each bag of the decomposition $\mathcal{T}_{1, 1}$.
The resulting decomposition is obviously a distance-$1$ pairing decomposition of width
$2k+1$ and order $2$.
Eventually, for $d \geq 2$, $k \geq 2$, we create the graph $G_{d,k}$ and the corresponding
decomposition $\mathcal{T}_{d, k}$ by applying the procedure $\mathsf{Combine}$:
$$ (G_{d,k}, \mathcal{T}_{d, k}) := \mathsf{Combine}((G_{d-1,k}, \mathcal{T}_{d-1,k}), (G_{d,k-1}, \mathcal{T}_{d,k-1})). $$
We can easily verify that the input to this procedure complies with Corollary \ref{combine-any-tw},
and leads to the construction of a graph with a distance-$d$ pairing decomposition
of width $2k+1$,
whose order is equal to the product of the orders of $\mathcal{T}_{d-1, k}$ and $\mathcal{T}_{d, k-1}$.
\vspace{0.5em}
For $d, k \geq 1$ we set $\ell_{d, k}$ as the order of $\mathcal{T}_{d, k}$.
\begin{lemma}
\label{large-tw-order-lemma}
For each $d, k \geq 1$, the following holds:
$$ \ell_{d, k} = 2^{\displaystyle \binom{d + k - 2}{k - 1}}. $$
\begin{proof}
The formula can be directly verified for $d = 1$ and for $k = 1$.
For $d, k \geq 2$, we know that the order of $\mathcal{T}_{d, k}$ is the product of the orders of
$\mathcal{T}_{d-1, k}$ and $\mathcal{T}_{d, k-1}$.
Therefore, by applying a simple induction on $d$ and $k$, we compute that
\[
\log_2 \ell_{d, k} = \log_2 \ell_{d-1,k} + \log_2 \ell_{d, k-1} =
\binom{d + k - 3}{k - 1} + \binom{d + k - 3}{k - 2} = \binom{d + k - 2}{k - 1}.
\]
\end{proof}
\end{lemma}
Lemma \ref{large-tw-order-lemma} immediately leads to the following conclusion:
\begin{theorem}
\label{tw-lower-bound}
For every even $d \geq 2$ and odd $t \geq 3$, there exists a graph with
treewidth not exceeding $t$ that contains a distance-$d$ half graph of order
$$ 2^{\displaystyle \binom{\frac12(d + t - 5)}{\frac12(t-3)}}. $$
\begin{proof}
We consider the graph $G_{\frac{d}{2}, \frac{t-1}{2}}$ together with its distance-$\frac{d}{2}$
pairing decomposition $\mathcal{T}_{\frac{d}{2}, \frac{t-1}{2}}$.
The decomposition has order $\ell_{\frac{d}{2}, \frac{t-1}{2}}$
(Lemma \ref{large-tw-order-lemma}), which matches the formula in the statement
of the theorem; and width $t$, which ensures that the graph has treewidth not exceeding $t$.
Eventually, by the properties of pairing decompositions,
$\mathsf{Leaves}(\mathcal{T}_{\frac{d}{2}, \frac{t-1}{2}})$
is a distance-$d$ half graph of order $\ell_{\frac{d}{2}, \frac{t-1}{2}}$.
\end{proof}
\end{theorem}
We also remark the asymptotic version of this theorem.
\begin{corollary}
\label{tw-lower-bound-asym}
Fix $t \geq 3$.
Then for $d \geq 2$, the maximum order of a distance-$d$ half graph in the class
of graphs with treewidth at most $t$ is bounded from below by
$ 2^{\displaystyle d^{\Omega(t)}}. $
\end{corollary}
This discovery immediately leads to a lower bound in the class of $K_t$-minor-free graphs:
\begin{theorem}
\label{kt-lower-bound}
For every even $d \geq 2$ and odd $t \geq 5$, there exists a $K_t$-minor-free graph
containing a distance-$d$ half graph of order
$$ 2^{\displaystyle \binom{\frac12(d + t - 7)}{\frac12(t-5)}}. $$
\begin{proof}
Theorem \ref{tw-lower-bound} asserts the existence of a graph with treewidth not exceeding
$t-2$ containing a distance-$d$ half graph of order
$2^{\binom{\frac12(d + t - 7)}{\frac12(t-5)}}. $
By Theorem \ref{tw-minor-free}, this graph is $K_t$-minor-free.
\end{proof}
\end{theorem}
We immediately infer the following asymptotic result:
\begin{corollary}
\label{kt-lower-bound-asym}
Fix $t \geq 5$.
Then for $d \geq 2$, the maximum order of a distance-$d$ half graph in the class
of $K_t$-minor-free graphs is bounded from below by
$ 2^{\displaystyle d^{\Omega(t)}}. $
\end{corollary}
\section{Introduction}\label{introduction-chapter}
\input{introduction}
\section{Preliminaries}\label{preliminaries-chapter}
\input{preliminaries}
\section{Lower bounds on the orders of half graphs}\label{lower-bounds-chapter}
\input{lower-bounds}
\section{Polynomial bound on neighborhood complexity in planar graphs}\label{planar-neighborhood-chapter}
\label{noose-profile-lemma-section}
\input{planar-neighborhood}
\section{Upper bound on the orders of semi-ladders in planar graphs}
\label{planar-upper-bound-section}
\input{planar-upper-bound}
\section{Upper bounds in other classes of graphs}\label{other-upper-bounds-chapter}
\input{other-upper-bounds}
\section{Conclusions}\label{conclusions-chapter}
\input{conclusions}
\bibliographystyle{abbrv}
\subsection{Graphs of bounded degree}
\label{degree-up-section}
The following simple theorem presents an upper bound on the maximum semi-ladder order
in graphs with maximum degree bounded by $\Delta$.
The main idea of the proof is that in a distance-$d$ semi-ladder $a_1, a_2, \dots, a_\ell,
b_1, b_2, \dots, b_\ell$, vertex $b_1$ must remain at distance at most $d$
from vertices $a_2, a_3, \dots, a_\ell$.
\begin{theorem}
\label{degree-upper-bound}
For each $\Delta \geq 2$, $d \geq 1$,
the order of every distance-$d$ semi-ladder in a graph with maximum degree bounded by
$\Delta$ is bounded from above by $\Delta^d + 1$.
\begin{proof}
Fix a graph $G$ in which the maximum degree of a vertex is bounded from above by $\Delta$,
and let $a_1, a_2, \dots, a_\ell, b_1, b_2, \dots, b_\ell$ be a distance-$d$ semi-ladder in $G$
of order $\ell \geq 2$.
By the properties of semi-ladders, we infer that for each $i \in \{2, 3, \dots, \ell\}$, we have that
$\mathrm{dist}(b_1, a_i) \leq d$ --- that is, there are $\ell - 1$ vertices (different than $b_1$)
in the distance-$d$ neighborhood of $b_1$.
Since each vertex $a_2, a_3, \dots, a_\ell$ is different than $b_1$
(by the definition of a distance-$d$ semi-ladder in Section \ref{preliminaries-chapter}),
it means that each of them is at distance at least $1$ and at most $d$ from $b_1$.
Obviously, there are at most $\Delta(\Delta - 1)^k$ vertices at distance exactly $k$
($k \geq 1$) from $b_1$.
Summing this over all $k \in \{1, 2, \dots, d\}$, we get that
\begin{equation*}
\begin{split}
\ell - 1 & \leq \sum_{k = 1}^d \Delta (\Delta - 1)^{k-1} = \Delta + (\Delta-1) \sum_{k=2}^d
\Delta(\Delta-1)^{k-2} \leq \Delta + (\Delta-1) \sum_{k=1}^{d-1} \Delta^k = \\
& = 1 + (\Delta - 1) \sum_{k=0}^{d-1} \Delta^k = 1 + \frac{\Delta^d - 1}{\Delta - 1}(\Delta - 1) =
\Delta^d.
\end{split}
\end{equation*}
\end{proof}
\end{theorem}
We contrast the $\Delta^d + 1$ upper bound with the $\left\lfloor\frac{\Delta}{2}\right\rfloor^{
\left\lceil \frac{d}{2} \right\rceil}$ lower bound (Theorem \ref{degree-lower-bound})
proved in Section \ref{lower-bounds-chapter}.
\subsection{Graphs with bounded pathwidth}
\label{pw-up-section}
We begin this section by reminding about a classic combinatorial result, first proved
by Erd\H{o}s and Rado \cite{sunflower_first}: the \textbf{Sunflower Lemma}.
\begin{definition}
\label{sunflower-def}
Suppose $\Omega$ is a universe and $\mathcal{F} = (F_1, F_2, \dots, F_n)$ is a family of
(not necessarily different) subsets of $\Omega$.
Then $\mathcal{F}$ is a \textbf{sunflower} if there exists a set $C$ (which we call the \textbf{core} of
the sunflower) such that for every two different indices $i, j \in [1, n]$, we have
$F_i \cap F_j = C$.
The \textbf{order} of a sunflower is the number of sets in it, that is, $|\mathcal{F}| = n$.
\end{definition}
\begin{theorem}[Sunflower Lemma]
\label{sunflower-lemma}
Let $\mathcal{G}$ be a family of $b!a^{b+1}$ (not necessarily different) subsets of $\Omega$
in which each subset has at most
$b$ elements. Then $\mathcal{G}$ contains a subfamily $\mathcal{F} \subseteq \mathcal{G}$ which
is a sunflower of order $a$.
\end{theorem}
The ``textbook proof'' of this lemma can be found e.g. in the book by Cygan et al.
\cite{ParamAlgo}.
\medskip
In order to prove an upper bound on the maximum semi-ladder order in the class of graphs with
bounded pathwidth, we first need to generalize the Sunflower Lemma.
\subsubsection*{Labeled Sunflower Lemma}
We wish to generalize the Sunflower Lemma (Theorem \ref{sunflower-lemma})
by allowing the sets in the family to assign \textbf{labels} to the elements of the set.
We first need to describe formally what this labeling means.
\begin{definition}
For a finite set of labels $\Sigma$ and a universe $\Omega$,
a \textbf{labeled subset} $A \subseteq \Omega$ over $\Sigma$
is a subset of $\Omega$ in which each element is also assigned a
label from $\Sigma$.
The \textbf{cardinality} of $A$ is the number of elements belonging to $A$.
In other words, a labeled subset is a partial function $A : \Omega \rightharpoonup \Sigma$,
and the cardinality of $A$ is the size of its domain.
\end{definition}
The definition of a sunflower now naturally generalizes to the families of labeled subsets:
\begin{definition}
For a finite set of labels $\Sigma$ and a universe $\Omega$, a family $\mathcal{F}$ of
(not necessarily different) labeled subsets of $\Omega$ over $\Sigma$ is a
\textbf{labeled sunflower} if:
\begin{itemize}
\item $\mathcal{F}$ is a sunflower (as in Definition \ref{sunflower-def}),
whose core we will call $C$, and
\item for each element $v \in C$, each labeled subset $A \in \mathcal{F}$ assigns the same label to $v$;
that is, for each $v \in C$, there exists a label $\rho \in \Sigma$ such that $A(v) = \rho$
for each $A\in\mathcal{F}$.
\end{itemize}
\end{definition}
It turns out that the textbook proof of the Sunflower Lemma \cite{ParamAlgo} can be
generalized to produce labeled sunflowers in a straightforward manner.
\begin{lemma}[Labeled Sunflower Lemma]
\label{labeled-sunflower-lemma}
For a finite set of labels $\Sigma$, a universe $\Omega$ and two integers $a \geq 1$,
$b \geq 0$, any family of $ab!(a|\Sigma|)^b$ (not necessarily different) labeled subsets of
$\Omega$ over $\Sigma$, each of cardinality at most $b$,
contains a labeled sunflower of order $a$ as a subset.
\begin{proof}
We apply an induction on $b$.
If $b = 0$, then the family contains at least $ab!(a|\Sigma|)^b = a$ empty sets and already
is a labeled sunflower.
Now, assume that $b \geq 1$, and let $\mathcal{F}$ be the family as in the statement of the lemma.
We consider two cases:
\begin{itemize}
\item There exists an element $v \in \Omega$ belonging to at least $(b-1)!(a|\Sigma|)^b$
labeled sets in~$\mathcal{F}$.
Hence, there exists a label $\rho \in \Sigma$ and a subfamily $\mathcal{F}' \subseteq \mathcal{F}$
such that we have $|\mathcal{F}'| \geq a(b-1)!(a|\Sigma|)^{b-1}$, and each set $A \in \mathcal{F}'$
contains $v$ and satisfies $A(v) = \rho$.
We create a modified universe $\Omega' := \Omega \setminus \{v\}$, and form a family
$\mathcal{F}''$ from $\mathcal{F}'$ by removing $v$ from each of the sets within $\mathcal{F}'$.
Then, Labeled Sunflower Lemma applies inductively to $\mathcal{F}''$ and parameters $a$ and $b-1$.
Hence, we can find a labeled sunflower $S$ of order $a$ as a subset of $\mathcal{F}''$.
By reintroducing $v$ to each of the sets in $S$, we find a labeled sunflower $S'$ of order $a$
as a subset of $\mathcal{F}'$.
\item Each element $v \in \Omega$ occurs in fewer than $(b-1)!(a|\Sigma|)^b$
labeled sets in $\mathcal{F}$.
Since $(b-1)!(a|\Sigma|)^b \leq \frac{1}{ab} |\mathcal{F}|$, we can find a family $\mathcal{G}$ of $a$ pairwise
disjoint labeled sets in $\mathcal{F}$ greedily.
In each of $a$ steps, we extend $\mathcal{G}$ by any labeled set $A \in \mathcal{F}$, and remove
from $\mathcal{F}$ all labeled sets intersecting $A$.
As each step removes at most $b!(a|\Sigma|)^b \leq \frac1a |\mathcal{F}|$ elements from $\mathcal{F}$,
we can see that this is a valid construction of $\mathcal{G}$.
Since the labeled sets in $\mathcal{G}$ are pairwise disjoint, they form a labeled sunflower.
\end{itemize}
In both cases, we construct a labeled sunflower of order $a$ as a subset of $\mathcal{F}$, so the
proof is complete.
\end{proof}
\end{lemma}
We remark that the lemma requires a relatively small multiplicative overhead on the size of
the initial family of subsets, compared to the original statement of the lemma (Theorem
\ref{sunflower-lemma}):
$$ \frac{ab!(a|\Sigma|)^b}{b!a^{b+1}} = |\Sigma|^b. $$
As a sidenote, there exists a simpler proof of a looser upper bound:
find a sunflower of order $a|\Sigma|^b$ using the sunflower lemma,
and then find a subset of this sunflower of order $a$ which is a~labeled sunflower
(which is an easy task since there are at most $|\Sigma|^b$ labelings of the core of the
sunflower).
This proof, however, requires the multiplicative overhead equal to $|\Sigma|^{b(b+1)}$
compared to the Sunflower Lemma.
If we used this version of the Labeled Sunflower Lemma later instead of the version
we have just proved in Lemma \ref{labeled-sunflower-lemma}, we would ultimately derive
the $d^{O(p^2)}p^{O(p)}$ upper bound on the maximum distance-$d$ semi-ladder size
in graphs with pathwidth bounded by $p$, which is unfortunately too high for our needs.
\subsubsection*{Upper bound proof}
In the first part of our proof, we will define a structure whose occurrence in a graph
proves that the graph both contains a large semi-ladder and has low pathwidth.
\begin{definition}
In a graph $G$, for $p, d, k, \ell \geq 1$,
a path decomposition $(W_1, W_2, \dots, W_k)$ of width $p$, together with $2\ell$
different vertices $a_1, a_2, \dots, a_\ell, b_1, b_2, \dots, b_\ell$,
and $\ell$ different indices $t_1, t_2, \dots, t_\ell \in [1, k]$,
is a \textbf{distance-$d$ alignment} of order $\ell$ if:
\begin{itemize}
\item vertices $a_1, a_2, \dots, a_\ell, b_1, b_2, \dots, b_\ell$ form a distance-$d$
semi-ladder in $G$;
\item vertices $a_1, a_2, \dots, a_\ell$ belong to the bags $W_{t_1}, W_{t_2}, \dots,
W_{t_\ell}$, respectively.
\end{itemize}
We denote a distance-$d$ alignment in the following way:
$$ \mathsf{Alignment}_d\left( (W_i)_{i=1}^k, (a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, (t_i)_{i=1}^\ell\right).$$
\end{definition}
We note that given a distance-$d$ alignment
$\mathsf{Alignment}_d\left( (W_i)_{i=1}^k, (a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, (t_i)_{i=1}^\ell\right)$,
one can easily take a subset of the underlying semi-ladder, given by indices
$i_1, i_2, \dots, i_m$ such that $1 \leq i_1 < i_2 < \dots < i_m \leq \ell$,
and form a distance-$d$ alignment with order $m$:
$\mathsf{Alignment}_d(\allowbreak
(W_i)_{i=1}^k, (a_{i_j})_{j=1}^m, (b_{i_j})_{j=1}^m, (t_{i_j})_{j=1}^\ell)$.
In our proof, we will transform a graph with bounded pathwidth, and containing a large distance
distance-$d$ semi-ladder, into a distance-$d$ alignment containing this semi-ladder.
Then, we will find a reasonably large subset of this alignment having necessary structural
properties.
The following definition formalizes these properties:
\begin{definition}
For $p, d, k, \ell \geq 1$, a distance-$d$ alignment of width $p$ and order $\ell$:
$$\mathsf{Alignment}_d(\allowbreak (W_i)_{i=1}^k, (a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, (t_i)_{i=1}^\ell)$$
is also a \textbf{distance-$d$ sunflower alignment} if the following additional
properties hold:
\begin{itemize}
\item bags $W_{t_1}, W_{t_2}, \dots, W_{t_\ell}$ form a sunflower, whose core we will
denote by $C$;
\item in $G$, the distance-$d$ profiles on $C$ are identical for each vertex
$a_1, a_2, \dots, a_\ell$.
\end{itemize}
We will refer to distance-$d$ sunflower alignment in the following way:
$$ \mathsf{SunflowerAlignment}_d\left( (W_i)_{i=1}^k, (a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell,
(t_i)_{i=1}^\ell\right).$$
The set $C$ is the \textbf{core} of the decomposition.
\end{definition}
We are now ready to find large distance-$d$ sunflower alignments in the graphs
with large distance-$d$ semi-ladders.
\begin{lemma}
\label{large-sunflower-lemma}
For $p, d, \ell \geq 1$,
every graph with pathwidth not exceeding $p$ and containing a semi-ladder of order
$\ell(p+1)! [\ell(d+2)]^{p+1}$
also contains a distance-$d$ sunflower path decomposition of order $\ell$.
\begin{proof}
Let $L := \ell(p+1)! [\ell(d+2)]^{p+1}$.
Fix a graph $G$, together with its distance-$d$ semi-ladder $a_1, a_2, \dots, a_L$,
$b_1, b_2, \dots, b_L$.
Since $\pw{G} \leq p$, there exists a path decomposition $W = (W_1, W_2, \dots,
W_k)$ of $G$ of width at most $p$; that is, we have $|W_i| \leq p + 1$ for each $i \in [1, k]$.
Moreover, we can assume that $W$ is a \textbf{nice path decomposition}; that is, we have
$W_1 = W_k = \varnothing$, and for
each index $i \in \{2, 3, \dots, k\}$, either of the following conditions is satisfied:
\begin{itemize}
\item $W_i$ \textbf{introduces} a vertex $v \in V(G)$; that is, $W_i = W_{i-1} \cup \{v\}$;
\item $W_i$ \textbf{forgets} a vertex $v \in V(G)$; that is, $W_i = W_{i-1} \setminus \{v\}$.
\end{itemize}
It can be easily shown that each path decomposition can be converted into a
nice path decomposition of the same width \cite{ParamAlgo},
so we can safely assume that $W$ is a nice path decomposition.
For each vertex $a_j$ ($1 \leq j \leq L$) of the semi-ladder, we can locate the bag
$W_{t_j}$ introducing $a_j$ to the decomposition.
Since the path decomposition is nice, the values $t_j$ are different for all $j \in [1, L]$.
Therefore, the following describes a distance-$d$ alignment of order $L$:
$$ \mathsf{Alignment}_d\left((W_i)_{i=1}^k, (a_i)_{i=1}^L, (b_i)_{i=1}^L, (t_i)_{i=1}^L \right). $$
We will now find a subset of this distance-$d$ alignment which is a distance-$d$
sunflower alignment.
We first create a family $\mathcal{F}$ of $L$ labeled subsets of $V(G)$ over $\{0, 1, 2, \dots, d, +\infty
\}$: for each $i \in [1, L]$, we let the $i$-th labeled subset in the family to be the bag
$W_{t_i}$ (containing the vertex $a_i$), where each vertex $v \in W_{t_i}$ has the label
$\pi_d[a_i, W_{t_i}](v)$.
Secondly, since each set in $\mathcal{F}$ contains at most $p + 1$ elements, the cardinality
of the set of labels is equal to $d + 2$, and $|\mathcal{F}| = L = \ell(p+1)! [\ell(d+2)]^{p+1}$,
we infer from the Labeled Sunflower Lemma
(Lemma \ref{labeled-sunflower-lemma}) that there exists a subfamily $\mathcal{F}' \subseteq \mathcal{F}$,
which is a labeled sunflower of order $\ell$.
Finally, we let $\mathcal{F}' = (W_{t_{i_1}}, W_{t_{i_2}}, \dots, W_{t_{i_\ell}})$ for $i_1 < i_2 < \dots < i_\ell$.
We can now easily verify that the following structure is a distance-$d$ sunflower alignment
of order $\ell$:
\[ \mathsf{SunflowerAlignment}_d\left( (W_j)_{j=1}^k, (a_{i_j})_{j=1}^\ell, (b_{i_j})_{j=1}^\ell,
(t_{i_j})_{j=1}^\ell \right). \]
\end{proof}
\end{lemma}
Now, it turns out that we can give an explicit upper bound on the order of every
distance-$d$ sunflower alignment:
\begin{lemma}
\label{no-large-sunflower-lemma}
For $d \geq 1$, no graph can contain a distance-$d$ sunflower alignment of order $2d + 3$.
\begin{proof}
Fix $\ell := 2d + 3$ and a graph $G$ containing a distance-$d$ sunflower alignment
of order $\ell$ and width $p$:
$$\mathsf{SunflowerAlignment}_d\left( (W_i)_{i=1}^k, (a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell,
(t_i)_{i=1}^\ell \right). $$
We will prove that the shortest path connecting $b_1$ with $a_i$ for some $i \in [2, \ell]$
has length greater than $d$, which contradicts the assumption that
$a_1, a_2, \dots, a_\ell, b_1, b_2, \dots, b_\ell$ is a distance-$d$ semi-ladder.
Let $C$ be the core of the sunflower alignment.
Firstly, we will prove that no shortest path from $b_1$ to $a_i$ for $i \in [2, \ell]$ passes
through $C$.
Assume for contradiction that for some $i \in [2, \ell]$, the shortest path from $b_1$ to $a_i$
contains a vertex $x \in C$ (Figure \ref{pw-core-intersection-fig}).
Since $\mathrm{dist}(x, a_i) \leq d$ and $\pi_d[a_1, C] = \pi_d[a_i, C]$, we infer that the vertex $x$ is
equidistant from $a_1$ and $a_i$.
Hence,
$$ \mathrm{dist}(b_1, a_1) \leq \mathrm{dist}(b_1, x) + \mathrm{dist}(x, a_1) = \mathrm{dist}(b_1, x) + \mathrm{dist}(x, a_i) = \mathrm{dist}(b_1, a_i)
\leq d. $$
We have a contradiction as $\mathrm{dist}(b_1, a_1) > d$ is required by the definition of a semi-ladder.
We note that this fact means that, in particular, neither $b_1$ nor any of the vertices $a_2, a_3,
\dots, a_\ell$ belongs to $C$.
\begin{figure}[h]
\centering
\input{figures/pw-core-intersection.tex}
\caption{The setup in the proof that no shortest path from $b_1$ to $a_i$ intersects $C$.}
\label{pw-core-intersection-fig}
\end{figure}
Next, we arrange the vertices $a_2, a_3, \dots, a_\ell$ in the order in which they appear in $W$.
Formally, we define a permutation $\sigma = (\sigma_1, \sigma_2, \dots, \sigma_{\ell-1})$ of
$\{2, 3, \dots, \ell\}$ such that $t_{\sigma_1} < t_{\sigma_2} < \dots < t_{\sigma_{\ell - 1}}$.
This way, for each pair of indices $i, j$ ($i, j \in [1, \ell - 1]$) with $i < j$,
the bag $W_{t_{\sigma_i}}$ containing $a_{\sigma_i}$ appears earlier in $W$ than the
bag $W_{t_{\sigma_j}}$ containing $a_{\sigma_j}$ (as $t_{\sigma_i} < t_{\sigma_j}$).
Let us find the vertex $b_1$ in the path decomposition.
We already know that $b_1 \not\in C$.
Since $W_{t_{\sigma_{d+1}}} \cap W_{t_{\sigma_{d+2}}} = C$, we deduce that $b_1$ may
belong to at most one of the bags $W_{t_{\sigma_{d+1}}}$, $W_{t_{\sigma_{d+2}}}$.
As the definition of a path decomposition requires that $b_1$ belongs to the family of the
bags forming a subinterval of the path decomposition,
we get that at least one of the following cases is satisfied:
\begin{enumerate}[(a)]
\item $b_1$ does not belong to any of the bags
$W_1, W_2, W_3, \dots, W_{t_{\sigma_{d+1}}}$ of the decomposition;
\item $b_1$ does not belong any of the bags $W_{t_{\sigma_{d+2}}}, \dots,
W_{k-2}, W_{k-1}, W_k$ of the decomposition.
\end{enumerate}
As these cases are symmetrical, we assume without loss of generality that the case (a) holds.
With this assumption, we consider the shortest path between $b_1$ and $a_{\sigma_1}$.
We remark two facts about this path:
\begin{itemize}
\item it cannot pass through $C$, and
\item it has to intersect each of the bags $W_{t_{\sigma_1}}, W_{t_{\sigma_2}}, \dots,
W_{t_{\sigma_{d+1}}}$ of the decomposition
(since $t_{\sigma_1} < t_{\sigma_2} < \dots < t_{\sigma_{d+1}}$, and
$a_{\sigma_1} \in W_{t_{\sigma_1}}$).
\end{itemize}
Since each pair of the bags $W_{t_{\sigma_1}}, W_{t_{\sigma_2}}, \dots, W_{t_{\sigma_{d+1}}}$
intersects exactly at $C$, and the path cannot pass through $C$,
we conclude that the path has to intersect each $W_{t_{\sigma_1}},
W_{t_{\sigma_2}}, \dots, W_{t_{\sigma_{d+1}}}$ at a~different vertex.
By our assumption that case (a) holds, $b_1$ does not belong to any of these bags.
We conclude that the path must contain at least $d + 2$ vertices,
hence its length is at least $d+1$ --- a contradiction.
This contradiction completes the proof of the lemma.
\end{proof}
\end{lemma}
This fact immediately allows us to conclude with a concrete upper bound.
\begin{theorem}
\label{pw-upper-bound}
For $p \geq 1$, $d \geq 1$, no graph with pathwidth bounded from above by $p$
contains a distance-$d$ semi-ladder of order
$$ (2d + 3)(p + 1)! [(2d + 3)(d + 2)]^{p + 1}. $$
\begin{proof}
If a graph with pathwidth bounded by $p$ contained a distance-$d$ semi-ladder of this
order, it would also contain a distance-$d$ sunflower alignment of order
$2d + 3$ (Lemma~\ref{large-sunflower-lemma}).
However, by Lemma \ref{no-large-sunflower-lemma}, such an alignment cannot exist.
\end{proof}
\end{theorem}
We also remark the asymptotic version of this bound.
\begin{corollary}
\label{pw-upper-bound-asym}
There exists a constant $\delta > 0$ such that for each $p, d \geq 2$, the maximum order
of a distance-$d$ semi-ladder in the class of graphs with pathwidth bounded by $p$
is bounded from above by $(pd)^{\delta p}$.
\end{corollary}
We recall the construction attesting the $d^{\Omega(p)}$ lower bound in graphs
with pathwidth bounded by $p$ (Corollary \ref{pw-lower-bound-asym}).
\subsection{Graphs with bounded treewidth and minor-free graphs}
\label{kt-up-section}
In this part, we will prove an upper bound on the maximum order of a distance-$d$
semi-ladder in the class of graphs excluding $K_t$ as a minor; an analogous bound for graphs
with bounded treewidth will follow.
We begin by introducing two concepts of Sparsity that will become useful in the proof:
\textbf{weak coloring numbers} and \textbf{uniform quasi-wideness}.
\begin{definition}[weak coloring numbers]
\label{wcol-def}
We follow the definition by Zhu \cite{DBLP:journals/dm/Zhu09}.
Let $\Sigma_{V(G)}$ denote the set of all permutations of $V(G)$.
For a permutation $\sigma \in \Sigma_{V(G)}$ and two vertices $u, v \in V(G)$, we write
$u <_\sigma v$ if $u$ occurs in $\sigma$ before~$v$.
For a fixed distance $d \geq 1$, we say that $v$ is \textbf{weakly $d$-reachable} from $u$
with respect to $\sigma \in \Sigma_{V(G)}$ if $v \leq_\sigma u$ and
there exists a path of length at most $d$
connecting $u$ and $v$ such that $v$ is the minimum vertex on this path with respect to
$\sigma$.
We remark that $u$ is weakly $d$-reachable from itself for every $d \in \mathbb{N}$.
We denote the set of vertices weakly $d$-reachable from $u$ with respect to $\sigma$
as $\mathrm{WReach}_d[G, \sigma, u]$ (Figure \ref{weak-reach-def-fig}).
\begin{figure}[h]
\centering
\input{figures/weak-reach-def.tex}
\caption{An example setup. In a permutation $\sigma$, for a vertex $u$ (red),
$\mathrm{WReach}_4[G, \sigma, u] \setminus \{u\}$ is marked green.}
\label{weak-reach-def-fig}
\end{figure}
Given a graph $G$ and an order $\sigma \in \Sigma_{V(G)}$ we define the weak coloring number
of $G$ with respect to $\sigma$ as $$\wcol_d(G, \sigma) :=
\max_{u \in V(G)} \left|\mathrm{WReach}_d[G, \sigma, u]\right|.$$
Finally, given a graph $G$, we define the \textbf{weak coloring number} of $G$ as
$$\wcol_d(G) := \min_{\sigma \in \Sigma_{V(G)}} \wcol_d(G, \sigma).$$
\end{definition}
\begin{definition}[uniform quasi-wideness]
\label{uniform-quasi-wideness-def}
A class $\mathcal{C}$ of graphs is \textbf{uniformly quasi-wide} with margins $N\,:\,\mathbb{N}\times\mathbb{N}\to\mathbb{N}$ and
$s\,:\,\mathbb{N}\to\mathbb{N}$ if for every $m, d \geq 1$, graph $G\in\mathcal{C}$ and a subset $A$ of vertices such that
$|A| \geq N(m, d)$, there exists a set of vertices $S \subseteq V(G)$, $|S| \leq s(d)$ and
a~subset $B \subseteq A-S$, $|B| \geq m$, which is a distance-$d$ independent set in
$G - S$.
\end{definition}
It turns out that a subgraph-closed class $\mathcal{C}$ of graphs is uniformly quasi-wide for any margins
if and only if it is nowhere dense \cite{DBLP:journals/jsyml/NesetrilM10}.
For more properties and applications of uniform quasi-wideness, we refer to the lecture notes
from the University of Warsaw \cite{SparsityUWNotes}.
In this section, we may provide the margins $N, s$ as partial functions, defined only
for distances $d$ from an infinite subset $D \subsetneq \mathbb{N}$.
It is straightforward to see that these margins can be easily extended to total functions:
given $m, d \in N$, we set $d' := \min \{x \in D\,\mid\,x \geq d\}$, and we put
$N(m, d) := N(m, d')$ and $s(d) := s(d')$.
\medskip
In the proof of the upper bound for $K_t$-minor-free graphs,
we will use the upper bound by Fabiański et al.~\cite{fabiaski2018progressive},
applicable to every uniformly quasi-wide class of graphs:
\begin{lemma}[{{\cite[Lemma 29]{fabiaski2018progressive}}}]
\label{semi-ladder-from-uqw}
In every uniformly quasi-wide class of graphs $\mathcal{C}$ with margins $N\,:\,\mathbb{N} \times \mathbb{N} \to \mathbb{N}$ and
$s\,:\,\mathbb{N} \to \mathbb{N}$, each semi-ladder in every graph $G \in \mathcal{C}$ has its order bounded by
$N(2 \cdot (d + 2)^{s(2d)} + 1,\, 2d)$.
\end{lemma}
We will now prove that the class of $K_t$-minor-free graphs is uniformly quasi-wide by
utilizing the generalized coloring numbers.
Precisely, we will use the following upper bound on the weak coloring numbers in this class,
proved by van den Heuvel et al. \cite{DBLP:journals/endm/HeuvelMRS15}.
\begin{lemma}[\cite{DBLP:journals/endm/HeuvelMRS15}]
\label{kt-wcol-bound}
For $t \geq 4$ and any graph $G$ which excludes $K_t$ as a minor, we have that
$\wcol_d(G) \leq \binom{d+t-2}{t-2}(t - 3)(2d + 1)$.
\end{lemma}
We only need to prove that if a class has fairly low weak coloring numbers, then it is
also uniformly quasi-wide with reasonably low margins.
\begin{lemma}
\label{wcol-gives-uqw}
Assume that a class of graphs $\mathcal{C}$ has a finite weak coloring number
$wcol_d(\mathcal{C})$ for each $d \geq 1$.
Then $\mathcal{C}$ is also uniformly quasi-wide with margins
$$N(m, d) = (\wcol_d(\mathcal{C}))!\,(m+1)^{\wcol_d(\mathcal{C}) + 1}, \quad
s(d) = \wcol_d(\mathcal{C}) \quad \text{for each }d \geq 1,\, m \geq 2. $$
\begin{proof}
Fix integers $d \geq 1, m \geq 2$, a graph $G\in\mathcal{C}$, and a subset $A$ of the vertices of $G$
containing at least $N(m, d)$ vertices.
We will prove the lemma by showing that we can erase at most $\wcol_d(\mathcal{C})$ vertices
from $G$ in order to find a distance-$d$ independent set $B \subseteq A$
of size $m$ in the remaining part of the graph.
In $G$, we can find an ordering $\sigma$ of its vertices for which
$\wcol_d(G, \sigma) \leq \wcol_d(\mathcal{C})$.
Knowing that, we define a family $\mathcal{F}$ of subsets of vertices:
$$ \mathcal{F} := \{R_v\,\mid\, v \in S\} \qquad\text{where }R_v := \mathrm{WReach}_d[G, \sigma, v]
\text{ for } v \in S. $$
Since each set in the family contains at most $\wcol_d(\mathcal{C})$ elements and
$|\mathcal{F}| \geq N(m, d) = (\wcol_d(\mathcal{C}))!\,(m+1)^{\wcol_d(\mathcal{C}) + 1}$,
the Sunflower Lemma (Theorem \ref{sunflower-lemma})
lets us find a subfamily $\mathcal{F}' \subseteq \mathcal{F}$ which is a sunflower of order $m + 1$.
We let $\mathcal{F}' = \{R_{v_1}, R_{v_2}, \dots, R_{v_{m+1}}\}$ for $m+1$ different vertices
$v_1, v_2, \dots, v_{m+1}$. We denote the core of $\mathcal{F}'$ as $D$.
Without loss of generality, we assume that the vertices $v_1, v_2, \dots, v_{m+1}$ are ordered
decreasingly with respect to the order $\sigma$: $v_{m+1} <_\sigma v_m <_\sigma \dots
<_\sigma v_1$.
By the definition of weak reachability in Definition \ref{wcol-def},
for each $i \in [1, m + 1]$, $v_i$ is the maximum element of $R_{v_i}$
with respect to $\sigma$.
Since for $i \in [1, m]$ we have $v_i >_\sigma v_{m + 1}$, and the core $D$ must be a subset
of $R_{v_{m+1}}$, we infer that $v_i \not\in D$ for each $i \in [1, m]$.
Therefore, the set $\{v_1, v_2, \dots, v_m\}$ of vertices is disjoint with $D$.
We now focus on the sunflower $\mathcal{F}'' := \{R_{v_1}, R_{v_2}, \dots, R_{v_m}\}$ of order $m$,
whose core is naturally $D$.
Obviously, $|D| \leq \wcol_d(\mathcal{C})$.
We define the graph $G' := G - D$.
We will now prove that $\{v_1, v_2, \dots, v_m\}$ is a distance\nobreakdash-$d$
independent set in $G'$.
Assume for contradiction that there exists a path of length at most $d$ connecting two
different vertices of the set --- say, $v_i, v_j$ for two different indices $i, j \in [1, m]$.
Let $w_{\min}$ be the vertex on this path which is minimal with respect to $\sigma$.
This, however, implies that $w_{\min}$ belongs to both $\mathrm{WReach}_d[G, \sigma, v_i]$
and $\mathrm{WReach}_d[G, \sigma, v_j]$, and thus $w_{\min} \in R_{v_i} \cap R_{v_j}$.
Since $\mathcal{F}'' = \{R_{v_1}, R_{v_2}, \dots, R_{v_m}\}$, we infer that
$w_{\min}$ belongs to $D$ --- the core of $\mathcal{F}''$.
This is a contradiction since $D$ is disjoint with $G'$.
\end{proof}
\end{lemma}
We remark that a combination of Lemmas \ref{semi-ladder-from-uqw}, \ref{kt-wcol-bound} and
\ref{wcol-gives-uqw} can already provide us a concrete upper bound on the maximum
order of a distance-$d$ semi-ladder in the class of $K_t$-minor-free graphs.
However, the produced bound will be insufficient for our purposes --- it can be verified that
it would result in the $d^{O(d^{2t - 2})}$ upper bound for each fixed $t \geq 4$, while
we aim at the $d^{O(d^{t - 1})}$ bound.
In order to prove a tighter upper bound, we will improve the margins $N, s$ with which the
class of $K_t$-minor-free graphs is uniformly quasi-wide using the lemma below.
This lemma is inspired by Lemma 3.16 from the work of Nešetřil and Ossona de Mendez
\cite{DBLP:journals/jsyml/NesetrilM10}.
However, we significantly modified the original lemma in order to ensure a huge drop of the
margin $s$ while keeping the margin $N$ relatively low.
\begin{lemma}
\label{kt-reduce-uqw}
Fix $t \geq 4$. Assume that a class of graphs $\mathcal{C}$:
\begin{itemize}
\item excludes the complete bipartite graph $K_{t-1, t-1}$ as a minor, and
\item is uniformly quasi-wide with margins $N\,:\,\mathbb{N}\times \mathbb{N}\to\mathbb{N}$, $s\,:\,\mathbb{N}\to\mathbb{N}$.
\end{itemize}
Then $\mathcal{C}$ is also uniformly quasi-wide with margins $\widehat{N}\,:\,\mathbb{N} \times \mathbb{N} \to \mathbb{N}$
and $\widehat{s}\,:\,\mathbb{N} \to \mathbb{N}$, where $\widehat{s}$~is a constant function,
$\widehat{s} \equiv t - 2$, and
$$ \widehat{N}(m, 2d) = N\left(\binom{s(2d) + 1}{t - 1}(m+t),\,2d\right) \quad
\text{for each }m, d \geq 1.$$
\begin{proof}
\vspace{0.5em}
We fix a graph $G \in \mathcal{C}$, integers $m, d \geq 1$, and a set of vertices $A \subseteq V(G)$ of
size at least $\widehat{N}(m, 2d)$.
By our assumption, there exists a~subset $S \subseteq V(G)$ with $|S| \leq s(2d)$
and a~subset $B \subseteq A-S$ with $|B| \geq \binom{s(2d) + 1}{t - 1}(m+t)$
such that $B$ is a distance-$2d$ independent set in $G - S$.
Similarly to \cite[Lemma 3.16]{DBLP:journals/jsyml/NesetrilM10},
for each $v \in B$, we let $L_v$ to be a minimal subset of $S$
such that in $G - L_v$, there is no path of length $d$ or less from $v$
to any vertex from $S \setminus L_v$; such a subset exists since $S$ itself satisfies
this requirement.
Now, we will define a new set $L'_v$ in the following way:
if $|L_v| \leq t - 2$, then we set $L'_v := L_v$; otherwise, we take $L'_v$ to be any subset of
$L_v$ of size exactly $t - 1$.
Since $L'_v \subseteq S$, $|L'_v| \leq t - 1$ and $|S| \leq s(2d)$, we conclude that there
are at most
$$\binom{s(2d)}{0} + \binom{s(2d)}{1} + \dots + \binom{s(2d)}{t - 1} =\binom{s(2d) + 1}{t - 1}$$
different possible sets $L'_v$.
It follows that for some set $C \subseteq S$, $|C| \leq t - 1$, there are at least $m + t$
different vertices $v_1, v_2, \dots, v_{m + t}$ for which $L'_{v_1} = L'_{v_2} = \dots =
L'_{v_{m+t}} = C$.
We consider two cases, distinguished by the cardinality of $C$:
\begin{itemize}
\item If $|C| \leq t - 2$, then $L_{v_1} = L_{v_2} = \dots = L_{v_{m + t}} = C$.
Now, assume there are two different vertices $v_i, v_j$ ($i, j \in [1, m + t]$) at distance
at most $2d$ in $G - C$.
Since $v_i$ and $v_j$ are at distance greater than $2d$ in $G - S$, the shortest path
between these two vertices in $G - C$ must pass through some vertex $x \in S \setminus C$.
This, however, means that $x$ is at distance at most $d$ from one of the vertices $v_i$,
$v_j$ in $G - C$ --- a contradiction since $x \not\in L_{v_i}$ and $x \not\in L_{v_j}$.
Therefore, $\{v_1, v_2, \dots, v_{m+t}\}$ is a distance-$2d$ independent set in $G - C$,
where $|C| \leq t - 2$.
\item If $|C| = t - 1$, then we will find $K_{m + t, t - 1}$ as a minor in $G$, which will lead
to a contradiction with $G \in \mathcal{C}$.
Namely, for each $x \in \{v_1, v_2, \dots, v_{m+t}\}$, we construct a tree $Y_x$ rooted at $x$
with depth not exceeding $d$ whose set of leaves is $L_x$ and that does not contain
any other vertices of $S$.
Such a tree exists as the minimality of $L_x$ implies that for each $v \in L_x$,
the distance between $x$ and $v$ in $G - (L_x \setminus \{v\})$ does not exceed $d$.
We see that no pair of trees $Y_x$, $Y_y$ can intersect at any vertex outside of $S$
--- otherwise, we would be able to construct a path of length at most $2d$
between $x$ and $y$ avoiding $S$.
This is, of course, impossible as $x, y \in A$.
Finally, we can find $K_{m+t, t-1}$ as a minor of $G$ by contracting all subgraphs
$Y_x - S$ into single vertices, and then observing
that for each $x \in \{v_1, v_2, \dots, v_{m+t}\}$ and $y \in C$, the vertex $y$ is adjacent
to the contracted subgraph $Y_x - S$.
We have a contradiction since we assumed $G$ to be $K_{t-1, t-1}$-free.
\end{itemize}
\end{proof}
\end{lemma}
We remark that Lemma \ref{kt-reduce-uqw} also applies if $\mathcal{C}$ excludes $K_t$ as a minor
for some fixed $t \geq 4$, for such classes of graphs exclude $K_{t-1, t-1}$ as a minor as well.
With our additional lemma in hand, we can prove the following upper bound:
\begin{theorem}
\label{kt-upper-bound}
There exists a polynomial $p$ such that for $t \geq 4$, $d \geq 2$,
there is no distance-$d$ semi-ladder of order larger than
$$ d^{p(t) \cdot (2d+1)^{t-1}} $$
in any $K_t$-minor-free graph.
\begin{proof}
In this proof, $\poly(t)$ will denote any polynomial of $t$ with constant coefficients independent
on $d$ or $t$.
However, each occurrence of this term in any equation might mean a different polynomial.
Fix $t \geq 4$ and $d \geq 2$, and consider the class $\mathcal{C}$ of graphs excluding $K_t$ as
a minor.
We first bound the weak coloring number of $\mathcal{C}$ using Theorem \ref{kt-wcol-bound}:
\begin{equation}
\label{kt-wcol-ineq}
\begin{split}
\wcol_d(\mathcal{C}) &\leq \binom{d + t - 2}{t - 2}(t - 3)(2d + 1) =
\frac{(d + 1)(d + 2) \dots (d+t-2)}{(t - 2)!} (t - 3)(2d + 1) = \\
&= \frac{d+1}{1} \cdot \frac{d+2}{2} \cdot \ldots \cdot \frac{d+t-2}{t-2} \cdot
(t - 3)(2d + 1) \leq \\ &\leq (d + 1)^{t-2}(t-3)(2d+1) \leq
\poly(t) \cdot (d + 1)^{t - 1}.
\end{split}
\end{equation}
By Lemma \ref{wcol-gives-uqw}, $\mathcal{C}$ is uniformly quasi-wide with margins
\begin{equation}
\label{kt-init-nmd-ineq}
\begin{split}
N(m, d) & = (\wcol_d(\mathcal{C}))!(m + 1)^{\wcol_d(\mathcal{C}) + 1} \leq
[(m + 1)\wcol_d(\mathcal{C})]^{\wcol_d(\mathcal{C}) + 1} = \\
& \stackrel{(\ref{kt-wcol-ineq})}{=}
[m \cdot \poly(t) \cdot (d + 1)^{t - 1}]^{\poly(t) \cdot (d + 1)^{t - 1}} \leq
(md)^{\poly(t) \cdot (d + 1)^{t - 1}}
\end{split}
\end{equation}
and
\begin{equation}
\label{kt-init-sd-ineq}
s(d) = \wcol_d(\mathcal{C}) \stackrel{(\ref{kt-wcol-ineq})}{\leq} \poly(t) \cdot (d + 1)^{t - 1}.
\end{equation}
In order to apply Lemma \ref{kt-reduce-uqw}, we first bound the following expression for
$m \geq 1$:
\begin{equation}
\label{kt-init-binom-ineq}
\begin{split}
\binom{s(2d) + 1}{t - 1}(m + t) & \leq
[s(2d) + 1]^{t - 1} (m + t) \stackrel{(\ref{kt-init-sd-ineq})}{\leq}
[\poly(t) \cdot (2d + 1)]^{(t - 1)^2} (m + t) \leq \\
& \leq m \cdot [d \cdot \poly(t)]^{(t - 1)^2}.
\end{split}
\end{equation}
Now, we get that $\mathcal{C}$ is also uniformly quasi-wide with margins $\widehat{s} \equiv t - 2$ and
\begin{equation}
\label{kt-later-nmd-ineq}
\begin{split}
\widehat{N}(m, 2d) & = N\left(\binom{s(2d) + 1}{t - 1}(m+t),\,2d\right)
\stackrel{(\ref{kt-init-binom-ineq})}{\leq}
N\left(m \cdot [d \cdot \poly(t)]^{(t - 1)^2},\, 2d\right) \leq \\
& \stackrel{(\ref{kt-init-nmd-ineq})}{\leq}
\left\{ m \cdot [d \cdot \poly(t)]^{(t - 1)^2} \cdot 2d \right\}^{\poly(t) \cdot
(2d + 1)^{t - 1}} \leq (md)^{\poly(t) \cdot (2d + 1)^{t - 1}}.
\end{split}
\end{equation}
Finally, we apply Lemma \ref{semi-ladder-from-uqw} and infer that the maximum order
of any distance-$d$ semi-ladder is bounded from above by
$$ \widehat{N}\left(2 \cdot (d + 2)^{t - 2} + 1, 2d\right) \stackrel{(\ref{kt-later-nmd-ineq})}{\leq}
d^{\poly(t) \cdot (2d + 1)^{t - 1}}. $$
Hence, there exists a polynomial $p$ for which this maximum order is bounded from
above by $d^{p(t) \cdot (2d+1)^{t - 1}}$ for all $t \geq 4$, $d \geq 2$.
\end{proof}
\end{theorem}
We also infer the following asymptotic version of Theorem \ref{kt-upper-bound}:
\begin{corollary}
\label{kt-upper-bound-asym}
For each fixed $t \geq 4$, the maximum order of a distance-$d$ semi-ladder in the class
of graphs excluding $K_t$ as a minor is bounded from above by $d^{O(d^{t - 1})}$.
\end{corollary}
We contrast this result with the $2^{d^{\Omega(t)}}$ lower bound
(Corollary \ref{kt-lower-bound-asym}) in the class of $K_t$-minor-free graphs.
\medskip
By Theorem \ref{tw-minor-free}
(each graph $G$ with $\tw(G) \leq t$ is also $K_{t+2}$-minor-free),
we immediately prove the following result from Corollary \ref{kt-upper-bound-asym}:
\begin{corollary}
\label{tw-upper-bound-asym}
For each fixed $t \geq 2$, the maximum order of a semi-ladder in the class of graphs with
treewidth not exceeding $t$ is bounded from above by $d^{O(d^{t + 1})}$.
\end{corollary}
Similarly, we recall the $2^{d^{\Omega(t)}}$ lower bound on the maximum order
of distance-$d$ semi-ladders in the class of graphs with treewidth bounded by $t$
(Corollary \ref{tw-lower-bound-asym}).
\subsection{Statement of the Noose Profile Lemma}
In order to state Noose Profile Lemma, we first need to define nooses in plane graphs.
\begin{definition}
For any graph $G$ embedded in the plane,
a {\bf noose} is a closed curve in the plane that passes through vertices and faces of this graph
that does not intersect itself or the interiors of any edges.
Note that this definition disallows the curve to pass through any vertex multiple times.
\end{definition}
We let the \textbf{length} of a noose to be the number of vertices on it.
For any noose $\mathcal{L}$ in a plane graph $G$, we define the set of vertices on the noose $V(\mathcal{L})$.
Moreover, for each $v \in V(G)$, we define the distance-$d$ profile of $v$ on $\mathcal{L}$ in $G$:
$\pi_d[v, \mathcal{L}] := \pi_d[v, V(\mathcal{L})]$.
Also, we define the subgraph $G_\mathcal{L}$ as the graph containing all vertices and edges
within the bounded closed region whose boundary is $\mathcal{L}$ (Figure \ref{gl-subgraph-fig}).
The vertices and edges of $G_\mathcal{L}$ are said to be \textbf{enclosed} by~$\mathcal{L}$.
\begin{figure}[h]
\centering
\begin{minipage}[b]{0.5\textwidth}
\centering
\input{figures/gl-subgraph-def-a.tex}
(a)
\end{minipage}\begin{minipage}[b]{0.5\textwidth}
\centering
\input{figures/gl-subgraph-def-b.tex}
(b)
\end{minipage}
\caption{(a) --- an example graph $G$ with a noose $\mathcal{L}$ (blue); (b) --- the graph $G_\mathcal{L}$,
with $V(\mathcal{L})$ marked red.}
\label{gl-subgraph-fig}
\end{figure}
We are now ready to present the lemma in question:
\begin{theorem}[Noose Profile Lemma]
\label{noose-profile-lemma}
Consider any graph $G$ together with its embedding in the plane, and fix any noose
$\mathcal{L}$ containing $c \geq 1$ vertices of $G$.
The set $\{\pi_d[v, \mathcal{L}]\, \mid\, v \in V(G_\mathcal{L})\}$
of different distance-$d$ profiles on $\mathcal{L}$,
measured from the vertices enclosed by $\mathcal{L}$,
has at most $c^3 (d+2)^4$ elements.
\end{theorem}
We remark that if $c$ is bounded by a polynomial of $d$, then the theorem above implies
that the number of distance-$d$ profiles on $\mathcal{L}$ is also
polynomially bounded on $d$.
Subsections \ref{closeness-def-section} through \ref{noose-profile-lemma-conclusion-subsection} are devoted to the proof of the lemma.
\subsection{Definition and properties of closeness}
\label{closeness-def-section}
Let us first describe some helpful notation.
For a closed region $\Omega \subseteq \mathbb{R}^2$ of the plane,
we denote $\partial \Omega$ as the topological boundary of $\Omega$,
and $\Int\Omega$ as its interior.
We also introduce the following majorization relation on distance-$d$ profiles in $G$:
\begin{definition}
For a graph $G$, a subset of vertices $S \subseteq V(G)$, and two vertices
$s, t \in V(G)$, we say that the distance-$d$ profile $\pi_d[s, S]$ {\bf majorizes} $\pi_d[t, S]$ if
$\pi_d[s, S](v) \geq \pi_d[t, S](v)$ for all $v \in S$.
We denote this partial order as $\pi_d[s, S] \succcurlyeq \pi_d[t, S]$.
\end{definition}
As in the statement of the lemma, fix any graph $G$ and a noose $\mathcal{L}$.
Let $v_1, v_2, \dots, v_c$ be the vertices of $\mathcal{L}$, listed
in the clockwise order.
For simplicity, we set $v_0 = v_c$ and $v_{c+1} = v_1$.
Let also $\mathcal{L}[i, j] \subseteq \mathcal{L}$
be the curve from $v_i$ to $v_j$ following the noose clockwise.
That is, $\mathcal{L}[i, j]$ contains vertices $v_i, v_{i+1}, \dots, v_j$ in this order if $i \leq j$,
and $v_i, v_{i+1}, \dots, v_c, v_1, v_2, \dots, v_j$ otherwise.
Moreover, let $\mathcal{L}(i, j) := \mathcal{L}[i, j] \setminus
\{v_i, v_j\}$.
Let us say that a vertex $s \in V(G_\mathcal{L})$ is \textbf{close} to a vertex $v_i \in \mathcal{L}$ if the distance
between these two vertices in $G$ does not exceed $d$, and no shortest path connecting
$v_i$ and $s$ contains any vertex from $\mathcal{L}$ as an internal vertex.
Otherwise, we say that $s$ is \textbf{far} from $v_i$.
For such vertex $s$ we also set $\mathrm{Close}(s) = \{v \in \mathcal{L}\,\mid\,
s\text{ is close to }v\}$.
\begin{lemma}
\label{lemma-majorization-close}
If for any two vertices $s, t \in V(G_\mathcal{L})$ we have $\pi_d[s, \mathrm{Close}(s)] \succcurlyeq
\pi_d[t, \mathrm{Close}(s)]$, then $\pi_d[s, \mathcal{L}] \succcurlyeq \pi_d[t, \mathcal{L}]$.
\begin{proof}
Take any $v \in \mathcal{L}$. If also $v \in \mathrm{Close}(s)$, then
$$ \pi_d[s, \mathcal{L}](v) = \pi_d[s, \mathrm{Close}(s)](v) \geq
\pi_d[t, \mathrm{Close}(s)](v) = \pi_d[s, \mathcal{L}](v). $$
If however $v \not\in \mathrm{Close}(s)$, then either of the following cases holds:
\begin{itemize}
\item The distance between $s$ and $v$ is longer than $d$.
In this case, $\pi_d[s, \mathcal{L}](v) = +\infty \geq \pi_d[t, \mathcal{L}](v)$.
\item The shortest path between $s$ and $v$ has length at most $d$, and
some such shortest path passes through another vertex of $\mathcal{L}$.
Pick a vertex of the noose $v' \in \mathcal{L}$ on any such shortest path.
In case there are multiple such vertices, we pick any vertex minimizing its distance from $s$.
As no shortest path between $s$ and $v'$ contains any other vertex of $\mathcal{L}$
(otherwise, such vertex would be even closer to $s$),
we have that $v' \in \mathrm{Close}(s)$.
Hence,
\begin{equation*}
\begin{split}
\pi_d[s, \mathcal{L}](v) &= \mathrm{dist}(s, v) = \mathrm{dist}(s, v') + \mathrm{dist}(v', v) = \pi_d[s, \mathrm{Close}(s)](v') +
\mathrm{dist}(v', v) \geq \\ &\geq \pi_d[t, \mathrm{Close}(s)](v') + \mathrm{dist}(v', v) =
\mathrm{dist}(t, v') + \mathrm{dist}(v', v) \geq \\
&\geq \mathrm{dist}(t, v) = \pi_d[t, \mathcal{L}](v).
\end{split}
\end{equation*}
\end{itemize}
In all cases, we proved that $\pi_d[s, \mathcal{L}](v) \geq \pi_d[t, \mathcal{L}](v)$.
Thus, $\pi_d[s, \mathcal{L}] \succcurlyeq \pi_d[t, \mathcal{L}]$.
\end{proof}
\end{lemma}
This immediately leads to the following corollary:
\begin{corollary}
\label{only-close-profile}
If for any two vertices $s, t \in V(G_\mathcal{L})$ we have $\mathrm{Close}(s) = \mathrm{Close}(t)$
and $\pi_d[s, \mathrm{Close}(s)] = \pi_d[t, \mathrm{Close}(t)]$, then
$\pi_d[s, \mathcal{L}] = \pi_d[t, \mathcal{L}]$.
\end{corollary}
Hence, $\pi_d[s, \mathcal{L}]$ can be uniquely deduced from the distances between $s$ and
each vertex from $\mathrm{Close}(s)$.
This allows us to safely replace the graph $G$ with $G_\mathcal{L}$ (that is, to remove
all vertices and edges not enclosed by $\mathcal{L}$); this replacement does not change
$\mathrm{Close}(s)$ or any of the distances to the close vertices.
\vspace{1em}
In $G_\mathcal{L}$, let
$\mathcal{C}_i := \{s \in V(G_\mathcal{L})\,\mid\, |\mathrm{Close}(s)| = i\}$.
First, we examine the behavior of the vertices from $\mathcal{C}_0$ and $\mathcal{C}_1$.
Note that $\mathcal{L} \subseteq \mathcal{C}_1$.
\begin{lemma}
There are at most $c(d + 1) + 1$ distinct distance-$d$ profiles on $\mathcal{L}$ measured
from the vertices in $\mathcal{C}_0 \cup \mathcal{C}_1$.
\begin{proof}
Obviously, no vertex from $\mathcal{C}_0$ can reach $\mathcal{L}$ by a path consisting
of at most $d$ edges,
so each such vertex generates the same distance-$d$ profile on $\mathcal{L}$:
the constant function $\lambda v.(+\infty)$.
Now consider any vertex $s \in \mathcal{C}_1$. Its distance-$d$ profile on $\mathcal{L}$
can be unambiguously deduced from the only vertex $v_i \in \mathrm{Close}(s)$
and the distance $\mathrm{dist}(s, v_i) \in [0, d]$ (Corollary \ref{only-close-profile}).
This leads to a maximum of $c(d + 1)$ distinct profiles created by $\mathcal{C}_1$.
Hence, at most $c(d+1) + 1$ distinct distance-$d$ profiles can be generated by the
vertices in $\mathcal{C}_0 \cup \mathcal{C}_1$.
\end{proof}
\end{lemma}
From now on, we only consider remaining vertices.
\subsection{Rightmost shortest paths}
We will now extend slightly the definitions by Klein \cite{10.5555/1070432.1070454}.
\begin{definition}
\label{left-of-def}
Fix any vertex $v \in \mathcal{L}$.
We define a strict partial order $\ll$ on oriented paths originating from $v$, but not necessarily
terminating at the same vertex.
We say that $P_1 \ll P_2$ (or: \textbf{''$P_1$ is left of $P_2$''}) if:
\begin{itemize}
\item neither of the paths is a prefix of another,
\item $P_1$ and $P_2$ have a common prefix $x_1, x_2, \dots, x_k$, where $v = x_1$,
\item $P_i$ contains an oriented edge $x_k \to w_i$ for $i = 1, 2$,
\item edge $x_k \to w_1$ is ``to the left'' of edge $x_k \to w_2$; formally,
edges $x_kx_{k-1}$, $x_kw_1$ and $x_kw_2$ are in the clockwise order around $x_k$
(Figure \ref{figure-to-the-left}(a)).
However, if $k = 1$, the paths do not contain $x_0$.
In order to cope with this problem, we imagine an auxiliary vertex $x_0$
outside of the region enclosed by
$\mathcal{L}$ and connect it by an edge to $x_1$, placed
strictly outside of this region (Figure \ref{figure-to-the-left}(b)).
\end{itemize}
We can also interchangeably say $P_2 \gg P_1$ (or: \textbf{``$P_2$ is right of $P_1$''}.)
\end{definition}
\begin{figure}[h]
\centering
\begin{minipage}[b]{0.5\textwidth}
\centering
\input{figures/to-the-left-a.tex}
(a)
\end{minipage}\begin{minipage}[b]{0.5\textwidth}
\centering
\input{figures/to-the-left-b.tex}
(b)
\end{minipage}
\caption{(a) --- the path containing $w_1$ is to the left of the path containing $w_2$. \\
(b) --- if the first edges of two compared paths differ, we imagine an auxiliary vertex
$x_0$ and an auxiliary edge $x_0x_1$ which we prepend to both paths.
We then compare the paths as in (a).}
\label{figure-to-the-left}
\end{figure}
The relation $\ll$ was defined in \cite{10.5555/1070432.1070454}
only between the simple paths originating at $v$ and terminating at a fixed vertex $s$.
Then $\ll$ is a linear order.
In that setup, if $v$ and $s$ are in the same connected component of the graph,
this relation limited only to the shortest paths between $v$ and $s$ contains the
maximal element $P_{v, s}$, which we call the \textbf{rightmost shortest path}.
However, Definition \ref{left-of-def} naturally extends $\ll$ to any two paths $P_1$, $P_2$ which both originate
at $v$ and neither is a prefix of the other, but which do not have to terminate at the
same vertex.
We also define the rightmost shortest path tree rooted at $v$ as in
\cite{10.5555/1070432.1070454}.
Notably, for any vertex $s$ of the tree, the path between $v$ and $s$ in this tree is $P_{v, s}$.
Obviously, if $v \in \mathcal{L}$ and for some vertices $a, b \in V(G_\mathcal{L})$,
$a$ belongs to $P_{v, b}$, then $P_{v, a} = P_{v, b}[v, a]$.
Moreover, for $v \in \mathcal{L}$ and $s \in V(G_\mathcal{L})$, we obviously have that
$\mathrm{len}(P_{v,s}) = \mathrm{dist}(v, s)$.
\begin{lemma}
\label{prefix-paths}
For any two distinct vertices $s, t \in \mathcal{L}$, paths
$P_{a,s}$ and $P_{a,t}$ share a common prefix and are vertex-disjoint after removing
this prefix.
\begin{proof}
Consider the rightmost shortest path tree rooted at $a$.
The tree contains paths $P_{a,s}$ and $P_{a,t}$.
The root $a$ belongs to both paths, hence they both
must intersect at a common prefix and nowhere else.
\end{proof}
\end{lemma}
\begin{lemma}
\label{suffix-paths}
Fix any $a, b \in \mathcal{L}$ and $s \in V(G_\mathcal{L}) \setminus V(\mathcal{L})$
such that $a, b \in \mathrm{Close}(s)$.
Paths $P_{a,s}$ and $P_{b,s}$ share a common suffix as a subpath, and
are vertex-disjoint after removing this suffix.
\begin{proof}
Take the first vertex $x \in P_{a,s} \cap P_{b,s}$ on the path between $a$ and $s$,
that is, the one minimizing $\mathrm{dist}(x, a)$.
If $x = s$, we are done.
In the opposite case, we set $a^*$ and $b^*$ as the next vertices after $x$ on the paths
$P_{a,s}$ and $P_{b,s}$, respectively.
Moreover, we set $a_p$ and $b_p$ as the last vertices before $x$ on these paths.
Vertices $a_p$ and $b_p$ exist since $P_{a,s}$ cannot pass through $b$ (otherwise,
$s$ would not be close to $a$), and similarly $P_{b,s}$ cannot pass through $a$.
Hence, $x \not \in \{a, b\}$ --- that is, $x$ cannot be the initial vertex of either
of these paths.
Obviously, the length of each of the paths $P_{a,s}[x,s]$ and $P_{b,s}[x,s]$
must be the same, otherwise we would be able to swap one of the suffixes with another
in one of the paths $P_{a,s}, P_{b,s}$, reducing its length.
This is, however, impossible as we require $P_{a,s}$ and $P_{b,s}$ to be the
shortest paths connecting the corresponding pairs of vertices.
Also, note that paths $P_{a,x}$ and $P_{b,x}$ are vertex-disjoint apart from their common
endpoint $x$.
Consider the closed region $\Omega$ bounded by $P_{a,x}$, $P_{b,x}$ and the part of
the noose between $a$ and $b$ --- either $\mathcal{L}[a, b]$ or $\mathcal{L}[b, a]$ ---
chosen so that $s \in \Int\Omega$.
(Obviously, $s$ cannot belong to $\mathcal{L}$, $P_{a,x}$ or $P_{b,x}$.)
Assume now that $a^* \not\in \Omega$ (Figure \ref{figure-suffix-paths}(a)).
Then, the path $P_{a, s}[a^*, s]$ must intersect $\partial \Omega$.
Hence, one of the following cases occurs:
\begin{itemize}
\item The path intersects $P_{a,x}$ (Figure \ref{figure-suffix-paths}(b)).
In this case, the path $P_{a, s}$ would intersect itself.
\item The path intersects $P_{b,x}$ at some point $y \neq x$
(Figure \ref{figure-suffix-paths}(c)).
In this case, $P_{a,s}$ contains vertices
$x, y$ in this order, while $P_{b, s}$ contains these vertices in the opposite order.
Hence,
$$ \mathrm{len}(P_{a,s}[y, s]) < \mathrm{len}(P_{a,s}[x, s]) = \mathrm{len}(P_{b,s}[x, s]) < \mathrm{len}(P_{b,s}[y, s]). $$
Therefore, $P_{b,s}$ could be shortened by replacing its suffix $P_{b,s}[y, s]$ by
$P_{a, s}[y, s]$.
\item The path enters $\Omega$ through an edge whose either endpoint is in
$\mathcal{L} \setminus \{a, b\}$.
This is impossible as this edge would not be enclosed
by the noose and therefore would not belong to $G_\mathcal{L}$.
\end{itemize}
\begin{figure}[h]
\centering
\begin{minipage}[b]{0.33\textwidth}
\centering
\input{figures/suffix-paths-fig-a.tex}
(a)
\end{minipage}\begin{minipage}[b]{0.33\textwidth}
\centering
\input{figures/suffix-paths-fig-b.tex}
(b)
\end{minipage}\begin{minipage}[b]{0.33\textwidth}
\centering
\input{figures/suffix-paths-fig-c.tex}
(c)
\end{minipage}
\caption{(a) --- an example setup. The noose $\mathcal{L}$ is a gray dashed circle.
The region $\Omega$ is shaded.
Green path is $P_{b,s}$, and the blue path is the prefix of $P_{a,s}$. \\
(b) --- a case where $P_{a,s}[a^*, s]$ intersects $P_{a,x}$. \\
(c) --- a case where $P_{a,s}[a^*, s]$ intersects $P_{b,x}$.}
\label{figure-suffix-paths}
\end{figure}
We arrived at a contradiction in each of the cases above.
Therefore $a^* \in \Omega$, and analogously $b^* \in \Omega$.
Assume now that $a^* \neq b^*$.
Then, we remind that $P_{a,s}$ is rightmost among all shortest paths from $a$ to $s$.
Consider the path $Q_a = P_{a,x} \cdot P_{b,s}[x, s]$.
As $\mathrm{len}(P_{a, s}[x, s]) = \mathrm{len}(P_{b, s}[x, s])$, we also have that
$\mathrm{len}(Q_a) = \mathrm{len}(P_{a, s})$.
Since $Q_a \neq P_{a, s}$, we get that $Q_a \ll P_{a,s}$.
Notice that $a_p$ and $x$ are two last common vertices of $Q_a$ and $P_{a,s}$, while
$b^*$ is the first vertex of $Q_a$ not belonging to $P_{a,s}$, and
$a^*$ is the first vertex of $P_{a,s}$ not belonging to $Q_a$.
By the definition of $\ll$, edges $xa_p$, $xb^*$ and $xa^*$
form a clockwise order around $x$.
We similarly deduce that edges $xb_p$, $xa^*$ and $xb^*$ form
a clockwise order around $x$.
This implies the clockwise order of four edges around $x$: $xa_p, xb^*, xb_p, xa^*$.
As $a_px$ and $xb_p$ are two consecutive edges on the boundary of $\Omega$,
we conclude that this boundary separates $a^*$ and $b^*$.
That is however impossible as $a^*, b^* \in \Omega$.
From the contradiction above, $a^* = b^*$.
This means that $P_{a,s}$ and $P_{b,s}$ share an oriented edge $xa^*$.
We now prove that they must share the remaining suffix of the path from $x$ to $s$.
Otherwise, there would be an oriented edge $fg$ shared by both $P_{a,s}$ and $P_{b,s}$,
followed by an oriented edge $gh_a$ in $P_{a,s}$, and by an oriented edge $gh_b$
in $P_{a,s}$ ($h_a \neq h_b$).
Assume without loss of generality that the oriented edges $gf, gh_a, gh_b$ are oriented
clockwise around $g$.
By the Definition \ref{left-of-def}, this means that
$$ P_{a, s} = P_{a,s}[a, g] \cdot P_{a,s}[g, s] \ll P_{a,s}[a,g] \cdot P_{b,s}[g,s] $$
--- a contradiction.
Hence, these paths must share the remaining suffix of the path
from $x$ to~$s$.
As $P_{a,s}[a,x] \cap P_{b,s}[b,x] = \{x\}$ and $P_{a,s}[x,s] = P_{b,s}[x,s]$,
this finishes the proof.
\end{proof}
\end{lemma}
Fix any vertex $s \in \mathcal{C}_k$, $k \geq 2$ and assume that it is close to vertices
$v_{i_1}, v_{i_2}, \dots, v_{i_k}$ of the noose, listed in the clockwise order
($1 \leq i_1 < i_2 < \dots < i_k \leq c$).
For simplicity, we also denote $i_{k+1} = i_1$.
Now, consider $k$ paths $P_{v_{i_1}, s}, P_{v_{i_2}, s}, \dots, P_{v_{i_k}, s}$.
\begin{lemma}
\label{disjoint-paths}
Exactly one of the following conditions holds:
\begin{enumerate}[(1)]
\item There exists $j \in [1, k]$ such that paths
$P_{v_{i_j}, s}$ and $P_{v_{i_{j+1}}, s}$ are vertex disjoint
apart from~$s$,
\item There exists a vertex $s' \neq s$ such that all the paths
$P_{v_{i_1}, s}, P_{v_{i_2}, s}, \dots, P_{v_{i_k}, s}$ contain $s'$.
This vertex is adjacent to $s$ and is the penultimate vertex in each of these paths.
\end{enumerate}
\begin{proof}
Obviously, condition (2) implies that (1) is false.
We only need to prove the opposite implication.
Assume that property (1) holds for no $j \in [1, k]$.
Therefore, by Lemma \ref{suffix-paths}, we see that for each $j \in [1,k]$, paths
$P_{v_{i_j},s}$ and $P_{v_{i_{j+1}}, s}$ share the common suffix, containing at least
two vertices.
Hence, each path $P_{v_{i_1},s}, P_{v_{i_2},s}, \dots, P_{v_{i_k},s}$ shares the same
common suffix, having at least two vertices.
The penultimate vertex in this suffix is $s'$ as in property (2).
\end{proof}
\end{lemma}
Let $V_1$ be the set of vertices from $\mathcal{C}_2 \cup \mathcal{C}_3 \cup \dots \cup
\mathcal{C}_c$ for which the first condition in Lemma~\ref{disjoint-paths} holds,
and $V_2$ --- the analogous set for the second condition.
\begin{lemma}
\label{profile-shift}
For every $s \in V_2$, there exists a vertex $s' \in V_1$ and an integer
$m \in \{1, 2, \dots, d\}$ such that
$$\forall_{v \in \mathcal{L}}\ \pi_d[s, \mathcal{L}](v) = \mathrm{Cap}_d\left(\pi_d[s',
\mathcal{L}](v) +
m\right), $$
where
$$\mathrm{Cap}_d(x) = \begin{cases}
x & \text{ if } x \leq d, \\
+\infty & \text{ otherwise.}
\end{cases}$$
\begin{proof}
If $s \in V_2$, then there exists a sequence $(s_0, s_1, \dots, s_{m-1}, s_m)$ where
$s = s_m$ and $m \geq 1$, which is the longest common suffix of all the paths
$P_{v_{i_1}, s}, P_{v_{i_2}, s}, \dots, P_{v_{i_k}, s}$.
The rightmost shortest paths from $v_{i_1}, v_{i_2}, \dots, v_{i_k}$ to $s_0$ can be
obtained by dropping $m$ last vertices in each of the paths.
In this setup, we have $s_0 \in V_1$ --- otherwise, we would be able to prepend the sequence
defined above by the common neighbor of $s_0$ on all the paths terminating at $s_0$.
We will now prove that $s' = s_0$ and $m$ satisfy the condition stated in the lemma.
Pick any vertex $v \in \mathcal{L}$ and consider the following cases:
\begin{itemize}
\item If $s$ is close to $v$, then $\mathrm{dist}(s, v) = \mathrm{dist}(s_0, v) + m$ (because of the common
prefix above).
\item If $s$ is far from $v$ and $\pi_d[s, \mathcal{L}](v) = \infty$, then
$\mathrm{dist}(s, v) > d$.
Hence, $\mathrm{dist}(s_0, v) > d-m$ as $\mathrm{dist}(s, v) \leq \mathrm{dist}(s, s_0) + \mathrm{dist}(s_0, v) = m + \mathrm{dist}(s_0, v)$.
To put it in the other way, $\mathrm{dist}(s_0, v) + m > d$.
Therefore $\pi_d[s_0, \mathcal{L}](v) + m > d$, which is consistent with the condition
$\pi_d[s, \mathcal{L}](v) = \infty$ required by the statement of the lemma.
\item If $s$ is far from $v$ and $\pi_d[s, \mathcal{L}](v) \leq d$, then by definition of closeness
some shortest path from $s$ to $v$ passes through another vertex $v' \in V(\mathcal{L})
\setminus \{v\}$.
Assume that $v'$ is one of the vertices closest to $s$ with this property.
We see that $s$ is close to $v'$.
Thus, $v' \in \{v_{i_1}, \dots, v_{i_k}\}$, so $P_{v',s}$ is one of the paths in the set
$\{P_{v_{i_1}, s}, \dots, P_{v_{i_k}, s}\}$, and as such, it contains $s_0$.
Therefore, some shortest path from $v$ to $s$ contains $v, v', s_0, s$ in this order.
Hence, $\pi_d[s, \mathcal{L}](v) = \mathrm{dist}(s, v) = \mathrm{dist}(s, s_0) + \mathrm{dist}(s_0, v) = m + \mathrm{dist}(s_0, v) =
\pi_d[s_0, \mathcal{L}](v) + m$.
\end{itemize}
Therefore, the distance-$d$ profile $\pi_d[s, \mathcal{L}]$ is constructed by considering
the profile $\pi_d[s_0, \mathcal{L}]$ where $s_0 \in V_1$,
and increasing each entry in the profile by $m$,
while remembering to replace each integer exceeding $d$ by~$\infty$.
\end{proof}
\end{lemma}
\begin{corollary}
\label{profile-shift-cor}
If
\[ |\{\pi_d[v, \mathcal{L}]\, \mid\, v \in V_1\}| = B \quad\text{for an integer }B,\]
then
\[ |\{\pi_d[v, \mathcal{L}]\, \mid\, v \in V_1 \cup V_2\}| \leq B \cdot (d + 1). \]
\begin{proof}
By Lemma \ref{profile-shift}, the profile of a vertex $v \in V_2$ can be deduced
from a distance-$d$ profile of a vertex $v' \in V_1$ and an integer $m \in \{1, 2, \dots, d\}$.
Hence,
\[ |\{\pi_d[v, \mathcal{L}]\, \mid\, v \in V_2\}| \leq
|\{\pi_d[v, \mathcal{L}]\, \mid\, v \in V_1\}| \cdot |\{1, 2, \dots, d\}| = B \cdot d. \]
We also include the vertices in $V_1$ into this inequality and get:
\[ |\{\pi_d[v, \mathcal{L}]\, \mid\, v \in V_1 \cup V_2\}| \leq
|\{\pi_d[v, \mathcal{L}]\, \mid\, v \in V_1\}| + |\{\pi_d[v, \mathcal{L}]\, \mid\, v \in V_2\}| \leq B \cdot (d+1). \]
\end{proof}
\end{corollary}
Corollary \ref{profile-shift-cor} allows us to focus on
bounding the number of different distance-$d$ profiles
measured only from the vertices in $V_1$.
\subsection{Buckets}
We will now group all the vertices in $V_1$ into a reasonably small number of buckets.
The buckets will be chosen in such a way that all the vertices within one group expose
similar properties in $G$.
This will eventually allow us to bound the number of different distance-$d$ profiles measured
by each individual bucket.
\begin{definition}
For a vertex $s \in V_1$, we define the \textbf{bucket} of $s$ as any quadruple
$(a, b, d_a, d_b)$ satisfying the following conditions (Figure \ref{bucket-def-figure}):
\begin{itemize}
\item $a, b \in V(\mathcal{L})$ and $a, b \in \mathrm{Close}(s)$,
\item $\mathcal{L}(b, a) \cap \mathrm{Close}(s) = \varnothing$; in other words,
each vertex $v \in \mathcal{L}(b, a)$ is far from $s$,
\item paths $P_{a, s}$ and $P_{b, s}$ intersect only at $s$,
\item $d_a = \mathrm{dist}(a, s)$ is the distance between $a$ and $s$ in $G_{\mathcal{L}}$,
and $1 \leq d_a \leq d$,
\item $d_b = \mathrm{dist}(b, s)$ is the distance between $b$ and $s$ in $G_{\mathcal{L}}$,
and $1 \leq d_b \leq d$.
\end{itemize}
\noindent Lemma \ref{disjoint-paths} proves that such an assignment exists since $s \in V_1$.
\end{definition}
\begin{figure}
\centering
\input{figures/bucket-def.tex}
\caption{Definition of a bucket assigned to a vertex $s$. Here, $d_a = 3$ and $d_b = 2$.
Vertex $s$ is far from any vertex on the dashed part of the noose.}
\label{bucket-def-figure}
\end{figure}
Notice that there at most $c(c - 1) d^2$ possible quadruples
$(a, b, d_a, d_b)$ --- $a$ and $b$ are two distinct vertices of the noose in some order,
and $d_a, d_b$ are two positive distances not exceeding $d$.
Fix a bucket $(a, b, d_a, d_b)$ and consider the set $\mathcal{S} =
\mathcal{S}(a, b, d_a, d_b)$ of
vertices $s$ that are assigned to the bucket.
Remember that each $s \in \mathcal{S}$ is far from each vertex of
$\mathcal{L}(b, a)$.
\vspace{1em}
\begin{lemma}
\label{hard-cross-paths}
For any two different vertices $s, t \in \mathcal{S}$, if paths
$P_{a,t}$ and $P_{b,s}$ intersect at any vertex $x$, then $P_{a,s} \gg P_{a,t}$,
$P_{b,t} \gg P_{b,s}$, and $\mathrm{dist}(x, t) = \mathrm{dist}(x, s) > 0$ (Figure \ref{hard-cross-paths-config}).
\begin{figure}[h]
\centering
\input{figures/cross-lemma-config.tex}
\caption{A possible configuration in Lemma \ref{hard-cross-paths}. Paths
$P_{a,s}$ and $P_{b,s}$ are marked blue, while $P_{a,t}$ and $P_{b,t}$ are green.}
\label{hard-cross-paths-config}
\end{figure}
\begin{proof}
Assume that $P_{a, t}$ and $P_{b, s}$ intersect at $x$.
Then we have a couple of simple equalities:
$$
\mathrm{dist}(a, t) = \mathrm{dist}(a, x) + \mathrm{dist}(x, t) \qquad\text{and}\qquad
\mathrm{dist}(b, s) = \mathrm{dist}(b, x) + \mathrm{dist}(x, s).
$$
From the triangle inequality and the fact that $s, t \in \mathcal{S}(a, b, d_a, d_b)$, we infer:
\begin{equation}
\label{xs-geq-xt-eq}
\mathrm{dist}(a, x) + \mathrm{dist}(x, s) \geq \mathrm{dist}(a, s) = d_a = \mathrm{dist}(a, t) = \mathrm{dist}(a, x) + \mathrm{dist}(x, t),
\end{equation}
\begin{equation}
\label{xt-geq-xs-eq}
\mathrm{dist}(b, x) + \mathrm{dist}(x, s) = \mathrm{dist}(b, s) = d_b = \mathrm{dist}(b, t) \leq \mathrm{dist}(b, x) + \mathrm{dist}(x, t).
\end{equation}
We infer that $\mathrm{dist}(x, s) \geq \mathrm{dist}(x, t)$ from (\ref{xs-geq-xt-eq}) and
$\mathrm{dist}(x, s) \leq \mathrm{dist}(x, t)$ from (\ref{xt-geq-xs-eq}).
Therefore, $\mathrm{dist}(x, s) = \mathrm{dist}(x, t)$ and all the inequalities above are satisfied
with equality.
As $x \neq s$ (otherwise we would have $x = s = t$), obviously $\mathrm{dist}(x, s) > 0$.
Hence, $\mathrm{dist}(a, s) = \mathrm{dist}(a, x) + \mathrm{dist}(x, s)$ and $\mathrm{dist}(b,t) = \mathrm{dist}(b,x) +
\mathrm{dist}(x,t)$.
We now see two shortest paths from $a$ to $s$: the rightmost path $P_{a,s}$, and
another path $Q := P_{a,x} \cdot P_{b, s}[x, s]$.
Notice that $P_{a,s}$ cannot be the prefix of $P_{a,x}$ as it is strictly longer than $P_{a,x}$.
Also $P_{a,x}$ cannot be the prefix of $P_{a,s}$
because $x$ lies on $P_{b,s}$ (which is vertex disjoint with $P_{a,s}$ apart from $s$,
and $x \neq s$).
Hence, we have either $P_{a,s} \ll P_{a,x}$ or $P_{a,s} \gg P_{a,x}$.
We however cannot have $P_{a,s} \ll P_{a,x}$,
or otherwise we would have $P_{a,s} \ll P_{a,x} \cdot P_{b,s}[x,s] = Q$,
which is impossible by the definition of $P_{a,s}$.
Therefore $P_{a,s} \gg P_{a,x}$.
As $P_{a,x} = P_{a,t}[a, x]$, we also get $P_{a,s} \gg P_{a,t}$.
An analogous argument shows that $P_{b, t} \gg P_{b, s}$.
\end{proof}
\end{lemma}
\begin{corollary}
For any two distinct vertices $s, t \in \mathcal{S}$, if paths
$P_{a,s}$ and $P_{b,t}$ intersect at any vertex $x$, then $P_{a,t} \gg P_{a,s}$,
$P_{b,s} \gg P_{b,t}$, and $\mathrm{dist}(x, t) = \mathrm{dist}(x, s) > 0$.
\label{hard-cross-paths-sym}
\begin{proof}
In the statement of Lemma \ref{hard-cross-paths}, swap $s$ and $t$.
\end{proof}
\end{corollary}
\begin{corollary}
\label{hard-cross-paths-both}
It is impossible for $P_{a,t}$ and $P_{b,s}$ to intersect, and for $P_{a,s}$ and
$P_{b,t}$ to intersect at the same time.
\begin{proof}
The former condition would imply $P_{a,s} \gg P_{a,t}$ (Lemma \ref{hard-cross-paths}),
while the latter --- $P_{a,t} \gg P_{a,s}$ (Corollary \ref{hard-cross-paths-sym}).
\end{proof}
\end{corollary}
\subsection{Gamma-regions}
We fix any bucket $\mathcal{S} = \mathcal{S}(a, b, d_a, d_b)$.
We will now assign a region of the plane to each vertex $w \in S$.
\begin{lemma}
For any vertex $w \in \mathcal{S}$, the curve $\mathcal{L}[a, b] \cup P_{a,w} \cup P_{b,w}$
is a closed Jordan curve.
\begin{proof}
Notice that $w \not\in V(\mathcal{L})$ and
$w$ is close to $a$, so $P_{a,w}$ cannot contain vertices from $\mathcal{L}$
as internal vertices. Therefore,
$P_{a,w} \cap \mathcal{L}[a, b] = \{a\}$. Analogously,
$P_{b,w} \cap \mathcal{L}[a, b] = \{b\}$. Finally,
$P_{a,w} \cap P_{b,w} = \{w\}$ due to the disjointness of these paths in the sense of
Claim \ref{disjoint-paths}.
Thus the union of these curves is a closed Jordan curve.
\end{proof}
\end{lemma}
\begin{definition}
For any vertex $w \in \mathcal{S}$, we define the \textbf{gamma-region}
$\Gamma_w$ as the
closed, bounded region of the plane whose boundary is $\mathcal{L}[a, b] \cup P_{a,w} \cup P_{b,w}$
(Figure \ref{gamma-def-fig}).
\end{definition}
\begin{figure}[h]
\centering
\begin{minipage}[t]{0.48\textwidth}
\centering
\input{figures/cross-lemma-area-a.tex}
(a)
\end{minipage}\begin{minipage}[t]{0.04\textwidth}\
\end{minipage}\begin{minipage}[t]{0.48\textwidth}
\centering
\input{figures/cross-lemma-area-b.tex}
(b)
\end{minipage}
\caption{Gamma regions in the configuration from Figure \ref{hard-cross-paths-config}:
(a) --- $\Gamma_t$, (b) --- $\Gamma_s$.}
\label{gamma-def-fig}
\end{figure}
We will now prove the potential of this definition.
Intuitively, for any two vertices $s, t \in \mathcal{S}$ in the bucket,
we will either have $t \in \Gamma_s$, which will imply a serious structural relation
between the gamma-regions $\Gamma_s$ and $\Gamma_t$,
or we will have $t \not\in \Gamma_s$, which will in turn have major implications
for the distance-$d$ profiles $\pi_d[s, \mathcal{L}]$ and $\pi_d[t, \mathcal{L}]$.
\begin{lemma}
\label{gamma-contain}
For any two different vertices $s, t \in \mathcal{S}$, if $t \in \Gamma_s$, then
$\Gamma_t \subsetneq \Gamma_s$.
\begin{proof}
Assume that $t \in \Gamma_s$.
We will first prove a couple of helper claims.
\begin{claim}
\label{gamma-contain-claim-b}
\renewcommand{\qed}{\cqedsymbol}
If $P_{b,t}$ is disjoint with $P_{a,s}$,
then $P_{b,t} \gg P_{b,s}$ and $P_{b,t}$ is fully contained within $\Gamma_s$.
\begin{claimproof}
Assume that $P_{b,t}$ is disjoint with $P_{a,s}$.
As $\mathrm{dist}(b, t) = \mathrm{dist}(b, s)$ and $s \neq t$,
neither of paths $P_{b,s}$ and $P_{b,t}$ is a prefix of another and thus
they are ordered by $\ll$.
We notice that $P_{b,s}$ follows $\partial \Gamma_s$ clockwise.
This is because we defined $\mathcal{L}[a, b]$ to run clockwise from $a$ to $b$ on
$\mathcal{L}$, and $P_{b,s}$ is a directed path originating from $b$, where
$\mathcal{L}[a, b]$ terminated.
Hence, both $P_{b,s}$ and $\mathcal{L}[a, b]$ have to be oriented the same way
on $\partial \Gamma_s$.
Let $(y_1, y_2, \dots, y_{k-1}, y_k)$ ($y_k = t$) be the maximal suffix of $P_{b,t}$
which is disjoint with $P_{b,s}$.
For any choice of $i \in \{1, 2, \dots, k\}$, we have that
$y_i \not\in P_{a,s}$ since $P_{b,t}$ is disjoint with $P_{a,s}$,
and $y_i \not\in \mathcal{L}[a,b]$ as $\mathcal{L}[a,b] \cap P_{b,t} = \{b\}$.
Hence $\{y_1, y_2, \dots, y_k\} \cap \partial \Gamma_s = \varnothing$, and thus
these vertices are either all strictly inside of $\Gamma_s$, or all strictly outside of it.
Now, as $P_{b,s}$ is oriented clockwise, it can be easily seen that $y_1 \in \Gamma_s\
\Leftrightarrow\ P_{b,y_1} \gg P_{b,s}$;
in other words, the interior of $\Gamma_s$ is ``to the right'' of $P_{b,s}$.
If $P_{b,y_1} \gg P_{b,s}$, then $P_{b,t} \gg P_{b,s}$ and $P_{b,s}$ is fully within
$\Gamma_s$.
If $P_{b,y_1} \ll P_{b,s}$, then $P_{b,t} \ll P_{b,s}$. Because $y_1 \not\in
\Gamma_s$, we have that $\{y_1, y_2 \dots, y_k\}$ is disjoint with $\Gamma_s$.
In particular, $t \not\in \Gamma_s$.
This however contradicts our assumption that $t \in \Gamma_s$.
\end{claimproof}
\end{claim}
\begin{claim}
\label{gamma-contain-claim-a}
\renewcommand{\qed}{\cqedsymbol}
If $P_{a,t}$ is disjoint with $P_{b,s}$,
then $P_{a,t} \ll P_{a,s}$ and $P_{a,t}$ is fully contained within $\Gamma_s$.
\begin{claimproof}
The proof of this claim follows mostly the proof of Claim \ref{gamma-contain-claim-b}.
However, $P_{a,s}$ follows $\partial \Gamma_s$ anti-clockwise.
This is because $\mathcal{L}[a, b]$ runs clockwise along the noose from $a$ to $b$,
and both $\mathcal{L}[a, b]$ and $P_{a, s}$ originate from the same vertex $a$.
Hence, these two paths are oriented in the opposite way along $\partial \Gamma_s$.
This means that the interior of $\Gamma_s$ is ``to the left'' of $P_{a,s}$.
Hence, $t \in \Gamma_s$ if and only if $P_{a,t} \ll P_{a,s}$.
\end{claimproof}
\end{claim}
Note that if both $P_{b,t}$ is disjoint with $P_{a,s}$, and $P_{a,t}$ is disjoint with $P_{b,s}$,
then by Claims \ref{gamma-contain-claim-b} and \ref{gamma-contain-claim-a}
we get that $\partial\Gamma_t \subseteq \Gamma_s$ and thus $\Gamma_t \subseteq
\Gamma_s$.
Assume that $t \in \Gamma_s$, but $\Gamma_t \not\subseteq \Gamma_s$.
As $\partial\Gamma_t$ is a Jordan curve, there exists a vertex $y$ on
$\partial\Gamma_t$ not belonging to $\Gamma_s$.
We will consider multiple cases, depending on which part of $\partial\Gamma_t$
this vertex belongs to.
\vspace{1em}
\underline{Case 1}: $y \in \mathcal{L}[a, b]$. This is however impossible as $\mathcal{L}[a, b]
\subseteq \Gamma_s$.
\vspace{1em}
\underline{Case 2a}: $y \in P_{b,t}$ and $P_{b,t} \gg P_{b,s}$.
In this case, $P_{b,t}$ cannot intersect $P_{a,s}$ by Corollary~\ref{hard-cross-paths-sym}.
Hence, by Claim~\ref{gamma-contain-claim-b}, we have that $P_{b,t}$ is fully contained
within $\Gamma_s$ --- a contradiction because $y \in P_{b,t}$ must lie outside
of $\Gamma_s$.
\vspace{1em}
\underline{Case 2b}: $y \in P_{b,t}$ and $P_{b,t} \ll P_{b,s}$.
In this case, Claim \ref{gamma-contain-claim-b} requires
that the intersection between $P_{b,t}$ and $P_{a,s}$ must exist.
Hence, we also get $P_{a,t} \gg P_{a,s}$ by Corollary \ref{hard-cross-paths-sym}.
Now, $P_{a,t}$ cannot intersect $P_{b,s}$ as this is forbidden by Corollary
\ref{hard-cross-paths-both}.
This leads to a contradiction due to Claim~\ref{gamma-contain-claim-a}.
\vspace{1em}
\underline{Case 3a}: $y \in P_{a,t}$ and $P_{a,t} \gg P_{a,s}$.
Similarly to the first part of Case 2b, we deduce that $P_{a,t}$ must intersect $P_{b,s}$.
However, by Lemma \ref{hard-cross-paths}, we get that $P_{a,t} \ll P_{a,s}$ ---
a contradiction.
\vspace{1em}
\underline{Case 3b}: $y \in P_{a,t}$ and $P_{a,t} \ll P_{a,s}$.
For our convenience, we take $y$ to be the first vertex of $P_{a,t}$ not in $\Gamma_s$.
We again deduce that $P_{a,t}$ intersects $P_{b,s}$; otherwise, Claim
\ref{gamma-contain-claim-a} would imply that $P_{a,t}$ is
contained within $\Gamma_s$, which contradicts the choice of $y$.
Let $x_1$ and $x_2$ be the first and the last intersection of $P_{a,t}$ with $P_{b,s}$,
respectively.
Notice that $y$ cannot precede $x_1$ on $P_{a,t}$; as $P_{a,t} \ll P_{a,s}$, then
$P_{a,y} \ll P_{a,s}$.
As $P_{a,y}$ would not intersect $P_{b,s}$, we could prove (analogously to the proofs
of Claims \ref{gamma-contain-claim-b} and \ref{gamma-contain-claim-a})
that $P_{a,y}$ is fully contained within $\Gamma_s$,
which contradicts our assumption.
Vertex $y$ cannot also appear after $x_2$ on $P_{a,t}$ --- in this case,
$y \not \in \Gamma_s$ would imply $t \not\in \Gamma_s$
(note that $P_{a,t}[y, t]$ would not be able to intersect $\partial\Gamma_s$),
which again is impossible.
Since vertices $a, x_1, y, x_2, t$ appear on $P_{a,t}$ in this order,
we have that $x_1 \in P_{a, x_2}$.
Also, by Lemma \ref{hard-cross-paths} and the fact that $\mathrm{dist}(x_2, t) < \mathrm{dist}(x_1, t)$,
we get that
\begin{equation*}
\begin{split}
\mathrm{dist}(b, x_1) &= \mathrm{dist}(b,s) - \mathrm{dist}(x_1, s) = \mathrm{dist}(b,s) - \mathrm{dist}(x_1, t) < \mathrm{dist}(b,s) - \mathrm{dist}(x_2, t) =\\
&= \mathrm{dist}(b,s) - \mathrm{dist}(x_2, s) = \mathrm{dist}(b, x_2).
\end{split}
\end{equation*}
We infer that $x_1 \in P_{b,s}[b, x_2] = P_{b, x_2}$.
Now, consider two paths: $P_{a,x_2} = P_{a,t}[a, x_2]$ and $P_{b,x_2} = P_{b,s}[b, x_2]$.
By Lemma \ref{suffix-paths}, these two paths must intersect on their common suffix
and nowhere else.
As $x_1 \in P_{a,x_2} \cap P_{b,x_2}$, we get that $P_{a,x_2}[x_1, x_2] = P_{b,x_2}[x_1, x_2]$.
This means that $P_{b,s}$ shares its vertices with $P_{a,t}$ on the segment between
$x_1$ and $x_2$.
Hence,
$$ P_{a,t}[x_1, x_2] = P_{a, x_2}[x_1, x_2] = P_{b, x_2}[x_1, x_2] =
P_{b, s}[x_1, x_2] \subseteq P_{b,s} \subseteq \partial \Gamma_s. $$
However, we get a contradiction because of our assumptions that
$y \in P_{a, x_2}[x_1, x_2]$ and $y \not\in \Gamma_s$.
\vspace{1em}
After considering all cases above, we have that $\Gamma_t \subseteq \Gamma_s$.
Moreover, $t \not\in P_{a,s}$ (since $\mathrm{dist}(a,s) = \mathrm{dist}(a,t)$) and analogously $t \not\in P_{b,s}$, and
$t \not\in V(\mathcal{L})$ (otherwise $t$ would only be close to itself).
Thus, $t \not\in \partial \Gamma_s$.
Since obviously $t \in \partial\Gamma_t$, we immediately
get that $\Gamma_s \neq \Gamma_t$.
Therefore, $\Gamma_t \subsetneq \Gamma_s$.
\end{proof}
\end{lemma}
\vspace{1em}
The claim above described the case $t \in \Gamma_s$.
Now we try to see what happens when $t \not\in \Gamma_s$.
\begin{lemma}
\label{majorization-lemma}
If $t \not\in \Gamma_s$ for some $s, t \in \mathcal{S}$, then
$\pi_d[t, \mathcal{L}] \succcurlyeq \pi_d[s, \mathcal{L}]$.
\begin{proof}
We will prove that $\pi_d[t, \mathrm{Close}(t)] \succcurlyeq \pi_d[s, \mathrm{Close}(t)]$.
Lemma \ref{lemma-majorization-close} will then conclude our proof.
Recall, by the choice of $a$ and $b$, that $\mathrm{Close}(t) \subseteq \mathcal{L}[a, b]$.
We will now prove that $\mathrm{dist}(v, s) \geq \mathrm{dist}(v, t)$ for each $v \in \mathcal{L}[a, b]$ such that
$v \in \mathrm{Close}(t)$.
For $v \in \{a, b\}$ the inequality is satisfied with equality; thus, we only need to care
about the case $v \in \mathcal{L}(a, b) \cap \mathrm{Close}(t)$.
Notice that $v \in \Gamma_s$, but on the other hand $t \not\in \Gamma_s$.
Therefore, we can take $x$ as the last intersection of $P_{v,t}$ with
$\partial \Gamma_s$.
We cannot have $x = v$, otherwise the edge connecting $x$
with the next vertex on the path would lie outside of the noose
since $v \in \mathcal{L}(a, b)$.
Also, since $v \in \mathrm{Close}(t)$, we get that $P_{v, t} \cap V(\mathcal{L}) = \{v\}$;
hence, $P_{v, t}$ cannot intersect $\mathcal{L}$ at any vertex other than $v$.
Therefore, $x \in P_{a,s} \cup P_{b,s}$.
Without loss of generality, assume that $x \in P_{a, s}$.
As $x$ lies both on the shortest path from $a$ to $s$, and the shortest path from
$v$ to $t$, we have the following equalities:
$$\mathrm{dist}(v, t) = \mathrm{dist}(v, x) + \mathrm{dist}(x, t) \qquad\text{and}\qquad
\mathrm{dist}(a, s) = \mathrm{dist}(a, x) + \mathrm{dist}(x, s).$$
Moreover, $\mathrm{dist}(a, t) = \mathrm{dist}(a, s) = d_a$.
From the triangle inequality and the equations above, we get
$$ \mathrm{dist}(a, x) + \mathrm{dist}(x, t) \geq \mathrm{dist}(a, t) = \mathrm{dist}(a, s) = \mathrm{dist}(a, x) + \mathrm{dist}(x, s), $$
or equivalently, $\mathrm{dist}(x, t) \geq \mathrm{dist}(x, s)$.
Then, from the conditions above and another use of triangle inequality,
we have
\[ \mathrm{dist}(v, t) = \mathrm{dist}(v, x) + \mathrm{dist}(x, t) \geq \mathrm{dist}(v, x) + \mathrm{dist}(x, s) \geq \mathrm{dist}(v, s). \]
\end{proof}
\end{lemma}
\subsection{Conclusion of the proof of Noose Profile Lemma}
\label{noose-profile-lemma-conclusion-subsection}
Assume there are $M$ vertices
$s_1, s_2, \dots, s_M \in \mathcal{S}$ with pairwise distinct distance-$d$ profiles
on $\mathcal{L}$.
Pick any vertices $s_i, s_j$, $i \neq j$, and let us describe their relation with respect to
the regions $\Gamma_{s_i}, \Gamma_{s_j}$ defined by them:
\begin{itemize}
\item If $s_i \not\in \Gamma_{s_j}$ and $s_j \not\in \Gamma_{s_i}$, then from
Lemma \ref{majorization-lemma} we get $\pi_d[s_i, \mathcal{L}] = \pi_d[s_j, \mathcal{L}]$ ---
a contradiction.
\item If $s_i \in \Gamma_{s_j}$ and $s_j \in \Gamma_{s_i}$, the from Lemma
\ref{gamma-contain}
we get $\Gamma_{s_i} \subsetneq \Gamma_{s_j} \subsetneq \Gamma_{s_i}$ ---
another contradiction.
\item Hence, either $\pi_d[s_i, \mathcal{L}] \prec \pi_d[s_j, \mathcal{L}]$
(if $s_j \not\in \Gamma_{s_i}$) or $\pi_d[s_j, \mathcal{L}] \prec \pi_d[s_i, \mathcal{L}]$
(if $s_i \not\in \Gamma_{s_j}$).
\end{itemize}
Therefore, the relation $\preccurlyeq$ defined on the distance-$d$ profiles for $s_1, s_2,
\dots, s_M$
is antisymmetric, transitive (by definition of $\preccurlyeq$) and connex
(by our considerations above).
Hence, it is a linear order and thus contains a chain of length $M$.
However, as $\pi_d$ is a function whose domain contains $c$ elements,
and its codomain contains $d+2$ possible values,
the maximum length of such a chain is $c(d+1) + 1$.
We thus get $M \leq c(d+1) + 1$.
Summing everything up, we proved that each set $\mathcal{S}(a, b, d_a, d_b)$
generates at most $c(d+1) + 1$ different distance-$d$ profiles.
There are at most $c(c-1)d^2$ such sets, as $a \neq b$ and $1 \leq d_a, d_b \leq d$.
Hence, the number of different profiles induced in $G$ by $V_1$ is bounded by
$$c(c - 1)d^2 \cdot [c(d+1) + 1] \leq c^3 (d+1)^3.$$
The number of profiles in $\mathcal{C}_2 \cup \mathcal{C}_3 \cup \dots \cup
\mathcal{C}_c = V_1 \cup V_2$ is then bounded by
$c^3 (d+1)^4$ (Corollary \ref{profile-shift-cor}).
The vertices from $\mathcal{C}_0 \cup \mathcal{C}_1$ induce at most
$c(d + 1) + 1$ additional profiles.
The total number of profiles can be thus bounded by
$$ c^3 (d+1)^4 + c(d + 1) + 1 \leq c^3(d+2)^4. $$
This concludes the proof of the Noose Profile Lemma.
We note a simple corollary which is a direct consequence of it:
\begin{corollary}
\label{noose-profille-lemma-rev}
Consider any graph $G$ together with its embedding in the plane, and fix any noose
$\mathcal{L}$ containing $c \geq 1$ vertices of $G$.
The set $\{\pi_d[v, \mathcal{L}]\, \mid\, v \not\in V(G_\mathcal{L})\}$
of different distance-$d$ profiles on $\mathcal{L}$,
measured from the vertices \textbf{not enclosed} by $\mathcal{L}$,
has at most $c^3 (d+2)^4$ elements.
\begin{proof}
Let us take the embedding of $G$ in the plane, and apply to it an inversion
with any positive radius
and a center in any point enclosed by $\mathcal{L}$ that does not lie on any vertex or
edge of $G$.
After this transformation,
the images of all vertices of $G$ that have not been enclosed by $\mathcal{L}$
in the original embedding will now be enclosed by the inversive image $\mathcal{L}'$ of the noose.
Noose Profile Lemma applies to the inversed embedding as well,
which allows us to reason that there are at most $c^3 (d+2)^4$ different distance-$d$
profiles on $\mathcal{L}$, measured from the vertices whose images are enclosed by $\mathcal{L}'$
--- or, in other words, measured from the vertices which were not enclosed by $\mathcal{L}$
in the original embedding.
\end{proof}
\end{corollary}
\subsection{Proof of Theorem \ref{neighborhood-complexity-planar}}
\label{beyond-noose-profile-lemma-section}
We now lift the Noose Profile Lemma to the general setting, where the noose can
be replaced with any non-empty set of vertices.
For convenience, we restate the theorem here.
\neighborhoodcomplthm*
\begin{proof}
We fix $G$ and embed it in the plane.
We also fix the set $A$ as in the statement of the theorem.
Let $V_d = \{v \in V(G)\,\mid\,\exists_{s\in A} \,\mathrm{dist}(v, s) \leq d\}$ be the set of vertices
of $G$ which are at~distance at most $d$ from any vertex in $A$.
We observe that for each vertex $v \not\in V_d$, the distance-$d$ profile
$\pi_d[v, A]$ is the constant function equal to $+\infty$.
Now, we define the graph $G_d = G[V_d]$ induced by $V_d$.
We can easily see that for each vertex $v \in V_d$, the distance-$d$ profile of $v$ on $A$
in $G_d$ is identical to the distance-$d$ profile of $v$ on $A$ in $G$.
Hence, the number of different distance-$d$ profiles on $A$ in $G_d$ is at most $1$ less
than the number of different distance-$d$ profiles on $A$ in $G$.
We first assume that $G_d$ is connected;
we will resolve the case where $G_d$ is disconnected at the end of the proof.
Let $\mathcal{T}$ be the minimum Steiner tree on $A$ in $G_d$; that is, the smallest possible tree
which is a connected subgraph of $G_d$ and spans all vertices of $A$.
\begin{claim}
\label{claim-small-steiner-tree}
$\mathcal{T}$ has at most $(c-1)(2d+1)$ edges.
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
Let $G_A$ be the complete weighted graph whose set of vertices is $A$, and for every
pair of vertices $u, v \in A$, the edge between these vertices has weight $\mathrm{dist}_{G_d}(u, v)$.
Let also $\mathcal{T}_A$ be the minimum-weight spanning tree of $G_A$.
We now prove that no edge of $\mathcal{T}_A$ has weight greater than $2d + 1$.
Assume for contradiction that $uv \in E(\mathcal{T}_A)$ is an edge with weight at least $2d + 2$.
In this case, take a shortest path from $u$ to $v$ in $G_d$:
$(x_0, x_1, x_2, \dots, x_\delta)$, where $x_0 = u$, $x_\delta = v$, $\delta \geq 2d+2$.
We have that $\mathrm{dist}_{G_d}(x_{d+1}, u) = d + 1$ and $\mathrm{dist}_{G_d}(x_{d+1}, v) = \delta - (d+1)$.
As $x_{d+1} \in V_d$, there exists a vertex $s \in A$ at distance at most $d$ from $x_{d+1}$.
By the triangle inequality, we infer that
\begin{equation*}
\begin{split}
\mathrm{dist}_{G_d}(s, u)& \leq \mathrm{dist}_{G_d}(s, x_{d+1}) + \mathrm{dist}_{G_d}(x_{d+1}, u) \leq
d + (d + 1) < \delta, \\
\mathrm{dist}_{G_d}(s, v)& \leq \mathrm{dist}_{G_d}(s, x_{d+1}) + \mathrm{dist}_{G_d}(x_{d+1}, v) \leq
d + (\delta - (d+1)) < \delta.
\end{split}
\end{equation*}
Hence, $G_A$ contains a three-vertex cycle $(u, v, s)$, in which the edge $uv$ is strictly
the heaviest.
Therefore, $uv$ cannot belong to $\mathcal{T}_A$ --- a contradiction.
\smallskip
Now, for each edge $uv \in \mathcal{T}_A$, we connect $u$ with $v$ in $G_d$ using the shortest
path between these two vertices.
We can easily see that the union of these paths is a connected subgraph of $G_d$ containing
all the vertices in $A$.
Hence, $\mathcal{T}$, the minimum Steiner tree on $A$, is at most as long as the union of these paths.
Since we used $|A|-1 = c - 1$ paths, and each of them has length at most $2d + 1$,
we infer that $\mathcal{T}$ has at most $(c-1)(2d+1)$ edges.
\end{claimproof}
\end{claim}
\newcommand{G_{\mathrm{cut}}}{G_{\mathrm{cut}}}
We now create a new graph $G_{\mathrm{cut}}$, which is a modified version of $G_d$,
by ``cutting the plane open'' along the Steiner tree $\mathcal{T}$ (Figure \ref{cutting-fig}).
This process is inspired by a similar idea by Pilipczuk et al.
\cite{DBLP:journals/talg/PilipczukPSL18}.
Formally, $G_{\mathrm{cut}}$ is the result of the following process:
\begin{figure}[h]
\centering
\begin{minipage}[b]{0.5\textwidth}
\centering
\input{figures/cut-tree-a.tex}
(a)
\end{minipage}\begin{minipage}[b]{0.5\textwidth}
\centering
\input{figures/cut-tree-b.tex}
(b)
\end{minipage}
\caption{Creating $G_{\mathrm{cut}}$. (a) --- original graph $G_d$, with tree $\mathcal{T}$ (blue).
(b) --- the resulting graph, with an Euler tour of $\mathcal{T}$.}
\label{cutting-fig}
\end{figure}
\begin{enumerate}
\item We find an Euler tour of $\mathcal{T}$ which does not intersect itself in the plane embedding
of $G_d$. This tour traverses each edge of $\mathcal{T}$ twice, in the opposite directions.
\item For each vertex $v \in V(\mathcal{T})$, we let $s_1, s_2, \dots, s_\Delta$ to be the neighbors of
$v$ in $\mathcal{T}$, ordered anti-clockwise around $v$.
For simplicity, we assume $s_{\Delta+1} = s_1$.
If $\Delta \geq 2$, we create $\Delta$~copies of $v$ (including the original vertex $v$):
$v_1, v_2, \dots, v_\Delta$, and we put the $i$-th copy, $v_i$, very close to the
original vertex $v$, and
between the edges $vs_i$ and $vs_{i+1}$ in the embedding of $G_d$.
Moreover, for each neighbor $x$ of $v$ such that $vx \not \in E(\mathcal{T})$, we find the only
index $i$ such that the edges $vs_i$, $vx$, $vs_{i+1}$ are ordered anti-clockwise around
$v$;
then, we replace the edge $vx$ with $v_ix$.
\item We duplicate each edge $uv$ of the Euler tour of $\mathcal{T}$, so that we have one copy for
each orientation of $uv$ in the Euler tour.
We then use both copies to connect the corresponding copies of vertices $u, v$
in $G_{\mathrm{cut}}$.
We can easily see that all new edges form a cycle enclosing~$\mathcal{T}$, which we call $C$.
Naturally, $C$ has twice as many edges as $\mathcal{T}$.
\item We remove the edges of $\mathcal{T}$ from the graph.
\end{enumerate}
Let $V(C)$ be the set of vertices of $C$, and $E(C)$ --- the set of edges of $C$.
Since $|E(\mathcal{T})| \leq (c-1)(2d+1)$ (Claim \ref{claim-small-steiner-tree}),
we have that $|E(C)| = 2|E(\mathcal{T})| \leq 2(c-1)(2d+1)$.
Also, for every vertex $v \in V(\mathcal{T})$, we let $\operatorname{deg}_\mathcal{T}(v)$ to be the degree of $v$ in $\mathcal{T}$.
Hence, for $v \in V(\mathcal{T})$, the graph $G_{\mathrm{cut}}$ contains vertices $v_1, \dots, v_{\operatorname{deg}_\mathcal{T}(v)}$.
\begin{claim}
\label{claim-steiner-dist-profile}
For any two different vertices $p, q \in V(G_{\mathrm{cut}}) \setminus V(C)$,
if $\pi_d[p, V(C)] = \pi_d[q, V(C)]$ in $G_{\mathrm{cut}}$, then
$\pi_d[p, V(\mathcal{T})] = \pi_d[q, V(\mathcal{T})]$ in $G_d$.
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
We will show that the distance-$d$ profile of any vertex $p \in V(G_{\mathrm{cut}}) \setminus V(C)$
on $V(C)$ in $G_{\mathrm{cut}}$ uniquely determines the distance-$d$ profile of $p$ on $V(\mathcal{T})$
in $G_d$.
The statement of the lemma will follow.
We first remark that for each $x \in V(\mathcal{T})$ and $i \in [1, \operatorname{deg}_\mathcal{T}(v)]$, we have that
$\mathrm{dist}_{G_{\mathrm{cut}}}(p, x_i) \geq \mathrm{dist}_{G_d}(p, x)$.
This is true since we can pick a shortest path from $p$ to $x_i$ in $G_{\mathrm{cut}}$, and replace
each vertex of this path belonging to $V(C)$ with the corresponding vertex of $V(\mathcal{T})$
in $G_d$.
The resulting path connects $p$ with $x$ in $G_d$, and has length $\mathrm{dist}_{G_{\mathrm{cut}}}(p, x_i)$.
We fix a vertex $v \in V(\mathcal{T})$, and we want to determine $\pi_d[p, V(\mathcal{T})](v)$ in $G_d$ from
$\pi_d[p, V(C)]$ in $G_{\mathrm{cut}}$.
Obviously, for each $x \in V(\mathcal{T})$ and $i \in [1, \operatorname{deg}_\mathcal{T}(v)]$ we have
$$ \mathrm{dist}_{G_d}(p, v) \leq \mathrm{dist}_{G_d}(p, x) + \mathrm{dist}_{G_d}(x, v) \leq
\mathrm{dist}_{G_{\mathrm{cut}}}(p, x_i) + \mathrm{dist}_{G_d}(x, v). $$
On the other hand, we pick a shortest path $P$ from $p$ to $v$ in $G_d$.
We let $x$ to be the first intersection of $P$ with $V(\mathcal{T})$, and $y$ --- the vertex
immediately preceding $x$ on $P$.
Since $y \not\in V(\mathcal{T})$, then by the construction of $G_{\mathrm{cut}}$ we infer that $y$ is adjacent to
a copy of $x$ in $G_{\mathrm{cut}}$ --- say, $x_i$ for some $i \in [1, \operatorname{deg}_\mathcal{T}(x)]$.
For this choice of $x$ and $i$ we have that
\begin{equation*}
\begin{split}
\mathrm{dist}_{G_d}(p, v) &= \mathrm{dist}_{G_d}(p, y) + 1 + \mathrm{dist}_{G_d}(x, v) =
\mathrm{dist}_{G_{\mathrm{cut}}}(p, y) + \mathrm{dist}_{G_{\mathrm{cut}}}(y, x_i) + \mathrm{dist}_{G_d}(x, v) \geq \\
&\geq \mathrm{dist}_{G_{\mathrm{cut}}}(p, x_i) + \mathrm{dist}_{G_d}(x, v).
\end{split}
\end{equation*}
We conclude that
$$ \mathrm{dist}_{G_d}(p, v) = \min \{ \mathrm{dist}_{G_{\mathrm{cut}}}(p, x_i) + \mathrm{dist}_{G_d}(x, v)\,\mid\,
x \in V(\mathcal{T}), i \in [1, \operatorname{deg}_\mathcal{T}(x)]\}. $$
It is now straightforward to determine $\pi_d[p, V(\mathcal{T})](v)$ in $G_d$ from
$\pi_d[p, V(C)]$ in $G_{\mathrm{cut}}$ and the distances in $G_d$ between each pair of vertices
of $\mathcal{T}$ (which are independent on the choice of~$p$).
\end{claimproof}
\end{claim}
We now observe that $C$ is a cycle in $G_{\mathrm{cut}}$, which does not enclose any
other vertices of $G_{\mathrm{cut}}$; hence, there exists a noose
$\mathcal{L}$, closely following $C$, that passes through each vertex of $C$ exactly once
and that does not enclose any other vertex of $G_{\mathrm{cut}}$.
The variant of Noose Profile Lemma (Corollary \ref{noose-profille-lemma-rev}) applies
to $\mathcal{L}$.
Hence, there are at most $|C|^3 (d+2)^4$ different distance-$d$ profiles on $C$ in
$G_{\mathrm{cut}}$, measured from the vertices not enclosed by $\mathcal{L}$.
We fix two vertices $p, q \in V(G_{\mathrm{cut}}) \setminus V(C)$ such that
$\pi_d[p, V(C)] = \pi_d[q, V(C)]$ in $G_{\mathrm{cut}}$.
Firstly, we see that neither $p$ nor $q$ are enclosed by $\mathcal{L}$.
We know from Claim \ref{claim-steiner-dist-profile} that $\pi_d[p, V(\mathcal{T})] = \pi_d[q, V(\mathcal{T})]$
in $G_d$.
Since $A \subseteq V(\mathcal{T})$, we infer that $\pi_d[p, A] = \pi_d[q, A]$ in $G_d$.
By the construction of $G_d$, we also get that $\pi_d[p, A] = \pi_d[q, A]$ in $G$.
Since there are at most $|C|^3 (d+2)^4$ different distance-$d$ profiles on $C$
in $G_{\mathrm{cut}}$, measured from the vertices not enclosed by $\mathcal{L}$,
we get that there are at most $|C|^3 (d+2)^4$ different distance-$d$ profiles on $A$
in $G_d$, measured from the vertices in $V(G_d) \setminus V(\mathcal{T})$.
Therefore, $G_d$ has at most $|C|^3 (d+2)^4 + |V(\mathcal{T})|$ different distance-$d$ profiles
on $A$ in total.
Recall that $G$ has at most one more distance-$d$ profile on $A$ compared to $G_d$
--- that is, the constant function equal to $+\infty$.
Hence, the number of distance-$d$ profiles on $A$ in $G$ is bounded by
\begin{equation*}
\begin{split}
|C|^3 (d+2)^4 + |V(\mathcal{T})| + 1 &\leq
[2(c-1)(2d+1)]^3(d+2)^4 + (c-1)(2d+1) + 1 \leq \\ &\leq
8c^3[(2d+1)^3(d+2)^4 + (2d+1) + 1] \leq 64c^3(d+2)^7.
\end{split}
\end{equation*}
Let us finally consider the case where $G_d$ is disconnected.
Assume that the vertices of $A$ are spread among $k$ different connected components
in $G_d$, and the $i$-th connected component contains $c_i$ vertices of $A$ for each
$i \in [1, k]$ ($c_1, c_2, \dots, c_k \geq 1$, $\sum c_i = c$).
Then, we apply this theorem to each connected component of $G_d$ separately.
We get that the number of different distance-$d$ profiles on $A$ in $G_d$ is bounded by
$$ \sum_{i=1}^k 64c_i^3(d+2)^7 < 64c^3(d+2)^7. $$
Hence, the number of different distance-$d$ profiles on $A$ in $G$ is also bounded by
$64c^3(d+2)^7$.
\end{proof}
\subsection{Quasi-cages and cages}
\label{quasi-cages-subsection}
We begin by introducing a prototype for cages --- quasi-cages.
In order to do this, we first need to define a special kind of a rooted tree.
\begin{definition}
Oriented paths $P_1, P_2, \dots, P_\ell$ in a planar graph $G$ create a \textbf{geodesic tree}
$\mathcal{T} = \bigcup P_i = \mathsf{Tree}(P_1, P_2, \dots, P_\ell)$ of
order $\ell$ rooted at a vertex $r$ if the following conditions hold:
\begin{itemize}
\item the union of all the paths is an oriented subtree $\mathcal{T}$ of $G$,
\item all paths $P_i$ are shortest paths in $G$ and have the same length,
not exceeding $d$,
\item each path $P_i$ originates at $r$ and terminates at a different leaf of the tree.
\end{itemize}
We say that $\mathcal{T}$ \textbf{avoids} $s$ if none of the paths contain $s$ as a vertex.
Also, if for all different $i, j$, the intersection of $P_i$ and $P_j$ is equal to $\{r\}$,
we call $\mathcal{T}$ a \textbf{simple geodesic tree}.
\end{definition}
We also use the following notation:
$\mathsf{Root}(\mathcal{T})$ is the root $r$ of the geodesic tree, and
$\mathsf{Path}(\mathcal{T}, i)$ is the oriented path $P_i$.
Moreover, for any two vertices $u, v \in \mathcal{T}$, we define
$\lca_\mathcal{T}(u, v)$ as the lowest common ancestor of these two vertices in $\mathcal{T}$,
where $\mathcal{T}$ is considered rooted at $r$.
We may write $\lca$ instead of $\lca_\mathcal{T}$ if the tree is clear from the context.
\medskip
We can now define a quasi-cage:
\begin{definition}
\label{def-quasi-cage}
A \textbf{quasi-cage} of order $\ell$ in a planar graph $G$ is a structure consisting of:
\begin{itemize}
\item a semi-ladder of order $\ell$ consisting of distinct vertices
$a_1, a_2, \dots, a_\ell$, and $b_1, b_2, \dots, b_\ell$,
\item two distinct root vertices $p, q \not\in \{a_1, a_2, \dots, a_\ell, b_1, b_2, \dots, b_\ell\}$,
\item shortest paths $P_1, P_2, \dots, P_\ell$, where $P_i$ is an oriented path from $p$ to $a_i$ for
each $i \in [1, \ell]$, which form a simple geodesic tree $\mathcal{P} = \mathsf{Tree}(P_1, P_2, \dots, P_\ell)$
rooted at $p$ and avoiding $q$,
\item shortest paths $Q_1, Q_2, \dots, Q_\ell$, where $Q_i$ is a directed path from $q$ to $a_i$
for each $i \in [1, \ell]$, which form a geodesic tree $\mathcal{Q} = \mathsf{Tree}(Q_1, Q_2, \dots, Q_\ell)$
rooted at $q$ and avoiding $p$.
\end{itemize}
We stress that while $\mathcal{P}$ must be a simple geodesic tree, $\mathcal{Q}$ is not necessarily simple
(Figure~\ref{quasi-cage-sample-fig}).
With the notation above, we denote a quasi-cage by
$$\mathsf{QuasiCage}((a_1, a_2, \dots, a_\ell), (b_1, b_2, \dots, b_\ell), \mathcal{P}, \mathcal{Q}). $$
\end{definition}
\begin{figure}[h]
\centering
\input{figures/quasi-cage-img.tex}
\caption{An example quasi-cage of order $6$. Tree $\mathcal{P}$ is marked blue and tree $\mathcal{Q}$ is
marked green. Vertices $b_1, b_2, \dots, b_6$ were omitted from the figure.
Note that trees $\mathcal{P}$ and $\mathcal{Q}$ can share vertices and edges, but $\mathcal{P}$ must not contain
$q$, and $\mathcal{Q}$ must not contain $p$.}
\label{quasi-cage-sample-fig}
\end{figure}
We remark that the definitions of semi-ladders, geodesic trees, simple
geodesic trees, and quasi-cages are closed to taking subsets.
Formally, fix a subsequence of indices $i_1, i_2, \dots, i_m$ ($1 \leq i_1 < i_2 < \dots < i_m
\leq \ell$).
Then:
\begin{itemize}
\item For a semi-ladder $(a_1, a_2, \dots, a_\ell), (b_1, b_2, \dots, b_\ell)$,
vertices
$(a_{i_1}, a_{i_2}, \dots, a_{i_m})$, $(b_{i_1}, b_{i_2}, \dots, b_{i_m})$ form
a semi-ladder of order $m$.
\item For a geodesic tree $\mathsf{Tree}(P_1, P_2, \dots, P_\ell)$ of order $\ell$, also
$\mathsf{Tree}(P_{i_1}, P_{i_2}, \dots, P_{i_m})$ is a geodesic tree of order $m$.
If the original geodesic tree was simple, its subset is simple as well.
\item For a quasi-cage of order $\ell$
$$\mathsf{QuasiCage}((a_1, a_2, \dots, a_\ell), (b_1, b_2, \dots, b_\ell),
\mathsf{Tree}(P_1, P_2, \dots, P_\ell), \mathsf{Tree}(Q_1, Q_2, \dots, Q_\ell)), $$
the following describes a quasi-cage of order $m$:
$$\mathsf{QuasiCage}((a_{i_1}, \dots, a_{i_m}), (b_{i_1}, \dots, b_{i_m}),
\mathsf{Tree}(P_{i_1}, \dots, P_{i_m}), \mathsf{Tree}(Q_{i_1}, \dots, Q_{i_m})). $$
\end{itemize}
This fact will also be true for each further refinement of the definition of a quasi-cage.
Therefore, from now on, we will refer to the subsets of any object (semi-ladder, geodesic tree,
quasi-cage and any its refinement) by taking the original object
and specifying the indices $i_1, i_2, \dots, i_m$.
\vspace{1em}
As the first step of our proof, we will demonstrate that planar graphs with large distance-$d$
semi-ladders also contain large quasi-cages.
\begin{lemma}
\label{quasi-cage-exists}
If $G$ contains a distance-$d$ semi-ladder of order $d(d\ell + 2)^d + 1$, then
$G$ also contains a quasi-cage of order $\ell$.
\begin{proof}
We will state and prove a series of claims, each imposing more structure on the semi-ladder.
We will call a distance-$d$ semi-ladder $(a_1, a_2, \dots, a_k), (b_1, b_2, \dots, b_k)$ of order $k$,
together with another vertex $r$,
\textbf{R-equidistant} if:
\begin{itemize}
\item $r \not\in \{a_1, a_2, \dots, a_k, b_1, b_2, \dots, b_k\}$,
\item each vertex $a_i$ is at the same distance from $r$, not exceeding $d$.
\end{itemize}
We will denote such semi-ladder as $\mathsf{RSemiLadder}((a_1, \dots, a_k), (b_1, \dots, b_k),
r)$.
\begin{claim}
\label{quasi-cage-exists-r-claim}
Every distance-$d$ semi-ladder of order $d\ell + 1$ contains an R-equidistant semi-ladder of order $\ell$
as a subset.
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
Take a distance-$d$ semi-ladder of order $d\ell + 1$ in $G$: $(a_1, a_2, \dots, a_{d\ell + 1}),
(b_1, b_2, \dots, b_{d\ell + 1})$.
Notice that $1 \leq \mathrm{dist}(a_i, b_1) \leq d$ for each $i \geq 2$.
This means that the set $\{a_2, a_3, \dots, a_{d\ell + 1}\}$ of vertices contains
a subset with at least $\frac{(d\ell + 1) - 1}{d} = \ell$ elements
where each element is at the same distance from $b_1$, not exceeding $d$.
Let this subset be $a_{i_1}, a_{i_2}, \dots, a_{i_\ell}$ ($2 \leq i_1 < i_2 < \dots < i_\ell \leq
d\ell + 1$).
Then, the following structure is an R-equidistant semi-ladder:
$$ \mathsf{RSemiLadder}((a_{i_1}, \dots, a_{i_\ell}), (b_{i_1}, \dots, b_{i_\ell}), b_1). $$
By our definition of a semi-ladder, the vertices of any semi-ladder must be different.
Hence, $b_1 \not\in \{a_{i_1}, \dots, a_{i_\ell}, b_{i_1}, \dots, b_{i_\ell}\}$.
\end{claimproof}
\end{claim}
A \textbf{simple geodesic semi-ladder} of order $k$ is a distance-$d$ semi-ladder
$(a_1, a_2, \dots, a_k)$, $(b_1, b_2, \dots, b_k)$, together with a simple geodesic tree
$\mathcal{P} = \mathsf{Tree}(P_1, P_2, \dots, P_k)$,
where for each $i \in [1, k]$, the path $P_i$ terminates at $a_i$.
We denote such a simple geodesic semi-ladder as
$\mathsf{SGSemiLadder}((a_1, \dots, a_k), (b_1, \dots, b_k), \mathcal{P})$.
\begin{claim}
\label{quasi-cage-exists-sg-claim}
Every R-equidistant semi-ladder of order $\ell^d$ contains a
simple geodesic semi-ladder of order $\ell$ as a subset.
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
Take an R-equidistant semi-ladder of order $\ell^d$:
$$\mathsf{RSemiLadder}((a_1, \dots, a_{\ell^d}), (b_1, \dots, b_{\ell^d}), r).$$
Let $\delta := \mathrm{dist}(r, a_1)$. We also take
$\mathcal{T}$ as a shortest paths tree rooted at $r$ whose leaves are exactly
$a_1, a_2, \dots, a_{\ell^d}$; this tree exists since all hypothetical leaves
are at the same distance $\delta \leq d$ from $r$.
This tree has depth $\delta$ and $\ell^d$ leaves.
Thus, $\mathcal{T}$ contains a vertex which has at least $\ell^{d / \delta} \geq \ell$ children.
Let $p$ be any such vertex.
Since $p$ has at least $\ell$ children in $\mathcal{T}$, and each child is a root of a subtree
in $\mathcal{T}$ containing at least one leaf of $\mathcal{T}$,
we can pick a subset $A = \{a_{i_1}, a_{i_2}, \dots, a_{i_\ell}\}$ ($1 \leq i_1 < i_2 < \dots <
i_\ell \leq \ell^d$)
of leaves of $\mathcal{T}$ where each leaf is in a different subtree of $\mathcal{T}$ rooted at a child of $p$.
Also, for each $j \in [1, \ell]$, we define $P_j$ as the shortest oriented path in $\mathcal{T}$
which originates at $p$ and terminates at $a_{i_j}$.
By the choice of $A$, all paths $P_1, P_2, \dots, P_\ell$ are vertex-disjoint apart
from their common origin~$p$.
They also have the same length since all leaves of $\mathcal{T}$ are at the same depth,
and all leaves in $A$ are in the subtree of $\mathcal{T}$ rooted at $p$.
Finally, they are shortest paths in $G$ by the choice of $\mathcal{T}$ as a shortest paths tree.
Therefore, $\mathsf{Tree}(P_1, P_2, \dots, P_\ell)$ is a simple geodesic tree.
We can now see that the following structure is a simple geodesic semi-ladder:
\[ \mathsf{SGSemiLadder}((a_{i_1}, \dots, a_{i_\ell}), (b_{i_1}, \dots, b_{i_\ell}),
\mathsf{Tree}(P_1, P_2, \dots, P_\ell)). \]
\end{claimproof}
\end{claim}
A simple geodesic semi-ladder
$\mathsf{SGSemiLadder}((a_1, \dots, a_k), (b_1, \dots, b_k), \mathcal{P})$ of order $k$,
together with another vertex $q$, is \textbf{Q-equidistant} if:
\begin{itemize}
\item $\mathcal{P}$ avoids $q$,
\item $q \not\in \{a_1, a_2, \dots, a_k, b_1, b_2, \dots, b_k\}$,
\item $q$ is at the same distance from each vertex $a_i$, and
\item $\mathrm{dist}(q, \mathsf{Root}(\mathcal{P})) + \mathrm{dist}(\mathsf{Root}(\mathcal{P}), a_i) > d$ for each $i \in [1, k]$.
\end{itemize}
We use the following notation for a Q-equidistant simple geodesic semi-ladder:
$\mathsf{QSemiLadder}(\allowbreak (a_1, \dots, a_k),\allowbreak (b_1, \dots, b_k),\allowbreak \mathcal{P}, q)$.
\begin{claim}
\label{quasi-cage-exists-q-claim}
Every simple geodesic semi-ladder of order $d\ell + 2$ contains
a Q-equidistant simple geodesic semi-ladder of order $\ell$
as a subset.
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
Take a simple geodesic semi-ladder of order $d\ell + 2$:
$$ \mathsf{SGSemiLadder}((a_1, \dots, a_{d\ell + 2}), (b_1, \dots, b_{d\ell + 2}), \mathcal{P}) \qquad
\text{where }\mathcal{P} = \mathsf{Tree}(P_1, P_2, \dots, P_{d\ell + 2}).$$
Notice that $b_1 \neq \mathsf{Root}(\mathcal{P})$; otherwise, we would have
$d < \mathrm{dist}(b_1, a_1) = \mathrm{dist}(\mathsf{Root}(\mathcal{P}), a_1) = \mathrm{dist}(\mathsf{Root}(\mathcal{P}), a_2) =
\mathrm{dist}(b_1, a_2) \leq d$.
Since paths $P_2, \dots, P_{d\ell + 2}$ are vertex-disjoint apart from $\mathsf{Root}(\mathcal{P})$,
this means that at most one of them passes through $b_1$.
Hence, at least $d\ell$ such paths do not contain $b_1$.
Moreover, for each $i \in [2, d\ell + 2]$, we have $\mathrm{dist}(a_i, b_1) \in [1, d]$.
By the pigeonhole principle, we can fix $\ell$ indices $i_1, i_2, \dots, i_\ell$
($2 \leq i_1 < i_2 < \dots < i_\ell \leq d\ell + 2$) with the following properties:
\begin{itemize}
\item for each $j \in [1, \ell]$, the path $P_{i_j}$ does not contain $b_1$,
\item $b_1$ is at the same distance from each vertex $a_{i_j}$ ($j \in [1, \ell]$).
\end{itemize}
We will prove that the following structure is a Q-equidistant simple geodesic semi-ladder:
$$ \mathsf{QSemiLadder}((a_{i_1}, \dots, a_{i_\ell}), (b_{i_1}, \dots, b_{i_\ell}),
\mathsf{Tree}(P_{i_1}, \dots, P_{i_\ell}), b_1). $$
Since the choice of the indices $i_1, \dots, i_\ell$ already met the first and the third
condition in the definition of a Q-equidistant simple geodesic semi-ladder,
we only need to verify the remaining requirements.
As any two vertices in the semi-ladder are different,
we have $b_1 \neq a_{i_j}$ and $b_1 \neq b_{i_j}$ for each $j \in [1, \ell]$, which
confirms the second condition.
Moreover, for every $j \in [1, \ell]$, we have that
\begin{equation*}
\begin{split}
\mathrm{dist}(b_1, \mathsf{Root}(\mathcal{P})) + \mathrm{dist}(\mathsf{Root}(\mathcal{P}), a_{i_j}) &=
\mathrm{dist}(b_1, \mathsf{Root}(\mathcal{P})) + \mathrm{dist}(\mathsf{Root}(\mathcal{P}), a_1) \geq \\ &\geq
\mathrm{dist}(b_1, a_1) > d.
\end{split}
\end{equation*}
All the required conditions are satisfied, so the structure defined above
is a Q-equidistant simple geodesic semi-ladder.
\end{claimproof}
\end{claim}
Now we will see that a large Q-equidistant simple geodesic semi-ladder in $G$
directly witnesses the existence of a large quasi-cage in $G$.
\begin{claim}
\label{quasi-cage-exists-qc-claim}
Every graph with a Q-equidistant simple geodesic semi-ladder of order $\ell$ also
contains a quasi-cage of order $\ell$.
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
Fix a Q-equidistant simple geodesic semi-ladder as in the statement of the claim:
$$\mathcal{L} = \mathsf{QSemiLadder}((a_1, \dots, a_\ell),\allowbreak (b_1, \dots, b_\ell), \mathcal{P}, q).$$
Let also $\mathcal{S}$ denote the semi-ladder $a_1, \dots, a_\ell$, $b_1, \dots, b_\ell$ underlying
$\mathcal{L}$, and set $p := \mathsf{Root}(\mathcal{P})$.
Let us also take $\mathcal{Q}$ as any shortest-path tree rooted at $q$ whose leaves
are $a_1, a_2, \dots, a_\ell$.
We will now verify that according to Definition \ref{def-quasi-cage}, the following structure
is a quasi-cage:
$$ \mathsf{QuasiCage}((a_1, \dots, a_\ell), (b_1, \dots, b_\ell), \mathcal{P}, \mathcal{Q}). $$
We first note that $p \not\in \mathcal{S}$ since $\mathcal{L}$ is also an R-equidistant semi-ladder.
Similarly, $q$ is disjoint with $\mathcal{S}$, which follows immediately from the definition of $\mathcal{L}$ as
a Q-equidistant simple geodesic semi-ladder.
The geodesic tree $\mathcal{P}$ is simple (since $\mathcal{L}$ is a simple geodesic semi-ladder)
and avoids $q$ (since $\mathcal{L}$ is a Q-equidistant simple geodesic semi-ladder).
We only need to prove that $\mathcal{Q}$ avoids $p$.
Assume for contradiction that for some $i \in [1, \ell]$, a path $Q_i = \mathsf{Path}(\mathcal{Q}, i)$
contains $p$ as a vertex.
This would mean that the shortest path between $q$ and $a_i$ contains
$p$ as a vertex.
However, by the definition of a Q-equidistant simple geodesic semi-ladder:
$$ \mathrm{dist}(q, a_i) = \mathrm{dist}(q, p) + \mathrm{dist}(p, a_i) = \mathrm{dist}(q, \mathsf{Root}(\mathcal{P})) + \mathrm{dist}(\mathsf{Root}(\mathcal{P}), a_i) > d $$
--- a contradiction.
\end{claimproof}
\end{claim}
We can now combine the claims above to prove our lemma.
Take any distance-$d$ semi-ladder $L_1$ in $G$ of order $d(d\ell + 2)^d + 1$.
By Claim \ref{quasi-cage-exists-r-claim}, $L_1$ contains an R-equidistant semi-ladder
$L_2$ of order $(d\ell + 2)^d$ as a subset.
By Claim \ref{quasi-cage-exists-sg-claim}, $L_2$ contains a simple geodesic semi-ladder
$L_3$ of order $d\ell + 2$ as a subset.
By Claim \ref{quasi-cage-exists-q-claim}, $L_3$ contains a Q-equidistant
simple geodesic semi-ladder $L_4$ of order $\ell$ as a subset.
Hence, by Claim \ref{quasi-cage-exists-qc-claim}, $L_4$ asserts the existence of
a quasi-cage of order $\ell$ in $G$.
\end{proof}
\end{lemma}
Next, we refine the definition of a quasi-cage by defining cages --- variants of
quasi-cages ensuring that both geodesic trees in a definition of a quasi-cage intersect
in a controlled way.
\begin{definition}
A \textbf{cage} of order $\ell$ is a quasi-cage
$\mathsf{QuasiCage}((a_1, \dots, a_\ell), (b_1, \dots, b_\ell), \mathcal{P}, \mathcal{Q})$
in which for every two indices $i, j \in [1, \ell]$, the paths $\mathsf{Path}(\mathcal{P}, i)$ and $\mathsf{Path}(\mathcal{Q}, j)$
have a non-empty intersection if and only if $i = j$.
We denote this structure in the following way:
$$ \mathsf{Cage}((a_1, \dots, a_\ell), (b_1, \dots, b_\ell), \mathcal{P}, \mathcal{Q}). $$
\end{definition}
\begin{figure}[h]
\centering
\input{figures/cage-img.tex}
\caption{An example cage.
This cage is a subset of the quasi-cage from Figure \ref{quasi-cage-sample-fig}.
The pair of vertices $(a_2, b_2)$ has been removed from the original semi-ladder,
and the remaining indices have been renumbered.
Analogously to Figure \ref{quasi-cage-sample-fig}, vertices $b_1, b_2, \dots, b_5$ were
removed from the picture.}
\label{cage-sample-fig}
\end{figure}
To see that the definition of a cage is slightly stronger than the one of a quasi-cage,
we can verify that a quasi-cage in Figure \ref{quasi-cage-sample-fig} is not a cage ---
its path connecting $q$ with $a_6$ intersects the path connecting $p$ with $a_2$.
However, a large subset of it is a cage (Figure \ref{cage-sample-fig}).
This is not a coincidence, as proved in the following lemma.
\begin{lemma}
\label{cage-exists}
Every graph with a quasi-cage of order $(2d - 1)\ell$
contains a cage of order $\ell$ as a subset.
\begin{proof}
Fix a quasi-cage:
$$\mathsf{QuasiCage}((a_1, a_2, \dots, a_{(2d - 1)\ell}),
(b_1, b_2, \dots, b_{(2d - 1)\ell}), \mathcal{P}, \mathcal{Q})$$
where $\mathcal{P} = \mathsf{Tree}(P_1, \dots, P_{(2d-1)\ell})$,
$\mathcal{Q} = \mathsf{Tree}(Q_1, \dots, Q_{(2d-1)\ell})$.
Firstly, note that for every $i \in [1, (2d-1)\ell]$, paths $P_i$ and $Q_i$ intersect, because
they share their final vertex $a_i$.
Our aim is now to find a subset of indices $I \subseteq \{1, 2, \dots, (2d - 1)\ell\}$
such that $|I| = \ell$ and for any two different indices $i, j \in I$, paths
$P_i$ and $Q_j$ do not intersect.
As soon as we achieve this, the subset of the quasi-cage given by the set of indices $I$
will form the sought cage.
Let us create an auxiliary directed graph $H$ where $V(H) = \{1, 2, \dots, (2d - 1)\ell\}$,
such that $H$ contains an oriented edge $i \to j$ for $i \neq j$ if and only if
$P_i$ and $Q_j$ intersect.
Let also $\widehat{H}$ be the undirected graph underlying $H$.
We plan to find an independent set $I \subseteq V(\widehat{H})$ of size at least $\ell$.
Then for any two indices $i, j \in I$, we will have that paths $P_i$ and $Q_j$ are disjoint,
as well as paths $P_j$ and $Q_i$.
Therefore, $I$ will be a subset of indices forming a cage.
We note that each path $Q_j$ has length at most $d$.
As $Q_j$ does not pass through $p$ (the root of the simple geodesic tree $\mathcal{P}$),
each vertex other than its origin $q$ can lie on at most one of the paths $P_i$.
Thus, $Q_j$ intersects at most $d$ different paths in $\mathcal{P}$.
Since $Q_j$ intersects with $P_j$ for every $j \in [1, (2d-1)\ell]$, we get that
$Q_j$ has a non-empty intersection with at most $d-1$ paths $P_i$ for $i \neq j$.
This means that no vertex of $H$ has in-degree larger than $d-1$.
In every non-empty subset $S$ of vertices of $\widehat{H}$,
the total number of edges in the subgraph
of $\widehat{H}$ induced by $S$ does not exceed $|S| \cdot (d-1)$;
this is because in the subgraph of $H$ induced by $S$, each vertex has in-degree not
exceeding $d-1$.
Thus, $\mathcal{S}$ contains a vertex with degree not exceeding the average degree of the vertices
in $S$, which can be bounded from above by
$$\frac{2 \cdot [|S| \cdot (d - 1)]}{|S|} = 2d - 2.$$
Hence, $\widehat{H}$ is $(2d-2)$-degenerate \cite{lick_white_1970}.
Since $(2d-2)$-degenerate graphs are $(2d-1)$-colorable~\cite{SZEKERES19681},
$\widehat{H}$ contains an independent set of size at least
\[\frac{|V(\widehat{H})|}{2d-1} = \ell.\]
\end{proof}
\end{lemma}
\subsection{Ordered cages}
\label{ordered-cages-section}
So far, the definition of a cage does not involve any topological properties of the plane.
In this subsection, we will introduce the topology to the cages by defining
ordered cages.
We will, however, need some notation beforehand.
\begin{definition}
For a cage $\mathcal{C} := \mathsf{Cage}((a_1, \dots, a_\ell), (b_1, \dots, b_\ell), \mathcal{P}, \mathcal{Q})$
of order $\ell$ in a graph $G$, and an index $i \in \{1, 2, \dots, \ell\}$, we define:
\begin{itemize}
\item the \textbf{$i$-th splitting vertex} $\mathsf{Split}(\mathcal{C}, i)$
as the vertex of the intersection of $\mathsf{Path}(\mathcal{P}, i)$ and $\mathsf{Path}(\mathcal{Q}, i)$
which is the closest to $\mathsf{Root}(\mathcal{P})$ (this vertex is unique since $\mathsf{Path}(\mathcal{P}, i)$ is
a shortest path in $G$);
\item the \textbf{$i$-th splitting path} $\mathsf{SPath}(\mathcal{C}, i)$
as the oriented simple path originating at $\mathsf{Root}(\mathcal{P})$,
following the prefix of $\mathsf{Path}(\mathcal{P}, i)$ until $\mathsf{Split}(\mathcal{C}, i)$,
and then --- the prefix of $\mathsf{Path}(\mathcal{Q}, i)$ in the opposite direction.
Formally,
$$ \mathsf{SPath}(\mathcal{C}, i) = \mathsf{Path}(\mathcal{P}, i)[\mathsf{Root}(\mathcal{P}),
\mathsf{Split}(\mathcal{C}, i)]\ \cdot\ (\mathsf{Path}(\mathcal{Q}, i))^{-1}[\mathsf{Split}(\mathcal{C}, i),
\mathsf{Root}(\mathcal{Q})].$$
\end{itemize}
\end{definition}
The definitions are also explained in Figure \ref{splitting-sample-fig}.
\begin{figure}[h]
\centering
\input{figures/splitting-img.tex}
\caption{Example splitting vertices and splitting paths in the cage $\mathcal{C}$ from
Figure~\ref{cage-sample-fig}.
Objects $\mathsf{Split}(\mathcal{C}, 2)$ and $\mathsf{SPath}(\mathcal{C}, 2)$ are marked yellow,
objects $\mathsf{Split}(\mathcal{C}, 4)$ and $\mathsf{SPath}(\mathcal{C}, 4)$ are marked orange,
and $\mathsf{SPath}(\mathcal{C}, 1)$ is marked green.}
\label{splitting-sample-fig}
\end{figure}
We derive the following facts about splitting paths:
\begin{lemma}
\label{two-splitting-paths-lemma}
Fix a cage $\mathcal{C} = ((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q})$,
two different indices $i, j \in [1, \ell]$ and a vertex $x \in V(\mathcal{Q})$.
If $x \in Q_i$ and $x \in Q_j$, then $x \in \mathsf{SPath}(\mathcal{C}, i) \cap \mathsf{SPath}(\mathcal{C}, j)$.
\begin{proof}
Note that $\mathsf{Split}(\mathcal{C}, i) \in P_i \cap Q_i$.
Hence, path $Q_j$ cannot contain $\mathsf{Split}(\mathcal{C}, i)$ or otherwise
paths $P_i$ and $Q_j$ would intersect.
Therefore, $x$ is an ancestor of $\mathsf{Split}(\mathcal{C}, i)$ in $\mathcal{Q}$, so
$$x \in (\mathsf{Path}(\mathcal{Q}, i))^{-1}[\mathsf{Split}(\mathcal{C}, i), \mathsf{Root}(\mathcal{Q})].$$
Thus, $x \in \mathsf{SPath}(\mathcal{C}, i)$.
We prove that $x \in \mathsf{SPath}(\mathcal{C}, j)$ analogously.
\end{proof}
\end{lemma}
\begin{lemma}
\label{splitting-path-intersection}
For a cage $\mathcal{C} = ((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q})$ in a graph $G$,
and two different indices $i, j \in [1, \ell]$:
$$ \mathsf{SPath}(\mathcal{C}, i) \cap \mathsf{SPath}(\mathcal{C}, j)\ =\ \{\mathsf{Root}(\mathcal{P})\} \cup
\mathsf{SPath}(\mathcal{C}, i)[\lca_{\mathcal{Q}}(a_i, a_j), \mathsf{Root}(\mathcal{Q})]. $$
In other words, any two distinct paths $\mathsf{SPath}(\mathcal{C}, i)$, $\mathsf{SPath}(\mathcal{C}, j)$
intersect exactly in their first vertex $p$ and in their common suffix.
\begin{proof}
We first note that the following condition is simple to verify.
By Lemma \ref{two-splitting-paths-lemma}, we have that
$$\mathsf{SPath}(\mathcal{C}, i)[\lca_{\mathcal{Q}}(a_i, a_j), \mathsf{Root}(\mathcal{Q})] =
\mathsf{SPath}(\mathcal{C}, j)[\lca_{\mathcal{Q}}(a_i, a_j), \mathsf{Root}(\mathcal{Q})].$$
Hence:
$$ \mathsf{SPath}(\mathcal{C}, i) \cap \mathsf{SPath}(\mathcal{C}, j)\ \supseteq\ \{\mathsf{Root}(\mathcal{P})\} \cup
\mathsf{SPath}(\mathcal{C}, i)[\lca_{\mathcal{Q}}(a_i, a_j), \mathsf{Root}(\mathcal{Q})]. $$
We only need to prove the $\subseteq$ part of the equality.
Let $\mathcal{P} = \mathsf{Tree}(P_1, P_2, \dots, P_\ell)$ and $\mathcal{Q} = \mathsf{Tree}(Q_1, Q_2, \dots,
Q_\ell)$, and fix two different indices $i, j$.
By the definition of a cage, paths $P_i$ and $Q_j$ are vertex-disjoint,
and paths $P_j$ and $Q_i$ are vertex-disjoint.
Since $\mathsf{SPath}(\mathcal{C}, i) \subseteq P_i \cup Q_i$ and $\mathsf{SPath}(\mathcal{C}, j) \subseteq P_j \cup Q_j$, we
conclude that
$$ \mathsf{SPath}(\mathcal{C}, i) \cap \mathsf{SPath}(\mathcal{C}, j) \subseteq (P_i \cap P_j) \cup (Q_i \cap Q_j). $$
We conclude the proof by noting that $P_i \cap P_j = \{p\}$ ($\mathcal{P}$ is a simple geodesic tree)
and $Q_i \cap Q_j = \mathsf{SPath}(\mathcal{C}, i)[\lca_\mathcal{Q}(a_i, a_j), \mathsf{Root}(\mathcal{Q})]$.
\end{proof}
\end{lemma}
In the example in Figure \ref{splitting-sample-fig}, paths $\mathsf{Split}(\mathcal{C}, 2)$
and $\mathsf{Split}(\mathcal{C}, 4)$ intersect at $p$ and $q$ only,
whereas paths $\mathsf{Split}(\mathcal{C}, 1)$ and $\mathsf{Split}(\mathcal{C}, 4)$ intersect
at $p$ and their common suffix, $\mathsf{Split}(\mathcal{C}, 4)[x, q]$
where $x = \lca_\mathcal{Q}(a_1, a_4)$.
\vspace{1em}
We will now introduce the concept of an order of a cage $\mathcal{C}$.
Roughly speaking, if we let $\mathcal{C} = \mathsf{Cage}((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q})$, then
the paths $\mathsf{Path}(\mathcal{P}, 1), \mathsf{Path}(\mathcal{P}, 2), \dots, \mathsf{Path}(\mathcal{P}, \ell)$ originate at the common vertex
$\mathsf{Root}(\mathcal{P})$ and are vertex disjoint otherwise.
Therefore, we can order all these paths cyclically around $\mathsf{Root}(\mathcal{P})$.
We stress that this cyclic order might not necessarily be consistent with
the numbering of the paths.
Fortunately, it turns out that we can order these paths in such a way that
the paths $\mathsf{Path}(\mathcal{Q}, 1), \mathsf{Path}(\mathcal{Q}, 2), \dots, \mathsf{Path}(\mathcal{Q}, \ell)$ are also sorted
in a meaningful way.
This is formalized by the following definition:
\begin{definition}
\label{order-def}
In a cage $\mathcal{C} = \mathsf{Cage}((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q})$ of order $\ell$ in a graph $G$
embedded in the plane, where $\mathcal{P} = \mathsf{Tree}(P_1, \dots, P_\ell)$,
$\mathcal{Q} = \mathsf{Tree}(Q_1, \dots, Q_\ell)$,
an \textbf{order} is a permutation $\sigma = (\sigma_1, \sigma_2, \dots, \sigma_\ell)$ of
$\{1, 2, \dots, \ell\}$ such that:
\begin{itemize}
\item the first edges on paths $P_{\sigma_1}, P_{\sigma_2}, \dots, P_{\sigma_\ell}$
are ordered anti-clockwise around $\mathsf{Root}(\mathcal{P})$ in the embedding of $G$ in the plane, and
\item for each vertex $v \in V(\mathcal{Q})$, there exist two indices $L, R$
($1 \leq L \leq R \leq \ell$) such that
$v$ lies on paths $Q_{\sigma_L}, Q_{\sigma_{L+1}}, \dots, Q_{\sigma_R}$ and on no other path
$Q_i$.
\end{itemize}
\end{definition}
For instance, the cage in Figure \ref{splitting-sample-fig} has an order; permutations
$\sigma = (1, 4, 5, 2, 3)$ and $\sigma = (5, 2, 3, 1, 4)$ are example orders.
However, not all cyclic shifts of $(1, 4, 5, 2, 3)$ are correct orders --- for instance,
$\sigma = (4, 5, 2, 3, 1)$ is \emph{not} an order because the vertex marked $x$ in
Figure \ref{splitting-sample-fig} would belong to paths $P_{\sigma_1}$ and $P_{\sigma_5}$
and no other paths.
Using Definition \ref{order-def}, we can naturally refine the definition of a cage.
\begin{definition}
\label{ordered-cage-def}
An \textbf{ordered cage} of order $\ell$ in a graph $G$ embedded in the plane
is a cage together with its order $\sigma$.
We denote this structure as
$$ \mathsf{OrderedCage}((a_1, \dots, a_\ell), (b_1, \dots, b_\ell), \mathcal{P}, \mathcal{Q}, \sigma). $$
\end{definition}
We are now ready to present a lemma which allows us to turn each cage into an ordered cage:
\begin{lemma}
\label{order-lemma}
Each cage in a graph $G$ embedded in the plane has an order.
\begin{proof}
Fix a cage $\mathcal{C} = ((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q})$ in $G$.
We let $\mathcal{P} = \mathsf{Tree}(P_1, \dots, P_\ell)$, $\mathcal{Q} = \mathsf{Tree}(Q_1, \dots, Q_\ell)$,
$p = \mathsf{Root}(\mathcal{P})$, $q = \mathsf{Root}(\mathcal{Q})$.
If $\ell = 1$, the lemma is trivial.
From now on, we assume that $\ell \geq 2$.
Consider a permutation $\mu^1 = (\mu^1_1, \mu^1_2, \dots, \mu^1_\ell)$ of
$\{1, 2, \dots, \ell\}$ for which the first edges on paths $P_{\mu^1_1}, P_{\mu^1_2}, \dots,
P_{\mu^1_\ell}$ are ordered anti-clockwise around $p$.
We also consider all cyclic shifts of $\mu^1$ --- for each $k \in [1, \ell]$, we define
$\mu^k = (\mu^k_1, \mu^k_2, \dots, \mu^k_\ell)$ as follows:
$$ \mu^k = (\mu^1_k, \mu^1_{k+1}, \dots, \mu^1_\ell, \mu^1_1, \mu^1_2, \dots, \mu^1_{k-1}). $$
Clearly, for each $k \in [1, \ell]$, the first edges on the paths
$P_{\mu^k_1}, P_{\mu^k_2}, \dots, P_{\mu^k_\ell}$ are ordered anti-clockwise around $p$.
We will prove that at least one of the permutations $\mu^1, \mu^2, \dots, \mu^\ell$ is an order.
We begin by taking a vertex $v \in V(\mathcal{Q})$ and describing the set
of paths $Q_i$ containing $v$.
\begin{claim}
\label{order-lemma-claim-no-interleave}
For every $v \in V(\mathcal{Q})$,
no cyclic shift $\mu^k$ ($k \in [1,\ell]$) of $\mu^1$ contains four distinct indices
$\mu^k_x, \mu^k_y, \mu^k_z, \mu^k_t$ ($1 \leq x < y < z < t \leq \ell$) such that
$$ v \in Q_{\mu^k_x}, \quad v\not\in Q_{\mu^k_y}, \quad v \in Q_{\mu^k_z}, \quad
v \not\in Q_{\mu^k_t}. $$
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
For the sake of contradiction let us pick a vertex $v \in V(\mathcal{Q})$, an index $k \in [1, \ell]$,
and indices $1 \leq x < y < z < t \leq \ell$ for which the conditions above hold.
We simplify the notation by setting $\ddot{x} = \mu^k_x$, $\ddot{y} = \mu^k_y$,
$\ddot{z} = \mu^k_z$, $\ddot{t} = \mu^k_t$ (Figure \ref{no-interleave-claim-fig}(a)).
We first remark that since $q$ is the root of $\mathcal{Q}$, it belongs to all paths $Q_i$.
Therefore, we must have that $v \neq q$.
\begin{figure}
\centering
\begin{minipage}[b]{0.33\textwidth}
\centering
\input{figures/ordering-a.tex}
(a)
\end{minipage}\begin{minipage}[b]{0.33\textwidth}
\centering
\input{figures/ordering-b.tex}
(b)
\end{minipage}\begin{minipage}[b]{0.33\textwidth}
\centering
\input{figures/ordering-c.tex}
(c)
\end{minipage}
\caption{(a) --- the setup in the proof of Claim \ref{order-lemma-claim-no-interleave}. \\
(b) --- the edges added in $G'$ (green). \\
(c) --- sets {$\color{green!70!white}A_1$},
{$\color{cyan!90!white}A_2$},
{$\color{pink!90!black}A_3$},
{$\color{brown!90!black}A_4$},
{$\color{violet!80!white}A_5$}
of vertices used in locating the $K_5$ clique as a minor of $G'$. }
\label{no-interleave-claim-fig}
\end{figure}
We will create another planar graph $G'$ which is a version of $G$ with some edges added
and some edges removed.
Let $f_{\ddot{x}}$, $f_{\ddot{y}}$, $f_{\ddot{z}}$, $f_{\ddot{t}}$ be the second
vertices on each of the paths $P_{\ddot{x}}$, $P_{\ddot{y}}$,
$P_{\ddot{z}}$, and $P_{\ddot{t}}$, respectively --- that is, the vertices immediately
following $p$ on the corresponding paths.
We create a graph $G'$ from $G$ with the same set of vertices and the same
embedding in the plane, but with the following
modifications (Figure \ref{no-interleave-claim-fig}(b)):
\begin{itemize}
\item We disconnect $p$ (the root of $\mathcal{P}$) from all its neighbors apart
from $f_{\ddot{x}}$, $f_{\ddot{y}}$, $f_{\ddot{z}}$, $f_{\ddot{t}}$.
\item We add the following edges to $G'$: $f_{\ddot{x}}f_{\ddot{y}}$,
$f_{\ddot{y}}f_{\ddot{z}}$, $f_{\ddot{z}}f_{\ddot{t}}$, and
$f_{\ddot{t}}f_{\ddot{x}}$.
\end{itemize}
Removing edges from the graph does not spoil its planarity.
Afterwards, four edges are inserted to $G'$.
In this graph, the anti-clockwise cyclic order of all edges incident to $p$ is
$pf_{\ddot{x}}, pf_{\ddot{y}}, pf_{\ddot{z}}, pf_{\ddot{t}}$.
Each new edge $f_if_j$ connects a neighbor of $p$ with its next neighbor
in this cyclic order.
In order to preserve the planarity of $G'$, we draw an edge $f_if_j$ so that
the triangle created by oriented edges $f_if_j$, $f_jp$, $pf_i$ is oriented anti-clockwise,
and $f_if_j$ lies very close to edges $pf_i$ and $pf_j$ in the embedding
(Figure \ref{no-interleave-claim-fig}(b)).
Since $p$ has only four neighbors in $G'$, we can draw each edge without breaking
the planarity of the embedding of $G'$.
\vspace{0.5em}
We will now find the clique $K_5$ as a minor of $G'$.
We define five subgraphs of $G'$, induced by the following sets of vertices
(Figure \ref{no-interleave-claim-fig}(c)):
\begin{equation*}
\begin{split}
A_1 &= \{p\}, \\
A_2 &= \mathsf{SPath}(\mathcal{C}, \ddot{x})[f_{\ddot{x}}, v], \\
A_3 &= \mathsf{SPath}(\mathcal{C}, \ddot{y})[f_{\ddot{y}}, q], \\
A_4 &= \mathsf{SPath}(\mathcal{C}, \ddot{z})[f_{\ddot{z}}, v]\ \setminus\ A_2, \\
A_5 &= \mathsf{SPath}(\mathcal{C}, \ddot{t})[f_{\ddot{t}}, q]\ \setminus\ A_3. \\
\end{split}
\end{equation*}
Since $v \in Q_{\ddot{x}}$ and $v \in Q_{\ddot{z}}$,
Lemma \ref{two-splitting-paths-lemma} asserts that
$v \in \mathsf{SPath}(\mathcal{C}, \ddot{x})$ and $v \in \mathsf{SPath}(\mathcal{C}, \ddot{z})$.
It is also obvious that all other ends of paths in the definitions of $A_2, A_3, A_4, A_5$
belong to the respective paths.
Hence, the sets above are defined correctly.
These sets are also non-empty since
$$ p \in A_1,\ \ f_{\ddot{x}} \in A_2,\ \ f_{\ddot{y}} \in A_3,\ \ f_{\ddot{z}} \in A_4,\ \
f_{\ddot{t}} \in A_5. $$
We now prove that each of the induced subgraphs $G'[A_1], G'[A_2], G'[A_3], G'[A_4], G'[A_5]$
is connected.
This fact is obvious for $A_1$, $A_2$, and $A_3$.
For $A_4$, we need to observe that because of Lemma \ref{splitting-path-intersection},
paths $\mathsf{SPath}(\mathcal{C}, \ddot{x})$ and $\mathsf{SPath}(\mathcal{C}, \ddot{z})$
intersect exactly at $p$ and their common suffix.
Therefore, removing $A_2$ from $\mathsf{SPath}(\mathcal{C}, \ddot{z})[f_{\ddot{z}}, v]$
erases a suffix from the path, and leaves a subpath as a result.
An analogous argument applies to $A_5$.
Therefore, each of the subgraphs is connected.
\vspace{0.5em}
We can also prove the pairwise disjointness of $A_1, \dots, A_5$.
Obviously, $A_1$ is disjoint with all the remaining sets $A_2, A_3, A_4, A_5$.
Also, $A_2$ is disjoint with $A_4$ by the definition of $A_4$,
and $A_3$ is disjoint with $A_5$ by the definition of $A_5$.
Now, take any indices $i \in \{\ddot{x}, \ddot{z}\}$, $j \in \{\ddot{y}, \ddot{t}\}$, and let us prove
that paths $\mathsf{SPath}(\mathcal{C}, i)[f_i, v]$ and $\mathsf{SPath}(\mathcal{C}, j)[f_j, q]$
are vertex-disjoint.
By Lemma \ref{splitting-path-intersection} we have that
\begin{equation}
\label{k5-spath-intersection-eq}
\mathsf{SPath}(\mathcal{C}, i) \cap \mathsf{SPath}(\mathcal{C}, j) = \{p\} \cup \mathsf{SPath}(\mathcal{C}, i)[\lca_\mathcal{Q}(a_i, a_j), q]
\end{equation}
(where $\mathsf{SPath}(\mathcal{C}, i)[\lca_\mathcal{Q}(a_i, a_j), q]$ is the common suffix of $\mathsf{SPath}(\mathcal{C}, i)$ and
$\mathsf{SPath}(\mathcal{C}, j)$).
Naturally, $p \not\in \mathsf{SPath}(\mathcal{C}, i)[f_i, v]$.
Moreover, since $v \not\in Q_j$, we infer that
$v \not\in \mathsf{SPath}(\mathcal{C}, i)[\lca_\mathcal{Q}(a_i, a_j), q]$,
so $\mathsf{SPath}(\mathcal{C}, i)[f_i, v]$ is also disjoint with
$\mathsf{SPath}(\mathcal{C}, i)[\lca_\mathcal{Q}(a_i, a_j), q]$.
Hence, by \ref{k5-spath-intersection-eq}, $\mathsf{SPath}(\mathcal{C}, i)[f_i, v]$ is disjoint with
$\mathsf{SPath}(\mathcal{C}, j)$ as well.
This means that we proved the vertex-disjointness of each pair of sets $A_1, \dots, A_5$.
\vspace{0.5em}
We are left to see that there is an edge between each pair of sets:
\begin{itemize}
\item There is a direct edge $pf_{\ddot{x}}$ connecting sets $A_1$ and $A_2$;
we analogously show edges connecting $A_1$ with each remaining set.
\item There is a direct edge $f_{\ddot{x}}f_{\ddot{y}}$ connecting sets $A_2$ and $A_3$;
we analogously show edges connecting $A_3$ with $A_4$, $A_4$ with $A_5$,
and $A_5$ with $A_2$.
\item Since the sets $A_2 = \mathsf{SPath}(\mathcal{C}, \ddot{x})[f_{\ddot{x}}, v]$ and
$\mathsf{SPath}(\mathcal{C}, \ddot{z})[f_{\ddot{z}}, v]$ induce connected graphs and
have a non-empty intersection, then
naturally $A_4 = \mathsf{SPath}(\mathcal{C}, \ddot{z})[f_{\ddot{z}}, v] \setminus A_2$ is connected
by an edge with $A_2$.
We analogously show that $A_3$ and $A_5$ are connected by an edge.
\end{itemize}
\vspace{0.5em}
Summing everything up, we created a modified planar graph $G'$ and indicated
five non-empty connected subgraphs such that each pair of subgraphs is vertex-disjoint,
yet there exist edges connecting each pair of subgraphs.
Therefore, $G'$ contains $K_5$ as a minor and hence --- by Wagner's theorem
\cite{agnarsson2007graph} --- it cannot be planar.
The contradiction concludes the proof of the claim.
\end{claimproof}
\end{claim}
As a direct consequence of Claim \ref{order-lemma-claim-no-interleave},
we can see that no cyclic shift $\mu^k$ of $\mu^1$ can contain four direct indices
$\mu^k_x, \mu^k_y, \mu^k_z, \mu^k_t$ (defined as in Claim
\ref{order-lemma-claim-no-interleave}) such that
$$ v \not\in Q_{\mu^k_x}, \quad v\in Q_{\mu^k_y}, \quad v \not\in Q_{\mu^k_z}, \quad
v \in Q_{\mu^k_t}. $$
If this set of conditions was true, we could consider the cyclic shift of $\mu^k$
with $\mu^k_y$ at the first position.
We can easily see that this cyclic shift would be contradictory with
Claim \ref{order-lemma-claim-no-interleave}.
\vspace{1em}
For a vertex $v \in V(\mathcal{Q})$ and integer $k \in [1, \ell]$,
we set $\mathcal{K}^k_v := \{i \in [1, \ell]\, \mid\,
v \in Q_{\mu^k_i}\}$; in other words, $\mathcal{K}^k_v$ is the set of positions $i$
in the permutation $\mu^k$ for which the corresponding path $Q_{\mu_i^k}$
contains $v$ as a vertex.
Note that for every $k_1, k_2 \in [1, \ell]$ and every vertex $v \in V(\mathcal{Q})$,
set $\mathcal{K}^{k_1}_v$ is a cyclic shift of $\mathcal{K}^{k_2}_v$; this is because the permutations
$\mu^{k_1}$ and $\mu^{k_2}$ are also mutual cyclic shifts.
\begin{claim}
\label{order-lemma-cyclic-interval}
Each set $\mathcal{K}^k_v$ is a cyclic interval in $[1, \ell]$; that is, it is either an interval or
a set of the form $[x, \ell] \cup [1, y]$ for some $x > y$.
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
Fix a vertex $v \in V(\mathcal{Q})$, integer $k \in [1, \ell]$,
and the corresponding set $\mathcal{K}^k_v$.
Assume that $\mathcal{K}^k_v$ is not a (non-cyclic) interval in $[1, \ell]$.
In this setup, there must exist
three indices $x, y, z$ ($1 \leq x < y < z \leq \ell$) for which
$x \in \mathcal{K}^k_v$, $y \not\in \mathcal{K}^k_v$, and $z \in \mathcal{K}^k_v$.
Without loss of generality, we can assume that $[x+1, z-1]$ is disjoint with $\mathcal{K}^k_v$.
Note that there cannot exist an index $t > z$ such that $t \not\in \mathcal{K}^k_v$ as this would
directly contradict Claim \ref{order-lemma-claim-no-interleave}.
Therefore, we have $[z, \ell] \subseteq \mathcal{K}^k_v$.
Also, there cannot exist an index $t < x$ such that $t \not\in \mathcal{K}^k_v$ as this would
pose a contradiction with the direct consequence of Claim
\ref{order-lemma-claim-no-interleave}.
Thus, we have $[1, x] \subseteq \mathcal{K}^k_v$.
Since $[1,x] \subseteq \mathcal{K}^k_v$, $[x+1, z-1] \cap \mathcal{K}^k_v = \varnothing$, and
$[z, \ell] \subseteq \mathcal{K}^k_v$, we have that $\mathcal{K}^k_v = [1, x] \cup [z, \ell]$.
\end{claimproof}
\end{claim}
In order to complete our proof, we also need to know how the cyclic intervals
$\mathcal{K}^k_v$ interact with each other.
It turns out that these intervals form a laminar family:
\begin{claim}
\label{order-lemma-laminar-family}
For any two vertices $u, v \in V(\mathcal{Q})$ and $k \in [1, \ell]$, the sets $\mathcal{K}^k_u$ and
$\mathcal{K}^k_v$ are either disjoint, or one of them is a subset of the other.
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
We remark that for $v \in V(\mathcal{Q})$, we have the following equivalent definition
of $\mathcal{K}^k_v$:
$$ \mathcal{K}^k_v = \{i \in [1, \ell]\, \mid\, a_{\mu^k_i}\text{ is in the subtree of }
\mathcal{Q}\text{ rooted at }v\}. $$
This is true since the path $Q_{\mu^k_i}$ in the original definition of $\mathcal{K}^k_v$
originates at $\mathsf{Root}(\mathcal{Q})$ and terminates at $a_{\mu^k_i}$ (a leaf in $\mathcal{Q}$).
Hence, $v$ belongs to this path if and only if its endpoint --- $a_{\mu^k_i}$ ---
is in the subtree rooted at $v$.
It is however well-known that the family of sets of leaves in every rooted tree $T$, where each
set corresponds to a subset of leaves in a rooted subtree of $T$, is laminar.
The proof of the claim follows.
\end{claimproof}
\end{claim}
Having proved all the necessary observations, we can find the cyclic shift $\mu^k$ of $\mu^1$
which forms an order in the embedding of the graph.
Fix any vertex $v^* \in V(\mathcal{Q})$ for which the cyclic interval $\mathcal{K}^1_{v^*}$
is not equal to $[1, \ell]$, but otherwise contains the largest number of indices.
Such a vertex exists since $\ell \geq 2$, so the leaves in $\mathcal{Q}$ do not cover the whole interval
$[1, \ell]$.
We now take the cyclic shift $\mu^k$ for which $\mathcal{K}^k_{v^*}$ is a prefix of $[1, \ell]$;
this is possible since $\mathcal{K}_{v^*}$ is a cyclic interval in $\mu^1$.
\begin{claim}
\label{order-lemma-found-claim}
$\mu^k$ is an order in $\mathcal{C}$.
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
Let $M$ be an integer such that $\mathcal{K}^k_{v^*} = [1, M]$.
We will now prove that $\mu^k$ is an order.
Firstly, since $\mu^k$ is a cyclic shift of $\mu^1$, the first edges on the paths
$P_{\mu^k_1}, P_{\mu^k_2}, \dots, P_{\mu^k_\ell}$ form an anti-clockwise order
around $p$.
In order to comply with Definition \ref{order-def},
we still need to prove that for each vertex $v \in V(\mathcal{Q})$, there exist two indices $L, R$
($1 \leq L \leq R \leq \ell$) such that $v$ lies exactly on paths
$Q_{\mu^k_L}, Q_{\mu^k_{L+1}}, \dots, Q_{\mu^k_R}$.
Fix a vertex $v \in \mathcal{Q}$.
Note that $\mathcal{K}^k_v$ is a cyclic interval (Claim \ref{order-lemma-cyclic-interval}).
If $\mathcal{K}^k_v = [1, \ell]$, then the proposition we are proving is trivial.
On the other hand, assume that $\mathcal{K}_v \neq [1, \ell]$.
From our assumptions, we have that $|\mathcal{K}^1_v| \leq |\mathcal{K}^1_{v^*}|$, so
also $|\mathcal{K}^k_v| \leq |\mathcal{K}^k_{v^*}|$.
From Claim \ref{order-lemma-laminar-family}, we get that $\mathcal{K}^k_v$ is either disjoint
or fully contained within $\mathcal{K}^k_{v^*}$; it cannot contain $\mathcal{K}^k_{v^*}$ strictly due to
$|\mathcal{K}^k_v| \leq |\mathcal{K}^k_{v^*}|$.
Recall that $\mathcal{K}^k_{v^*} = [1, M]$.
If $\mathcal{K}^k_v$ is disjoint with $\mathcal{K}^k_{v^*}$, then $\mathcal{K}^k_v \subseteq [M+1, \ell]$,
and $\mathcal{K}^k_v$ is a non-cyclic interval.
If $\mathcal{K}^k_v$ is fully contained within $\mathcal{K}^k_{v^*}$, then $\mathcal{K}^k_v \subseteq [1, M]$,
and again $\mathcal{K}^k_v$ is a non-cyclic interval.
Hence, every $v \in V(\mathcal{Q})$ can be assigned a subinterval $
\mathcal{K}^k_v = [L, R] \subseteq [1, \ell]$
such that $v$ lies exactly on paths $Q_{\mu^k_L}, Q_{\mu^k_{L+1}}, \dots, Q_{\mu^k_R}$.
This finishes the proof that $\mu^k$ is an order.
\end{claimproof}
\end{claim}
Claim \ref{order-lemma-found-claim} finishes the proof of the lemma.
\end{proof}
\end{lemma}
While it is possible to proceed to the next parts of the proof
using ordered cages, the fact that we need to use
two different orderings --- one imposed by the semi-ladder, and one imposed by
the order $\sigma$ in the ordered cage --- will be excessively unwieldy.
In order to remedy this inconvenience, we will introduce a~variant of ordered cages unifying
both orderings.
This variant will lead us to a slightly weaker upper bound on the maximum semi-ladder size,
though the bound will still remain asymptotically the same.
\begin{definition}
An \textbf{identity ordered cage} of order $\ell$ is an ordered cage
$$\textsf{OrderedCage}(\allowbreak(a_1, \dots, a_\ell), (b_1, \dots, b_\ell), \mathcal{P}, \mathcal{Q}, \sigma)\ \ \text{where }\sigma = (1, 2, \dots, \ell)\text{ is the identity permutation.}$$
\noindent We denote this structure as
$$ \textsf{IdOrderedCage}((a_1, \dots, a_\ell), (b_1, \dots, b_\ell), \mathcal{P}, \mathcal{Q}). $$
\end{definition}
We immediately follow with a proof that large identity ordered cages exist in planar graphs
given that large ordered cages exist.
We, however, remark that the proof might alter the embedding of a graph in the plane.
\begin{lemma}
\label{identity-ordered-cage-exists}
If a graph $G$ embedded in the plane contains an ordered cage of order $(\ell - 1)^2 + 1$
for $\ell \geq 1$,
then there exists an embedding of $G$ in the plane in which $G$ contains an
identity ordered cage of order $\ell$.
\begin{proof}
Take any graph $G$ with an ordered cage $\mathcal{C}$ of order $(\ell-1)^2 + 1$:
$$\mathcal{C} = \mathsf{OrderedCage}((a_i)_{i=1}^{(\ell-1)^2+1},
(b_i)_{i=1}^{(\ell-1)^2+1}, \mathcal{P}, \mathcal{Q}, \sigma).$$
By Erd\H{o}s-Szekeres Theorem \cite{10.1007/978-1-4612-0801-3_9},
$\sigma$ contains either an increasing subsequence
of length $\ell$, or a decreasing subsequence of length $\ell$.
If $\sigma$ contains an increasing subsequence $\sigma_{\mathrm{inc}}$ of length $\ell$,
then a subset of $\mathcal{C}$ with indices $\sigma_{\mathrm{inc}}$
is an identity ordered cage of order $\ell$ in $G$ with the original embedding in the plane.
Assume now that $\sigma$ contains a decreasing subsequence $\sigma_{\mathrm{dec}}$
of length $\ell$.
In this case, we modify the embedding of $G$ in the plane by reflecting it through
any line in the Euclidean plane.
Since in the original embedding, the first edges on paths $P_{\sigma_1}, P_{\sigma_2}, \dots,
P_{\sigma_{(\ell-1)^2+1}}$ were ordered anti-clockwise around $\mathsf{Root}(\mathcal{P})$,
these edges are ordered clockwise in the reflected embedding.
Hence, the reversed permutation $\sigma^{\rev} =
(\sigma_{(\ell-1)^2 + 1}, \sigma_{(\ell-1)^2}, \dots, \sigma_1)$ is an order in the
modified embedding, since
the first edges on paths $P_{\sigma_{(\ell-1)^2+1}}, P_{\sigma_{(\ell-1)^2}}, \dots, P_{\sigma_1}$
are ordered anti-clockwise in the altered embedding.
The remaining condition in Definition \ref{ordered-cage-def} can be verified in a
straightforward way.
Now, we notice that $\sigma_{\mathrm{dec}}^{\rev}$ (the reversed subsequence
$\sigma_{\mathrm{dec}}$) is an increasing subsequence in the newly formed order
$\sigma^{\rev}$.
Hence, the subset of $\mathcal{C}$ indicated by $\sigma_{\mathrm{dec}}^{\rev}$
in the transformed embedding is an identity ordered cage.
\end{proof}
\end{lemma}
An example identity ordered cage is depicted in Figure \ref{figure-neighbor-areas}(a).
In identity ordered cages, the following useful fact holds:
\begin{lemma}
\label{lca-composition-lemma}
Fix an identity ordered cage $\mathsf{IdOrderedCage}((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q})$
in a graph $G$ and three indices $i, j, k$ ($1 \leq i < j < k \leq \ell$).
In the set $\{\lca_\mathcal{Q}(a_i, a_j), \lca_\mathcal{Q}(a_j, a_k)\}$,
one of the elements is equal to $\lca_\mathcal{Q}(a_i, a_k)$ and is an ancestor of
the other element in the set (it can be, in particular, equal to it).
\begin{proof}
Since both elements of the set $\{\lca_\mathcal{Q}(a_i, a_j), \lca_\mathcal{Q}(a_j, a_k)\}$
are the ancestors of $a_j$ in $\mathcal{Q}$, one of these elements is an ancestor of the other.
Without loss of generality, assume that $\lca_\mathcal{Q}(a_i, a_j)$ is an ancestor of the other
element of the set.
This means that $a_k$ is in the subtree rooted at $\lca_\mathcal{Q}(a_i, a_j)$.
As both $a_i$ and $a_k$ are in this subtree, we infer that $\lca_\mathcal{Q}(a_i, a_j)$ is an ancestor
of $\lca_\mathcal{Q}(a_i, a_k)$.
Since $\lca_\mathcal{Q}(a_i, a_k) \in Q_i$, $\lca_\mathcal{Q}(a_i, a_k) \in Q_k$, and $j \in [i, k]$,
by the definition of an identity ordered cage we also have $\lca_\mathcal{Q}(a_i, a_k) \in Q_j$.
Therefore, $\lca_\mathcal{Q}(a_i, a_k)$ is also an ancestor of $a_j$ in $\mathcal{Q}$.
Hence, $\lca_\mathcal{Q}(a_i, a_k)$ is an ancestor of $\lca_\mathcal{Q}(a_i, a_j)$.
We conclude that $\lca_\mathcal{Q}(a_i, a_j) = \lca_\mathcal{Q}(a_i, a_k)$.
\end{proof}
\end{lemma}
\subsection{Neighbor areas}
\label{neighbor-area-section}
Until now, we were concerned about the structure imposed only by
some vertices of the semi-ladder --- that is, the vertices $a_1, a_2, \dots, a_\ell$.
It is now time to include the corresponding vertices $b_1, b_2, \dots, b_\ell$ in the picture.
It turns out that each sufficiently large ordered cage contains a smaller ordered cage as a subset
in which for every $i$, the vertex $b_i$ is, in some topological sense, \emph{near} $a_i$.
This is where the upper bounds on the neighborhood complexity in planar graphs proved in Section
\ref{noose-profile-lemma-section}, will come into play.
First, we need to design technical tools allowing us to formalize this idea.
\begin{definition}
Let $\mathcal{C} = \mathsf{IdOrderedCage}((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q})$ be an identity ordered
cage of order $\ell$ in $G$.
For every two integers $i, j$ ($ 1\leq i < j \leq \ell$), we set $v_{i,j} = \lca_\mathcal{Q}(a_i, a_j)$.
Note that by Lemma \ref{splitting-path-intersection}, $v_{i,j}$ is the first vertex of the common
suffix of $\mathsf{SPath}(\mathcal{C}, i)$ and $\mathsf{SPath}(\mathcal{C}, j)$.
For these integers $i, j$,
we define the \textbf{neighbor area} $\mathsf{Area}(\mathcal{C}, i, j)$ as the closed
part of the plane whose boundary is traversed anti-clockwise by the following directed cycle:
$$ \mathsf{SPath}(\mathcal{C}, i)[\mathsf{Root}(\mathcal{P}), v_{i, j}] \cdot
(\mathsf{SPath}(\mathcal{C}, j))^{-1}[v_{i, j}, \mathsf{Root}(\mathcal{P})]. $$
\end{definition}
Note that neighbor areas are not necessarily bounded (Figure \ref{figure-neighbor-areas}).
\begin{figure}[h]
\centering
\begin{minipage}[b]{0.33\textwidth}
\centering
\input{figures/neighbor-area-a.tex}
(a)
\end{minipage}\begin{minipage}[b]{0.33\textwidth}
\centering
\input{figures/neighbor-area-b.tex}
(b)
\end{minipage}\begin{minipage}[b]{0.33\textwidth}
\centering
\input{figures/neighbor-area-c.tex}
(c)
\end{minipage}
\caption{(a) --- an example identity ordered cage $\mathcal{C}$ of order $8$ embedded in the plane. \\
(b) --- neighbor areas $\mathsf{Area}(\mathcal{C}, 1, 2)$ (green), $\mathsf{Area}(\mathcal{C}, 2, 4)$ (violet), and
$\mathsf{Area}(\mathcal{C}, 5, 8)$ (orange). \\
(c) --- an unbounded neighbor area $\mathsf{Area}(\mathcal{C}, 2, 7)$ (blue). The area is unbounded
since its boundary is traversed anti-clockwise first by $\mathsf{SPath}(\mathcal{C}, 2)$, and later
by $(\mathsf{SPath}(\mathcal{C}, 7))^{-1}$.}
\label{figure-neighbor-areas}
\end{figure}
We can easily see from Figure \ref{figure-neighbor-areas} that the union
of two neighbor areas $\mathsf{Area}(\mathcal{C}, 1, 2)$ and $\mathsf{Area}(\mathcal{C}, 2, 4)$ in the presented example is
$\mathsf{Area}(\mathcal{C}, 1, 4)$, and that the intersection of these is a prefix of $\mathsf{SPath}(\mathcal{C}, 2)$.
It turns out that this observation is satisfied in general:
\begin{lemma}
\label{area-sum-lemma}
In an identity ordered cage $\mathcal{C}$ of order $\ell$, for every indices $i, j, k$ such that
$1 \leq i < j < k \leq \ell$, we have that:
\begin{equation*}
\begin{split}
\mathsf{Area}(\mathcal{C}, i, j) \cup \mathsf{Area}(\mathcal{C}, j, k) &= \mathsf{Area}(\mathcal{C}, i, k), \\
\mathsf{Area}(\mathcal{C}, i, j) \cap \mathsf{Area}(\mathcal{C}, j, k) &= \partial\mathsf{Area}(\mathcal{C},i,j) \cap \partial\mathsf{Area}(\mathcal{C},j,k) \subseteq
\mathsf{SPath}(\mathcal{C}, j).
\end{split}
\end{equation*}
\begin{proof}
We first define vertices $v_{i, j} = \lca_\mathcal{Q}(a_i, a_j)$, $v_{j, k}=\lca_\mathcal{Q}(a_j, a_k)$
as in the definition of neighbor areas.
We also let $\mathcal{C} = \mathsf{IdOrderedCage}((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q})$,
$p := \mathsf{Root}(\mathcal{P})$, and $\mathcal{Q} = \mathsf{Tree}(Q_1, \dots, Q_\ell)$.
These definitions tell us that
\begin{equation*}
\begin{split}
\partial\mathsf{Area}(\mathcal{C}, i, j) &= \mathsf{SPath}(\mathcal{C}, i)[p, v_{i, j}] \cdot
(\mathsf{SPath}(\mathcal{C}, j))^{-1}[v_{i, j}, p], \\
\partial\mathsf{Area}(\mathcal{C}, j, k) &= \mathsf{SPath}(\mathcal{C}, j)[p, v_{j, k}] \cdot
(\mathsf{SPath}(\mathcal{C}, k))^{-1}[v_{j, k}, p].
\end{split}
\end{equation*}
Since $v_{i, j}$ and $v_{j, k}$ are both ancestors of $a_j$ in $\mathcal{Q}$, either of these is
an ancestor of the other (in particular, we might have $v_{i, j} = v_{j, k}$).
Without loss of generality, we assume that $v_{j, k}$ is an ancestor of $v_{i, j}$ in $\mathcal{Q}$
or equal to $v_{i, j}$ (Figure \ref{area-sum-layout-fig}).
Then, $\mathsf{SPath}(\mathcal{C}, j)[p, v_{i, j}] \subseteq \mathsf{SPath}(\mathcal{C}, j)[p, v_{j, k}]$.
Moreover, by Lemma \ref{lca-composition-lemma}, $v_{i,k} := \lca(a_i, a_k)$ is equal to $v_{j,k}$.
\begin{figure}[h]
\centering
\input{figures/area-sum-layout.tex}
\caption{The configuration assumed in Lemma \ref{area-sum-lemma}. The vertices
$v_{i,j}$ and $v_{j,k}$ may overlap. The blue area is $\mathsf{Area}(\mathcal{C}, i, j)$. The green area is
$\mathsf{Area}(\mathcal{C}, j, k)$. The brown path is $\mathsf{SPath}(\mathcal{C}, j)$.}
\label{area-sum-layout-fig}
\end{figure}
\vspace{0.5em}
We first note that $\partial\mathsf{Area}(\mathcal{C}, i, j) \cap \partial\mathsf{Area}(\mathcal{C}, j, k) \subseteq \mathsf{SPath}(\mathcal{C}, j)$;
this is because any intersection of both boundaries outside of $\mathsf{SPath}(\mathcal{C}, j)$ would
have to be an intersection of $\mathsf{SPath}(\mathcal{C}, i)$ with $\mathsf{SPath}(\mathcal{C}, k)$.
These paths intersect only at $p$ and $\mathsf{SPath}(\mathcal{C}, i)[v_{i, k}, q]$ (Lemma
\ref{splitting-path-intersection}).
However, $v_{i, k} = v_{j, k} \in \mathsf{SPath}(\mathcal{C}, j)$, so also $\mathsf{SPath}(\mathcal{C}, i)[v_{i, k}, q] \subseteq
\mathsf{SPath}(\mathcal{C}, j)$.
Obviously, $p \in \mathsf{SPath}(\mathcal{C}, j)$ as well.
Therefore, no intersection of $\partial\mathsf{Area}(\mathcal{C}, i, j)$ and $\partial\mathsf{Area}(\mathcal{C}, j, k)$ can occur
outside of $\mathsf{SPath}(\mathcal{C}, j)$.
Thanks to this fact, we can now compute $\partial\mathsf{Area}(\mathcal{C}, i, j) \cap \partial\mathsf{Area}(\mathcal{C}, j, k)$:
\begin{equation*}
\begin{split}
\partial\mathsf{Area}(\mathcal{C}, i, j) & \cap \partial\mathsf{Area}(\mathcal{C}, j, k) = \\
& = (\partial\mathsf{Area}(\mathcal{C}, i, j) \cap \mathsf{SPath}(\mathcal{C}, j)) \cap (\partial\mathsf{Area}(\mathcal{C}, j, k) \cap \mathsf{SPath}(\mathcal{C}, j))
= \\
& = \mathsf{SPath}(\mathcal{C}, j)[p, v_{i, j}] \cap \mathsf{SPath}(\mathcal{C}, j)[p, v_{j, k}] = \mathsf{SPath}(\mathcal{C}, j)[p, v_{i, j}]
\end{split}
\end{equation*}
--- that is, this intersection is a prefix of $\mathsf{SPath}(\mathcal{C}, j)$.
Therefore, the two boundaries intersect at exactly one segment.
We can use this information to prove that the interiors of $\mathsf{Area}(\mathcal{C}, i, j)$ and $\mathsf{Area}(\mathcal{C}, j, k)$
are disjoint.
Let us name $f_i, f_j, f_k$ as the second vertices on the paths $P_i, P_j, P_k$, respectively;
that is, the vertices immediately following $p = \mathsf{Root}(\mathcal{P})$ on the respective paths.
Since the counter-clockwise orientation of $\partial\mathsf{Area}(\mathcal{C}, i, j)$ contains
oriented edges $f_jp$ and $pf_i$ in this order,
and the counter-clockwise orientation of $\partial\mathsf{Area}(\mathcal{C}, j, k)$ contains
oriented edges $f_kp$ and $pf_j$ in this order,
we only need to verify the cyclic order of the edges $pf_i, pf_j, pf_k$ around vertex $p$.
These edges are ordered anti-clockwise around $p$ (by the definition of an ordered
cage), so the interiors of the areas $\mathsf{Area}(\mathcal{C}, i, j)$, $\mathsf{Area}(\mathcal{C}, j, k)$
are disjoint (Figure \ref{area-sum-layout-fig}).
From the considerations above, we conclude that
$$ \mathsf{Area}(\mathcal{C}, i, j) \cap \mathsf{Area}(\mathcal{C}, j, k) = \partial\mathsf{Area}(\mathcal{C}, i, j) \cap \partial \mathsf{Area}(\mathcal{C}, j, k)
\subseteq \mathsf{SPath}(\mathcal{C}, j). $$
Moreover, since the interiors of both neighbor areas are disjoint,
given the anti-clockwise orientations of $\partial\mathsf{Area}(\mathcal{C}, i, j)$ and
$\partial\mathsf{Area}(\mathcal{C}, j, k)$, both starting and finishing at their common vertex $p$,
we can compute the anti-clockwise orientation of $\partial[\mathsf{Area}(\mathcal{C}, i, j) \cup
\mathsf{Area}(\mathcal{C}, j, k)]$ by composing the anti-clockwise orientations of
$\partial\mathsf{Area}(\mathcal{C}, i, j)$ and $\partial\mathsf{Area}(\mathcal{C}, j, k)$:
\begin{equation*}
\begin{split}
& \partial[\mathsf{Area}(\mathcal{C}, i, j) \cup \mathsf{Area}(\mathcal{C}, j, k)] = \\
& = \mathsf{SPath}(\mathcal{C}, i)[p, v_{i, j}] \cdot (\mathsf{SPath}(\mathcal{C}, j))^{-1}[v_{i, j}, p] \cdot
\mathsf{SPath}(\mathcal{C}, j)[p, v_{j, k}] \cdot (\mathsf{SPath}(\mathcal{C}, k))^{-1}[v_{j, k}, p] = \\
& = \mathsf{SPath}(\mathcal{C}, i)[p, v_{i, j}] \cdot \mathsf{SPath}(\mathcal{C}, j)[v_{i, j}, v_{j, k}] \cdot
(\mathsf{SPath}(\mathcal{C}, k))^{-1}[v_{j, k}, p] \stackrel{(\star)}{=} \\
& \stackrel{(\star)}{=} \mathsf{SPath}(\mathcal{C}, i)[p, v_{i, j}] \cdot \mathsf{SPath}(\mathcal{C}, i)[v_{i, j}, v_{j, k}] \cdot
(\mathsf{SPath}(\mathcal{C}, k))^{-1}[v_{j, k}, p] = \\
& = \mathsf{SPath}(\mathcal{C}, i)[p, v_{j, k}] \cdot (\mathsf{SPath}(\mathcal{C}, k))^{-1}[v_{j, k}, p] = \\
& =
\mathsf{SPath}(\mathcal{C}, i)[p, v_{i, k}] \cdot (\mathsf{SPath}(\mathcal{C}, k))^{-1}[v_{i, k}, p] =
\partial\mathsf{Area}(\mathcal{C}, i, k).
\end{split}
\end{equation*}
In the equality $(\star)$, we use the definition of $v_{i, j}$ --- it is the first vertex
of the common suffix of $\mathsf{SPath}(\mathcal{C}, i)$ and $\mathsf{SPath}(\mathcal{C}, j)$.
Therefore, $\mathsf{Area}(\mathcal{C}, i, j) \cup \mathsf{Area}(\mathcal{C}, j, k) = \mathsf{Area}(\mathcal{C}, i, k)$.
\end{proof}
\end{lemma}
We can immediately infer the following fact from Lemma \ref{area-sum-lemma}:
\begin{corollary}
\label{area-int-lemma}
In any identity ordered cage $\mathcal{C}$ of order $\ell$, for every triple of indices $i, j, k$ such that
$1 \leq i < j < k \leq \ell$, we have that:
$$ \mathsf{Area}(\mathcal{C}, i, j) \cap \mathrm{Int}\,\mathsf{Area}(\mathcal{C}, j, k) = \varnothing,
\qquad \mathrm{Int}\,\mathsf{Area}(\mathcal{C}, i, j) \cap \mathsf{Area}(\mathcal{C}, j, k) = \varnothing. $$
\begin{proof}
Since areas $\mathsf{Area}(\mathcal{C}, i, j)$ and $\mathsf{Area}(\mathcal{C}, j, k)$ intersect only at their boundaries,
the interior of either neighbor area is disjoint with the other neighbor area.
\end{proof}
\end{corollary}
Now we will examine the importance of neighbor areas in identity ordered cages.
For an identity ordered cage $\mathcal{C}$ of order $\ell$ and two indices $i, j$ ($i < j$),
we can observe which vertices of the semi-ladder underlying $\mathcal{C}$:
$a_1, a_2, \dots, a_\ell, b_1, b_2, \dots, b_\ell$ belong to $\mathsf{Area}(\mathcal{C}, i, j)$,
and which do not.
It turns out that there cannot be too many pairs of vertices $(a_k, b_k)$ for $k \in [1, \ell]$
such that one vertex in the pair belongs to $\mathsf{Area}(\mathcal{C}, i, j)$ and the other does not.
For simplicity of the further part of the proof, we use the following definition:
\begin{definition}
\label{separated-from-def}
Fix a neighbor area $\mathsf{Area}(\mathcal{C}, i, j)$ in an identity ordered cage $\mathcal{C}$.
For a~pair of vertices $u, v$, if exactly one of them belongs to $\mathsf{Area}(\mathcal{C}, i, j)$,
we will say that $u$ \textbf{is separated from} $v$ by $\mathsf{Area}(\mathcal{C}, i, j)$.
\end{definition}
For instance, in Figure \ref{figure-neighbor-areas}, $a_5$ is separated from $a_3$ by
$\mathsf{Area}(\mathcal{C}, 2, 4)$, but $a_5$ is not separated from $a_7$ by the same neighbor area.
It turns out that the definition of ``being separated'' is connected in a non-trivial way
to the distinctness of distance-$d$ profiles.
This will allow us to employ the Noose Profile Lemma (Theorem \ref{noose-profile-lemma}),
which bounds the neighborhood complexity of nooses in planar graphs,
in order to limit the number of pairs
of the vertices of the semi-ladder separated by neighbor areas.
\begin{lemma}
\label{neighbor-separation-lemma}
In an identity ordered cage $\mathcal{C} = \mathsf{IdOrderedCage}((a_i)_{i=1}^\ell,
(b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q})$ of order~$\ell$, for every pair of indices $i, j$ ($1 \leq i < j \leq
\ell$), the neighbor area $\mathsf{Area}(\mathcal{C}, i, j)$ separates at most $128d^3(d+2)^4$ distinct pairs
of vertices $(a_k, b_k)$ for $k \in [1, \ell]$.
\begin{proof}
Fix two integers $i, j$ ($1 \leq i < j \leq \ell$) for the proof.
Denote the set of vertices on the boundary of $\mathsf{Area}(\mathcal{C}, i, j)$ as $B$.
\begin{claim}
\label{large-neighbor-small-noose}
$|B| \leq 4d$.
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
We first note that $|E(\mathsf{SPath}(\mathcal{C}, k))| \leq 2d$ for each $k \in [1, L]$ since
$\mathsf{SPath}(\mathcal{C}, k)$ is the concatenation of subpaths of two paths,
$\mathsf{Path}(\mathcal{P}, k)$ and $\mathsf{Path}(\mathcal{Q}, k)$, whose lengths do not exceed $d$.
The boundary of $\mathsf{Area}(\mathcal{C}, i, j)$ is a cycle and
consists of two prefixes of paths $\mathsf{SPath}(\mathcal{C}, i)$ and $\mathsf{SPath}(\mathcal{C}, j)$.
Therefore,
\[ |B| = |V(\partial \mathsf{Area}(\mathcal{C}, i, j))| = |E(\partial \mathsf{Area}(\mathcal{C}, i, j))| \leq
|E(\mathsf{SPath}(\mathcal{C}, i))| + |E(\mathsf{SPath}(\mathcal{C}, j))| \leq 4d. \]
\end{claimproof}
\end{claim}
Let $I$ denote the set of indices $k$ for which $a_k$ is separated from $b_k$ by
$\mathsf{Area}(\mathcal{C}, i, j)$; we need to prove that $|I| \leq 128d^3(d + 2)^4$.
For each $k \in I$, two cases are possible --- either $a_k$ belongs to $\mathsf{Area}(\mathcal{C}, i, j)$,
which implies that $b_k \not\in \mathsf{Area}(\mathcal{C}, i, j)$; or $a_k \not\in \mathsf{Area}(\mathcal{C}, i, j)$, which
implies that $b_k \in \mathsf{Area}(\mathcal{C}, i, j)$.
We will partition $I$ into two subsets --- $I_1$ and $I_2$ --- depending on which
case holds for a given $k$:
$$ I_1 = \{k \in I\, \mid\, a_k \in \mathsf{Area}(\mathcal{C}, i, j),\ b_k \not\in \mathsf{Area}(\mathcal{C}, i, j)\}, $$
$$ I_2 = \{k \in I\, \mid\, a_k \not\in \mathsf{Area}(\mathcal{C}, i, j),\ b_k \in \mathsf{Area}(\mathcal{C}, i, j)\}. $$
We will prove that both $I_1$ and $I_2$ contain no more than $64d^3(d + 2)^4$ indices;
the statement of the lemma will follow immediately.
\begin{claim}
\label{large-neighbor-distinct-profiles}
For any $t \in \{1, 2\}$ and two different indices $x, y \in I_t$,
vertices $a_x$ and $a_y$ have different distance-$d$ profiles on $B$.
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
Assume on the contrary that $a_x$ and $a_y$ have identical distance-$d$ profiles on $B$.
Without loss of generality, assume that $x < y$.
Because vertices $a_x, a_y, b_x, b_y$ form a distance-$d$ semi-ladder of order $2$,
it follows that
$$
\mathrm{dist}(a_y, b_x) \leq d, \quad\text{ but }\quad \mathrm{dist}(a_x, b_x) > d.
$$
\begin{figure}[h]
\centering
\input{figures/separating-profiles.tex}
\caption{The configuration in Claim \ref{large-neighbor-distinct-profiles}.}
\label{separating-profiles-fig}
\end{figure}
Since $x, y \in I_k$, we have that $a_y$ is separated from $b_x$ by $\mathsf{Area}(\mathcal{C}, i, j)$.
Therefore, the shortest path
between these two vertices must pass through a vertex of $\partial \mathsf{Area}(\mathcal{C}, i, j)$ ---
that is, some vertex $z \in B$ (Figure \ref{separating-profiles-fig}).
Thus,
$$
\mathrm{dist}(a_y, b_x) = \mathrm{dist}(a_y, z) + \mathrm{dist}(z, b_x).
$$
It follows that $\mathrm{dist}(a_y, z) \leq d$ and hence $\pi_d[a_y, B](z) = \mathrm{dist}(a_y, z)$.
Because distance-$d$ profiles of $a_y$ and $a_x$ on $B$ are equal, this implies that
$\pi_d[a_x, B](z) = \pi_d[a_y, B](z) = \mathrm{dist}(a_y, z)$.
Since also $\pi_d[a_x, B](z) \leq d$, we get that $\mathrm{dist}(a_x, z) = \pi_d[a_x, B](z) = \mathrm{dist}(a_y, z)$,
so the following inequality follows from the triangle inequality:
$$
\mathrm{dist}(a_x, b_x) \leq \mathrm{dist}(a_x, z) + \mathrm{dist}(z, b_x) = \mathrm{dist}(a_y, z) + \mathrm{dist}(z, b_x) = \mathrm{dist}(a_y, b_x)
\leq d
$$
--- a contradiction.
Therefore, $a_x$ and $a_y$ must have distinct distance-$d$ profiles on $B$.
\end{claimproof}
\end{claim}
A combination of both claims above provides us with a link between the notion of cages and
the Noose Profile Lemma.
Assume for contradiction that for an integer $t \in \{1, 2\}$, the set $I_t$ contains more than
$64 d^3 (d+2)^4$ elements.
By Claim \ref{large-neighbor-distinct-profiles}, we infer that
$\left|\{\pi_d[a_x, B]\, \mid\, x \in I_k\}\right| > 64 d^3 (d + 2)^4$.
We also remark that since $B$ is a cycle in $G$, there exists a noose $\mathcal{L}$ in the embedding
of $G$ in the plane passing through vertices in $B$ and no other vertices
($\mathcal{L}$ should closely follow the cycle $B$, passing through each vertex of $B$ in the
same order as $B$, but not touching the edges of the graph).
$\mathcal{L}$ is now subject to the Noose Profile Lemma.
We can see that either all vertices in $\{a_k\,\mid\, k \in I_t\}$ are enclosed by $\mathcal{L}$, or
none of them are enclosed by $\mathcal{L}$ (depending on the value of $t$ and whether
$\mathsf{Area}(\mathcal{C}, i, j)$ is bounded or unbounded).
If these vertices are all enclosed by $\mathcal{L}$, then Noose Profile Lemma (Theorem
\ref{noose-profile-lemma}) applies, so the number of different distance-$d$ profiles
seen from $\mathcal{L}$ is bounded from above by
$$ |B|^3 \cdot (d+2)^4 \leq (4d)^3 \cdot (d + 2)^4 = 64d^3 (d+2)^4 $$
--- a contradiction.
Analogously, if none of vertices in $\{a_k\,\mid\, k \in I_t\}$ are enclosed by $\mathcal{L}$,
then a variant of the Noose Profile Lemma (Corollary \ref{noose-profille-lemma-rev}) applies,
and we contradict our assumption in the same fashion.
Therefore, $|I_t| \leq 64d^3 (d+2)^4$.
Hence, $|I| = |I_1| + |I_2| \leq 128d^3 (d+2)^4$.
\end{proof}
\end{lemma}
We will also prove that in an identity ordered cage $\mathcal{C}$, for each $i \in [2, \ell - 1]$,
we can expect to find the vertex $a_i$ in the interior of the neighbor area $\mathsf{Area}(\mathcal{C},i-1,i+1)$
--- roughly speaking, ``near'' the path $\mathsf{SPath}(\mathcal{C}, i)$.
\begin{lemma}
\label{neighbor-cage-ai-good-lemma}
In an identity ordered cage $\mathcal{C} =
\mathsf{IdOrderedCage}((a_1, \dots, a_\ell), (b_1, \dots, b_\ell), \mathcal{P}, \mathcal{Q})$ in graph $G$,
for every $i \in [2, \ell - 1]$,
we have that $a_i \in \mathrm{Int}\, \mathsf{Area}(\mathcal{C}, i-1, i+1)$.
\begin{proof}
For the sake of contradiction assume that $a_i \not\in \mathrm{Int}\, \mathsf{Area}(\mathcal{C}, i-1, i+1)$.
For all $j \in [1, \ell]$, we choose $f_j$ as the second vertex on $\mathsf{Path}(\mathcal{P}, j)$ --- that is,
the vertex on this path immediately following $\mathsf{Root}(\mathcal{P})$.
We also let $p := \mathsf{Root}(\mathcal{P})$,
$\mathcal{P} = \mathsf{Tree}(P_1, \dots, P_\ell)$,
and $\mathcal{Q} = \mathsf{Tree}(Q_1, \dots, Q_\ell)$.
Since edges $pf_{i-1}, pf_i, pf_{i+1}$ are ordered anti-clockwise around $p$ (by the
definition of an ordered cage), and because the boundary of $\mathsf{Area}(\mathcal{C}, i-1, i+1)$,
when ordered anti-clockwise, contains edges $f_{i+1}p$ and $pf_{i-1}$ in this order,
we have that $pf_i \subseteq \mathsf{Area}(\mathcal{C}, i-1, i+1)$ (Figure~\ref{ai-acw-ordering-fig}).
Thus, $f_i \in \mathsf{Area}(\mathcal{C}, i-1, i+1)$.
Since $a_i \not\in \mathrm{Int}\, \mathsf{Area}(\mathcal{C}, i-1, i+1)$, the path $P_i[f_i, a_i]$ must intersect
$\partial\mathsf{Area}(\mathcal{C}, i-1, i+1)$.
\begin{figure}[h]
\centering
\input{figures/ai-acw-ordering.tex}
\caption{A simple geodesic tree $\mathcal{P}$ (a part of the identity ordered cage $\mathcal{C}$)
with important vertices in Lemma \ref{neighbor-cage-ai-good-lemma}.
$\mathsf{Area}(\mathcal{C}, i-1, i+1)$ is shaded.}
\label{ai-acw-ordering-fig}
\end{figure}
By the definition of neighbor areas, $\partial\mathsf{Area}(\mathcal{C}, i-1, i+1) \subseteq
P_{i-1} \cup P_{i+1} \cup Q_{i-1} \cup Q_{i+1}$.
However, $P_i[f_i, a_i]$ is vertex-disjoint with $P_j$ for each $j \neq i$ (since
by the definition of a quasi-cage, paths $P_i$ and $P_j$ are vertex-disjoint apart
from $p$).
Similarly, $P_i$ is vertex-disjoint with $Q_j$ for each $j \neq i$ (by the
definition of a cage).
Hence, $P_i[f_i, a_i]$ is vertex-disjoint with $\partial\mathsf{Area}(\mathcal{C}, i-1, i+1)$ --- a contradiction.
\end{proof}
\end{lemma}
\subsection{Neighbor cages}
\label{neighbor-cages-section}
We are now ready to use the tools developed in Section \ref{neighbor-area-section}
to define neighbor cages and explore their properties.
\begin{definition}
\label{neighbor-cage-def}
An identity ordered cage $\mathcal{C} = \mathsf{IdOrderedCage}((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q})$
of order $\ell$ is also a \textbf{neighbor cage}
if for each index $i \in \{2, 3, \dots, \ell - 1\}$, the vertex $b_i$ belongs to
$\mathsf{Area}(\mathcal{C}, i - 1, i + 1)$.
We denote neighbor cages in the following way:
$$ \mathsf{NeighborCage}((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q}). $$
\end{definition}
Figure \ref{neighbor-examples-fig} shows an example of a neighbor cage.
Unnecessary parts of the graph (including the edges connecting the vertices $b_i$
with the remaining part of the graph) have been omitted.
\begin{figure}[h]
\centering
\begin{minipage}[b]{0.33\textwidth}
\centering
\input{figures/neighbor-a.tex}
(a)
\end{minipage}\begin{minipage}[b]{0.33\textwidth}
\centering
\input{figures/neighbor-b.tex}
(b)
\end{minipage}\begin{minipage}[b]{0.33\textwidth}
\centering
\input{figures/neighbor-c.tex}
(c)
\end{minipage}
\caption{(a) --- An example neighbor cage of order $5$, with edges connecting
$b_1, \dots, b_5$ with the remaining part of the graph removed. Note that $b_1$ and $b_5$ may
be anywhere in the graph. \\
(b) --- The neighbor area which must contain $b_2$ is shaded. \\
(c) --- The neighbor area which must contain $b_3$ is shaded.}
\label{neighbor-examples-fig}
\end{figure}
We will now employ the toolchain we have developed to prove that large identity ordered cages
contain large neighbor cages as subsets.
\begin{lemma}
\label{large-neighbor-lemma}
Each identity ordered cage of order $[256d^3(d+2)^4 + 2] \ell + 2$ contains a neighbor cage
of order $\ell$ as a subset.
\begin{proof}
Let $L := [256d^3(d+2)^4 + 1] \ell + 2$,
and fix an identity ordered cage of order $L$:
$$\mathcal{C} = \mathsf{IdOrderedCage}((a_i)_{i=1}^L, (b_i)_{i=1}^L, \mathcal{P}, \mathcal{Q}).$$
We build a permutation $\pi$ of vertices of the semi-ladder $\{a_1, a_2, \dots, a_L,
b_1, b_2, \dots, b_L\}$ in the following way:
\begin{itemize}
\item $\pi$ contains vertices $a_1, a_2, \dots, a_L$ in this order; immediately after each $a_i$
(for $i \in [1, L]$), we add a (possibly empty) sequence $\Gamma_i$ which is a
permuted subset of $\{b_1, b_2, \dots, b_L\}$. That is,
$$ \pi = (a_1) \cdot \Gamma_1 \cdot (a_2) \cdot \Gamma_2 \cdot \dots \cdot (a_L) \cdot
\Gamma_L, $$
where $\cdot$ denotes the concatenation of sequences.
\item For each index $i \in [1, L - 1]$, $\Gamma_i$ contains those vertices $b_1, \dots, b_L$
which belong to $\mathsf{Area}(\mathcal{C}, i, i+1)$,
but do not belong to any previous sequence $\Gamma_1, \dots, \Gamma_{i-1}$.
Formally, the set of vertices in $\Gamma_i$ is
$$ \left[\{b_1, b_2, \dots, b_L\} \cap \mathsf{Area}(\mathcal{C}, i, i+1)\right] \setminus (\Gamma_1 \cup
\dots \cup \Gamma_{i-1}). $$
\item $\Gamma_L$ contains all vertices in $\{b_1, b_2, \dots, b_L\}$ which do not belong
to any previous sequence $\Gamma_1, \dots, \Gamma_{L-1}$.
\item Each sequence $\Gamma_i$ (for $i \in [1, L]$) is ordered arbitrarily.
\end{itemize}
It can be clearly seen that the procedure above produces a permutation $\pi$.
\vspace{1em}
We will now find a large subsequence of $\pi$ with the following property:
if $a_i$ belongs to the subsequence for some $i \in [1,L]$, then $b_i$ is a neighbor of $a_i$
in this subsequence; and conversely, if $b_i$ belongs to this subsequence, then
$a_i$ neighbors $b_i$ in this subsequence.
For all integers $i \in [1, L]$, we define the values $\alpha(i)$ and $\beta(i)$
so that $a_i = \pi_{\alpha(i)}$ and $b_i = \pi_{\beta(i)}$.
Note that by the definition of $\pi$, we have $\alpha(1) < \alpha(2) < \dots < \alpha(L)$.
This definition allows us to define the \textbf{conflict interval} $X_i$ for each $i \in [2, L-1]$ ---
a closed interval whose endpoints are at $\alpha(i)$ and $\beta(i)$.
Each conflict interval is a subinterval of the interval $[1, 2L]$.
We stress that we do not define $X_1$ or $X_L$.
We note the following property of the conflict intervals:
\begin{claim}
\label{large-neighbor-separation-claim}
For every two different integers $s, t$ ($s \in [2, L-1]$, $t \in [2, L]$),
$a_s$ is separated from $b_s$ by $\mathsf{Area}(\mathcal{C}, 1, t)$
if and only if $\alpha(t) \in X_s$.
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
Let us first remark that
\begin{equation}
\label{prefix-area-sum-eq}
\mathsf{Area}(\mathcal{C}, 1, t) = \mathsf{Area}(\mathcal{C}, 1, 2) \cup \mathsf{Area}(\mathcal{C}, 2, 3) \cup \dots \cup \mathsf{Area}(\mathcal{C}, t-1, t)
\end{equation}
(Lemma \ref{area-sum-lemma}).
Therefore, if $\beta(s) < \alpha(t)$, then $b_s$ was added to $\pi$ before $a_t$;
it follows that $b_s$ belongs to one of the subsequences $\Gamma_1, \Gamma_2, \dots,
\Gamma_{t-1}$.
Hence, $b_s$ belongs to $\mathsf{Area}(\mathcal{C}, i, i+1)$ for some $i < t$.
By (\ref{prefix-area-sum-eq}), we conclude that $b_s \in \mathsf{Area}(\mathcal{C}, 1, t)$.
Conversely, if $b_s \in \mathsf{Area}(\mathcal{C}, 1, t)$, then $b_s \in \mathsf{Area}(\mathcal{C}, i, i+1)$ for some $i < t$.
If we fix $i$ to be the smallest index for which $b_s \in \mathsf{Area}(\mathcal{C}, i, i+1)$, we will
get that $b_s \in \Gamma_i$, where $i < t$, so also $\beta(s) < \alpha(t)$.
We conclude that
\begin{equation}
\label{large-neighbor-separation-bs}
b_s \in \mathsf{Area}(\mathcal{C}, 1, t)\ \Leftrightarrow\ \beta(s) < \alpha(t).
\end{equation}
Now, let us compare $\alpha(s)$ with $\alpha(t)$.
Naturally, we have $\alpha(s) < \alpha(t)$ if and only if $s < t$.
Also, by Lemma \ref{neighbor-cage-ai-good-lemma}
we have that $a_s \in \mathrm{Int}\,\mathsf{Area}(\mathcal{C}, s-1, s+1)$.
If $s < t$, we immediately get that $a_s \in \mathsf{Area}(\mathcal{C}, 1, t)$.
However, if $s > t$, then we infer the following relation from Corollary~\ref{area-int-lemma}:
$$ \mathsf{Area}(\mathcal{C}, 1, s-1) \cap \mathrm{Int}\,\mathsf{Area}(\mathcal{C}, s-1, s+1) = \varnothing. $$
Hence, $a_s \not\in \mathsf{Area}(\mathcal{C}, 1, s - 1)$, so also $a_s \not\in \mathsf{Area}(\mathcal{C}, 1, t)$.
We now proved that
\begin{equation}
\label{large-neighbor-separation-as}
a_s \in \mathsf{Area}(\mathcal{C}, 1, t)\ \Leftrightarrow\ \alpha(s) < \alpha(t).
\end{equation}
It is obvious that $\alpha(t) \in X_s$ if and only if exactly one of the conditions
$\alpha(s) < \alpha(t)$, $\beta(s) < \alpha(t)$ holds.
From (\ref{large-neighbor-separation-bs}) and (\ref{large-neighbor-separation-as})
it follows that this is equivalent to exactly one of the conditions
$a_s \in \mathsf{Area}(\mathcal{C}, 1, t)$, $b_s \in \mathsf{Area}(\mathcal{C}, 1, t)$ being satisfied.
A verification with Definition \ref{separated-from-def} concludes the proof.
\end{claimproof}
\end{claim}
This claim enables us to prove that the conflict intervals do not intersect \emph{too frequently}:
\begin{claim}
\label{large-neighbor-sparse-conflicts}
For each $x \in \mathbb{R}$, at most $256d^3(d+2)^4 + 2$ conflict intervals contain $x$.
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
Fix $x \in \mathbb{R}$, and consider the set $I = \{i \in [2, L-1]\,\mid\, x \in X_i\}$ of all indices
for which the corresponding conflict interval contains $x$.
We partition $I$ into two subsets, depending on whether $\alpha(i)$ is the left or the right
endpoint of the conflict interval $X_i$:
\begin{equation*}
\begin{split}
I_{\alpha\beta} &= \{i \in I\,\mid\, \alpha(i) < \beta(i)\}, \\
I_{\beta\alpha} &= \{i \in I\,\mid\, \alpha(i) > \beta(i)\}.
\end{split}
\end{equation*}
Let $m = |I_{\alpha\beta}|$ and $I_{\alpha\beta} = \{i_1, i_2, \dots, i_m\}$ where
$2 \leq i_1 < i_2 < \dots < i_m \leq L-1$.
Since $\alpha(i_1) < \alpha(i_2) < \dots < \alpha(i_m)$ and each interval $X_{i_j}$ for
$j \in [1, m]$ has its left endpoint at $\alpha(i_j)$, we conclude that
$\alpha(i_m)$ also belongs to each conflict interval $X_{i_1}, X_{i_2}, \dots, X_{i_m}$.
Hence, by Claim \ref{large-neighbor-separation-claim}, each pair of vertices
$a_{i_j}, b_{i_j}$ for $j \in [1, m - 1]$ is separated by $\mathsf{Area}(\mathcal{C}, 1, i_m)$.
By Lemma \ref{neighbor-separation-lemma} we conclude that $m - 1 \leq
128d^3(d+2)^4$, so $|I_{\alpha\beta}| \leq 128d^3(d+2)^4 + 1$.
We can prove in a similar fashion that $|I_{\beta\alpha}| \leq 128d^3(d+2)^4 + 1$ ---
if $I_{\beta\alpha} = \{j_1, j_2, \dots, j_n\}$ for some $n \in \mathbb{N}$
and $2 \leq j_1 < j_2 < \dots < j_n \leq L-1$,
then $\alpha(j_1)$ belongs to each conflict interval $X_{j_1}, X_{j_2}, \dots, X_{j_n}$,
and the remaining part of the argument follows.
Therefore, $|I| = |I_{\alpha\beta}| + |I_{\beta\alpha}| \leq 256d^3(d+2)^4 + 2$.
\end{claimproof}
\end{claim}
We now consider an auxiliary undirected graph $H$ where $V(H) = \{2, 3, \dots, L-1\}$ and
vertices $i$ and $j$ are connected by an edge if the conflict intervals $X_i$ and $X_j$
intersect.
This is a well-known definition of an interval graph.
Every interval graph is also a perfect graph \cite{west2001introduction},
so $H$ has a proper coloring where the number of colors is equal
to the maximum size of a clique in $H$.
In interval graphs, the maximum size of a clique is equal to the maximum number of intervals
which intersect at a single point.
This number is bounded by Claim \ref{large-neighbor-sparse-conflicts} by
$256d^3(d+2)^4 + 2$,
and therefore $H$ can be colored using that many colors.
Since $L = [256d^3(d+2)^4 + 2] \ell + 2$, we have
$|V(H)| = [256d^3(d+2)^4 + 2] \ell$ and there exists a color that has been used for at least
$\ell$ vertices of $H$.
Therefore, $H$ contains an independent set of size $\ell$, or in other words,
there exists a set of $\ell$ pairwise disjoint conflict intervals
$X_{d_1}, X_{d_2}, \dots, X_{d_\ell}$ ($2 \leq d_1 < d_2 < \dots < d_\ell \leq L-1$).
\vspace{0.5em}
We create a modified identity ordered cage $\mathcal{C}'$ which is a subset of $\mathcal{C}$
given by indices $d_1, d_2, \dots, d_\ell$.
\begin{claim}
\label{large-neighbor-found}
$\mathcal{C}'$ is a neighbor cage.
\begin{claimproof}
\renewcommand{\qed}{\cqedsymbol}
We fix an index $i \in \{2, 3, \dots, \ell - 1\}$, and we prove that
$b_{d_i}$ belongs to $\mathsf{Area}(\mathcal{C}, d_{i - 1}, d_{i + 1})$.
Naturally, $\mathsf{Area}(\mathcal{C}, d_{i-1}, d_{i+1}) = \mathsf{Area}(\mathcal{C}', i-1, i+1)$, so this is enough to
complete the proof of the claim.
Lemma \ref{neighbor-cage-ai-good-lemma} asserts that $a_{d_i} \in \mathrm{Int}\,\mathsf{Area}(
\mathcal{C}, d_i-1, d_i+1) \subseteq \mathrm{Int}\,\mathsf{Area}(\mathcal{C}, d_{i-1}, d_{i+1})$.
Hence, $a_i \in \Int\mathsf{Area}(\mathcal{C}, 1, d_{i+1})$.
Moreover, from Corollary \ref{area-int-lemma} we deduce that
$\mathsf{Area}(\mathcal{C}, 1, d_{i-1}) \cap \Int\mathsf{Area}(\mathcal{C}, d_{i-1}, d_{i+1}) = \varnothing$.
Hence, $a_i \not\in \mathsf{Area}(\mathcal{C}, 1, d_{i-1})$.
Now, we apply Claim \ref{large-neighbor-separation-claim}.
Since the conflict intervals $X_{d_1}, X_{d_2}, \dots, X_{d_\ell}$ are pairwise disjoint,
we get that $\alpha(d_i) \not\in X_{d_{i-1}}$ and $\alpha(d_i) \not\in X_{d_{i+1}}$, and therefore
$a_{d_i}$ is separated from $b_{d_i}$ by neither $\mathsf{Area}(\mathcal{C}, 1, d_{i-1})$ nor
$\mathsf{Area}(\mathcal{C}, 1, d_{i+1})$.
Due to the fact that $a_{d_i} \in \Int\mathsf{Area}(\mathcal{C}, d_{i-1}, d_{i+1})$, we get that
$b_{d_i} \not\in \mathsf{Area}(\mathcal{C}, 1, d_{i-1})$ and $b_i \in \mathsf{Area}(\mathcal{C}, 1, d_{i+1})$.
Now, we observe that
$$\mathsf{Area}(\mathcal{C}, 1, d_{i + 1}) = \mathsf{Area}(\mathcal{C}, 1, d_{i-1}) \cup \mathsf{Area}(\mathcal{C}, d_{i-1}, d_{i+1})$$
(Lemma \ref{area-sum-lemma}).
Since $b_{d_i} \in \mathsf{Area}(\mathcal{C}, 1, d_{i+1})$ and $b_{d_i} \not\in \mathsf{Area}(\mathcal{C}', 1, d_{i-1})$, we
infer that $b_{d_i} \in \mathsf{Area}(\mathcal{C}, d_{i-1}, d_{i+1})$.
Hence, $\mathcal{C}'$ is a neighbor cage of order $\ell$.
\end{claimproof}
\end{claim}
Claim \ref{large-neighbor-found} completes the proof.
\end{proof}
\end{lemma}
Let us now verify a few basic properties of neighbor cages.
\begin{lemma}
\label{neighbor-cage-spread-lemma}
Fix a neighbor cage $\mathcal{C} = \mathsf{NeighborCage}((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q})$ in
a graph $G$ embedded in the plane, and consider an edge $uv \in E(G)$.
Assume that for some $L, R$ ($2 \leq L < R < \ell$), we have that
$u \in \mathsf{Area}(\mathcal{C}, L, R)$, but $u \not\in V(\mathcal{Q}) \cup \{p\}$.
Then $v \in \mathsf{Area}(\mathcal{C}, L-1, R+1)$.
\begin{proof}
Let $\mathcal{P} = \mathsf{Tree}(P_1, P_2, \dots, P_\ell)$.
Since $\mathsf{Area}(\mathcal{C}, L, R) \subseteq \mathsf{Area}(\mathcal{C}, L-1, R+1)$ (a consequence of Lemma
\ref{area-sum-lemma}),
we have that $u \in \mathsf{Area}(\mathcal{C}, L-1, R+1)$.
We now want to prove that $u \in \Int\mathsf{Area}(\mathcal{C}, L-1, R+1)$.
Assume on the contrary that $u \in \partial\mathsf{Area}(\mathcal{C}, L-1, R+1)$.
As $\mathsf{Area}(\mathcal{C}, L, R) \subseteq \mathsf{Area}(\mathcal{C}, L-1, R+1)$ and $u \in \mathsf{Area}(\mathcal{C}, L, R)$,
it follows that $u \in \partial\mathsf{Area}(\mathcal{C}, L, R)$.
Hence,
$$ u \in \left[\partial\mathsf{Area}(\mathcal{C}, L-1, R+1) \cap \partial\mathsf{Area}(\mathcal{C}, L, R)\right] \setminus \left[
V(\mathcal{Q}) \cup \{p\}\right]. $$
Since $\partial\mathsf{Area}(\mathcal{C}, L, R)\,\subseteq\,V(\mathcal{P}) \cup V(\mathcal{Q})$, we infer from the definition
of a neighbor area that
$$u \in \partial\mathsf{Area}(\mathcal{C}, L, R) \setminus V(\mathcal{Q})\quad\Rightarrow\quad
u \in \partial\mathsf{Area}(\mathcal{C}, L, R) \cap V(\mathcal{P})\quad\Rightarrow\quad
u \in P_L \cup P_R. $$
Analogously, $u \in P_{L-1} \cup P_{R+1}$.
However, as $\mathcal{P}$ is a simple geodesic tree,
every pair of different paths $P_i, P_j$ ($1 \leq i, j \leq \ell$) intersects only at $p$.
Hence, $u = p$ --- a contradiction, since we assumed that $u \neq p$.
\end{proof}
\end{lemma}
Therefore, short paths can only reach very local parts of the neighbor cage without
intersecting $\mathcal{Q}$ or passing through $p$.
This fact is explored in the following lemmas:
\begin{lemma}
\label{semiladder-path-no-root}
Fix a neighbor cage $\mathcal{C} = \mathsf{NeighborCage}((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q})$
and two indices $i, j$ ($1 \leq i < j \leq \ell$).
No shortest path between $b_i$ and $a_j$ can pass through $\mathsf{Root}(\mathcal{P})$.
\begin{proof}
If any shortest path connecting $b_i$ and $a_j$ contains $\mathsf{Root}(\mathcal{P})$ as a vertex, then
\begin{equation*}
\begin{split}
d &< \mathrm{dist}(b_i, a_i) \leq \mathrm{dist}(b_i, \mathsf{Root}(\mathcal{P})) + \mathrm{dist}(\mathsf{Root}(\mathcal{P}), a_i) = \\
&= \mathrm{dist}(b_i, \mathsf{Root}(\mathcal{P})) + \mathrm{dist}(\mathsf{Root}(\mathcal{P}), a_j) = \mathrm{dist}(b_i, a_j) \leq d
\end{split}
\end{equation*}
--- a contradiction.
\end{proof}
\end{lemma}
\begin{lemma}
\label{path-first-intersection-lemma}
Fix a neighbor cage $\mathcal{C} = \mathsf{NeighborCage}((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q})$ in $G$
and two indices $i, j$ ($i < j$, $i \in [d+2, \ell-d-1]$).
Take an oriented shortest path $R$ from $b_i$ to $a_j$.
Note that this path intersects $\mathcal{Q}$ because $a_j \in V(\mathcal{Q})$.
The first intersection of $R$ with $\mathcal{Q}$ belongs
to $\mathsf{Area}(\mathcal{C}, i-d-1, i+d+1)$.
\begin{proof}
From the definition of a neighbor cage, we have that $b_i \in \mathsf{Area}(\mathcal{C}, i-1, i+1)$.
Let $R = (v_0, v_1, \dots, v_\delta)$ be the shortest path from $b_i$ to $a_j$,
where $v_0 = b_i$, $v_\delta = a_j$, and $\delta \leq d$ (as required by the definition
of a semi-ladder).
Let also $v_k$ be the first vertex of this path belonging to $V(\mathcal{Q})$.
Since $p \not\in (v_0, v_1, \dots, v_\delta)$ (Lemma \ref{semiladder-path-no-root}),
by applying Lemma~\ref{neighbor-cage-spread-lemma}
we inductively deduce that $v_t \in \mathsf{Area}(\mathcal{C}, i-t-1, i+t+1)$ for each $t \in \{0, 1, \dots, k\}$.
Therefore, $v_k \in \mathsf{Area}(\mathcal{C}, i-k-1, i+k+1)$.
As $k \leq \delta \leq d$, we infer that $v_k \in \mathsf{Area}(\mathcal{C}, i-d-1, i+d+1)$.
\end{proof}
\end{lemma}
Now, for a vertex $v$ belonging to a geodesic tree $\mathcal{T}$, we define
the \textbf{depth} $\mu_\mathcal{T}(v)$ of $v$ as the distance from $v$ to $\mathsf{Root}(\mathcal{T})$ in $\mathcal{T}$.
Note that it is implied by the definition of a geodesic tree that $\mu_\mathcal{T}(v)$ is also
equal to the distance between $v$ and $\mathsf{Root}(\mathcal{T})$ in $G$.
We remark a few simple facts about $\mu_\mathcal{T}$:
\begin{itemize}
\item $\mu_\mathcal{T}(\mathsf{Root}(\mathcal{T})) = 0$.
\item $\mu_\mathcal{T}$ is constant on the set of leaves of $\mathcal{T}$.
\item If a vertex $u$ is an ancestor of another vertex $v$ in $\mathcal{T}$, then
$\mathrm{dist}(u, v) = \mu_\mathcal{T}(v) - \mu_\mathcal{T}(u)$.
\item More generally, for any two vertices $u, v \in V(\mathcal{T})$,
we have $\mathrm{dist}(u, v) \geq |\mu_\mathcal{T}(u) - \mu_\mathcal{T}(v)|$.
\item On any oriented simple path in $\mathcal{T}$, the depths of vertices are first decreasing,
and then increasing. In other words, there do not exist three vertices $x, y, z$ lying
on an oriented simple path in $\mathcal{T}$ in this order,
for which $\mu_\mathcal{T}(x) < \mu_\mathcal{T}(y) > \mu_\mathcal{T}(z)$.
\end{itemize}
\vspace{0.5em}
We already know from Lemmas \ref{semiladder-path-no-root} and
\ref{path-first-intersection-lemma} that each shortest path $R$ connecting the vertices
$b_i$ and $a_j$ of the semi-ladder ($i < j$) must avoid $\mathsf{Root}(\mathcal{P})$ and the first intersection
of $R$ with $\mathcal{Q}$ occurs inside of $\mathsf{Area}(\mathcal{C}, i-d-1, i+d+1)$.
It turns out that this first intersection imposes serious restrictions on each following intersection
of $R$ with $\mathcal{Q}$.
\begin{lemma}
\label{intersection-depth-lower-bound-lemma}
Fix a neighbor cage $\mathcal{C} = \mathsf{NeighborCage}((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q})$
and two indices $i, j$ ($1 \le i < j \le \ell$).
Consider any shortest path from $b_i$ to $a_j$: $R = (v_0, v_1, v_2, \dots, v_\delta)$ for some
$\delta \leq d$, $v_0 = b_i$, $v_\delta = a_j$.
Suppose that for some indices $0 \leq x \leq y \leq \delta$ we have $v_x, v_y \in V(\mathcal{Q})$.
Then $\mu_\mathcal{Q}(v_y) > \mu_\mathcal{Q}(\mathrm{lca}_\mathcal{Q}(v_x, a_i))$.
\begin{proof}
We set $\mu := \mu_\mathcal{Q}$, $\lca := \lca_\mathcal{Q}$.
For the sake of contradiction let us fix a shortest path $R$
from $b_i$ to $a_j$ and two indices $x, y$ as above such that
$\mu(v_y) \leq \mu(\lca(v_x, a_i))$.
We consider a path $G$ from $b_i$ to $a_i$ which first follows $R$ from $b_i$ to $v_x$,
then goes up the tree $\mathcal{Q}$ from $v_x$ to $\lca(v_x, a_i)$, and then goes down the tree
$\mathcal{Q}$ from $\lca(v_x, a_i)$ to $a_i$ (Figure \ref{intersection-depth-setup-fig}).
\begin{figure}[h]
\centering
\begin{minipage}[b]{0.49\textwidth}
\centering
\input{figures/depth-lca-a.tex}
(a)
\end{minipage}\begin{minipage}[b]{0.49\textwidth}
\centering
\input{figures/depth-lca-b.tex}
(b)
\end{minipage}
\caption{The setup in Lemma \ref{intersection-depth-lower-bound-lemma}. \\
(a) --- The shortest path $R$ from $b_i$ to $a_j$ (red) crosses $\mathcal{Q}$ twice.
We are going to prove
that there exists a path $G$ from $b_i$ to $a_i$ (green) which is not longer than $R$. \\
(b) --- Both $R$ and $G$ have been split into three parts: red, blue and green. $R$ and
$G$ share the red fragment. (\ref{intersection-depth-eq-b}) proves that the blue segment
in $G$ is not longer than the blue segment in $R$. (\ref{intersection-depth-eq-c}) proves
that the green segment in $G$ is not longer than the green segment in $R$.}
\label{intersection-depth-setup-fig}
\end{figure}
We obviously have that
\begin{equation}
\label{intersection-depth-main-eq}
\mathrm{dist}(b_i, a_i) \leq \mathrm{len}(G) = \mathrm{len}(G[b_i, v_x]) + \mathrm{len}(G[v_x, \lca(v_x, a_i)]) +
\mathrm{len}(G[\lca(v_x, a_i), a_i]).
\end{equation}
As $G$ follows $R$ on the fragment between $b_i$ and $v_x$, we have that
\begin{equation}
\label{intersection-depth-eq-a}
\mathrm{len}(G[b_i, v_x]) = \mathrm{len}(R[b_i, v_x]).
\end{equation}
Next, $\lca(v_x, a_i)$ is an ancestor of $v_x$ in $\mathcal{Q}$ and thus
\begin{equation}
\label{intersection-depth-eq-b}
\begin{split}
\mathrm{len}(G[v_x, \mathrm{lca}(v_x, a_i)]) & = \mu(v_x) - \mu(\mathrm{lca}(v_x, a_i)) \leq
\mu(v_x) - \mu(v_y) \leq \mathrm{dist}(v_x, v_y) = \\ &= \mathrm{len}(R[v_x, v_y]).
\end{split}
\end{equation}
Analogously, $\mathrm{lca}(v_x, a_i)$ is an ancestor of $a_i$ in $\mathcal{Q}$.
Therefore,
\begin{equation}
\label{intersection-depth-eq-c}
\begin{split}
\mathrm{len}(G[\mathrm{lca}(v_x, a_i), a_i]) & = \mu(a_i) - \mu(\mathrm{lca}(v_x, a_i)) \leq
\mu(a_i) - \mu(v_y) = \mu(a_j) - \mu(v_y) \leq \\
& \leq \mathrm{dist}(v_y, a_j) = \mathrm{len}(R[v_y, a_j]).
\end{split}
\end{equation}
By substituting (\ref{intersection-depth-eq-a}), (\ref{intersection-depth-eq-b}),
(\ref{intersection-depth-eq-c}) into (\ref{intersection-depth-main-eq}), we conclude that
\begin{equation*}
\begin{split}
\mathrm{dist}(b_i, a_i) & \leq \mathrm{len}(R[b_i, v_x]) + \mathrm{len}(R[v_x, v_y]) +
\mathrm{len}(R[v_y, a_j]) = \mathrm{len}(R) = \mathrm{dist}(b_i, a_j) = \\ &= \delta \leq d
\end{split}
\end{equation*}
--- a contradiction since the semi-ladder requires that $\mathrm{dist}(b_i, a_i) > d$.
\end{proof}
\end{lemma}
A less formal way of thinking about Lemma \ref{intersection-depth-lower-bound-lemma}
is that as soon as the shortest path from $b_i$ to $a_j$ touches any vertex of $\mathcal{Q}$,
all subsequent intersections of the path with $\mathcal{Q}$ need to happen
sufficiently deep in the tree.
There are also some limitations on where this path may intersect $\mathcal{Q}$ at all ---
by letting $x = y$ in the lemma above, we infer that each intersection $v_x$
of a shortest path from $b_i$ to $a_j$ must satisfy $v_x \neq \lca_\mathcal{Q}(v_x, a_i)$.
That is, no intersection of this path with $\mathcal{Q}$ can be an ancestor of $a_i$ in $\mathcal{Q}$.
The most important conclusion will become clear in a moment:
since the first intersection of every oriented shortest path from $b_i$ to $a_j$ ($i < j$)
with $\mathcal{Q}$ must happen topologically relatively close to $b_i$
(Lemma \ref{path-first-intersection-lemma}),
we should be able to infer a common lower bound on the depth of
every such intersection, no matter the path or value of $j$.
This is indeed possible, albeit with slightly stronger assumptions,
as proved in Lemma \ref{ladder-path-depth-bound-lemma} below.
In order to proceed, we need a small definition.
\begin{definition}
In a neighbor cage $\mathcal{C} = \mathsf{NeighborCage}((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q})$,
a neighbor area $\mathsf{Area}(\mathcal{C}, i, j)$ is \textbf{rootless} if $\mathsf{Root}(\mathcal{Q}) \not\in \Int\mathsf{Area}(\mathcal{C}, i, j)$.
Note that not all neighbor areas must be rootless, as seen in Figure \ref{rootless-def-figure}.
\begin{figure}[h]
\centering
\begin{minipage}[b]{0.4\textwidth}
\centering
\input{figures/rootless-def-a.tex}
(a)
\end{minipage}\begin{minipage}[b]{0.4\textwidth}
\centering
\input{figures/rootless-def-b.tex}
(b)
\end{minipage}
\caption{(a) --- An example neighbor cage $\mathcal{C}$ of order $5$. $\mathsf{Area}(\mathcal{C}, 3, 4)$ (green) is
rootless, but $\mathsf{Area}(\mathcal{C}, 1, 3)$ (red) is not. Vertices $b_1, \dots, b_5$ were omitted
for clarity. \\
(b) --- Another neighbor cage $\mathcal{D}$. Now, both $\mathsf{Area}(\mathcal{D}, 1, 3)$ and $\mathsf{Area}(\mathcal{D}, 3, 4)$ are
rootless.}
\label{rootless-def-figure}
\end{figure}
\end{definition}
We are now ready to introduce the promised lemma.
\begin{lemma}
\label{ladder-path-depth-bound-lemma}
Fix a neighbor cage $\mathcal{C} = \mathsf{NeighborCage}((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q})$
and an index $i$ ($i \in [d + 2, \ell - d - 1]$). If $\mathsf{Area}(\mathcal{C}, i-d-1, i+d+1)$ is rootless, then
each intersection $v$ of an oriented shortest path from $b_i$ to $a_j$ ($j > i$)
with $\mathcal{Q}$ satisfies
$$ \mu_\mathcal{Q}(v) > \mu_\mathcal{Q}(\lca_\mathcal{Q}(a_{i-d-1}, a_{i+d+1})). $$
\begin{proof}
We set $\mu := \mu_\mathcal{Q}$, $\lca := \lca_\mathcal{Q}$.
We also let $v_{\lca} := \lca(a_{i-d-1}, a_{i+d+1})$ and $\mathcal{Q} = \mathsf{Tree}(Q_1, \dots, Q_\ell)$.
Basing on the definition of neighbor areas, we infer that $v_{\lca}$ is the shallowest vertex
in $\mathcal{Q}$ belonging to $\partial\mathsf{Area}(\mathcal{C}, i-d-1, i+d+1)$.
We will now prove that $v_{\lca}$ is also the shallowest vertex in $\mathcal{Q}$ belonging to
$\mathsf{Area}(\mathcal{C}, i-d-1, i+d+1)$.
Assume for contradiction that there exists a vertex $x \in \mathsf{Area}(\mathcal{C}, i-d-1, i+d+1) \cap V(\mathcal{Q})$
for which $\mu(x) < \mu(v_{\lca})$.
Since $\mathsf{Root}(\mathcal{Q}) \not\in \Int\mathsf{Area}(\mathcal{C}, i-d-1, i+d+1)$,
the unique simple path in $\mathcal{Q}$ connecting $x$ with $\mathsf{Root}(\mathcal{Q})$ must intersect
$\partial\mathsf{Area}(\mathcal{C}, i-d-1, i+d+1)$ at some vertex $s \in V(\mathcal{Q})$.
Obviously, $\mu(s) \geq \mu(v_{\lca})$.
However, it means that the simple path in $\mathcal{Q}$ connecting $x$ with $\mathsf{Root}(\mathcal{Q})$
contains three vertices in the following order: $x, s, \mathsf{Root}(\mathcal{Q})$. But
$$ \mu(x) < \mu(v_{\lca}) \leq \mu(s) > \mu(\mathsf{Root}(\mathcal{Q})) = 0 \qquad
\Rightarrow \qquad \mu(x) < \mu(s) > \mu(\mathsf{Root}(\mathcal{Q})) $$
--- a contradiction.
Hence, $v_{\lca}$ is the shallowest vertex of $\mathsf{Area}(\mathcal{C}, i-d-1, i+d+1) \cap V(\mathcal{Q})$.
\vspace{0.5em}
We fix a shortest path $R$ from $b_i$ to $a_j$. Let $v_1$ be the first intersection of $R$
with $V(\mathcal{Q})$.
By Lemma \ref{path-first-intersection-lemma}, we have that
$v_1 \in \mathsf{Area}(\mathcal{C}, i-d-1, i+d+1)$.
\begin{figure}[h]
\centering
\input{figures/common-bound-setup.tex}
\caption{An example of the setup in Lemma \ref{ladder-path-depth-bound-lemma} ---
a cage $\mathcal{C}$, $d = 6$ and $i = 8$.
We consider $v_1$ ---
the first intersection of the shortest path between $b_8$ and $a_{11}$ (green) with $\mathcal{Q}$.
We prove that the simple path $S$ in $\mathcal{Q}$ connecting $v_1$ with $a_8$ (red) fully belongs
to $\mathsf{Area}(\mathcal{C}, 1, 15)$ (shaded).
It will follow that $\mu(\lca(v_1, a_8)) \geq \mu(v_{\lca})$, and Lemma
\ref{intersection-depth-lower-bound-lemma} will conclude the proof.}
\label{common-bound-setup-fig}
\end{figure}
We now prove (Figure \ref{common-bound-setup-fig})
that the simple path in $\mathcal{Q}$ between $v_1$ and $a_i$ --- call it $S$ --- is fully contained
within $\mathsf{Area}(\mathcal{C}, i-d-1, i+d+1)$.
Firstly, from the properties of neighbor cages, it follows that
$a_i \in \mathsf{Area}(\mathcal{C}, i-1, i+1)$; thus, $a_i \in \mathsf{Area}(\mathcal{C}, i-d-1, i+d+1)$.
Secondly, by the definition of neighbor areas, the intersection of
$\partial\mathsf{Area}(\mathcal{C}, i-d-1, i+d+1)$ with $\mathcal{Q}$ is the simple path in $\mathcal{Q}$
connecting $\mathsf{Split}(\mathcal{C}, i-d-1)$ with $\mathsf{Split}(\mathcal{C}, i+d+1)$.
Let us call this path $B$.
Therefore, if $S$ was not contained
within $\mathsf{Area}(\mathcal{C}, i-d-1, i+d+1)$, it would have to intersect $R$ at least twice ---
once when leaving the neighbor area, and once when reentering it.
This would, however, mean that $\mathcal{Q}$ contains a cycle --- which is impossible.
Hence, $S$ fully belongs to $\mathsf{Area}(\mathcal{C}, i-d-1, i+d+1)$.
It means in particular that
\begin{equation*}
\begin{split}
\mu(\lca(v_1, a_i)) &=
\min \{\mu(w)\,\mid\, w \in S\} \geq \\
&\geq \min\{\mu(w)\,\mid\, w \in \mathsf{Area}(\mathcal{C}, i-d-1, i+d+1)\,\cap\,V(\mathcal{Q})\} = \mu(v_{\lca}).
\end{split}
\end{equation*}
Therefore, by Lemma \ref{intersection-depth-lower-bound-lemma},
each intersection $v$ of $R$ with $\mathcal{Q}$ --- either $v_1$, or any
later intersection --- must satisfy
$$ \mu(v) > \mu(\lca(v_1, a_i)) \geq \mu(v_{\lca}). $$
\end{proof}
\end{lemma}
\subsection{Separating cages}
\label{separating-cages-lemma}
Lemma \ref{ladder-path-depth-bound-lemma}
allows us to introduce the final variant of a cage, which will eventually lead us
to a polynomial bound on the maximum order of any neighbor cage.
This in turn will produce an upper bound on the maximum order of any distance-$d$ semi-ladder.
\begin{definition}
A neighbor cage $\mathcal{C} = \mathsf{NeighborCage}((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q})$ in a graph $G$
is a \textbf{separating cage} if there exists an integer $\lambda \in \{0, 1, 2, \dots, d - 1\}$,
called \textbf{threshold}, such that the following properties hold
(Figure~\ref{separating-def-fig}):
\begin{itemize}
\item for every two different indices $i, j$ ($1 \leq i, j \leq \ell$),
paths $\mathsf{Path}(\mathcal{Q}, i)$ and $\mathsf{Path}(\mathcal{Q}, j)$ do not share any vertices
which are at depth larger than $\lambda$ in $\mathcal{Q}$;
\item for every pair of indices $i, j$ ($1 \leq i < j \leq \ell$),
no shortest path from $b_i$ to $a_j$ contains any vertex belonging to $\mathcal{Q}$ which is at
depth at most $\lambda$ in $\mathcal{Q}$.
\end{itemize}
We denote a separating cage in the following way:
$$ \mathsf{SeparatingCage}((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q}, \lambda). $$
\begin{figure}[h]
\centering
\begin{minipage}[b]{0.495\textwidth}
\centering
\input{figures/separating-def-a.tex}
(a)
\end{minipage}\begin{minipage}[b]{0.495\textwidth}
\centering
\input{figures/separating-def-b.tex}
(b)
\end{minipage}
\caption{An example separating cage $\mathcal{C}$ of order $9$ and threshold $\lambda = 2$.
The threshold is a blue dotted
line; no two paths connecting $\mathsf{Root}(\mathcal{Q})$ with a leaf of $\mathcal{Q}$ can intersect above the
line, and no path connecting $b_i$ with $a_j$ (for $i < j$)
can intersect $\mathcal{Q}$ at this line or below. \\
(a) --- Three valid paths connecting $b_i$ with $a_j$ for $i < j$ (green). \\
(b) --- Two invalid paths connecting $b_i$ with $a_j$ for $i < j$ (red).
These cannot occur in the separating cage because
each of them passes through a vertex of $\mathcal{Q}$ at depth $\lambda$ or less.}
\label{separating-def-fig}
\end{figure}
\end{definition}
We will now prove that graphs with large neighbor cages also contain large separating cages.
\begin{lemma}
\label{large-separating-cage-lemma}
Each neighbor cage of order $2(2d+3)((\ell-1)d + 1)$ contains a separating cage
of order $\ell$ as a subset.
\begin{proof}
Let $L := 2(2d+3)((\ell-1)d + 1)$ and
fix a cage $\mathcal{C} = \mathsf{NeighborCage}((a_i)_{i=1}^L,
(b_i)_{i=1}^L, \mathcal{P}, \mathcal{Q})$ of order $L$.
We let $\mathcal{Q} = \mathsf{Tree}(Q_1, Q_2, \dots, Q_L)$.
Let also $M := 2((\ell - 1)d + 1)$. We define a sequence of $M$ neighbor areas
$(A_1, A_2, \dots, A_M)$:
$$ A_i = \mathsf{Area}(\mathcal{C},\, (2d + 3)(i - 1) + 1,\, (2d + 3)i) \qquad \text{for each index }i \in [1, M]. $$
We remark that because the set $\{[(2d + 3)(i-1) + 1,\, (2d+3)i]\,\mid\, i \in \{1, \dots, M\}\}$
contains only pairwise disjoint segments,
we infer from Lemma \ref{area-int-lemma} that the interiors of the neighbor areas
$A_1, A_2, \dots, A_M$ are pairwise disjoint.
Hence, at least $M - 1 = 2(\ell - 1)d + 1$ out of neighbor areas $A_1, A_2, \dots, A_M$
are rootless.
For each neighbor area $A_i$, we define its depth $\mu(A_i) = \mu_\mathcal{Q}(\lca_\mathcal{Q}(
a_{(2d + 3)(i - 1) + 1},\, a_{(2d+3)i}))$.
Note that $\mu(A_i)$ is chosen specifically to match the conditions of Lemma
\ref{ladder-path-depth-bound-lemma}:
provided that $A_i$ is rootless, each intersection $v$ of a shortest path from
$b_{(2d+3)(i-1) + (d+2)}$ to $a_j$ (for $j > (2d+3)(i-1) + (d+2)$) with $\mathcal{Q}$ satisfies
$\mu_\mathcal{Q}(v) > \mu(A_i)$.
We also remark that $\mu(A_i) \in \{0, 1, 2, \dots, d-1\}$ for each $i \in [1, M]$.
\newcommand{\mathsf{Block}}{\mathsf{Block}}
The pigeonhole principle allows us to select $2\ell-1$ out of $(2\ell-2)d + 1$ rootless
neighbor areas so that the selected neighbor areas have the same depth $\mu$.
We fix this subset of rootless neighbor areas: $A_{t_1}, A_{t_2}, \dots, A_{t_{2\ell-1}}$ where
$1 \leq t_1 < t_2 < \dots < t_{2\ell-1} \leq M$. Note that
$$ \mu(A_{t_1}) = \mu(A_{t_2}) = \dots = \mu(A_{t_{2\ell-1}}) =: \lambda, \qquad
\mathsf{Root}(\mathcal{Q}) \not\in \Int\mathsf{Area}(A_{t_j})\text{ for }j\in[1,2\ell-1]. $$
We also define $m_j$ for $j \in [1, 2\ell-1]$ as the index of the central vertex of the semi-ladder
in the neighbor area $A_{t_j}$: $m_j = (2d + 3)(t_j - 1) + (d + 2)$.
Naturally, the sequence of indices $m_j$ is increasing: $m_1 < m_2 < \dots < m_{2\ell-1}$.
Also, for every pair of indices $i, j \in [1, 2\ell - 1]$ ($i < j$), each intersection $v$ of
a shortest path from $b_{m_i}$ to $a_{m_j}$ with $\mathcal{Q}$ satisfies $\mu_\mathcal{Q}(v) > \lambda$.
\vspace{0.5em}
Let $\mathcal{C}'$ be the neighbor cage of order $\ell$ which is a subset of $\mathcal{C}$ given by
the sequence of indices $m_1, m_3, m_5, \dots, m_{2\ell-1}$:
$$ \mathcal{C}' = \mathsf{NeighborCage}((a_{m_1}, a_{m_3}, \dots, a_{m_{2\ell-1}}),
(b_{m_1}, b_{m_3}, \dots, b_{m_{2\ell-1}}), \mathcal{P}', \mathcal{Q}'), \quad \mathcal{P}' \subseteq \mathcal{P},\
\mathcal{Q}' \subseteq \mathcal{Q}. $$
We verify that $\mathcal{C}'$ is a separating cage with threshold $\lambda$.
Firstly, we see that $\lambda = \mu(B_{t_1}) \in \{0, 1, 2, \dots, d-1\}$.
Secondly, we want to prove that no shortest path whose shortness is required
by the semi-ladder in $\mathcal{C}'$ contains any vertex belonging to $\mathcal{Q}$ that is at
depth at most $\lambda$ in $\mathcal{Q}$.
This is quickly resolved by Lemma \ref{ladder-path-depth-bound-lemma}.
Fix any two vertices of the semi-ladder in $\mathcal{C}'$ which require a short path:
$b_{m_i}, a_{m_j}$ ($i < j$, both $i, j$ odd), and fix a shortest path $R$ between
these two vertices.
As mentioned before, each intersection $v$ of $R$ with $\mathcal{Q}$ satisfies $\mu_\mathcal{Q}(v) > \lambda$.
Since $\mathcal{Q}' \subseteq \mathcal{Q}$, we obviously have $\mu_{\mathcal{Q}'}(v) > \lambda$ as well.
Finally, we want to prove that no two different oriented paths connecting $\mathsf{Root}(\mathcal{Q}')$
with the leaves of $\mathcal{Q}'$ intersect at any vertex at depth larger than $\lambda$.
We again fix two vertices of the semi-ladder in $\mathcal{C}'$: $a_{m_i}, a_{m_j}$
($i < j$, both $i, j$ odd), and consider paths $Q_{m_i}$ and $Q_{m_j}$, connecting
$\mathsf{Root}(\mathcal{Q})$ with $a_{m_i}$ and $a_{m_j}$, respectively.
Assume for contradiction that these paths intersect at a vertex $v$ such that
$\mu(v) > \lambda$.
This means that $v \in Q_{m_i}$ and $v \in Q_{m_j}$.
By the definition of identity ordered cages, we have that $v \in Q_k$ for every
$k \in [m_i, m_j]$.
However, since both $i$ and $j$ are odd, we have that $i + 1 < j$.
This means that $$[m_{i+1}-d-1, m_{i+1}+d+1] \subseteq [m_i, m_j].$$
Hence, $v \in Q_{m_{i+1}-d-1}$ and $v \in Q_{m_{i+1}+d+1}$ since $\mathcal{C}$ is an identity
ordered cage.
However, we verify that
$$ \mu_\mathcal{Q}\left(\lca_\mathcal{Q}(a_{m_{i+1}-d-1}, a_{m_{i+1}+d+1})\right) =
\mu(A_{t_{i+1}}) = \lambda. $$
This means that paths $Q_{m_{i+1}-d-1}$ and $Q_{m_{i+1}+d+1}$ do not intersect
at any vertex at depth greater than $\lambda$, yet $v$ is an intersection of these paths
at depth greater than $\lambda$ --- a contradiction.
Therefore, paths $Q_{m_i}, Q_{m_j}$ do not share any vertex at depth larger than $\lambda$.
Since these paths were chosen arbitrarily from $\mathcal{Q}'$,
all the paths connecting $\mathsf{Root}(\mathcal{Q})$ with a leaf of $\mathcal{Q}'$ are vertex-disjoint,
as long as vertices at depth larger than $\lambda$ are concerned.
Since all required properties of separating cages have been verified, $\mathcal{C}'$ together
with threshold $\lambda$ is a separating cage.
\end{proof}
\end{lemma}
In separating cages, we can prove a much more powerful variant of Lemma
\ref{neighbor-cage-spread-lemma}:
\begin{lemma}
\label{separating-cage-spread-lemma}
Consider a separating cage
$\mathcal{C} = \mathsf{SeparatingCage}((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q}, \lambda)$.
For every pair of indices $i, j$ ($1 \leq i < j \leq \ell$) and every edge $uv$ on a shortest
path between $b_i$ and $a_j$, if $u \in \mathsf{Area}(\mathcal{C}, L, R)$ for some integers $2 \leq L < R < \ell$,
then $v \in \mathsf{Area}(\mathcal{C}, L-1, R+1)$.
\begin{proof}
In a similar vein to the proof of Lemma \ref{neighbor-cage-spread-lemma}, we will prove that
$u \not\in \partial\mathsf{Area}(\mathcal{C}, L-1, R+1)$; the correctness of the statement of the lemma
will follow.
We remark that $u \in \mathsf{Area}(\mathcal{C}, L, R)$, and thus $u \in \mathsf{Area}(\mathcal{C}, L-1, R+1)$.
We assume for contradiction that $u \in \partial\mathsf{Area}(\mathcal{C}, L-1, R+1)$.
Since $\mathsf{Area}(\mathcal{C}, L, R) \subseteq \mathsf{Area}(\mathcal{C}, L-1, R+1)$, we also have that
$u \in \partial\mathsf{Area}(\mathcal{C}, L, R)$.
Therefore, both conditions below must be satisfied:
\begin{equation*}
\begin{split}
u \in \mathsf{SPath}(\mathcal{C}, L-1)\ \ &\vee\ \ u \in \mathsf{SPath}(\mathcal{C}, R+1), \\
u \in \mathsf{SPath}(\mathcal{C}, L)\ \ &\vee\ \ u \in \mathsf{SPath}(\mathcal{C}, R).
\end{split}
\end{equation*}
Hence, $v$ belongs to the intersection of $\mathsf{SPath}(\mathcal{C}, i)$ and $\mathsf{SPath}(\mathcal{C}, j)$
for $i \neq j$.
Therefore, by Lemma~\ref{splitting-path-intersection}, these paths intersect exactly at $p$
and their common suffix belonging to $\mathcal{Q}$.
However, since $u$ lies on the shortest path whose shortness is required by the
semi-ladder, Lemma \ref{semiladder-path-no-root} applies
and asserts that $u \neq p$.
It means that $u$ belongs to the intersection of paths $\mathsf{Path}(\mathcal{Q}, i)$ and $\mathsf{Path}(\mathcal{Q}, j)$.
But the definition of a separating cage requires that each such intersection must occur
at depth at most $\lambda$.
This means that the considered shortest path intersects $\mathcal{Q}$ at a vertex $u$
located at depth at most $\lambda$, which is explicitly forbidden by the definition
of a~separating cage --- a contradiction.
As $u \in \mathsf{Area}(\mathcal{C}, L-1, R+1)$, $u \not\in \partial\mathsf{Area}(\mathcal{C}, L-1, R+1)$, and $v$ is
connected to $u$ by an edge, we have that $v \in \mathsf{Area}(\mathcal{C}, L-1, R+1)$.
\end{proof}
\end{lemma}
The lemma above leads to a straightforward linear bound on the maximum order of any
separating cage:
\begin{lemma}
\label{no-large-separating-cage}
Every separating cage has order smaller than $2d+5$.
\begin{proof}
Assume for contradiction
that $\mathcal{C} = \mathsf{SeparatingCage}((a_i)_{i=1}^\ell, (b_i)_{i=1}^\ell, \mathcal{P}, \mathcal{Q}, \lambda)$
is a separating cage of order $\ell \geq 2d + 5$.
We consider a shortest path from $b_{d+2}$ to $a_{2d+4}$: $(u_0, u_1, u_2, \dots, u_\delta)$
where $u_0 = b_{d+2}$, $u_\delta = a_{2d+4}$ and $\delta \leq d$
(as required by the semi-ladder).
By the properties of neighbor cages, we have that $u_0 \in \mathsf{Area}(\mathcal{C}, d + 1, d + 3)$.
Using Lemma \ref{separating-cage-spread-lemma},
we prove inductively that $u_i \in \mathsf{Area}(\mathcal{C}, d - i + 1, d + i + 3)$ for each
$i \in \{0, 1, \dots, \delta\}$.
In particular, we infer that $a_{2d+4} = u_\delta \in \mathsf{Area}(\mathcal{C}, d - \delta + 1, d + \delta + 3)$.
Since $\delta \leq d$, we get that $a_{2d+4} \in \mathsf{Area}(\mathcal{C}, 1, 2d + 3)$.
However, Lemma \ref{neighbor-cage-ai-good-lemma} asserts
that $a_{2d+4} \in \mathrm{Int}\,\mathsf{Area}(\mathcal{C}, 2d+3, 2d+5)$.
Since
$$\mathsf{Area}(\mathcal{C}, 1, 2d+3) \cap \mathrm{Int}\,\mathsf{Area}(\mathcal{C}, 2d+3, 2d+5) = \varnothing$$
(Corollary \ref{area-int-lemma}), we have a contradiction.
\end{proof}
\end{lemma}
We can now finalize the proof of Theorem \ref{planar-upper-bound} bounding the maximum
distance-$d$ semi-ladder order in planar graphs:
\begin{corollary}
\label{planar-upper-bound-cor}
For $d \geq 1$,
all distance-$d$ semi-ladders in planar graphs have order smaller than
$$ d \cdot \left\{ d \cdot (2d - 1) \cdot
\left(\left\{[256d^3(d+2)^4 + 2] \cdot 2(2d+3)[(2d+4)d + 1]
+ 1\right\}^2 + 1\right)
+ 2 \right\}^d + 1. $$
\begin{proof}
We define the following polynomial functions:
\begin{equation*}
\begin{split}
\chi_1(d) &= 2d + 5, \\
\chi_2(d) &= 2(2d+3)[(\chi_1(d) - 1)d + 1], \\
\chi_3(d) &= [256d^3(d+2)^4 + 2]\chi_2(d) + 2, \\
\chi_4(d) &= (\chi_3(d) - 1)^2 + 1, \\
\chi_5(d) &= (2d-1)\chi_4(d).
\end{split}
\end{equation*}
It can be verified that the formula in the statement of the corollary simplifies to
$$d \left\{ d \cdot \chi_5(d) + 2\right\}^d + 1 =: M_d.$$
Assume that a distance-$d$ semi-ladder of order at least $M_d$ exists.
We take its subset which is a semi-ladder of order $M_d$, and call it $\mathcal{C}_1$.
Using Lemma \ref{quasi-cage-exists}, we find a quasi-cage $\mathcal{C}_2$ of order
$\chi_5(d)$ in the graph.
Using Lemma \ref{cage-exists}, we find a cage $\mathcal{C}_3$ of order $\chi_4(d)$ as
a subset of $\mathcal{C}_3$.
Using Lemma \ref{order-lemma}, we associate the cage $\mathcal{C}_3$ with an order and
create an ordered cage $\mathcal{C}_4$ underlying the same semi-ladder as $\mathcal{C}_3$.
Using Lemma \ref{identity-ordered-cage-exists}, we find an identity ordered cage $\mathcal{C}_5$ of
order $\chi_3(d)$ as a subset of $\mathcal{C}_4$.
Note that this may require altering the embedding of the graph in the plane.
Using Lemma \ref{large-neighbor-lemma}, we find a neighbor cage $\mathcal{C}_6$ of
order $\chi_2(d)$ as a subset of $\mathcal{C}_5$.
Using Lemma \ref{large-separating-cage-lemma}, we find a separating cage $\mathcal{C}_7$ of
order $\chi_1(d)=2d+5$ as a subset of $\mathcal{C}_6$.
Finally, Lemma \ref{no-large-separating-cage} contradicts our assumption since
it asserts that $\mathcal{C}_7$ cannot exist.
Hence, all distance-$d$ semi-ladders in the class of planar graphs must have
order smaller than $M_d$.
\end{proof}
\end{corollary}
We remark that this upper bound is of the form $d \cdot \rho(d)^d + 1$ where
$\rho(d)$ is a polynomial of degree $22$,
so the upper bound is of the form $d^{O(d)}$.
This concludes the proof of Theorem \ref{planar-upper-bound}.
|
{
"redpajama_set_name": "RedPajamaArXiv"
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Home Horse News Women Defend Their Show Jumping Battle of the Sexes Title
Women Defend Their Show Jumping Battle of the Sexes Title
Georgina Bloomberg helped the women secure victory with her win in the Six Bar class. Photo © 2010 Randi Muster/Mustphoto, Inc., Official Sport Photographer of the 2010 FTI Winter Equestrian Festival.
Energized is the only way to describe the Palm Beach International Arena at the 2010 FTI Winter Equestrian Festival on Saturday night for the $55,000 Nespresso Battle of the Sexes.
More than five thousand fans arrived for the signature Saturday Night Lights entertainment. The majestic Budweiser Clydesdales paraded in the arena with their loyal Dalmation leader Harley in an exhibition before the class. Fire blowers, chained escape artists, and knife juggling tight rope walkers from the famed Key West Sunset Carnival wowed the fans.
Yet the most amazing feats were performed by the Olympic and world-class riders in the spirited competition which pitted men against women and even husband against wife to see who would be the victorious team.
In the first speed round over fences, the men's team emerged with a lead of six winning rounds to four. But as two-time Olympic gold medalist Beezie Madden noted, "We were ready for a comeback."
In the side by side match race round over fences, where riders compete neck to neck, the women crossed the line with clear rounds first eight times out of ten. The last couple of riders to contest the match race were married couple, 2008 Olympic gold medalist Will Simpson and his wife Nicole Shahinian-Simpson.
As they rounded the bend to the final line, Will knew that his wife was gaining on him. "I saw her coming around the turn," he recalled. Nicole added, "I thought, 'Just go!' He's way too fast anyway. I can't pull on the reins!"
Nicole ended up just catching Will to win by hundredths of a second. "It was super fun! It was the way to do it. We gave it our all, and it all worked out," Nicole said.
With a handy lead of 12 to 8 going into the final six bar round where horses jump a series of six consecutive fences, two women and two men went clear. As the height was raised to 1.65m, Ali Niforushan and Will Simpson went clean again for the men and Georgina Bloomberg and Lauren Hough cleared it a second time as well.
The ladies led 20 to 16 as the fence bars raised one more time to 1.80m. Ali's horse knocked down the last bar then Georgina soared clearly over them all, securing the win for the ladies.
Bloomberg said that she and her horse Fiedi 3 had experience in this type of class. Bloomberg explained, "I did the six bar last year here with him, and it was my first class ever with him. I didn't trust him, and I leaned forward at a jump. Ever since then, I've been thinking about getting back here in this class."
She said of her team's win, "It's always fun when you win, but it's a fun class either way! Having this many people show up was amazing, and the atmosphere was great. They did a really good job putting on the class."
For a second year in a row the pretty in pink team proved the gals had the guts and the glory. The winning team led by captain Katie Prudent included Georgina Bloomberg, Debbie Stephens, Margie Engle, Beezie Madden, Laura Chapot, Lauren Hough, Casey Hodges, Cara Raether, Marilyn Meredith and Nicole Simpson. The men's team led by captain Henri Prudent included Pablo Barrios, Shane Sweetnam, Ali Nilforushan, Nick Dello Joio, Jorge Zamudio, Ramiro Quintana, Michael Morrissey, Charlie Jayne, Benjamin Meredith, and Will Simpson.
For full horse show results and information, please visit www.shownet.biz and www.equestriansport.com.
Previous articleRiding Arena Maintenance
Next articleHorseChannel Quizzes
https://www.horseillustrated.com
Horse Illustrated is the magazine for people who are passionate about horses. Each issue offers advice on horse health and care, plus user-friendly training tips for both English and western riders and engaging lifestyle features for horse lovers.
Biden Signs Five Animal Protection Measures into Law
Maryland 5* At Fair Hill Three-Day Event Preview
2022 FEI World Eventing Championships – Conclusion
Debbie February 2, 2010 at 7:24 am
Thanks for good article.
Jenna February 2, 2010 at 7:54 am
Go Girls! 🙂
Katie February 2, 2010 at 1:07 pm
Ya girls!!
Brianna February 2, 2010 at 6:50 pm
that'll show the guys:) i have a friend who thinks he's amazing at riding just cause he's the only boy at my stables. hahaha.wait til i show him this. u go girls and of the HORSES!
Galadriel February 2, 2010 at 11:05 pm
Yay for the women.
1999 Kentucky Derby Winner Charismatic Dies at Age 20
Leslie Potter - February 20, 2017
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
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## Never Binge Again™
### Reprogram Yourself to Think Like a Permanently
Thin Person™ on the Food Plan Of Your Choice!
### By Glenn Livingston, Ph.D.
Smashwords Edition
Copyright © 2015 by Glenn Livingston
Copyright © Psy Tech Inc.
"Never Binge Again™ and "Reprogram Yourself to Think Like a Permanently Thin Person™" are trademarks of Psy Tech Inc.
ALL RIGHTS RESERVED
DISCLAIMER: For education only. You are responsible for determining your own nutritional, medical, and psychological needs. If you require assistance with this task you must consult with a licensed physician, nutritionist, psychologist, and/or other professional. No medical, psychological, and/or nutritional advice is offered through this book. Even though the author is a licensed psychologist, he does not offer psychological services, psychological advice and/or psychological counsel in his role as author of this book. Psy Tech Inc. is only willing to license you the right to utilize this book in the event you agree with these terms. If you do not agree with these terms, please do not read the book, delete it from all electronic devices you own, and/or return it to your place of purchase for a full refund (where applicable).
Table of Contents
Chapter 1: The Outrageous Promise
Chapter 2: How to 'Deal' with Cravings
Chapter 3: What if You DO Binge?
Chapter 4: Changing Your Food Plan
Chapter 5: The Time Counting Trap
Chapter 6: Overcoming the Deprivation Trap
Chapter 7: Defeating the Food Industry
Chapter 8: "Hell is Other People" (Says Your Pig)
Chapter 9: The Pig is Powerless, Not You
Chapter 10: Twelve Hard to Recognize Pig Squeals!
Chapter 11: Discipline vs. Regret
Chapter 12: The Psychology of Bingeing, Not Bingeing, and Thinking Too Much About Food
Chapter 13: A Radical View on Guilt and Shame
Chapter 14: "Unconscious" Bingeing
Chapter 15: Your Personal Pig Squeal Journal
Chapter 16: Binge Anxiety
Chapter 17: What to Do When It's Not Working
Chapter 18: Alcohol Pigs, Drug Pigs, and Other Pigs Worth Dominating
Chapter 19: My Personal Food Plan
Chapter 20: Taking the Next Step
Notes
Chapter 1
### The Outrageous Promise
### **"This can't possibly be true"**
Sincerely, Your Fat-Thinking-Self
I'd like to make an outrageous, life-changing promise: Suspend judgment long enough to learn one crazy mental trick and you can achieve full control of your eating... _forever_.
NOT the painful, grit-your-teeth-and-bear-it control you've experienced while dieting before, but real control that lasts. Effortless control you feel secure about 24x7x365, without constant thought. Natural, lifelong control which represents true peace with food. So you can obtain the body you want, the health you deserve, and the sense of confidence and esteem which comes from sticking to a commitment.
Plus, once you learn this mental trick it will not only act to protect you against the thoughts which cause you to overeat today, but anything your "fat-thinking-self" might dream up tomorrow.
But fair warning: This trick-of-mind is fairly unusual, and you may have a negative reaction when you first hear it. Some people put the book down. Others call me a lunatic.
That's OK.
Go ahead and write in the margins, send me nasty emails, or whatever you need to do to voice your objections. My Mom will still love me even if you don't — and I'll just take your initial reactions as par for the course...
Because what you've been calling a weight problem _— or difficulty sticking with your best thinking about what to eat —_ is in reality a survival drive gone wrong. This is why all your rational attempts to keep to your commitments have failed, and why you keep getting derailed from your best-laid dietary and nutritional plans.
It's also why it seems like no matter how hard you try, you eventually find yourself eating in ways you swore you never would again. And it's why you may feel demoralized, dejected, and hopeless about ever successfully dealing with food.
When you start to rein in this survival-drive-run-amuck, it's going to fear for its life. But thankfully, there's ONE insight to which this seemingly unconquerable drive responds. One which can help you utterly dominate it, giving you full control of your eating from now on.
So feel free to entertain every critical voice in your head. In fact, becoming aware of your internal objections is an essential part of the process. I've actually set up the book to stimulate them.
All I'm asking is you give this a chance.
Give it a full read and promise yourself to withhold judgment. Try it out for a while, even if it seems nutty or doesn't quite work for you at first. If at that point you still think this idea is just not for you, that's fine. By then, you'll have made a fully informed decision, which is critical because _— as you'll soon realize —_ this is about a lot more than losing a few pounds. And it's about more than your health.
This is about accomplishing all your goals and dreams with more confidence and security than you ever thought possible.
What's at stake is everything you care about, as it is for everyone who's ever really struggled with food. And if you'll just pause to breathe for a moment, I know you'll nod your head in agreement. At minimum, you'll have to acknowledge how important it is to get control of this eating thing once and for all.
So please keep your mind as open as it's ever been.
After all... what if I'm right?
### Who am I?
I'm a formerly obese guy with very poor cardiovascular genetics...
A guy who almost ate himself to death despite a dozen warnings from doctors and other health professionals...
Who wasted years of his life believing he had a mysterious disease which caused him to compulsively overeat...
And who used to think he was powerless to resist bagels, pizza, chocolate, donuts, pasta, potato chips, and pretty much anything else which tasted good in mass quantities.
My ongoing food compulsions and preoccupations did not deter me, however, from earning a Ph.D. in clinical psychology, nor from building a large, very successful practice, nor even from funding my own food-preference research project with 40,000+ people.
And for the last 25 years I've been the CEO of companies which have provided tens of millions of dollars in research and consulting services for Fortune 500 companies. These firms have included major food manufacturers like Lipton, Kraft, Nabisco, etc.
Frankly, I'm a guy who couldn't stop thinking about food, even while he was working with psychotherapy patients and coaching clients...
Someone who spent most of his life feeling desperate to control his food problem. That is, until I discovered a child-like trick of mind which got me thinking like a permanently thin person...
A weird idea which got in my head and grew progressively stronger by itself, no matter how hard my fat-thinking-self tried to eliminate it!
WARNING:
Your Fat Thinking Alter-Ego Does
NOT Want You to Read This Book!
Your Fat-Thinking-Self will say anything to prevent you from reading this. For example, it may already be saying something like this:
"You've got to be kidding me! Another diet plan? There's NO way we could ever do this. You're too weak, you never stick with a hard and fast food rule. Besides, are we really just going to eat like rabbits for the rest of our life? C'mon. Just put the book down and let's go have us a little Bingeing party. Can we? Can we? Huh!!?"
So let me promise you something up front: This book is about cementing your ability to stick with the Food Plan of your choice. It's not about getting you to follow _(or not follow)_ any particular diet. Absolutely everything about what you eat, when you eat, and where you eat will be entirely up to you.
Your Fat-Thinking-Self will also object to drawing the clear "lines in the sand" required by this technique:
"Are you really NEVER going to cross the line again? That's just a set up for feeling guilty when you Binge and you know it. Do you really need more guilt in your life? Now just go get me some 'comfort food'...it'll be yummy!" – Your Fat Thinking Self
These guilt-threats need not frighten or control you. Because in this book we'll apply a very kindhearted, effective way to recover from mistakes without becoming preoccupied with guilt and shame. If you fall down, you'll just get up and resume where you left off. There's NO need to repeatedly smack yourself in the head with a spatula! _(Note your Fat-Thinking-Self's immediate excitement at the possibility of you falling down.)_
That said, since fear of guilt and failure stops many people before they've had a chance to really try this, let's talk a bit about how we'll handle mistakes in the Never Binge Again way of thinking. In short, we just treat ourselves the same way we'd treat a child who's genuinely trying to accomplish something important.
For example, suppose your 5 year old daughter has her heart set on riding her bicycle to the top of a very steep hill without stopping. Would you say "You'll never get to the top without stopping, little Sarah. That hill is WAY too steep. I don't want you to feel guilty and ashamed after you fail, so let's not even try, OK?"
Of course not! Instead, you'd help her set her sights on the goal with confidence and enthusiasm. And if she didn't make it, you'd be right by her side to figure out what went wrong so she could do better next time. You certainly wouldn't make her feel guilty for failing to reach the top, nor prevent her from setting the goal in the first place.
In this scenario, Sarah would know in her heart of hearts that if she did fail, you'd be right there to pick up the pieces and help her do better next time. But _—and this is the key—_ with your support and enthusiasm she'd peddle up the hill with confidence and determination. And eventually _—perhaps not on the first few tries—_ she WOULD make it...in large part because you protected her from becoming pre-occupied with the possibility of failure.
In a way, you'd have encouraged Sarah to purposefully "keep a secret" from herself, so that doubt and insecurity would not interfere with her energy and concentration on the goal.
**In my experience this is the mindset of people who stop bingeing**. Like little Sarah confidently peddling up that big hill, you'll learn to put even the remotest possibility of failure out of your mind...even if you DO at times fail on any given attempt. If you make a mistake, you'll just pick yourself up and get back to peddling in the right direction, speaking kindly to yourself the whole time.
It's almost impossible to Binge if you refuse to yell at yourself.
Uncertainty, doubt, and low self-esteem are the psychological cancers which fuel overeating behavior. But rather than take years to eliminate these problems using traditional psychological methods, we're going to cut right to the chase, remove the possibility of failure from our minds as we "peddle up that hill," and quickly face down the guilt if we happen to make a mistake.
Therefore, we can confidently tell your Fat Thinking Self it no longer has the power to undermine your efforts with the fear of failure, guilt, and shame. With the power of Never Binge Again you can set any reasonable food goal with confidence and keep pursuing it until you achieve it—no matter how many attempts it may require. _(At this point your Fat Thinking Self will get very excited about the possibility of you requiring multiple attempts to stop bingeing. Just ignore these thoughts for now)_
We'll go into more detail about dealing with the fear of failure, guilt about mistakes, etc. later in the book, but now that you understand the basic concept it should be a lot easier for you to keep reading.
There's one last objection your Fat-Thinking-Self will raise about this book to stop you from finishing it, however: It will suggest aggressively rejecting all your fat-thoughts is a form of self-cruelty. It would prefer you keep trying to "love yourself thin" instead.
I promise you'll be loving yourself MORE _—and beating yourself up LESS—_ when we're done.
In this context, it's very important you understand that...
It's Almost Impossible to "Love Yourself Thin!"
Identifying and caging your fat-thinking alter-ego is how YOU finally come to dominate all your food decisions and permanently reprogram yourself to think like a thin person. It's how to disempower the destructive thinking which has, to this point, caused you so much trouble with food.
As noted above, many people reject this mental maneuver because they want to love ALL parts of themselves, no matter what.
The problem with loving, feeding, and nurturing ALL your thoughts and feelings is that certain impulses are too strong to restrain when they're given even a tiny opening. For many people, the physical and biochemical set up when it comes to food and other survival drives makes it extremely difficult to "love themselves thin." In my experience this includes _most_ people who struggle with binge-eating and/or serious bouts of overeating.
The compassionate soul inside me wishes this weren't true.
Plus, a book called "Love Yourself Thin" would sell much better than the one you're about to read. It would also appeal to more than just male bingers, as it largely does now. _(The Never Binge Again philosophy works equally well for both genders, but most women reject it for the above reasons.)_
Now, our fat thoughts are indeed a part of us. So I understand why people may perceive this technique as unnecessarily harsh at first _._ But if you'll take the time to think about it, I know you'll agree these thoughts represent the _worst_ part of us...
The part which has repeatedly caused us to act against our own best judgment, and continually change our minds about our most serious food commitments.
These thoughts are worthy of permanent rejection.
In my experience, the act of recovering from Bingeing, serious overeating, and/or simply learning to stick to a diet is NOT like nurturing a wounded animal back to health. It's more like capturing and caging an aggressive Doberman Pincher. This dog must respect and fear you—or it will have its way every time!
In the 1993 movie "A Bronx Tale," Robert Deniro's character says "it's better to be feared than loved." And while we definitely want to treat other _people (and our own constructive thoughts)_ with the utmost kindness and respect, I'm afraid Mr. Deniro was bang-on regarding your fat-thinking alter-ego.
Interrupting and disempowering the thoughts which sustain your bingeing and overeating is not a game of mercy, it's a game of ruthless domination.
The fundamental reason people keep changing their minds about food commitments is because they are unknowingly giving their "fat-thinking-self" nurturance and love.
For all the reasons above, the mental entity which will hereafter house ALL your fat thinking shall be deemed "the Pig!™"
### What is 'The Pig'?
THE FIRST THING YOU NEED TO KNOW IS THIS: THE PIG IS NOT YOU!
You have dreams and aspirations, but the Pig lives only to Binge.
You enjoy everything life has to offer, but the Pig wants only its junk and will say whatever it takes to get you to feed it...
The Pig doesn't care about the consequences to your health, body, well-being, or happiness — because the Pig must get its stuff at any cost! You want to love, learn, laugh, and live your life to the fullest. But the Pig lives only for that "one more" precious Binge.
You can plan, organize, and accomplish amazing things. But the Pig sees life as one big food party and spends all its time and energy trying to convince you to indulge.
Thankfully, YOU are the only one who can feed it.
Understand this and you're half way to controlling your weight forever.
The other half is learning to _cold-heartedly_ ignore its Squeals.
When it comes down to it, either you or the Pig is going to suffer, and it's NOT going to be you!
The Pig is responsible for most of the misery in your life...
It convinced you to eat all the wrong foods, in the wrong portions, at the wrong times — downgrading your health, confidence, and quality of life most likely for decades by the time you became willing to read this.
The Pig has talked you out of every perfectly reasonable weight-loss plan you've ever made...
It's prevented you from nourishing your body, mind, and soul...
It's robbed you of not only the body you want, but the energy you need to build the life of your dreams.
It's the Pig that's caused you to live with this unnecessary weight burden...
It's the Pig that's drained your success, health, and happiness...
And it's the Pig that's making you feel hopeless about ever losing weight for good.
But the Pig couldn't care less.
It cares ONLY for its own pleasure, and will destroy everything you love without blinking an eye... just to get one more precious bite.
The Pig deserves NO love and NO compassion.
It is NOT your inner child, a cute little pet, or anything else YOU might truly value in life.
So don't you dare confuse "pig" _(small 'p')_ with the Pig _(capital 'P!')..._
Because pigs _(the real animals)_ are quite loving and adorable. Some people even keep them as pets. But the "Pig" _(with a capital 'P')_ is a pathetic creature which will destroy everything you love if you let it.
Unfortunately, we can't completely eliminate it from our lives because the Pig is intimately connected to an anatomical structure we need to survive _(the midbrain)._ But you can eternally dominate it as long as you don't confuse its Squeals for your own desires, and as long as you do what's otherwise necessary for your survival.
THE PIG IS NOT YOU!
As crazy as it sounds, you must learn to treat the Pig with the same contempt you'd feel for a serious criminal. Because every time you "cross the line" and Binge despite your best-laid plans, there's actually a little voice inside you _— the Pig's voice —_ working hard to make it "OK".
But it's NOT OK! And this trick of mind is how you finally get good and disgusted with the internal thoughts which _— until now —_ have been ruining so much of your life in exchange for a few moments of toxic pleasure.
For this reason, we're going to voluntarily and aggressively separate ourselves from the Pig in our own mental space, and in so doing we're going to gain 100% dominance over its destructive ideas.
The Pig is NOT you, and deserves only your contempt. Learn to hear its Squeals, then promptly ignore them.
### Am I a raving lunatic?
Not quite.
I don't believe there's a REAL pig inside anyone.
It's only a mental concept. A voluntary trick of mind.
But here's the thing: It's not "just" a trick of mind, it's THE trick of mind that works where others fail!
We may wish to acknowledge the trick in order to maintain our ability to think rationally. But in order to get the job done, once we've acknowledged this, it becomes imperative to treat the Pig as if it were real.
Therefore, this will be the only time I'll point out the Pig doesn't really exist.
It's a conceptual framework to help you separate from the thoughts and feelings which, until now, have derailed your best-laid plans. A way of thinking which helps you take control and live the life you deserve. But in order for it to work, it's got to seem 100% real to us during ALL potential moments of temptation.
You might struggle with this idea at first. Your Pig would certainly prefer you believed it didn't exist. Because then you'd think its Squeals were your own thoughts — and, as you'll soon discover, this is the ONLY way the Pig can get you to feed it.
Who cares...
Cage the Pig and let it suffer!
REMEMBER: It's your mind and you're allowed to organize your thoughts and feelings any way you want. The Pig exists because you SAY it exists, end of story.
### "Are you really taking any of this nonsense
seriously? C'mon... let's just go Binge!"
Sincerely - Your Pig
TAKE THE TEST:
Is It Worth Defining a "Fat Thinking Alter-Ego" Inside You?
If you're not sure whether you're ready to define a "Fat Thinking Alter Ego" _(Pig)_ from which to aggressively separate, find out how much damage it's already done by taking the test at www.NeverBingeAgain.com
### How to hear the Pig's Squeals
To truly dominate the Pig we need to distinguish its Squeals from our own rational hunger. You'll need to make a concrete Food Plan with a set of your own specific Food Rules _... and then definitively commit._
The Pig hates rules and will do it's very best to destroy the integrity of any you may set. This is why you must take 100% ownership and responsibility. It's also why every rule _— and your Food Plan as a whole —_ must be set with 100% clarity. Otherwise, the Pig can use "fuzzy lines" and "diets you're just trying out for a while" to mercilessly assail your integrity and confidence.
You simply must...
### Create your own Food Plan
You'll need to thoroughly embrace your own Food Plan, comprised solely of your own Food Rules. Why yours and not some diet guru's, nutritionist's, and/or weight loss doctor's? Because after you're five years old nobody can follow you around making sure you eat right, that's why.
Of course, you can and should get expert advice.
By all means, read health books, and work with experts you trust to inform your thinking. But if you're reading _this_ book, odds are you've already done so. In fact, I'd be willing to bet my left kidney _—and I'm rather fond of that one—_ you've got a pretty good idea of what a well-balanced, nourishing, and reasonable diet looks like.
It'd work too, if you'd only stick to it!
So let's skip all the "Mama said eat your vegetables" stuff and cut right to the "stick to it" part...
If you're finally going to stick to a plan, you'll need to OWN it — 100%.
After all, whose hands are going to grab the car keys, start the engine, drive to the market, put the food in the cart, take out the money, give it to the cashier, put the bags in the trunk, bring them inside, put them away, choose the meals, prepare them, get out the fork, stick it in, pick it up to your lips and put it in your mouth?
Yours.
Not your doctor's, nutritionist's, diet guru's, or therapist's hands, that's for sure! And it's a good thing, too, because for all their well-meaning advice and expertise, none of these people could follow you around 24 hours a day, even if they wanted to do so.
The ONLY way you're ever going to succeed is if you accept 100% responsibility for every bite and swallow. You see, "trying out" professional diet plans is a type of dependency which sets the Pig up to retake control like this:
### "Must've been a bad diet plan that nutritionist, doctor, or diet-guru recommended. You'll have to talk to them about it. Or maybe we need to find someone else to follow. Oh well, in the meantime we might as well just Binge. Yummy!!!"
— Sincerely, Your Pig
So, this one's up to you. You're completely and utterly responsible — 100%, not 99.999%. ONE HUNDRED PERCENT. Get it?
Breathe for a moment here and listen for your Pig's inevitable Squeal:
### "Wait just a minute here! This book itself is a diet book too, isn't it? After all Glenn's just another guy trying to make a buck with weight-loss advice. So go ahead, try it out for a while. Sooner or later you'll cheat like you always do, and then I'll be free to Binge again. Why wait? Let's do it NOW! Yippee!!!"
– Sincerely, Your Pig
What a Pig. Cage the Pig!
### How to own your Food Plan 100%
This might seem obvious but...
The best way to own your Food Plan is to write it down.
Every single Food rule... and the Plan as a whole.
100%, unambiguously.
That means, if 10 people were to review your plan and watch how you ate all day long, they'd _unanimously_ agree whether you were on it or off it. Not 9 of them. ALL of them.
However, your Food Plan is a very private matter. So this "would 10 people agree" test is only a thought experiment to help YOU judge whether you've articulated it clearly and precisely.
The reason you want to spell out your plan with enough precision that 10 people could agree is because ambiguity is the Pig's best friend...
Ambiguity is a yellow light, not a red one...
And the Pig will go 100 miles per hour from a quarter mile away to speed through a yellow light. You can count on it, every time.
When the specifics are laid out in incontrovertible detail, however, you convert fuzzy yellow lights into red, and it becomes impossible for the Pig to run the light without getting caught—because you'll immediately recognize any thought suggesting you run the light as Pig Squeal _(fat thinking)_...
...which you can promptly ignore — not argue or debate with, not console, not attend to in any way...
Ignore.
There's NO use trying to reason with The Pig. It doesn't care for your well-being. All it wants is to Binge, and it will twist around every last bit of information and attention you provide in order to persuade you to feed it. Therefore, we starve the Pig of information and attention at every turn.
If you simply ignore the Pig, the red lights will hold forever.
Why?
Because YOU are the only one who can put your foot on the gas and run the lights _— no matter how much the Pig may protest or try to convince you otherwise._
The only danger is in not recognizing Pig's Squeal for what it is. _The only danger is thinking the Pig is you._ That's why we're such sticklers for a precisely defined plan.
You do NOT have to follow anyone else's guidelines for writing up your Food Plan. Do it in whatever manner suits you best.
After all, it's your Plan. And as long as it's 100% unambiguous, clear, and nutritionally sound, it will suffice.
In a moment, I'll provide a simple set of guidelines for constructing your Food Plan. However, I must first warn you, your Pig will Squeal louder in response to this part of the book than any other. Just continue to ignore its objections and remember three important things:
(1) Even though we'll be talking about how to use "Never" and "Always" kinds of rules to provide clarity, these are NOT required elements of this program _—you can construct healthy and effective Food Plans entirely without them_. _(Download the free food plan starter templates from_ www.NeverBingeAgain.com _for examples)_...
(2) The goal is to create the _LEAST_ severe Food Plan which still protects you from previously troublesome food behaviors. Only you can know how to comprise this. But the purpose of the plan is to give you an unshakable sense of confidence, not turn you into a "Food Nazi"...
(3) Even though we'll push any semblance of a doubt in our ability to keep to your Food Plan out of our minds so we can "peddle up the hill" with 100% confidence, we do have a plan for gently forgiving ourselves and quickly resuming course if mistakes are made.
With this framework in mind, let's talk about:
### A Simple Set of Guidelines for Constructing a Food Plan
As long as your Food Plan is easy to remember, unambiguous, and nutritionally complete you _can_ make it work. Here are some simple categories of Food Rules you may wish to consider:
• **NEVERS:** What foods, drinks, and behaviors will you _never_ indulge in again as long as you live?
• **ALWAYS:** What will you _always_ do regarding food, drink, and food behaviors?
• **UNRESTRICTED:** What foods, drinks, and food behaviors will you permit yourself to have _without restriction?_
• **CONDITIONALS:** What foods, drinks, and behaviors will you permit only at certain times, in certain amounts, and/or restricted by other _conditions?_ _(Specify these in exquisite detail so there's no ambiguity about when the light is red vs. green. Avoid yellow lights because in the Pig's way of thinking, yellow = bright green.)_
There are a lot of different variables involved in constructing a Food Plan, so it's somewhat more difficult to quit Bingeing than to stop abusing drugs, cigarettes, or alcohol. With the latter you can just quit. But with food, you've got to keep eating _something_.
The Pig will try to defeat you with this fact. A good Food Plan eliminates the possibility.
Once you're armed with a crystal clear plan, you'll quickly catch on to your Pig's handful of sneaky strategies, no matter how long you've previously been fooled. Therefore, we're going to spend considerable time illustrating how to adopt Nevers, Always, Unrestricteds, and Conditionals, and make them stick.
Let's start with NEVER.
Never is the simplest and clearest red light of all. Creating even one Never is a great way to learn how to hear the Pig's Squeals because it clearly draws the line between your food vs. Pig Slop. Setting even one Never is how you begin your new life.
### "OK, OK. If you're going to insist on doing
something to slow down for a while, how about
we just quit Bingeing one day at a time?
I could definitely live with _that_. But whatever
you do just don't say NEVER!"
– Sincerely, Your Pig
### How to Never Do Something (Anything) Again
NEVER is a word you won't hear much in our culture when it comes to food, alcohol, drugs, or any other pleasurable substance. That's a shame, because it's one of the most powerful words for taking permanent control over the Pig.
If you can't say you'll NEVER do _something_ again _(or never engage in a particular food behavior again),_ the Pig knows it's only a matter of time until it gains the upper hand. If we define a "Binge" as engaging in any eating behavior which contradicts your Food Plan, then at very minimum we must be able to say we will NEVER Binge again.
So we will carefully define a livable and acceptable Food Plan and then NEVER break it again!
If you think about it, it's very odd how unwilling we've become to say NEVER when it comes to things which have caused so much misery in our lives. There are many behaviors we expect people never to engage in. So why not add one more when you have so much to gain?
• We expect responsible members of society to NEVER kill, rape, or steal...
• We expect people with life threatening allergies to avoid certain substances for the rest of their lives _(for example, there are some people who simply can't eat peanuts... EVER)...
_ • We expect people to NEVER act on their sexual impulses in public...
• And married persons are supposed to confine their romantic and sexual adventures to each other. We even have a legal contract _— the marriage license —_ which formalizes this understanding.
In fact, we've all learned to NEVER do many things just to get through everyday life:
• Never put your hand on a hot stove or in the electric socket
• Never threaten a political official with bodily harm
• Never grab a knife on the sharp end
And some of our 'Nevers' are so strongly ingrained we don't even realize they're learned behaviors. For example:
• Never pass gas at the table when dining with others
• Never grab a total stranger and kiss them on the lips
• Never sit at the teacher's desk in school
• Never take off your shoes and socks in church
• Never kick a policeman in the tushy
By the time most children are 10 years old they've naturally learned all of these things — and if they can do it, so can you. Adding one more 'Never' is child's play, no matter how much short-term pleasure one must sacrifice, and no matter what your Pig says!
### "Are you really going to let this guy tell us to
NEVER eat something again? C'mon, have a spine!!"
– Sincerely, Your Fat Thinking Pig
IMPORTANT: Despite what your Pig may say, nobody is telling you what to do. In fact, that's the whole point.
Until now you've allowed the Pig to impose its will as if you were its slave. The information in this section gives YOU the power to make _permanent_ decisions without the Pig's pernicious influence. The moment you put even one Never in your Food Rules, you've begun to cage the Pig!
### Always
Always is Never's best friend. Defining some things you will ALWAYS do _— and acting on these commitments —_ will give you even more confidence in your ability to cage the Pig.
Yes ALWAYS — you know, as in every day for the rest of your life.
Your 'Always' list can include general self-care in addition to food specific behaviors. For example, maybe you always start the day with a glass of water. Or maybe you always shower in the evening to help you get to sleep without extra food. Maybe you always meditate, exercise, or make fresh vegetable juice.
Maybe you always eat an apple before lunch...
Or maybe you don't _always_ do anything.
Whatever you put here, just remember "always" and "never" are sacred vows. They become something the Pig can't assail, no matter how hard it tries, because the motives behind any Squeal suggesting an exception will be recognized immediately.
But as soon as you declare an intention which interferes with the Pig's yummy Binges, it will begin trying hard to defeat you. That's its job. You see, the Pig genuinely believes it will die without its precious stuff. But you will prevail as long as you remember the Pig Squeals are not your own thinking.
For example, suppose you always drink 16 ounces of purified water when you wake up in the morning. Always! As soon as you declare this rule, your Pig may say something like:
"You can't say ALWAYS! How could you ever know that? One morning you'll wake up and forget. Or maybe you just won't feel like it. Some mornings you simply won't have the time. Then you'll have broken your silly vow. These ridiculous rules obviously don't matter since you can't possibly stick with them. We might as well just go BINGE!" —Sincerely, Your Pig
To prevail, you need only dismiss this as Pig Squeal.
Don't argue with the Pig.
Don't try to win a rational debate.
You don't need to, because the Pig is powerless to do anything without your consent. If the Pig could act on its own behalf it would immediately do so without asking. The very fact it talks _at all_ proves its only hope is to convince you with its lies.
All that's necessary is to ignore it.
Notwithstanding this, let's dispute its points one by one, just to show you how ridiculous the Pig's arguments can be:
### "You can't possibly mean 'Always'.
Nobody can ever know what they're always going to do!"
This is the Pig's first attempt to pull the wool over your eyes. It says "You can't always do _anything!_ " What a negative, confidence-destroying message.
Would you ever tell a young child: "Listen little Bobby, there's NO hope of remembering to brush your teeth, tie your shoes, and get dressed all by yourself every day. Just get that idea out of your head. You might as well just give up and accept you'll be a dependent little child the rest of your life... no matter what the big boys do."
Of course you wouldn't! Then why let the Pig talk to you that way?
The truth is there are many, many things people ALWAYS do daily...
• They turn off their alarm
• Roll out of bed
• Pee in the toilet
• Brush their teeth
• Etc.
• You can add one more ALWAYS anytime you want!
Let's go on...
### "One morning you'll wake up and forget.
And then you'll have broken your silly vow."
The Pig wants you to _plan to forget_ your vow. But the very nature of a vow is a _plan to remember_. Which is more constructive? Which is more likely to improve your life?
The answer is obvious. So why would anyone ever make a plan to forget when we, as human beings, have the ability to plan to remember? People don't do that. Pigs do!
Any doubt you have about your ability to ALWAYS do something is 100% driven by the Pig's desire to have you break your vow. It doesn't care what impact this has on your confidence, self-esteem, health, or loved ones. The Pig is an anarchist and will try to destroy any structure which interferes with its Binges — at the expense of all your goals and aspirations. It has only contempt for your higher plans. Which is why we owe it nothing but contempt in return.
The truth is there are many things we're perfectly capable of remembering to do every single day. For example, taking care of our children.
"Sorry little Sarah, I'm afraid I won't be giving you anything to eat or drink today. And you'll just have to stay up all night because Daddy can't possibly remember to put you to bed either" — _How your Pig would take care of a small child_
We also drive our cars home every day and park them in a safe spot – _instead of the lawn or the neighbor's rose garden_ – even though the latter might be more convenient _._ We eat and/or drink enough to sustain us through one more day. And we put ourselves to bed every night somewhere at least reasonably safe and comfortable _(as opposed to lying down outside in our front yards without a tent or sleeping bag)_
### "These rules are just silly... obviously they don't
matter at all since you can't possibly stick with them."
See how the Pig attempts to undermine even your simplest effort at positive, healthy change? It doesn't care if you die of dehydration. It must subvert your confidence and impulse control or else it won't get any more Pig Slop _(ever)._ Knowing this, it's clear we can't ever take it seriously.
### "You might as well just let me BINGE!"
The Pig's true nature comes out at last. The Binge is all it was after all along.
But just for argument's sake, suppose you DID break your plan to always drink 16 ounces of purified water every morning. Does it naturally follow you should go out and buy several bags of Doritos, a box of donuts, a pound of chocolate bars... and go to town on them all at once?
Of course not. If you forget to brush your teeth one morning, are you obligated to pick up a hammer and bang them all out? It's ridiculous.
**Pig Squeal may** _seem_ **rational on its surface, but it never is.** _(Never —as in never, ever, ever)_
The Pig can appear very appealing _at first_ because of its ability to leverage a vulnerability in your survival drive. But when you hold its Squeal up to the light of day it NEVER makes any sense.
Just ignore Pig Squeal when you hear it. Period, end of story.
### Unrestricted
Some people find it helpful to list out those things they can eat and/or drink in unlimited quantities without concern. Others just designate the 'Unrestricted' category as being everything that is not specifically listed on their restricted list.
Usually the 'Unrestricted' category is comprised of healthy "go to" foods you feel good about eating. For example, perhaps you want to allow as many leafy greens, cruciferous vegetables, green tea, beans, berries, clean water, etc., as you desire.
Or maybe you feel safer with NEVER and CONDITIONAL rules for everything... and prefer not to leave anything unrestricted. It's completely up to you!
However you handle your 'Unconditional' section, just be sure you remember the Pig's favorite con:
### "We simply MUST cheat this one time only or
else we will promptly starve to death!"
— Sincerely, Your Pig
Regardless of how you construct your 'Unrestricted' category you must always ensure there is enough leeway in your overall Food Plan so you'll have enough to eat. Otherwise the Pig's Squeals start to sound more alluring — and you must always be able to dismiss them outright.
Humans evolved during times of intermittent famine. Our bodies are set up to go for long periods without eating. It takes a minimum of several weeks without food for most people to starve to death. What are the odds you're going to die if you skip a meal? Slim to none!
There's NEVER a good reason to Binge.
The Pig is NOT trying to take care of you by suggesting you'll starve if you don't make an exception to your Food Plan. Its purpose is NOT to nourish your body but to destroy your Plan so it can go on an all-out Food Orgy.
Cage the Pig and let it suffer!
### Conditional
There are some foods and drinks that might work for you only in certain situations, at certain times, or when accompanying certain behaviors.
Maybe you only allow yourself sports drinks after a certain amount of exercise on a given calendar day.
Maybe you get to have a certain treasured meal only when dining out with friends, but no more than twice a week.
Maybe it's that you only eat chocolate on Saturdays.
Or maybe you just eat pretzels on days when you take your son or daughter to a major league baseball game.
The point of the 'Conditional' category is to acknowledge certain foods, drinks, and food behaviors are only troublesome when left unregulated _— or only in certain situations._
The limit on the conditions you impose only stems from your own imagination and experience. I'm not necessarily suggesting any of the examples above are good or bad. But I will leave you with one caution: Avoid letting your 'Conditional' section become _too_ complex. It's very difficult to remember complex rules when you're hungry, so the simpler the better.
Keep going over your conditions until they're expressed in the simplest possible language.
Fewer, clearer rules tend to work best.
For some people this is just a sentence or two, for others it's a whole page. Still others will have NO food or drink as 'Conditional' whatsoever.
The point is to go through the exercise and think through which foods, drinks, and food behaviors you don't need to give up entirely, but which still require _some_ degree of control. It can also help articulate in writing your rationale for each of these conditions to ensure the Pig is not sneaking in some Squeal.
Last, if you find you're repeatedly struggling to find the right condition for a particular food, drink, or behavior, the odds are you'd do better putting it into the 'Never' section. _(This paragraph can save you years of painful struggle so you might want to re-read it)_
There you have it.
Never, Always, Unrestricted, and Conditional.
Four beautifully simple categories to create your own personal, self-contained legal system for governing your eating from here on.
Go ahead and create a first draft of your Food Plan. But before you finalize it, let me expose you to some of the most violent Squeals you're likely to hear once you've set it down in black and white _._
See, your Pig absolutely hates the idea of a crystal clear Food Plan. It wants you to believe such a Plan will restrict your freedom. _But exactly the opposite is true_. Just as most great jazz players practice their scales for years before they can freely express their creative genius, so too will you need structure around food to truly enjoy not only your food, but ALL the freedom life has to offer:
THE QUESTION IS, WHO WILL BE FREE, YOU OR THE PIG?
The question isn't whether you'll have freedom of choice vs becoming enslaved to a Food Plan. The question is, will you choose to live your life as a slave to the Pig's impulses and demands, or put the animal in its cage so you can exercise your human freedom?
Besides, you already have a Food Plan whether you write it down or not! It's impossible to function each day without making decisions about what you'll never, always, sometimes, and conditionally eat. The problem is, most people make these decisions _unconsciously_.
For example, everyone _always_ stops overeating at a certain point, even if that point is unhealthy. They might eat a whole pizza, but not five. And they certainly don't eat the box the pizza came in.
Almost everyone also _always_ has their favorite treats too—consumed in just the right combinations and amounts.
And there are at least some things most people avoid entirely for reasons of taste, convenience, or health.
Since you already DO have a Food Plan, I'm only suggesting you take control. Make it conscious and evaluate it with the full force of your intellect. Write the darn thing down!
Now, I've purposefully avoided recommending any particular Food Plan and/or positioning myself as a dietary or nutritional expert because the moment I even hint at telling you what to eat, your Pig will inevitably Squeal "We could NEVER eat like that! You might as well stop right here"
See, your Pig would LOVE to turn this into a big nutritional debate because there's still a lot of controversy about what constitutes the ideal diet. And the Pig knows that immersing you in this controversy would distract you from the main point, which is permanently committing to a Food Plan of _your own_ design, using _your own_ best thinking.
But now you're aware of this Pig strategy, so you won't be vulnerable to it...
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Now, believe it or not if you've read this far, you've actually got enough information in your brain to defeat your fat-thinking-self forever:
• The Pig is NOT You. It is a conceptual, animalistic entity which misdirects your survival drive towards food behaviors that do NOT serve your best interests, and causes you to keep changing your mind about your commitments. Unfortunately, due to our anatomy we're all forced to spend a lifetime with this presence inside. But we _can_ choose to intellectually and emotionally sever it from our own definition of self. In so doing we separate from the onslaught of destructive urges and irrational thinking to which we were previously vulnerable. We can stop behaving against our own best judgment and pursue our goals and aspirations _without_ ongoing sabotage. We will lock the Pig in a cage and dominate it completely, showing it nothing but contempt. Many years of suffering have proven it will dominate _us_ if we do anything else.
• To accomplish this, you must take 100% responsibility for defining your own unambiguous Food Plan. You can draw inspiration from various experts and books, but nobody _— not even the most renowned diet expert —_ can follow you around to be sure you comply. For this reason, and because nobody knows how your body reacts as well as you do, the buck absolutely must stop with you. There are free starter templates available on the website.
• Define your Food Plan with 100% clarity so you can tell with certainty when you are ON versus OFF it.
• A Binge = even one bite and/or swallow outside of your Food Plan.
• You will NEVER Binge again.
• Pig Squeal _(fat thinking)_ is ANY thought, feeling, or impulse which suggests you may ever even consider the possibility of Bingeing again. Since you _(your thin-thinking-self)_ will NEVER do it _— and since there's just you and the Pig inside your head —_ anything which even remotely suggests you will do otherwise must be coming from the Pig.
• Pig Slop is anything which violates your Food Plan even 0.00001%. Bingeing = putting even the tiniest bit of Pig Slop in your mouth.
• Your Pig's Trough is where its Slop belongs. You never eat out of a Pig's Trough, so you will never eat Pig Slop again.
• From now on when the Pig Squeals for its Slop, you will just ignore it. Only Pigs eat Slop and you are not a Pig, so there's never any reason to engage or debate the Pig about the idea.
• In this way, you may defeat the Pig forever.
Even though the above is all you need to dominate your Pig, it will work hard to sneak Squeals past you in every possible manner. So let's review some of the most alluring Squeals you're likely to hear once you resolve to dominate the Pig. For example, your Pig may already be saying something like:
### "Glenn says you'll be weak and vulnerable until you've heard all of my best techniques. That means we can keep on Bingeing until you finish this book! Take your time because it's Yummy!!! Yipppeeeee!!!!"
— Sincerely, Your Pig
See what I mean?
What a Pig!
But still, in much the same way prisoners of war can be inoculated against brainwashing by pre-exposing them to the techniques their captors are likely to use, you can benefit from the accumulated wisdom of those who've defeated their own Pigs before you.
For this reason _— and even though NONE of the Pig's Squeals ever stand up to the light of reason —_ we will address and dispel your Pig's sneakiest Squeals as we progress.
In other words, I'll prepare you with foreknowledge of the many stupid, stupid ways the Pig will try to trick you.
Not surprisingly, the very first thing your Pig may say after you've sworn your sacred oath to your Food Plan is "You're just being silly now. How will you manage those inevitable, irresistible cravings?"
Chapter 2
### How to 'Deal' with Cravings
First of all...
### You do not have cravings –
your pig does! So when you
feel one coming on, just say:
### "I WILL NEVER EAT PIG SLOP AGAIN!"
(Then move on to a more valuable way to spend your time and
energy, or a healthier way to nourish your body, mind, and soul)
From where you sit right now, it might be hard to believe this is ALL you need for dominating any craving. But it's true. In fact, the conclusion flows naturally from the definition of the Pig itself:
THREE STEPS TO DEFEAT ANY CRAVING
1. **Remember:** Consuming even the most minuscule amount of Pig Slop _—anything even remotely off of your well defined Food Plan—_ is, by definition, a Binge.
2. **Recall:** All thoughts and feelings which suggest you may ever Binge again are Pig Squeal. Therefore _you_ do not have cravings, your Pig does. ALL cravings are Pig Squeal.
3. **Reiterate:** So just quietly but proudly say to yourself [1] "I will never eat Pig Slop again!" _(Some people like to add "And I shall remain 100% committed to my Food Plan until my dying breath")_ Then go on with your day, ignoring the Squeals.
That's all.
Or you can just use the shorthand:
"That's Pig Slop, and I NEVER eat Pig Slop!"
You might want to print this out and carry it around for a while.
Oh wait... did you hear that? Your Pig just got very excited:
### "Glenn says to Never Binge Again you need to carry around these three steps. That means if you ever forget them _— which you know you will —_ we can just Binge until you remember. Yummmmmy!!!"
— Sincerely, Your Pig
What a Pig!
Just remember ONE thing and you'll be fine:
### You Will Never Eat Pig Slop Again!
By definition, every craving is nothing more than a desire for Pig Slop — every last one. So just ignore it and go on with your life.
Let's make it even simpler: The one and only thing you need to do to ensure you do not Binge is 'not Binge!' Mind blowing, isn't it? Still, some people find it comforting to carry around the above three-step reminder. Enough said.
Now, other people tell me that even though they understand and agree with the definitions above, the cravings are too uncomfortable to tolerate. These people don't realize the Pig has convinced them of yet another insane proposition: That one must be comfortable at all times, and that Bingeing is the ONLY way to alleviate discomfort.
Unfortunately, we all must share our bodies with our Pigs. So, when the Pig has cravings, we indeed might feel uncomfortable — if we haven't taken a few precautions first. Sometimes even if we have.
Momentarily I'll tell you how to eliminate _most_ of this discomfort, but one critical point first:
**YOU DO NOT NEED TO BE COMFORTABLE TO STICK TO YOUR FOOD PLAN** _(FOREVER!)_
Because the Pig is a survival drive run amuck, it thinks it will literally die without comfort. This is why it will go to any length to get you to feed it. But comfort is not a "must have," only a "nice to have." Therefore, before your Pig will let up, it will need to know you're willing to tolerate ANY level of discomfort without Bingeing.
Of course, feeling bad for the sake of feeling bad would be masochistic, so we will definitely take steps to make ourselves comfortable. But if we're going to hold our Food Plans sacred, there _will_ be times we feel uncomfortable. So be it. Our Pigs must know we will NEVER consider these times Bingeing opportunities.
Let's do a little thought experiment to illustrate your in-born ability to tolerate enough discomfort to Never Binge Again. First, bring to mind some Slop your Pig would absolutely love to eat — its favorite junk.
Next, think of someone you love dearly — perhaps your son or your daughter, or maybe a spouse, sibling, parent, or beloved pet. _(If there's nobody in your life you love dearly right now, think of a role model or celebrity you care about.)_
Before you go any further, please be sure you really are thinking of a special person _—_ AND _—_ something your Pig craves with all of its disgusting essence. This exercise will only take a few moments, but you'll remember it the rest of your life. It can dramatically strengthen your ability to manage cravings, so don't let your Pig cheat you out of it by suggesting you skip this, OK?
OK!
Now assume an evil dictator is stalking the person you picked, and he presents you with a twisted choice: Although he will continue watching your special person forever, the dictator will never contact, influence, or harm them in any way _— provided you abstain from the Pig Slop under consideration until you draw your very last breath._
But if you ever indulge again _— no matter how far in the future, no matter how small the amount, and no matter what the circumstance —_ the evil dictator will kidnap and hold them in a prison for the rest of their lives. You'll always know the one indulgence you just "couldn't resist" was solely responsible for depriving your very special person of their freedom forevermore _._
Remember, this dictator has the resources of an entire country behind him, so the authorities are powerless to stop him. The ONLY way to keep your special person safe is to completely abstain from even one more bite or swallow of your Pig's favorite Slop — _forever._ You'll literally have to avoid it for the rest of your life as if it were poison because the consequences are so grave.
What would you do?
It's a no-brainer, isn't it?
When you care enough, tolerating any level of discomfort FOREVER is suddenly within your power. No matter how strong a craving the Pig might throw at you.
No matter how much the Pig may Squeal for its junk, I've got little doubt you'd keep your word in this situation.
Your Pig needs to know this! It must understand you're willing to tolerate any level of discomfort without ever Bingeing again. This does not mean you _must_ feel uncomfortable, just that if you do, so be it.
With this key distinction between the desirability and necessity of comfort behind us, let's talk about what you can actually do to make yourself more comfortable while you cage the Pig.
The key is recognizing there is a very real survival drive which the Pig hijacks and turns against us. Humans are wired to seek sustenance as a major priority in three situations: (1) when nutrients are depleted; (2) when we get too cold and; (3) when our blood sugar drops too low. Sometimes, we also confuse dehydration with hunger. Therefore:
You can keep the discomfort associated with cravings to a minimum by staying relatively warm and hydrated, and consuming regular, consistent, healthy meals.
Most people can almost totally eliminate the physiological experience of cravings when they attend to these elements of self-care.
There's one more very important thing you can do to ward off cravings: Acknowledge the difference between killing a craving and "getting high" with the hyper-palatable treats our modern food industry has engineered to overstimulate our brain's reward centers. Your Pig wants to get high with food, but your goal is _only_ to eliminate the craving so you can go on with your day.
Perhaps the concept of getting high with food is new to you. That wouldn't surprise me because our culture actually condones and reinforces the habit. It doesn't identify the experience for what it really is.
Economic incentives have sent the industry on a never-ending quest to make foods which push our evolutionary buttons — foods with high caloric density, and foods with progressively more addictive potential. Unfortunately this pursuit is so lucrative, things will probably only get worse in our lifetimes. It's unfortunately very difficult to stop a giant economic machine.
This likely is not news to you.
What most people don't realize, however, is WHY our economic infrastructure developed to support this type of activity in the first place. And, if we're going to have a more mature attitude about food _— and make the Pig's Squeals even less alluring —_ it's helpful to understand how these forces developed. Knowledge is power.
The very fabric of society once depended on its ability to refine food in this unnatural way. When it became necessary for larger tribes to send armies over longer distances, it was difficult to transport enough whole, natural food to feed the soldiers on the journey. And as our society developed specialization of labor, we required workers to spend whole days focused on their singular trade, rather than hunting and gathering for themselves.
This is why ultra-dense, portable sources of calories became an essential part of our civil structure. In many ways _— though there are now much better alternatives available —_ the survival and economic balance of nations once depended on these foods, and they've become firmly entrenched in our culture.
Beyond this, the prevalence of disease before modern medicine made being too thin much more of a risk than being too fat. And only recently have most societies become able to keep starvation at bay for a majority of the population.
These are among many of the stronger reasons it became a moral transgression to waste food in our society. And why just a few hundred years ago in Europe, being portly or chubby was a sign of higher status, as was the "luxury" of consuming white flour, and white sugar!
These forces _—in addition to the ridiculously delicious nature of those super-rewarding foods heavy in sugar, salt, and oil, etc.—_ caused us to develop cooking habits and social norms to ensure continued demand. For anyone to eat in another manner was a threat to society itself. The offender need either be reined in or cast out!
Moreover, "reining in" back then was much different than we think of it now. Today, acting differently than society as a whole is acceptable and even encouraged to a certain extent. But in the old days individualism was very dangerous because it threatened the survival of the tribe. While today you'll only be made to _feel_ like an outcast if you eat differently than everyone else, back then it was more like "step out of line and we'll kill you!" There was only a certain amount of food available, of a certain kind, at a particular time. So you ate what everyone else ate or you died. Period.
And even though things may be a _little_ better now thanks to the healthy foods movement, there's still a very strongly enculturated preference for gluttony _("Supersize that please")_ which is aided and abetted by big Agriculture with its nutritional denials and GMO modifications, not to mention the profits of big Pharma which treats the resulting diseases.
This is how our Pigs became fortified with (1) the extremely pleasurable drive to consume super-rewarding, ultra-processed foods _(the "Food High");_ (2) very strong social and familial support for indulgence; (3) traditions and Holidays which reinforce the use of these foods; (4) unspoken cultural prohibitions against abstaining; (5) the unspoken threat of becoming an outcast if you eat differently than the rest of society.
**In short, our society actually WANTS you to get high with food. The world around you is mostly on your Pig's side. To defeat the Pig, you must become willing to face this situation.** _(Once you do, it's easy!)_
The situation food abusers face today is very different than that faced by people who choose other substances. When a substance abuser indulges, they're making a choice to act _against_ societal pressures and norms. When they stop, they fall back into line with cultural norms, and more easily integrate into society.
The exact opposite is true with food.
Food abusers are actually supported by our culture to continue eating poorly. To get healthier, they must make a choice to act _against_ societal pressures and norms. To _stop_ abusing food means embracing _more_ unease and conflict with others. There are fewer restaurants you can easily eat in. Fewer markets to shop in. Family and friends will pressure you to eat the way they do. I could go on and on.
Thankfully there _is_ a growing community of healthy eaters where people who wish to stop getting high with food may find refuge. You can dominate the Pig regardless of social pressure as long as you know what's going on around you.
You can and will also learn to recognize the Pig Squeal stimulated by other people's Pigs and the food industry as a whole—even when nobody else acknowledges what's happening. All great progress begins with one person's willingness to stand against the crowd, and right here in this book you have all the necessary tools to do it.
In fact, it wouldn't matter if you were the only person in the world who wanted to eat healthy. As long as you're conscious of the social dilemma, you won't be fooled. Just recognize the voices of industry and culture you're surrounded by as Pig Squeal. And then remember you will never eat Pig Slop again, no matter what anyone else says!
Remember: All the Pig wants is one more Food High, and it will use the very fabric of society to back up its claims. It believes you will literally die if you don't Binge on some Slop, pronto!
But the Pig is wrong.
When you stick to your Food Plan and nourish your body you will NOT die.
But you won't get a Food High either.
You'll just kill the Craving and go on with your day.
This will NOT be exhilarating.
You'll experience life however life was meant to be on that particular day without a food high...
But YOU will be 100% in control.
This is the only way to get the results you want.
Killing a Craving is like pouring water on a fire in your back yard so you don't burn down the house. Getting high with food is like throwing gasoline on the fire and inhaling the fumes.
When you kill the Craving you're left with a few carefully contained, smoldering ashes which eventually die out on their own accord. But if you inhale the fumes, you'll obtain a brief sense of euphoria before being left with a much bigger problem to manage.
Another helpful analogy is contentment _(killing the Craving)_ vs. mania _(the Food High)._ Contentment is a gentle state of mind available to anyone who seeks it. It's not something people feel compelled to get up on the rooftops and shout about. Contentment is a solid, repeatable state which builds sustainable confidence, and a rational and responsible sense of well-being.
Mania, on the other hand, is inherently unstable. The Pig knows the Food High will eventually wear off, so it frantically Squeals to extend the high by Bingeing "just a little" more.
Mania is an unstable, temporary pleasure which becomes progressively more difficult to repeat. Just like with drugs, the Pig will require more Slop during each subsequent Binge in order to obtain the same high it experienced previously. This is what drug addicts call "chasing the dragon", and it destroys the Binger's confidence, health, and sense of wellbeing the longer it's allowed to occur.
So how do you deal with Cravings?
Cage the Pig, man... just cage it and let it suffer!
Your Pig has Cravings... you don't. And you will NEVER eat Pig Slop again.
Be willing to tolerate ANY level of discomfort to keep to your solemn vow—but stay nourished, warm, and hydrated to keep this to a minimum.
Kill Cravings, don't get high with food.
End of story.
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Chapter 3
### What if You DO Binge?
The first time you make a mistake you'll almost certainly hear something like this from your Pig:
### "You cheated! You cheated! You cheated!!! See? Your Food Plan doesn't mean anything at all! The Hell with this _'Never Binge Again!'_ stuff. You'll have to try something else to control me. YOU'VE BLOWN IT SO I AM NOW TOTALLY FREE TO BINGE AT WILL FROM NOW ON!!! Yippeeee!!! Yippeeee!!! Party Time!!! Let's Do It!!!!"
– Your Pig
This one Squeal causes more damage than virtually any other because it allows a small Binge to snowball into a full-blown Food Orgy, and seriously undermines confidence in your ability to control yourself.
This Squeal is wholly responsible for the "Screw it, you already blew it, just start again tomorrow" mentality. Or, in shorthand, the "F___ It" Squeal.
Learning to recognize and ignore the F__ It Squeal is, without a doubt, the most significant benefit of the Never Binge Again approach.
Thankfully this Squeal, like every other, is easily defeated once you see it for what it is. But because our culture actually supports Binge thinking, it can be hard to identify.
For example, I'm sure you've heard the idea of "progress, not perfection" bandied about by the so called experts. They may even quote scientific evidence which suggests perfectionism is a set up for a Binge.
While these are alluring ideas which can be helpful when placed in context, they unfortunately only tell HALF the story. What these half-truths fail to acknowledge is the significant difference in attitude required _before_ vs. _after_ a food mistake. Just like we can't walk on water or swim on dry land, we must maneuver very differently before vs. after a Binge. _(Remember, a Binge is even one bite or swallow outside of your very well defined Food Plan)_ :
• **BEFORE A BINGE:** Your Food Plan is 100% perfect and final. You Will NEVER Make a Mistake Again. You Will NEVER Binge Again!
• **AFTER A BINGE:** You are a fallible human being. You were _practicing_ a set of Food Rules, but that practice is now over and it's time for the big leagues. Analyze what went wrong, adjust your Food Plan if necessary, and THEN declare it perfect and final. You may have found it necessary to divorce the old Food Plan _(or simply failed to hear the Pig's Squeals about it),_ but now you're a changed person, ready to marry once again. You Will NEVER Binge Again!
The Pig wants to confuse these two situations so you'll reject your Food Plan as nonsensical. Why? So it can Binge of course!
I hope you're starting to see a pattern. Bingeing is ALL the Pig ever wants, and there's NEVER a reason to listen to it before, during, or after a mistake.
The Pig's "confuse and conquer" maneuver is easily defeated when you place your thinking in the right context.
**WHY PERFECTION IS THE BEST COMMITMENT TOOL** : Making a sacred commitment to your Food Plan is like getting married. And I've yet to hear these vows at a wedding ceremony:
" _I promise to love and be faithful...until an inevitable moment of weakness. I promise I'll do the best I can, but nobody's perfect and there sure are a lot of attractive people out there. I'm 80% sure I can be faithful forever, but anyone who promises you 100% is an unrealistic liar. A 'pretty good' promise is the best anyone can ever hope for, because you can't possibly know who you're going to sleep with next year, or in ten years. Just being honest. You want me to be honest, right?"_ _– The Vow Your Pig Would Make at Its Wedding!_
You'd never accept this kind of a wishy-washy promise from a mate...so why entertain it for your own commitments? Your Pig craves uncertainty, not you. It will exploit even the most miniscule crisis of confidence to tear at the very fabric of your most sacred vows.
Time for another thought experiment: Suppose your fiancé _—after realizing you wouldn't accept this level of uncertainty in the wedding vows—_ increased their confidence in a lifetime of fidelity from 80% to 90%. Would you marry them then?
What about 95%?
99%?
Kind of ruins the romance, doesn't it!
You wouldn't accept anything less than a 100% commitment, because perfection is the essence of commitment...all notions of human frailty aside.
PERFECTION IS ESSENCE OF COMMITMENT
**Allowing ANY possibility you will ever Binge again changes the commitment from "I will" to "I'll try"...which is NO commitment at all.** The "little engine that could" was in error **. "I think I can" is the wrong philosophy. "I know I can" is the only attitude which succeeds with impulse control because your Pig will use "I'll try" to destroy the very fabric of your Food Plan.**
Anything less than a plan for 100% adherence to your Food Plan is nothing more than the Pig's plan to Binge. You must authoritatively declare your Food Plan as 100% perfect or you are not committing to anything at all.
The philosophy behind "progress not perfection" as a _before_ tool is one of hopeless abandon to the Pig's impulses. To adopt the "progress not perfection" ideology is to believe it's literally impossible to dominate your Cravings.
Progress-not-perfection says there will eventually come an irresistible urge which forces you to indulge... it's just a matter of time.
Cravings are indeed a natural part of being alive. You can't escape them, but once you've drawn your perfect lines in the sand you need not fear them either!
Now, there actually IS scientific evidence that perfectionism is a set up for a Binge, but what'w missing from this analysis is context. Perfectionism is _only_ a set up for a Binge when you allow the Pig to use it to retrospectively assign powerlessness to you— _AFTER_ a mistake has ocurred:
### "Either you're perfect or you're nothing. Either you can perfectly control your food intake or you can't control it at all. You made a mistake and are therefore not perfect. Obviously, you are now completely out of control. I get to go on a big giant hairy Binge. Yippeeee!!!"
\- Your Pig
Perfectionism may be a set up for a Binge when you apply it after a mistake has occurred, but when you use it to lock in your commitments at the outset just the opposite is true. Perfectionism is the right approach to gain control of your eating forever when used as a commitment tool. In fact in this context I'd contend it is the ONLY approach that works. However, when applied as a post-Binge analysis tool it works in the Pig's best interest, not yours.
To Never Binge Again and permanently stick to our commitments we must recognize any and all insecurity as 100% Pig Squeal. By definition, it can't be any other way because Pig Squeal is any thought, feeling, or impulse which suggests you will _ever_ Binge again.
By definition, any and all doubt about your commitment to Never Binge Again is Pig Squeal.
**Now, what if you DO Binge?** Can you feel how excited your Pig is getting about the fact I'm even bothering to write this?
### "See, Glenn knows we ARE going to Binge again, otherwise he'd never put this section in the book. I'm so happy!!! Let's go already. Let's just do it!!!! C'mon already!!!"
– Your Pig
What if you DO Binge? What then???
Simple: Analyze what happened, adjust your sails, and then NEVER Binge again.
Why? Because the Pig must suffer, that's why!
Period, end of story.
Notwithstanding the simplicity and elegance of this instruction, many people feel the need for more direction to get back on track after a mistake. So let's talk about the right mental maneuvers to recover from a Binge.
First, please know that after a Binge your Pig will direct all its efforts to _building_ upon your mistake. And just as monsters are terrified of the light of day, the Pig prefers to hide in the dark. It knows under scrutiny you will become wise to its game, so it will try to get you to casually dismiss the mistake without examination—in hopes of keeping the errors in thinking and/or problematic Food Rules from being exposed.
In short, the Pig will martial all its efforts to stop you from carefully reflecting upon what happened and instead try to direct your energy towards Bingeing more.
Knowing the Pig's post-Binge goals, the first thing to do after a Binge is remember what a serious, solemn oath committing to our Food Plan actually was. After all, your ability to stick with your own commitments is your ability to keep your word, and without your word, you don't have much. So if you find you've made a mistake you must take it _very_ seriously and become willing to carefully reflect upon what went wrong.
On the other hand, creating the perfect set of Food Rules for any given individual is a complex matter... not unlike creating a set of laws to govern a large, interactive society.
Successful legal systems always contain a mechanism for self-correction. For example, although the framers of the United States Constitution fully intended it to govern as the law of the land, they understood it was still a potentially fallible document. So they included a mechanism for amending it over time.
But the process for amending the Constitution does _not_ allow for impulsivity. It requires a drawn out process of proposals, votes, and ratification. These delays ensure serious consideration is given to the ramifications of change, and make it difficult for any one crazed person _(or group)_ to seize power and undo all the good work.
Therefore, the first thing to do after a Binge is to examine what happened. Review your Food Plan with an eye towards determining whether you believe each Food Rule within it is still in your best interest.
Is the Food Plan as a whole still the most accurate representation of a perfect, healthy lifestyle? Or does something need to be amended?
**More often than not, Binges occur simply because you failed to hear the Pig's Squeal, NOT because of a problem with the Food Plan itself.** The Pig slipped in a few destructive words which you mistook for your own thinking, and you acted upon them.
This is called a "Simple Pig Attack" and requires NO changes to your Plan. If you've experienced a Simple Pig Attack just put the Pig back in its cage forever by re-committing in full to the exact Food Plan you just broke.
This is what we mean by "just Never Binge Again" as the best mechanism for fast and permanent recovery. But remember, your Pig will Squeal violently because it doesn't want to go back into its cage, once again locked away from its Slop forever. Listen for things like:
"You obviously can't lock me in my cage forever. You're too weak. I just got out, so of course I'll get out again. Maybe I can't beat you now but it's only a matter of time until we Binge again. Yippee!!!" _– Your Pig's response upon hearing you will Never Binge Again after a recent indulgence_
This is utter Pig Squeal and has NO constructive purpose. The Pig doesn't care about your well-being at all. It ONLY wants Slop, so why would you ever take its thoughts seriously?
Just ignore the Pig on this matter, don't debate it.
Notwithstanding the above, having rational answers for this nonsense is helpful to many people as they're first learning how to cage the Pig. So let's address the Pig's "points":
• "You're too weak" Making a renewed effort to eat more constructively is evidence of strength, not weakness. Even if you've repeatedly fallen down for years, continuing to get up until you succeed is a mark of fortitude and perseverance, not weakness. A weak person just listens to the Pig and gives up. A strong one resolves to lock the Pig back in its cage forever. Making a renewed vow of abstinence proves your strength. When you think about it this way, you'll see how truly pathetic it is that the Pig would attempt to use your renewed vow against you!
• "I just got out, so of course I'll get out again." It's extremely unusual for prisoners to break out of jail twice unless the jailor consciously and purposefully leaves the door open.
• "Maybe I can't beat you right now but it's only a matter of time until we Binge again." Since you have full control over what you buy, open, take out of the package with your hands, put in your mouth, chew, and swallow, you will _always_ have the 100% ability to keep the Pig in its cage. You don't have to worry about "later", only the present, and it is always the present.
That's how to defeat the Pig after a simple Pig Attack.
But what if you believe your Food Plan itself was at fault?
For example, what if YOU _(not your Pig!)_ believe you've erroneously committed to a Plan which is too restrictive and leaves you uncomfortably hungry and/or missing key nutrients?
If this is the case you're going to need to go ahead and change it. But before you do (a) be sure you've given yourself some time for the Pig Slop you've ingested to leave your system because it's hard to hear the Pig's Squeals when your body's full of Pig Slop; (b) Save a dated copy of your complete Food Plan before making any changes so you can roll it back later if you find the Pig has influenced the changes; (c) Take some serious, reflective time to "think on paper" about the specific changes you're planning to make _;_ (d) Consider whether any previous version of your Food Plan was better. It's not unusual for mistakes to have occurred because the Pig convinced you to abandon a perfectly good Food Plan. If this is the case, just revert to the old one. And since you save a dated copy of every version, this is easy to do.
Here's one more thing to consider as you re-examine your Food Plan: If you find you're repeatedly struggling with a food or drink in the Conditionals section, the odds are pretty good you need to move it to the Nevers. For many people, certain super-rewarding foods taste and feel too good to constrain with conditions and rules. But these same people _—who may have struggled for years or even decades with a particular food—_ find it remarkably easy to NEVER have it again. Certainly much easier than the ongoing, painful search for that one "magic rule" which will let them have their cake and eat it too.
Never can be a LOT easier than sometimes!
Last, during the "legislative process" _—the time during which you are re-examining your Food Plan—_ it's best if you allow the previous rules to govern, however imperfect they may be. The Pig craves the anarchy which underlies a Binge. Therefore, under no circumstances should you ever allow "the absence of a government" to exist—even for a micro-second.
And remember, you made a mistake, you didn't have a brain operation which disabled your ability to make good food choices, or to control your hands, arms, legs, mouth, and tongue. You have not had a mysterious curse laid upon you which prevents you from eating well. Space aliens have not abducted you and implanted electrodes which force you to eat Pig Slop. Whatever new rules you may consider, you are 100% in charge of feeding yourself throughout the entire process! Finally...
**After a serious analysis of what caused the mistake, promptly forgive yourself and make a 100% confident, renewed commitment to** _perfectly_ **follow your Food Plan forever.**
You are a fallible human being. You were _practicing_ a particular Food Plan, but now practice is over. It's time for the big leagues. You analyzed what went wrong, and made the necessary adjustments so...
You Will Never Binge Again!
And all you need to do to never binge again is never binge again.
You might consider reading the above sentence a few times because your Pig would very much like you to think otherwise, especially right after a Binge.
Cage the Pig and let it suffer!
In the next chapter we're going to tackle and defeat a serious paradox: You must simultaneously view your Food Plan as perfect AND remain amenable to change. _(So you can grow from experience and incorporate new information as it becomes available)_
FREE BINGE RECOVERY TOOLS
Here's a strange thought: Since you will Never Binge Again you actually won't ever need these tools. And your Pig loves that they exist because they suggest the possibility you might consider feeding it. Let the Pig suffer! All you need to do to never binge again is never binge again. Profound, isn't it?
However, because it can be a little tricky to master the two different ways of thinking required before vs. after a Binge, many people find having specific tools available for Binge recovery extremely helpful. Therefore, I've prepared a free workbook and accompanying MP3 for your smart phone to walk you through the re-establishment of your commitment—and more importantly your confidence!—after a Binge has occurred.
It's part of the FREE book upgrade available at www.NeverBingeAgain.com
Chapter 4
### Changing Your Food Plan
There's a big Paradox inherent in the idea of changing our Food Plan. On the one hand, to have _any_ chance of success we must 100% commit to the plan we swore at the outset. Otherwise the Pig will be able to tear the tiny hole we're leaving in the fabric of our Plan wide open, and burst out into a big giant Food Orgy.
On the other hand, experimentation and learning are the underpinning of all progress. We must always integrate new evidence as it becomes available. And we must be able to learn from our mistakes. The best Food Plans _evolve_ over time, so it's critical to retain the ability to adapt.
For example, a few weeks ago my doctor brought a new series of studies to my attention which suggested fruit is metabolized _faster_ in the presence of fatty foods, not slower as was previously thought. This meant my "only eat fruit with nuts and seeds" rule _—which was originally intended to keep my glycemic load down and manage my genetic predisposition to high triglycerides—_ was actually counterproductive. It would be foolhardy to insist on sticking to this rule in the context of this new information, even though I'd previously committed 100%.
Similarly, because the food industry spends billions on developing cheap, super-rewarding foods— _and very persuasive packaging_ —many people are unwilling to put certain types of Pig Slop in their Pig's trough vs. their human plates. Their Pig begs and pleads to keep its Slop in the Conditionals section of the Food Plan, putting forth endless variations of rules it says it will follow _"this time_ "... if we'll only give it one more chance.
Our natural inclination is to leave as much pleasure in our diets as possible. And because a good Food Plan should indeed also be pleasurable, it can take several rounds of experimentation to weed out the Pig's impulses for _toxic_ pleasure from your own innate healthy desires.
**Upon Serious Reflection You May Change Your Food
Plan At Any Time** _...But Your Pig Never Will Again!!_
We must adapt our Food Plan when the reasons are sound—even though each time we commit to it we have every intention of NEVER changing it again. But because the Pig will always do everything in its power to convince us Bingeing is perfectly rational, we must apply a simple procedure to ensure the changes are not Pig driven. So it's important to ask yourself these challenge questions before changing your Food Plan:
• Have you made a written copy of your existing Food Plan and saved it somewhere you can easily retrieve in case you need to "roll back" to your best previous plan? The Pig seeks anarchy so it can Binge. Saving and protecting "the law" in the event a repeal becomes necessary is something _people_ do, not Pigs.
• Have you taken the time to "think on paper" about your proposed change? Your Pig will insist most changes it desires are extremely urgent because it knows you're unlikely to decide in its favor if you think too much about what's being proposed. People treat changes to the law as serious matters worthy of careful reflection and analysis. Pigs want immediate change for immediate pleasure. People use their intellect and delay-of-gratification abilities to make wiser, healthier choices.
• Are you being very specific about the change itself? Generally speaking, Food Plans improve slowly and specifically over time _(like the law)._ But Pigs argue for vaguely articulated changes which are often sweeping and impulsive in nature.
• Can you articulate the detailed and specific _reason_ behind the change you wish to make? _(Not the change itself, but the reason for it)._ Poorly articulated reasons for change are more likely to be Pig driven. The Pig's primary rationale is "because it will taste/feel good." Because this reason is so primitive and transparent, the Pig prefers it not be articulated at all. So before changing your plan, ask yourself if the change you are contemplating represents a legitimate opportunity to improve your nutrition, comfort level, and well-being. Articulate the reason YOU believe this in detail, and then analyze that reason just to be sure no Pig Squeal has snuck in.
• Are you sure any change is necessary at all? Most often the reason for a Binge is a simple Pig Attack _(unrecognized Pig Squeal)_ , not a problem with the Food Plan itself. But the emotions and physiological disturbances associated with Bingeing can make us FEEL like something's horribly wrong which must change immediately. Would it be more constructive to just resume and 100% re-commit to your Food Plan as is?
• If the change under consideration was prompted by having Binged, has enough TIME passed for your body to rid itself of the physical influence of Pig Slop? This can require few days. In the interim you can't trust your biological hunger mechanisms... they've been temporarily corrupted by the Pig. You must take particular care to make _intellectually_ sound food choices after a Binge.
• Even if the change under consideration was NOT prompted by a Binge, have you given at least a few day's consideration to all the above?
If you can get through the above questions successfully, then it's almost certainly YOU who are making the change, not your Pig, and you should go forward once again with 100% confidence.
It's perfectly fine to change your Food Plan as long as you're sure YOU are doing it for good reason, and are not under the influence of the Pig. Moreover, notwithstanding the seeming Big Paradox, we must be able and willing to adapt as we learn.
Just use the challenge questions above to be sure it's YOU who's doing the adapting and not your Pig! _(Note: For a printable one-sheet you can hang on your wall with these criteria, please download the "How to Change Your Food Plan" cheat sheet at_ www.NeverBingeAgain.com _)_
Chapter 5
### The Time Counting Trap
Our culture emphasizes counting time to address addiction. Just as alcoholics are encouraged to know how long it's been since their last drink, people who love food may be tempted to keep track of the last time they Binged.
This is a serious mistake in my not-so-humble opinion.
Counting the number of days, months, or years it's been since you last Binged is like counting how long you've been obeying the law. In our society the law is the law and we simply expect people to comply _—we don't give them a medal when they do!_
Try this thought experiment: Imagine someone proclaiming "it's been three weeks since I ran a red light" or "it's been a whole year since I robbed a bank" and you'll see just how ridiculous counting time can become.
Unfortunately, this practice is more than just a silly game—it's actually harmful because it signals the Pig you are insecure and ambivalent about your commitment. Worse yet, it orients your entire life's identity squarely around your food problems, rather than your aspirations, abilities, and dreams.
Just like there's no reason to think about how long it's been since you last ran a red light, there's NO reason to count the number of days since you last Binged.
Medals and public recognition are not given out for how long you've obeyed the law. Obeying is just the price you're expected to pay for societal privileges—not the least of which include your freedom.
Counting time is the Pig's way of orienting your whole life around Pig Slop... and trying to convince you that your commitment will eventually collapse under the weight of "all those days."
Be 100% clear with your Pig: This is a life-long arrangement and you will Never Binge Again. Otherwise, you'd just be giving it a calendar to mark off the days in hopes of one day being released.
The Pig does not deserve a calendar.
The Pig had plenty of time to prove itself a worthy citizen during the years you were open to listening to it. All it did with this privilege was try to ruin your best laid plans, goals, and dreams.
Let the Pig suffer in its cage of toxic desires and unsatisfactory rewards forever!
You won't be getting up in the town square seeking recognition for how long it's been since you've run a red light. There's no "clock" to pin on yourself as a medal for public recognition.
Your Pig may want to define your whole life according to its last taste of Pig Slop, but compliance with your Food Plan is a normal and expected part of citizenship in your more objective, balanced, and respectful view of yourself. It's not something to be lauded and applauded in public. Deriving self-worth from other peoples' recognition of your compliance stacks the deck in the Pig's favor because the moment you make a mistake it can say:
### "You made a mistake and now you're going to lose ALL the public recognition you've worked so hard to obtain. Oh well, no use crying over spilled milk. Sure, you've lost face in the public's eye, but there's still ONE great thing we can do, right? Let's Binge Binge Binge Binge Binge!!! You're going to have to start over tomorrow anyway, so you might as well set me free. Yippee!!!"
– Sincerely, Your Pig
This is why your Food Plan and how long you've been on it is nobody's business but your own. You've made a permanent decision to become a law-abiding, non-Bingeing citizen.
One more thought experiment to drive home the point: Suppose you run a red light. Does this give you license to blaze through every subsequent one? Of course not!
Society expects you to stop at every red light no matter what you did at the last one. You're not excused from the responsibility of obeying normal traffic laws because you have some "red light running disease." **Making a mistake doesn't invalidate the law.** Your Food Plan remains law at every possible moment in time, no matter what no matter what no matter what.
The law is the law and your Pig will just have to live with that. Forever.
Counting time is a Pig's game designed to blow up any tiny mistake into a full-fledged Food Orgy.
But still, if you're not going to rely on counting time as evidence of your ability to abstain, how will you deal with insecurity?
After all, your Food Plan is sacred, so you must take any insecurity about complying with it as seriously as you would any impulse to disobey the law. Therefore, if you find the Pig is making you insecure about your ability to stick to your Plan _forever_ , make it a priority to identify the Squeal and restore your confidence 100%.
THE ONLY CAUSES OF BINGE ANXIETY
**1) Pig Squeal misidentified as your own thoughts.** To check for this ask yourself: "What _might_ the Pig be trying to get me to believe so I will Binge? What's it saying?" Be specific! Just articulate the Squeal to inoculate yourself in the future. Put it in a Squeal Journal if it helps. Pig Squeal _always_ loses its power in the light of day.
**2) Grey areas your Pig has snuck into your Food Plan.** If you find this is the case, evaluate the Food Plan as per the detailed instructions in the previous chapter.
Binge Anxiety is actually just your Pig's plan to Binge in disguise. Cage the Pig and let it suffer!
The question is, do you feel 100%, completely and totally secure in your Food Plan. More importantly, are you 100% confident in your ability to comply with it forever? If not, you either have to find-and-ignore the Pig Squeal or carefully change the Food Plan _(see previous chapter.)_ There are NO other options!
It's also important to note, however, that many people wait to get started until they can honestly say they FEEL 100% confident in their plans. These people are confusing their Pig's feelings for their own.
You don't have to FEEL 100% confident. You only have to intellectually believe your Food Plan represents your best thinking at a time when you were of sound mind and were motivated enough to put it all in black and white. Then you DECLARE yourself 100% confident and DECLARE all other thoughts and feelings as belonging to the Pig so you can reject them. And you just take the leap!
This is what I mean when I say Never Binge Again is a "trick of mind." It's just a way of thinking which makes the line between your thin-thinking-self and your fat-thinking alter-ego crystal clear so you can hear the Squeals.
It's a game we play to avoid distracting ourselves with ANY possibility of failure so we can concentrate 100% of our energy on achieving the goal.
Now, to _really_ lock down your ability to deal with doubt and insecurity, I'd like to give you a new perspective on deprivation. See, most people's Pigs suggest they won't be able to deal with the feelings of deprivation forever. But there's a LOT more to this notion than appears on the surface...
Chapter 6
### Overcoming the Deprivation Trap
### "You simply can't Never Binge Again. You'll feel way too deprived and eventually you'll just give up and feed me. Why wait? Let's Binge!!!
–Sincerely, Your Pig
### "There there now. You're very upset. Go get us some comfort food and let's have ourselves a little Binge. We'll feel SOOOOO much better!"
–Sincerely, Your Pig
There are actually TWO types of deprivation: (1) What you deprive yourself of by NOT having something and; (2) what you deprive yourself of by having it. _(To my knowledge, this was first pointed out by Geneen Roth)_
It's exceptionally rare for people to consciously choose between these two alternatives. In fact, most people never consider the second kind at all.
Just for illustration _—I'm NOT saying you have to adopt this rule!—_ let's take the notion of never eating donuts again. If you decide to never eat donuts again, you'll deprive yourself of the taste, texture, and mouth feel of a donut for the rest of your natural life. You will never experience donut-pleasure again. To a donut-loving Pig, this is most certainly a fate worse than death.
But if you decide to _continue_ eating donuts, you will deprive yourself of everything associated with _never_ eating donuts again including (a) acquiring the body of your dreams _(or something very close); (b)_ the "lightness of being" associated with life without all that extra weight; (c) the energy associated with more regular, healthy nourishment; (d) knowing what it's like to have consistent blood sugar levels and to live without sugar crashes; (e) the _confidence_ which comes from knowing you have the power to NEVER eat a donut again; (f) years near the end of your life which were meant to be pain-free and full of joy, but are instead filled with immobility and dysfunction due to strokes, heart attacks, etc.
Your Pig would love to have you concentrate only on the _short term_ effects of deprivation because it genuinely believes Pig Slop is the _only_ pleasure life has to offer. But the list of things we deprive ourselves of by _continuing_ a food behavior is often a lot longer, and much more painful!
To take advantage of this insight you only need to make a solid comparison between your two choices. What will you deprive yourself of if you continue to embrace the particular food _(or behavior)_ vs. assigning it to your Pig's trough?
And I'll tell you what, let's give your Pig a running start by letting it go first. Think about some treat you _just might_ want to consider avoiding from now on. Go ahead and tell the Pig to provide you with a long list of things you'll be depriving yourself of if you never eat it again.
Can you feel your Pig squirming? That's because there are only two things it can really put forward in this situation—taste and convenience. Oh, it will say you'll be depriving yourself of life itself _—that you'll starve to death in a matter of hours without its favorite Slop._
But by now your Pig knows you're on to _that_ game. So the best it can do is say "because it tastes good" or "it's so easy to just grab it and go."
Your Pig squirms at the mere thought of this exercise because it knows its ammunition pales in comparison to your side of the equation.
Make the Pig suffer...write down your list!
Let the Pig say as much as it wants about how deprived you'll feel when you move its Slop to the Nevers section of your Food Plan...
When you write these things down it should become clear to you the Pig is talking about itself. It will feel deprived, not you.
Then write down everything you can think of which YOU will be deprived of by keeping the Pig's Slop in your Plan.
A well-considered, informed decision between the two types of deprivation always favors you, no matter the specifics of the Food Rule under consideration...so just write down the facts and make your choices.
I remember the day I first realized what I was depriving myself of by continuing to eat Pig Slop in a particular situation. I'm kind of an outdoorsman. I haven't won any awards, but for the past 12 years I've driven up to the White Mountain National Forest _(in New Hampshire)_ several times a month for a long hike.
Now, a big part of what my Pig used to love about hiking was how much I could feed it without gaining weight. One of my favorite things to do was to hike a 5,000+ foot mountain with a pack full of junk food. And I'd really go to town on my feed bag before, during, and after the hike...
See, my Pig had me convinced there was NO reason to hike without a big sack of Pig Slop. It was as essential as my map, compass, headlamp, and other survival gear...
Then one day, after reading about the two types of deprivation, I realized I literally didn't know what it was like to hike _without_ junk food. I hadn't done it even one single day. And I began wondering what I might be missing. So instead of the traditional bags and boxes and bars of crap, I packed up some organic greens and blueberries, put some green tea in a thermos, and threw a bag of raw seeds in my pack.
Here's what happened: An incredible calmness I didn't know anyone could ever feel came over me. As I walked through the woods I felt I could really breathe the air, listen to the running water, appreciate the sites, and enjoy all the animals I encountered. It was one of the best days of my life. It gave me a feeling of "rightness" with the world which since then has been a more powerful lure than anything the Pig can throw at me.
It lasted several days.
I slept better. Felt less reactive to "emergencies" at work. Was better with my clients. Solved problems more easily.
In many ways I felt more present than I'd ever been.
And through this experience I realized it was my Pig who'd convinced me I needed junk food on every hike. But that was a big hairy Pig lie! I'd actually been depriving myself of who I was meant to be at my core.
Since then I've learned this experience of _contentment_ is just under the surface for anyone who really wants it. Sadly, most people let their Pigs keep it from them entirely. This upsets me to no end. Why would anyone _ever_ choose to Binge when they could just make the Pig suffer!!!???
My Pig wanted me to think hiking without Pig Slop was cruel and torturous deprivation. But it turns out I'd been so distracted by the delicious tastes, I had no idea how I truly _was_ depriving myself.
Now, if you walk away from this thinking I'm telling you to go hug some trees and avoid any particular food forever, you're missing the point. The point is there are TWO types of deprivation, and you are 100% free to choose either one in any circumstance.
YOU get to choose, not your Pig.
When the Pig says "you can't follow these Food Rules any longer, they're too depriving", pause to ask yourself what the Pig is really aiming to deprive _you_ of if you break them.
One last important point about all this...
You make the rules. So be sure you've created a Food Plan you're confident you can live with forever. One which allows you to pursue your dreams in the body you want, while striking the optimal balance between short term pleasures vs. longer term goals. Every rule you make is a compromise between these two ends. Only you can decide where the best line is for your own body—that's what freedom is about!
Here's another way to look at it: Every day we make choices between "Live Fast and Die Young" [2] vs. "Live Slow and Enjoy the Long Ride." Do you want to borrow life from tomorrow to live faster today, or forgo some short term pleasure to achieve a better long term outcome?
In a free country, we have every right to trade suffering _tomorrow_ for pleasure _today_ if this is what we truly desire. In fact, we've fought wars for this kind of freedom.
However, the problem is most people have allowed their Pigs to dominate these decisions, so they never make a conscious choice. And because they've never experienced long periods of Pig-free eating, they also haven't had the opportunity to make _informed_ decisions about these very critical food matters.
I might not agree, but I'd vehemently defend your right to say "I'm choosing to live a little faster right now for the sheer pleasure of it. I'm fully aware I'm probably going to die a little younger and/or suffer more at the end of my life because of this choice, but I'm of sound mind, adult years, and 100% capable of making this conscious choice."
The problem is, people making this tradeoff rarely do so consciously. Instead, they allow their Pigs and society as a whole to pull the wool over their eyes and keep them blind to these choices.
The ultimate responsibility of freedom is choosing whether to live fast and die young vs. enjoy the longer, slower ride. However you decide on any particular Food Rule, please be sure you've given yourself a chance to experience the slower side of the equation so you're making a truly informed choice.
Why? Because the Pig must suffer, that's why!
DEPRIVATION WORKSHEET
If you'd like to see exactly what your Pig has been depriving you of and really cement in your defense against the Deprivation Squeal, please download the FREE "Avoiding the Deprivation Trap" workbook at www.NeverBingeAgain.com
Chapter 7
### Defeating the Food Industry
One day about 15 years ago I was talking with my friend Ted [3] _—successful senior executive in a meal replacement bar company—_ about some of his biggest marketing insights. The answer was revealing: One of their most significant growth spurts began when the company REMOVED the vitamins so the bars would taste better, while they simultaneously made the packaging LOOK more nutritious and delicious.
Apparently, it's quite profitable to distract people into THINKING they're eating healthy.
Packaging is only one part of this trend. Another trick of the trade is to emphasize ONE ingredient with proven health benefits in order to distract you from the other harmful ones.
For example, I'm guessing most of you already know fat free foods can still be loaded with sugar. But did you know many "Heart Healthy Omega 3" packaged foods can still have very high levels of sodium? That although dry-roasted nuts may have fewer calories and be lower in unhealthy fats than nuts roasted in oil and sugar—the roasting process itself can still create cancer causing compounds in significant amounts? That "Whole Grain" labeled products can still be refined enough to spike your blood sugar and increase your risk of diabetes? _(And possibly even cancer?)_
These are just some of the perfectly legal ways the food industry bolsters your Pig's best ideas. It's a "confuse and conquer" strategy. Hundreds of intelligent, high-paid marketing executives, lawyers, consultants, and food scientists are hard at work giving your Pig more ammunition. [4] And why wouldn't they be? To them, your Pig is worth billions!
Thankfully, all the Food Industry tricks are transparent and easily defeated once you shift your perspective in the simple way I'll share in a moment. And as long as you don't fool yourself, it's perfectly OK to trade a little health for taste, convenience, and enjoyment if that's what YOU really want to do. As long as these are conscious choices made with your fully informed consent, it won't impact your ability to Never Binge Again.
But I need to tread carefully here because most people prefer to arrive at their own conclusions about what constitutes healthy food. And provided the conclusions you arrive at empower you to draw your own unambiguous line in the sand, you can and will make yourself immune to the food industry's tricks. We needn't agree on what constitutes healthy food... you only need to be 100% clear on it for yourself.
Your Pig may chime in here and say:
"Hey, wait just a minute here Bubba! Glenn said you could create your OWN Food Plan. He said it was entirely up to you... but now he is going to drone on about what's healthy food vs. what's junk. Not only is he lying... but who made _him_ the king of health information? See? What have I been telling you! This is all just a bunch of prairie poo. Why are you wasting your time reading it at all? For God's sake, let's just go Binge already, OK? Can we, can we, can we, can we....please!!!!????"
YOUR FOOD PLAN IS ENTIRELY UP TO YOU –I AM ONLY PROVIDING A SHORTCUT WHICH MIGHT SAVE YOU YEARS OF PAINFUL EXPERIMENTATION. SKIP THE REST OF THIS CHAPTER IF YOU THINK SEEING IT WILL INTERFERE WITH YOUR ABILITY TO INDEPENDENTLY DEFINE HEALTHY FOOD FOR YOURSELF:
**THE SIMPLEST WAY TO THINK ABOUT HEALTHY FOOD
** _(Skip the rest of this chapter if you prefer to come to your own conclusions)_
Whole, unprocessed, organic plant foods—and a modest amount of organic animal protein—are the ONLY truly healthy foods for humans on this planet. Everything else is a man-made refinement for taste, convenience, or enjoyment. Everything. The more refined, better tasting, and convenient a given food is, the more you're likely to be trading on your health for these benefits.
It's much easier to start with a small list of what's good for you _(an affirmative list)_ than to make an exhaustive list of what's harmful _(a punitive list of taboos.)_ The latter is much too long, complex, and provides the Pig way too much material to debate.
But none of this means you've got to be a saint and just eat dirt and rocks the rest of your life. It's perfectly fine for YOU—not your Pig!—to include choices for taste, convenience, and fun in your Food Plan, with full knowledge you're trading off some health when you do.
Just don't let your Pig fool you into believing the toxic-pleasure peddled by the Food Industry is actually healthy, because that is a recipe for disaster. Whatever you do, resolve right now to deprive your Pig of the constant barrage of well-funded Squeals provided by the food industry's billions.
There's one last critical fact we'll need in order to prevent the food industry from supporting your Pig. After living for decades in a society set up to feed the Pig at every turn, it's likely your natural hunger mechanisms are out of tune with what your body really needs. Your taste buds have been desensitized. The reward pathways in your brain don't fire as intensely in response to the natural foods for which they were designed. They've come to require the more super-rewarding stimulation of processed foods and other societally promoted junk.
But thankfully most of this is reversible. If you eat less sugar, fruit will begin to taste better. As you consume less junk _—as crazy as it sounds!—_ you'll begin to find yourself craving green vegetables. But you do NOT have to force these things to happen... and you shouldn't try. They're just a natural result of Never Bingeing Again. Just like someone who quits smoking begins to enjoy deep breaths of clean air like never before, so too will your natural food instincts begin to be revitalized.
The essence of a Pig-hijacked survival drive is the belief your Binge food is a fundamental requirement for life itself. To make room for this, the Pig rejects what nature actually has to offer. But when you cage the Pig, this process slowly but surely reverses itself.
One last thing on this point which your Pig will hate: There's overwhelming evidence which suggests raw, organic, leafy greens are to nutrition what oxygen is to your lungs. So if you want to speed up the recovery and re-normalization of your survival drive, just add some to your diet. You can throw them in the blender with a little water and drink them down like medicine. You don't have to enjoy them, you just need to get them in. When you add organic leafy greens, you begin to crowd out everything else.
But if you find this suggestion too aversive, please know it's not a requirement and there's NO need to force it. No matter what your Food Plan, if you keep making the Pig suffer you should naturally begin evolving towards healthy food.
The reason I'm so confident about this is because the places you'll naturally choose to cage the Pig are those in which you experience the most unpleasant side effects of toxic pleasure. As you eliminate more and more toxic pleasure from your diet, you'll naturally gravitate towards getting your nutrition from healthier foods. You can't help it any more than a smoker could help breathing in real oxygen after they quit poisoning their lungs with cigarettes.
When a smoker quits smoking, those large, slow, deep breaths of fresh air can make them a lot more comfortable. They can still quit forever regardless of whether they embrace this practice, but life is a lot easier if they do. Similarly, you can dominate the Pig forever without eating your stupid vegetables. But things will go faster and you'll make life easier if you do.
Enough said!
THE FOUR MOST COMMON FOOD INDUSTRY LIES
If you'd really like to bolster your defense against the food industry's Pig-feeding tricks, please download my free audio _(and word for word transcript):_ _"The Four Most Common Food Industry Lies and How to Defeat Them!"_ from www.NeverBingeAgain.com
Chapter 8
"Hell is Other People" [5]
(Says Your Pig)
In the past few decades psychologists have discovered our self-concept is intimately bound with how others see us. None of us seem to know who we are until we see it reflected in someone else's eyes. As if self-worth can only derive from the mirror of other people's thoughts, feelings, and opinions.
While it may be true we can't avoid having our self-concept _influenced_ by our relationships, your Pig takes this to a ludicrous extreme. It wants you to believe the slightest instability in your loved ones' opinions about you and/or your Food Plan will cause you to Binge.
In other words, your new Food Plan will upset your wife, your children, your mom, your husband, your grandma, your second cousin, your nephew, and of course your dog. _(Don't forget your dog!)_ And without their 100% unconditional acceptance of everything you do, the Pig says you'll be incapable of sticking to a simple commitment. So you might as well give up and Binge.
Pig Squeal!
• As a side note, it's also entirely possible you could upset your wife, mom, second cousin, _(or dog)_ by _including_ something in your Food Plan which they think should never be eaten. In fact, if we were truly dependent on other's opinions to stick to our Food Plan NO food would ever be acceptable _—because if you look hard enough you'll find someone who believes you should never have it._
Here's the thing: You are perfectly, 100% capable of drawing lines in the sand regardless of what anyone does around you. If you decide you're never going to eat a particular food again, then your wife, mother, father, grandfather and/or dog could bake the most delicious Pig Slop you can imagine and wave it in front of your nose saying "C'mon... just one little bite? It's really, really good. One little bite never killed anyone!"...
And you could still say "no thank you" from here to eternity.
**When others tempt you with food, just quietly say** _to yourself_ **"That's Pig Slop...and I Will Never Eat Pig Slop Again!"**
It's important to reiterate this is not something you share out loud. Your Food Plan is a very private and personal matter. You don't need to debate, justify, and/or explain it to another soul in the universe.
By extension, other people's Food Plans are also none of your business. Telling someone else they're eating Pig Slop is a great way to ruin a good relationship...
Everyone gets to decide for themselves what goes in their Pig's trough vs. their human plate. In fact, everyone gets to decide whether they want to separate their addictive mind from their more constructive thoughts and feelings in the first place.
We all also get to decide for ourselves whether to call a Pig into existence _at all._ So you've got NO way of knowing whether the person you're talking to wants to even acknowledge their own Pig...much less to discern how this person defines Pig Slop in their own personal Food Plan.
Only our own Pigs are truly knowable. To mess with other people's Pigs without their permission is an intrusive type of mind-reading.
Besides, having practiced psychology for decades, I can tell you mind-reading is NO easy feat. Just when I think I know what someone's thinking, I manage to hold off and listen a little while longer and discover I was actually way off the mark. Even with people I've known for years.
And even if you COULD see another person's Pig with 100% accuracy, that doesn't make it OK to point out. After all, Superman didn't go around telling everyone he knew what kind of underwear they were wearing even though he had x-ray vision.
So please resist the urge to tell other people they're eating Pig Slop.
If they push back when you say "no thank you" to something and you need more ammunition to make them stop annoying you, you can always say it's for medical reasons. The Food Plan you've adopted will always have something to do with your _physiological_ well-being, so you'll always have medical reasons for maintaining it—if for no other reason than a healthy Food Plan is almost certainly medically necessary to maintain a healthy body! _(Even one Binge of most types of Pig Slop can cause sharp spikes in numerous medical risk factors)_
If the other person asks "what medical reasons?" just say "Oh, I'm not dying or anything like that, but I kind of hate talking about it" and then change the topic. That'll usually do it unless your loved one is a real sicko with food. And if they _are_ a real sicko, why entertain their ideas in the first place?
People have food trouble with others in their social environment because they unknowingly allow their Pigs to go around seeking approval.
Remember, one of the biggest problems in food addiction is dependency, which provides the perfect excuse for a Binge:
"So and so seduced you into Bingeing, so you can't possibly blame yourself. It was just too hard to keep to your Food Plan given how much (s)he wanted you to eat ______. Besides, it was really yummy! Let's get more!!!" – How your Pig uses other people as an excuse
The defense against this is to make your Food Plan a 100% private matter. You don't need anyone to validate it.
You might seek education from your doctor, nutritionist, and other experts you respect. And you might read nutritional books to continue amassing information about healthy eating.
But there's NO reason to talk to anyone else about it.
In fact, you should be very careful even talking to experts unless and until you've fully vetted them, and are sure their opinions have not been overly distorted by the profit motive.
In the end, YOU assume full responsibility for your Food Plan, no matter how well informed you are by experts. After all, it's your body.
See, when it comes to eating, other people aren't "Hell", they're just a minor annoyance.
You could stand in a kitchen full of gourmet chefs _—completely surrounded with the most delicious appetizers, entrees, and deserts—_ while they all tempt your Pig for hours _...without breaking a single rule on your Food Plan!_ Because once you've eliminated ambiguity from your Food Plan then every tempting comment can immediately be recognized as Pig Squeal, and all the "treats" offered become obvious Pig Slop in _your_ model of the world.
Therefore, when others are tempting your Pig in a social dining environment just look at the treat and say to yourself "That is Pig Slop. And I Will Never Eat Pig Slop Again!" If the Pig keeps Squealing then give it the middle finger and coldly, cruelly say "That's just how it is, Pig!!!"
The more information you have about how to dominate the Pig, the more you're going to realize it's the PIG that's powerless, NOT you!!
**What Your Pig Says About Being Influenced by Others Around Food**
"Hell is other people! You can't be around other people and stick to your Food Plan because you'll upset them too much. We'll just have to have ourselves a yummy, yummy Binge when we see them and start over the next day."
**What YOU Say About Being Influenced by Others Around Food**
"The Hell with other people! There isn't one single soul on this planet who can convince me to eat Pig Slop because I will NEVER eat Pig Slop _again... and that's that!"_
Now, before we leave this chapter on dealing with other people, let me just say it IS possible to introduce willing participants to the Never Binge Again philosophy. Here's how you do it...
Wait until you come across someone who's actively concerned about their weight and/or eating behavior. In other words, they're experiencing the immediate, painful after-effects of toxic pleasure — OR — they are significantly impressed with your results.
In this situation, your friend may be amenable to hearing about the **results** you've achieved using a very different and powerful approach. Make sure they know this approach lets you define your own Food Plan and does NOT impose any particular dietary rules.
It's best if you can get them to read the book _(always available at_ www.NeverBingeAgain.com _)_ before going into too much detail, or their Pig may talk them out of reading it. Thereafter, if they seem intrigued and give you permission, it can be very gratifying to help them identify their Pig's Squeals...
But if they seem to be rejecting the Never Binge Again philosophy there's really not much you can do. In these cases it's best to say "I'm sorry it wasn't helpful" and politely change the topic.
Fighting with other people's Pigs is NOT a winnable war unless you have a clear ally, and the collateral damage is too great when you don't. When in doubt, just have your friend read the book and see what they think.
(Note: There's nothing wrong with telling a spouse or other loved one that their wellbeing impacts you and your family. Sometimes it takes the withdrawal of affection to get people to change. Sometimes they won't change no matter what you do, and you'll need to consider whether the relationship itself has become toxic. But you won't get anywhere by trying to force the Never Binge Again philosophy on them. In fact, doing so can ruin the possibility they'll consider it at a later juncture. "A man convinced against his will is of the same opinion still" – Samuel Butler)
Because the super-rewarding food our society has produced is indeed SUPER delicious, Never Binge Again is experienced as a pretty radical concept which most people will only be open to when they're really in pain. And when they are, it's necessary to get a LOT of information into their heads reasonably quickly with a certain amount of practiced finesse.
For this reason, it's better to leave the education to the book itself _(and/or the audios and videos on the_ www.NeverBingeAgain.com _website)_ when possible. Dominating your own Pig and teaching others to do the same are two entirely different matters. The ideas in Never Binge Again are NOT very contagious... most people unfortunately need to have been beaten down fairly seriously by their Pigs before they will be open to them.
Let's talk for a few minutes about what's necessary to TEACH someone else to Never Binge Again by reviewing how I got you to accept the idea while reading this book. _(I know, I know, your Pig may still Squeal that you haven't made up your mind yet—stupid Pig. Make the Pig suffer!)_
First, I carefully sold you on the concept of the Pig during the introduction. I explained how this could work for you where nothing had ever worked before. Then I made an outrageous promise: If you'd be willing to entertain a crazy idea _—with suspended judgment—_ I could give you control over your eating _forever_. And I explained you only needed to let me provide you with a weird idea to ponder for a while in order to benefit. It wasn't another grit-your-teeth-and-bear it exhausting diet.
Only with this motivation in place could we proceed to carefully define the Pig, outlining how it was possible to make this seemingly irrational leap without giving up your ability to think clearly. [6]
The next step was to forewarn you of the impending violent backlash you might experience against these ideas. I encouraged you to write your disbelief and arguments in the margins. Why? Because Pigs Squeal loudly and frantically as soon as they realize we're on to their game. And at that juncture you hadn't yet separated your own thoughts from Pig Squeal—so the Pig could have easily dissuaded you from reading further.
Because the Pig's best-first-line of attack is to destroy the concept before it even takes hold, we had to create a safe channel for the Pig Squeal while we educated you about its tricks. This was the first step in leading your Pig into its forever prison.
And this is perhaps the most difficult part about teaching other people to see their own Pigs: Before deciding to call a Pig into existence, people are in an undifferentiated state. They haven't yet separated from their own fat thinking thoughts. Before understanding the Never Binge Again concept, those thoughts are still an integral part of who they are and what they value as a human being. _Therefore, the idea of separating from this bothersome part of themselves is at first experienced as a very harsh criticism of their own personhood._
In other words, at the beginning a newbie's Pig's violent struggle for survival is perceived as _their own_. This makes them prone to arguing with you if you present the idea too forcefully. And since the Pig is a SURVIVAL drive run-amuck, the energy behind this argument is the same energy behind the thrashing of a drowning person. It may be politely hidden, but their Pigs will say and/or do ANYTHING to survive.
For all these reasons it's best to get this book into your prospective Pig Dominator's hands rather than undertake the battle yourself.
Notwithstanding the above, people can and will accept the notion of a Pig after they've taken a particularly strong beating by their food struggles. They have to really want results, and feel a little desperate to find a different solution. [7]
For all these reasons, for many people the Pig is a concept which just gets planted and grows over time. Be prepared for push back. And just like it's fruitless to argue and debate with your own Pig, don't become too argumentative with theirs. Let the book do the hard work...then let them have their say thereafter.
Some people will love you for this! And it's _very_ exciting to be around others who have truly committed to Never Binge Again.
But it's important to remember these people will probably define their own Food Plans very much differently than you defined yours. What sounds like Pig Squeal to you may indeed be healthy thinking for them. And what looks like Pig Slop to you may be perfectly good food in their view of the world. That's fine – you're separate and unique individuals with separate and unique Food Plans!
Others will want to push aside the concept and continue struggling as they have been, looking for that magic formula which allows them to have their cake and eat it too. It's OK. Let them. You've planted a seed which they may remember the next time they're stung by toxic pleasure.
Regardless of what other people in your life do, just Never Binge Again!
UNUSUAL WAYS TO NEUTRALIZE OTHER PEOPLE'S PIGS
If you'd like to supercharge your defense against other people's Pigs, download my free audio _(and transcript)_ "Unusual Ways to Neutralize Other People's Pigs" from www.NeverBingeAgain.com
Chapter 9
### The Pig is Powerless, Not You
A good portion of our society believes there's a mysterious disease which makes certain people completely powerless over food, alcohol, drugs, and other toxic pleasures. Spokespeople from the addiction treatment industry often suggest that super-rewarding foods trigger an irresistible impulse which "compulsive overeaters" are powerless to defend themselves against.
If you're one of these diseased people, as this line of reasoning goes, you can't ever hope to control yourself, and you certainly can't quit eating any particular food. The best you can hope for is "one day at a time" abstinence while you dedicate the rest of your life to hanging around with others _(who also can't control themselves)_ so you can all supposedly watch over one another...
And help each other through the inevitable string of "relapses" to come, since you are, after all, just a slave to your disease, doomed to a lifetime of Bingeing and recovery. _(An institutionalized rationale to remove responsibility and guilt, claim ongoing helplessness, and taking a permanent position as a victim)_
### "What a delicious disease!!!"
_(Says Your Pig)_
There's NO good scientific, empirical evidence for this mysterious disease.
The disease concept was originally put forth by Alcoholics Anonymous to reduce guilt and shame over indulgences which put the lives, finances, and wellbeing of not only the drinker but also their family at risk. It was easier for families to accept their loved one was suffering from a disease than to think of them as an arrogant and selfish person who risked life, limb, and the security of the family for just one more drinking binge.
The idea of powerlessness has now been extended to virtually every imaginable toxic pleasure. People say _—and our culture willingly accepts—_ there are diseases which make some of us powerless over alcohol, drugs, gambling, infidelity, sexual perversions, and pretty much anything else that feels good. [8]
Of course, this extends to food.
"It's not our fault and it's not a moral issue" says the current chorus of voices from the addiction treatment industry. "And relapse is an inevitable part of recovery"
Poppycock.
Here's the thing: Human beings are perfectly capable of abstaining from toxic pleasure. **Pigs are powerless over people, NOT the other way around.** And the most glaring evidence of this is that the Pig bothers to talk at all.
We already know the Pig wants only to Binge, and will SAY whatever it takes to convince you to feed it. But did you ever stop to think why it bothers with all the verbal mumbo jumbo in the first place? If all it wants is Pig Slop, why not just quietly go and take some? Why must it say anything at all?
Because the Pig CAN'T feed itself, that's why! It's a powerless creature whose only hope is to get you to go along with its warped thinking. That's why it's always desperately trying to convince you to get its junk. That's why it talks a blue streak until it realizes you will Never Binge Again.
THE VERY FACT THE PIG TALKS PROVES YOU ARE ITS JAILOR. IT'S COMPLETELY POWERLESS TO FEED ITSELF, SO IT'S ONLY HOPE FOR RELEASE IS VERBALLY CONVINCING YOU TO LET IT OUT OF PRISON.
Here's something very nice to know: Even _—and perhaps especially—_ if the Pig should ever happen to be correct about any particular point, you will still NEVER Binge again. You will NEVER grant it control over your arms, legs, or mouth.
Because regardless of what it says, the Pig only wants to indulge in toxic pleasures which will destroy everything you care about. So who cares if the Pig went out and got a degree from Harvard—or for that matter, if it found the cure for cancer? You'd still ignore every last Squeal because you know it has only this one destructive motive.
The Pig is a weak, pathetic creature which doesn't care about anything besides Bingeing. It will extract any price from your life to get at its Slop, but it's completely powerless to do so unless you listen to its Squeals.
The Pig is powerless and you are its master.
So turn a deaf ear and just Never Binge Again!
Chapter 10
### Twelve Hard to Recognize Pig Squeals!
Once you've begun to dominate the Pig, it will begin watching for an opportunity to break out of its cage. That's its job! So in this chapter we'll review some fairly common _—but hard to recognize—_ Pig Squeals which many people have trouble hearing at first.
Like all Squeals, these twelve fall apart when examined in the light of day. Nevertheless, arming yourself with foreknowledge of the most common Pig Costumes used shortly after resolving to Never Binge Again can be very helpful.
And although I'll take the time to disprove each of them, please remember this is overkill and simply for the point of illustration _—kind of like slicing a watermelon with a chainsaw when a simple knife would do..._
You do NOT need to memorize, recall and present these perfect arguments to your Pig because your mind is not a debate club or a democracy. It's a monarchy, and you are the King _(or Queen.)_ The Pig is nothing more than your terrified peasant. It must comply with your every rule no matter how silly or unnecessary it may seem.
You make the laws. The Pig has no choice but to obey.
For this reason, simply acknowledging Pig Squeal as Pig Squeal is more than sufficient to inoculate you against this peasant, your majesty...
But you do need to recognize them first. So let's start with the trickiest Squeal of all.
THE HARDEST SQUEAL TO RECOGNIZE
One of the early changes most people observe when they decide to cage the Pig is a remarkably improved ability to get back on track faster if they happen to make a mistake. What most people don't expect, however, is that the Pig will attempt to hijack this ability for its own purpose. As soon as the Pig realizes you're feeling more confident about getting back on track after a Binge it will say something like:
### "Hey! You're getting really good at putting me back in my cage using this new dominate the Pig stuff, so I really can't do too much harm anymore. After all, you can just lock me back up whenever you feel like it. So how about let's go have ourselves a great big hairy Bingeing party, you and me, OK? That's what we've been wanting all these years anyway, isn't it? Finally! A safe way to Binge! Thank God for Never Binge Again because now we can do it!!!"
–Your Pig
Listen, your word is sacred.
A Binge is ALWAYS a big deal.
You made a solemn oath to follow a Food Plan. It doesn't matter how small a transgression your Pig has in mind. Your word is your word. Period.
If you give the Pig an inch it will try to take a mile and you know it. Let it land on the beach and it will marshal all its troops to fortify its position and take as much of your territory as possible. The Pig will always do its best to turn "just one bite" into a week-long Food Orgy.
Which is why NEVER means NEVER.
Make the Pig suffer!!!
HARD TO RECOGNIZE SQUEAL #2
### "90% compliance is good enough. After all, you used to eat badly a LOT more often. Why not leave well-enough alone?"
– Your Pig
Giving the Pig 10% leeway only creates the opportunity for it to take more, and more, and more. And I can prove it:
• 90% today times 90% tomorrow brings you to 81% of your original goal. _(90% x 90% = 81%)
_ • The next day you're down to 72.9% _(81% x 90% = 72.9%)
_ • By the end of the week you'll be at LESS THAN HALF of your original plan. _(90% x 90% x 90% x 90% x 90% x 90% x 90% = 47.8%)_
• Follow this logic to its natural conclusion and in just one month you'll be at a miserable 4.2%
If you comply 90%, you'll be back in Full Binge Mode within thirty days!
• **90% is Pig Squeal, plain and simple.
• 100% is the ONLY possible solution.**
Anything less than a 100% commitment is nothing more than the Pig's plan to Binge.
• You don't set out to climb a mountain saying "maybe I will and maybe I won't." You visualize yourself on top and you commit.
• You don't get married saying "maybe this will work and maybe it won't." Either you feel strongly enough to commit 100% or you find yourself a different mate.
• You don't get in a car saying "maybe I'll get to my destination safely or maybe I'll crash." You commit 100% to avoiding other vehicles _(and anything else not-so-good-for-humans-in-cars.)_
• You don't drink clean water 90% of the time, but have yourself a big old swig from the toilet the other 10%.
A 90% committed athlete will almost never make it out of the minor leagues. To have any chance of taking home the gold you've got to give it your all.
Now let's talk about 100%.
100% commitment doesn't degrade over time. If you commit 100% today, you'll still be at 100% tomorrow because100% x 100% still equals 100%. And you know what? You'll be at 100% the next day too. _(100% x 100% x 100% = 100%)._ Ad infinitum.
Commit 100% each and every day and you'll be at 100% on the very last day of your life because 100% to the power of infinity is still 100%.
100% is the ONLY number which does this.
Even 99% eventually degrades to full Binge mode...it just takes a little longer. _(You'd be at less than half your plan in under three-months-time, and down to almost zero by the end of the year)_
Moreover, the slight edge you get from a 100% vs. 90% commitment may not seem like much the first few days, but it compounds over time.
A 100% committed athlete rises to the top of their game even though they may only edge out their competition by a nose on any particular day. Their slight edge day after day after day adds up. Because winning by just a nose every time is still winning, they _really_ stand out from the crowd. It's not unusual for such athletes to get ten times more recognition and compensation than their peers.
The slight edge in confidence YOU will get from complying 100% makes all the difference in your Pig understanding it will NEVER win vs. thinking it will only be a matter of time. And when the Pig knows it will NEVER win, it will eventually conclude it has no choice but to give up and leave you alone.
But at 90% compliance the Pig keeps Squealing. It drains your energy and confidence and wears you down. 90% always leads to a low self-esteem Binge mentality over time. At 90% the Pig never knows when it's going to hit that "lucky 10%." So it acts like a frantic gambler glued to a slot machine in Vegas, dedicating ALL its energy just to be sure it's still in the game to pull the lever when that "one big win" comes due.
Even at 99.9999% compliance the Pig will, in fact, continue this behavior. Because one chance in a million _—or a billion for that matter!—_ is enough to give the Pig hope. And a little hope is all the Pig needs to keep going.
Think of how many tens of millions of people buy lottery tickets each week because "Hey, you never know" _(NY lottery slogan)_ or "you've got to be in it to win it!"
But just as a prisoner serving a life sentence eventually decides hope is undesirable and painful, at 100% compliance your Pig will eventually let go of hope so you get on with your life.
And it happens a lot sooner than you might think!
Therefore, it's in your best interest to quash every last ray of hope your Pig may be holding onto in order to live a confident, Binge-free life... _forevermore._
When you accept 90% compliance, you're depriving yourself of the immense confidence and peace of mind which only 100% can bring.
100% is really the ONLY option.
You must be willing to pay ANY price to achieve 100% compliance with your own Food Plan... and your Pig must know this with certainty.
Remember, it's YOU who wrote the Food Plan in the first place! What's the point of not 100% complying with yourself? Isn't the whole point of freedom being able to chart ANY course you want and successfully reach the destination?
In this context, I hope you can see how STUPID the Pig is for incessantly trying to talk you out of this.
HARD TO RECOGNIZE SQUEAL #3
### "The sheer number of times you've previously Binged despite your most sacred promises and commitments _—even after reading this book—_ proves you'll never be able to stick to ANY Food Plan whatsoever. You're just too weak. Face it, you've already tried to dominate me and failed. How many more times are you going to do this before you accept it's impossible? Just give up and accept a life of Bingeing until our hearts are content. Yummmmmmm!!!!"
– Your Pig
Even if you've repeatedly fallen down for years, continuing to get up until you succeed is a mark of strength, not weakness!
A weak person gives in and gives up, but people who chose to keep renewing their vow to _forever_ lock the Pig in its cage until that lock becomes unbreakable can't help but succeed. Renewed commitment is a mark of fortitude and perseverance. It's something to be revered, not ridiculed!
The fact you've fought a biological error your whole life and experimented with dozens of ideas for a Food Plan before making your FINAL one is admirable...
And as long as you're 100% committed to utterly and completely dominating the Pig, you will continue to make steady progress until you beat it into permanent submission.
In fact, this occurred just after your _last_ Binge, no matter whether that was 5 seconds, 5 minutes, or 5 years ago!
The Pig would like to use your past mistakes as evidence of permanent weakness _—and it will most certainly jump on the chance to attack any mistakes you may make after reading this book—_ but in doing so it actually draws attention to your fortitude and persistence.
The Pig makes your point _for_ you.
Stupid Pig!
You are 100% capable of making an irreversible decision, regardless of how many times you may have reversed the same decision before. This is true even if, as a practical matter, some people require a multitude of attempts before arriving at their FINAL Food Plan.
**HARD TO RECOGNIZE SQUEAL #4
** _(The "Controlled Bingeing" Strategy)_
### The Pig says: "A planned and controlled Binge once in a while isn't so bad. That's what you intend to do anyway and you know it. You can Binge one out of ten meals and still get thin. So what's the problem? Let's go already, I'm ready when you are. And it'll be SO yummy!!!"
–Your Pig
A Binge is defined as even one bite or swallow outside of your carefully constructed Food Plan. Nobody told you what to put on this Plan. It represents your best thinking at a time when you were of sound mind and felt motivated enough to write it down. With great forethought, you defined a set of clear rules you firmly believed were in your best interest.
REMEMBER: There's nothing which says you can't have good tasting, delicious foods _on_ your Plan. It's even perfectly legitimate to include things you know are unhealthy if YOU want to make those trade-offs...
But it's _your_ plan, not the Pig's!
Which is why it's imperative you recognize this particular Squeal as the Pig's attempt to intrude on your best thinking. The Pig hates your well-considered ideas because the only way it will ever get fed is if it can get you to act on impulse. But...
There's absolutely NO need for "Cheat Days" and/or "Controlled Binges" on a well-considered Food Plan which nobody forced you to adopt in the first place.
You've already used your own best thinking to create a balanced plan for health, well-being, and enjoyment. If you're unhappy with it, go back and change it according to the procedure we've already discussed. But the sudden idea to have a controlled departure is nothing more than a plan to Binge. And you know where _that_ slovenly idea is coming from, don't you!?
Remember: If you plan it in as part of your Food Rules then it's NOT Pig Slop in the first place.
You Will Never Eat Pig Slop Again!
You Will Never Binge Again!
**HARD TO RECOGNIZE SQUEAL #5
** ("I Don't Really Exist")
### "You know there's not really a Pig inside you. Therefore none of this 'Dominate the Pig' stuff makes ANY sense at all. So why don't you just let me out and Binge already!!!?"
– Your Pig
As discussed previously, the Pig is a language gimmick. There's no _real_ Pig inside you. It's only a concept, even though the dynamic between you and the Pig can be characterized as that which exists between more recently evolved neocortical functions and the mid-brain, where survival impulses originate.
But the Pig is not "just" a language gimmick, it's an _incredibly effective_ language gimmick! In fact, it may be the ONLY way to thoroughly separate your thin-thinking-self from the fat thoughts and feelings which have sabotaged your efforts until this point in life.
And let's bring back our governmental analogy: The continually refined use of language is what allows humans to coordinate and control their impulses so they can participate in a civil society. Language is what separates us from the apes and allows us to articulate the laws which make it possible to live amongst one another.
Language is how we managed to step out of the jungle and move beyond "might makes right" to form a society.
Language is the very fabric of our civilization.
To negate the use of language for the purpose of controlling impulse is to advocate against society as a whole. To suggest the Pig is nonsense because it's "just" a language gimmick is to declare yourself an anarchist and set yourself on a mission of destruction.
Never Binge Again is a way of thinking which can restore full control over your eating, and eradicate the ridiculous notion that free will and responsibility don't exist when it comes to toxic pleasure.
The Pig would love you to declare it non-existent so it could Binge.
Cage the Pig and let it suffer!
**HARD TO RECOGNIZE SQUEAL #6
** (The "We Can Only Be Grateful Squeal")
### "Wanting and striving are useless. Learning to love what you have is the only thing which leads to happiness. Besides, there's ONE super-duper-wonderful thing we can always be grateful for...Pig Slop! Yummy!!!!! Gimmeee some!!!!"
– Your Pig
This Squeal is hard to recognize because it actually contains a significant half-truth: Being grateful for what you have IS an important part of a content and satisfied life. It starkly contrasts with harboring resentments, envy, and jealously for others' accomplishments and possessions.
That said, without striving and yearning nobody would ever accomplish _anything_. Feeling uncomfortable about the gap between where we are and where we want to be is what causes people to set goals and make plans in the first place.
A healthy person actively tolerates a certain amount of discomfort and uses it as motivation to change. They set clear goals and diligently work towards them over time. A well person admires the characteristics of others who've achieved and obtained things they themselves desire _—and tries to adopt these characteristics so they might achieve similarly_.
Yes, a well person IS grateful for what they have along the way, but they don't allow this gratefulness to interfere with their striving.
There are three ways people deviate from the well attitude described above... and each of them supports the Pig in its efforts:
• DEVIATION #1 – ENVY AND RAGE: Some people become driven by rage and envy in the face of other people's accomplishments. They harbor tremendous resentment and believe others aren't entitled to the success they've achieved. It's "unfair", they reason. "Those" people are just lucky, and they themselves can't ever catch a break. And they're not going to take this lying down, either! The envious, enraged person feels justified in attempting to destroy the accomplishments of others, or at least in preventing them from feeling good about what they've done. They want to steal the spoils of the accomplished person's efforts—or prevent them from accomplishing anything in the first place. Such people dedicate themselves to _getting even_ instead of being well. And this position fuels the Pig's argument that the only thing worth living for is Pig Slop.
• DEVIATION #2 – NEGATIVITY AND DEPRESSION: Other people become self-castigating. They wallow in negativity, depression, and self-criticism. The Pig then uses this as justification for indulging in Pig Slop as the _only_ good thing in life.
• DEIVATION #3 – EXCESSIVE GRATEFULNESS: The third way people can deal with the discomfort of the gap between where they are and where they'd like to be is Over-Gratefulness. It goes something like this:
–"Forget your big goals entirely. There's no point planning for anything long term because you never know when we're going to be spending days, weeks, or months in a full-fledged Food Orgy. The best we can ever hope for is to avoid becoming angry, resentful, or negative. Therefore, we should only focus on being grateful for the shadow of a life we can manage to cobble together between Bingeing episodes. Besides, there's always the next yummy Binge to look forward to, right? Right!!!"
– Your Pig
NONE of these three deviations are a smart idea.
It's all well and good to be grateful and shun negativity, but the Pig would have you focus on this exclusively. If it succeeds, it will remove your motivation to pursue longer terms goals with the diligence and discipline it takes to achieve them. And since you won't be accomplishing much to speak of using this Piggy philosophy of life, Pig Slop will start to seem like a good idea.
The Pig hates when you diligently plan and persevere towards your goals because it knows accomplishing them will make Pig Slop _—and all the suffering associated with it—_ progressively less attractive as time goes on.
Knowing You Will NEVER Binge Again, on the other hand, allows you to make plans and pursue dreams you couldn't even imagine while you were letting your Pig run the show.
• Aiming High + Planning + Diligence + Persistence + Gratefulness = Happy Life.
• Gratefulness Only = Stupid Pig.
Let the Pig suffer!!!
HARD TO RECOGNIZE SQUEAL #7
### "You just Binged. Shame on you! Now you must suffer with constant obsession and excessive guilt about all the bad foods you ate and what a bad person you are. _(At least we'll get to keep thinking about those delicious foods. And besides, once you've done enough penance you'll have paid the price and we'll be clear to Binge again. I can't wait!!!!)_ "
– Sincerely, Your Pig
It's only natural to feel a degradation in self-esteem and confidence when you've broken your solemn word to yourself or others. But normal, healthy guilt is only supposed to bring your attention to an area which needs improvement. Once you understand and commit to what needs to be improved _—for example if you've identified the specific Pig Attack and have recommitted to your Food Plan—_ then guilt has served its function and it's time to move on.
A well person feels guilt and shame when they let themselves or others down. They see it as a signal to examine their behavior and find significant ways to improve. But thereafter holding onto guilt is a Pig's game. _Excessive_ guilt is a type of penance the Pig wants you to focus on so you can "pay the price" for the _next_ Binge.
In your world there's NO price worth paying for a Binge. But the Pig thinks even one tiny bite or swallow of Pig Slop is worth ANY price. So it muddies the issue. What the Pig is really saying in this particular Squeal is:
### "Go ahead and beat yourself up while you keep thinking about all the delicious junk we ate. If that's the price we have to pay to get some Pig Slop again, so be it!"
– Your Pig
REMEMBER: To Never Binge Again all you need to do is Never Binge Again. You do not need to repeatedly smack yourself in the head with a spatula to prove you've suffered enough.
"Hey, there's an idea! Why don't we punish ourselves doubly hard for this last Binge? That way we'll have enough punishment stored up to get away with one more...FREE! Good thinking there Bubba!" [9] _– How your Pig motivates you to keep punishing yourself for a Binge_
You don't need to write a novel about your Binge. You don't need to go confess in the town square.
Yes, you allowed the Pig to misdirect your energy and harm your body with some Pig Slop. But after you've identified the Pig Attack _(or problem in your Food Plan)_ it's a complete waste of time to dwell on guilt and shame about the Binge because you will NEVER Binge again and that's that.
Your body will recover within a day or two, and along with it, your confidence.
**HARD TO RECOGNIZE SQUEAL #8
** ("You Can Exercise Off the Calories")
### "You'll exercise enough to justify this Binge later on today. Or maybe you already did. Or we could do it tomorrow. Who cares... it's yummy. Let's go!!!"
– Sincerely, Your Pig
One of the Pig's most idiotic arguments is that it's perfectly fine to eat Pig Slop because there's enough time left in the day to exercise off the calories. Or perhaps _after_ a good exercise session the Pig may suggest you've "earned it." Or maybe you will do enough exercise _tomorrow_. Or next year. Or maybe when you're 99 years old. _("Yeah, that's the ticket! Let's Binge until we're 99 and then spend one year making up for it at the end of our lives. That sounds like a plan, Stan!" – Your Pig)_
Here's the problem: Anything even .00001% off your Food Plan poisons everything important to you. There are always physical effects beyond calories and weight loss...such as fatigue, difficulty working the next day, and the need to eat more over and above the cheat to rebalance your blood sugar, sodium levels, etc.
Pig Slop is Pig Slop and a Binge is a Binge. It doesn't matter how much exercise you've done today, will do tomorrow, or plan to do sometime in the next 99 years. You will avoid Pig Slop from here to eternity as if it were poison. You'd never consciously consume some arsenic with the idea you could exercise it off later, so why do it with Slop?
HARD TO RECOGNIZE SQUEAL #9
### "You really must eat something off your plan
every once in a while or you'll starve!"
Sincerely – Your Pig
If you never eat Pig Slop again _—and you never will—_ the PIG will starve and YOU will thrive! Let the Pig suffer!!!
HARD TO RECOGNIZE SQUEAL #10
### "I'm not an idiot. I'm just as smart as you are. And, OK, I'll admit it... I DO exist inside you after all. So you really need to listen to my incredibly intelligent, complex arguments for Bingeing because I'm just as likely to be right as you are. Besides, you really _want_ to hear me out so we can Binge, don't you? Let's go!!!"
– Your Pig
Because the Pig derives from a survival drive which is indeed anatomically inside of you, it has access to the full force of your native intelligence. But that's NOT a good reason to listen to it!
YOU use intelligence to accomplish worthy goals and aspirations. The Pig uses it for destructive purposes only.
To engage in debate over the merit of the Pig's arguments is like talking to a serial killer about the merit of their deeds. Save your energy for those who have more constructive aims. Nothing good ever comes from letting a serial killer win an argument. Even if he's right!
Even if the Pig is not an idiot, you must treat it as if it were.
The Pig will use ALL the intellectual capacity it can borrow from your brain to argue for indulgence. Its ultimate aim is to obliterate your human ability to delay gratification and thoughtfully direct your behavior _—and instead have you behave like a dog in a meat factory._
No matter how smart your Pig may appear, it is NOT trying to win an intellectual debate at Harvard. There's only one purpose to its debate: To get you acting like a wild animal...
If you fail to treat the Pig like an idiot it will treat YOU like an idiot!
It's idiotic to give human rights and responsibilities to an animal. We don't give driver's licenses to dogs _(or let them vote.)_ We certainly don't give them free access to the refrigerator, the butcher's shop, or the supermarket.
There's never any point in debating with your Pig. It is an animal and must always be treated like one!
HARD TO RECOGNIZE SQUEAL #11
### "You know, you've been doing great lately. You've really been taking care of yourself with this 'Cage the Pig' stuff. You're looking and feeling a lot better. Therefore, you're finally thin and healthy enough to get away with a GREAT BIG GIANT HAIRY BINGE!!! Let's just do it, you and me, whaddyasay? Can we? Can we? Huh? PLEEEEEEEEEEASE!!!?"
– Your Pig
Let me answer this ridiculous Squeal with a serious question: Is your body a great big garbage can, the sole purpose of which is to process as much refuse as possible? And as soon as enough Pig Slop has been emptied from that canister, are you supposed to rush in and fill it up with more garbage?
—OR—
Or is your body a sacred vessel meant to carry you forward and supply you with energy, peace, and happiness in order to accomplish your goals and live your dreams?
You know the right answer...
And you know the Pig's answer too...
So you know what to do, right? _(Cage the Pig!)_
HARD TO RECOGNIZE SQUEAL #12
### "Hold on just a minute now, Bubba! This is about _willpower_ , and everyone knows you can't diet on willpower alone. All the latest studies have shown willpower is something you use up as you deal with stress and make decisions throughout the day. See? NOW I've gotcha. I've gotcha....I'VE GOTCHA!!! It's absolutely hopeless to rely on willpower. You're going to Binge. You are. You are. You ARE! And since the time will definitely come, why bother waiting? Let's do it now!!!"
– Your Pig
This _is_ a tricky Squeal because there's a wealth of evidence which does actually suggest willpower is a limited resource. Deciding between competing alternatives _(like eating junk vs. a healthy meal)_ really does tax our mental energy. And so people make increasingly poorer choices as the day goes on and stress wears them down.
On the surface then, it seems willpower may be doomed to fail, and Never Binge Again may be an impossible dream. But when you place these scientific findings _in context_ you'll see this idea is just the Pig at work...
The key is understanding willpower is only necessary when there's actually a choice to be made, but when your options are clearly constrained beyond all reasonable doubt, deciding requires virtually no effort at all.
Don't believe me? OK! Time for another thought experiment: How much willpower did it take for you NOT to rob a bank today? Did you spend a lot of the day agonizing about whether or not to do it? Worrying that one day when you're particularly tired and stressed, you just won't have the willpower to resist, even though you didn't rob one today?
Of course not!
Why?
Because you're NOT a bank robber.
You NEVER rob banks, so walking past a bank without robbing it is truly effortless. And here's the thing: It will NEVER take effort for you to resist robbing a bank, regardless of how stressed you may become or how much willpower you may have at any given moment _._ Why? Because you're a law abiding citizen. You're simply NOT the kind of person who robs banks.
I know the example is a little over the top, but the point is, you don't have to strain and struggle to resist doing something you've sworn NEVER to do... as long as the line is crystal clear.
The situation does become a little more difficult with the CONDITIONALS category of your Food Plan. But only a little, because you can actually translate every conditional into a never.
For example, "I only eat pretzels at baseball games" can become "I NEVER eat pretzels outside of a major league baseball stadium." "I can eat as many calories as I want on the weekends" can be translated to "I NEVER consume more than 2,750 calories per day during the work week."
ALWAYS can be translated to NEVER. For example "I always drink a glass of water as soon as I wake up" becomes "I NEVER leave my bedroom in the morning without drinking a glass of water."
See what I mean?
The trick is making sure every rule in your Food Plan is defined with crystal clarity. If you've got extraordinarily "bright lines" to define the boundaries, then it does NOT take any willpower to recognize and keep to them.
It's only when you've accepted the Pig's desires as actual, viable options that you'll need willpower to resist.
DETAILED INTERVIEW ON THE 12 SNEAKY PIG SQUEALS
For a much more detailed discussion of these 12 sneaky Pig Squeals please download the free audio _(and transcript)_ "12 Sneaky Pig Squeals" from www.NeverBingeAgain.com
Chapter 11
### Discipline vs. Regret
Jim Rohn said "A Life of Discipline is Better Than a Life of Regret," but your Pig vehemently disagrees. It wants you to think discipline restricts your freedom, when precisely the opposite is true.
Most people remember feeling like their whole world opened up when they first got their driver's license. They could finally just get in the car and go anywhere they desired. No longer were they dependent upon others.
But what these very same people forget is that in order to acquire this freedom, they first had to master a series of disciplines. They needed to learn the rules of the road, amass a certain number of supervised driving hours, and pass a written test. Only then could they take the live road test.
The keys to the driving kingdom are _only_ given to those who've proven themselves capable of following the rules of the road in earnest. Mastering rules and discipline is how we _increase_ freedom in our society, not restrict it!
Here's another way to look at it: Freedom isn't free! It's only for those willing to pay the price.
Your Pig says you're giving up freedom by imposing a disciplined Food Plan, but discipline itself is the price which must be paid for freedom. Without discipline, you will _never_ experience the freedom to:
• Eat without guilt...
• Live in the body of your dreams...
• Live with a minimum of dietary illnesses...
• Have the energy only a truly nourished body can provide...
• Enjoy confidence in your ability to master your own impulses _..._
• Choose what to eat, when to eat, and where to eat...
• Accomplish progressively more meaningful goals, fully confident you can count on yourself to stay on track until they are achieved...
A disciplined Food Plan doesn't restrict your freedom, it enhances it 100 fold. In actuality it is _the Pig_ which seeks to restrict your freedom. If it were given its way you'd be nothing more than a slave to its impulses, and your true freedom would go out the window.
It's your Pig who frames the problem as Freedom _versus_ Discipline in the first place. As if you had to choose one or the other, when in reality freedom ceases to exist in the absence of discipline.
The real question is whether you'll choose a life of discipline versus a life of regret. And when you frame it in this context, it doesn't seem like much of a choice at all, does it?
You know what to do.
(Let the Pig suffer!!!)
NO REGRETS WORKSHEET
If you'd like to more clearly see what the Pig may cause you to regret later on, please download the "No Regrets" worksheet. It's part of the free book upgrade available at www.NeverBingeAgain.com
Chapter 12
### The Psychology of Bingeing, Not Bingeing, and Thinking Too Much About Food
Many years ago when I first started to research food addiction, I wrote a book called "Eat with Your Head™" based in part on a self-funded survey with over 40,000 people on the relationship between personality and Binge food choices.
A few years later my wife and I developed a website called "EmotionalEatingSecrets.com." [10]
At the time, I was very taken with the idea that delving deep into one's personal psychology would yield powerful insight into why any given person Binged. Moreover, I believed it was necessary to acquire such insights in order to stop.
But now, many years later, I know I was unequivocally wrong!
It may be intriguing and psychologically valuable to figure out why your Pig prefers chocolate and pizza while other people's Pigs like donuts and potato chips, why you chose to let your Pig have its Slop in private while others prefer to Binge in the company of others, why anger triggers some people to Binge and loneliness triggers others, etc...
But the notion it's necessary to answer these kinds of questions before you can stop Bingeing is 100% Pig Squeal. From the Pig's perspective:
### "You know, Mama and Papa didn't love us nearly enough. They said and did some pretty awful things. And everyone deserves love, right? Oh well. I guess we'll just have to keep Bingeing to fill that big empty hole Mama and Papa left deep inside us. At least until ALL the tragic events from our past have been uncovered and we can find healthy substitutes for the love we missed out on. I know, I know, Pig Slop can't ever replace Mommy and Daddy's love. But it sure does taste good. Too bad, so sad. Let's Binge!!!"
– Your Pig
Or alternatively:
### "Our life is just too stressful. And our loved ones don't support our personal goals and dreams nearly enough. All we have to rely on in this world is Pig Slop. Maybe we'll be able to stop eating it when we have less stress or better coping mechanisms. But for now, we simply MUST Binge in order to cope. Oooooooooh!!! Oooooooooh!!! Oooooooooh!!! How yummy!!!!"
– Your Pig
Now, please don't get me wrong, I thoroughly support psychological and spiritual soul searching. In fact, a big part of the reason I myself have such a meaningful life is because of the years I've spent with therapists, coaches, and mentors digging deep into my own thoughts, feelings, and past experiences. I wouldn't give it up for the world.
But soul searching has absolutely nothing to do with your ability to quit Bingeing. Zero. Nada. Zilch.
This is a ridiculously simple concept which shouldn't have to be written—but because of the confusing culture in which we live I'm afraid it does...
You do NOT need to know why you Binge. You just need to stop.
It doesn't matter whether it's because nobody came to your fourth grade bowling party, because you saw your Momma in her underwear, or because grandpa forgot to pick you up at school when you were five.
You know how to eat healthy.
You know how to construct an unambiguous Food Plan, making well-considered, intellectual decisions to balance the tradeoff between short vs. long term gratification and health.
You know what a Binge is and what a Binge isn't.
So just don't Binge again...
Ever.
Even if everyone you love suddenly dies.
Even if you feel justifiably lonely, alienated, angry, depressed, anxious, and/or stressed beyond all hope and reason...
Just _Never Binge Again!_
Now, if you want to go back and examine the particular Slop the Pig talked you into for the purpose of more clearly hearing its Squeal next time...
Or if you want to do some soul searching to see why you were convincible at that particular time and in those particular circumstances...
Fine. More power to you.
But you don't need to wait for a good answer before you stop Bingeing.
You don't need to see a Shrink to stop Bingeing.
You don't need to go to a support group to stop Bingeing.
In fact, you don't even really need this book.
To stop, just draw 100% clear lines and stop.
That's ALL you need to know about the psychology of Bingeing.
It really _is_ that simple.
While Binges are often associated with emotional experiences _—and therefore serve as an excellent jumping off point for soulful exploration—_ they do NOT and cannot CAUSE you to Binge!
The notion that emotional upset _causes_ Binges is actually harmful, because it gives the Pig license to keep Bingeing until the upset is over and/or fully understood.
Remember, this is coming from a guy with a Ph.D. in psychology _—who grew up in a family of psychologists and therapists and still thinks of himself as a psychologist first and foremost—_ so I don't say this lightly!
Bingeing transforms you into a wild animal. It rejects the laws of humanity and returns you to the jungle where life is brutish, chaotic, and short.
Bingeing wipes out your spirit.
Don't spend years investigating WHY you Binge before you stop. Just stop.
Who cares if your Mummy and Daddy didn't love you enough?
Choose to stand for the domination of the human spirit over our animal nature so you can accomplish your dreams and pass your experiences on to your loved ones.
Which leads me to one last point about the psychology of Bingeing...
It's NOT a foregone conclusion that childhood adversity will traumatize a person and set them on a path of compulsive self-destruction. In fact, adversity _can_ result in both a strength of character AND a determined persistence to right the wrongs one has experienced.
Yes, there are victims of child abuse who wind up abusing drugs or becoming serious binge eaters. And there are those who choose to perpetuate the abuse cycle by victimizing their own children...
But there are also those who turn into incredibly gentle souls, passionate about helping others who've been through anything similar.
We all must make a decision in this life to either get well or get even.
Bingeing is glued to the revenge journey...
Your resolve to Never Binge Again puts you on the royal road to forgiveness and wellbeing.
To partake of everything life has to offer...
Cage the Pig!
Chapter 13
### A Radical View on Guilt and Shame
We've talked about this throughout the book in order to quiet your Pig enough so you could actually read it. In this short chapter, I want to put to rest any remaining fear you may have of guilt or shame for having made a mistake.
I've run into many people who say the Never Binge Again approach very much appeals to them, but they won't implement it because they fear a "guilt hangover" when they inevitably find themselves Bingeing again. But if you've been paying attention, you should recognize this as just another Pig Squeal:
### "Don't bother committing to a Food Plan because you can't ever hope to do it perfectly, and then I'll beat you up and make you feel horribly guilty...so you never try such a silly thing again. C'mon, are you really going to do this nonsense? Let's just Binge!!!"
– Sincerely, Your Pig
See, the Pig has a plan for you to FAIL.
But YOU have a plan to SUCCEED.
Just remember this distinction and ignore that vile creature.
The natural, healthy purpose of guilt and shame is to draw your attention to a bad behavior so you can correct it. Therefore, once you've made a 100% firm plan to never Binge again, there's absolutely NO purpose to holding onto your guilt or shame.
Guilt and shame about Bingeing are uncomfortable emotions which quickly dissipate in the absence of a plan to Binge again. Much like the pain you feel after touching a hot stove, these feelings exist to help you learn...and they go away quickly once you've done so.
You don't need to walk around for a month beating yourself up for touching the stove, you just say "I'll Never Do That Again"... and once you're 100% convinced of your commitment, you easily let it go.
Unfortunately the field of psychology has gone too far in its attempt to eliminate the guilt and shame which Victorian times imposed upon us for our natural human feelings _(mostly sexuality and anger)_...
And today popular wisdom suggests we should eradicate these emotions entirely...
But that's NOT entirely healthy either.
We should actually WANT to feel guilty when we break our commitments... or else we'd be removing our motivation to change, and denigrating the meaning of our word.
But we must also be willing to let go of these uncomfortable emotions once we've analyzed what went wrong and made a commitment to correct it in the future...
Holding onto guilt and shame for a well-analyzed and corrected mistake is the Pig's way of doing penance in advance for its plan to Binge again.
Don't let your Pig talk you into fearing your guilt...
Or hold onto it once you've fixed the problem.
Touching a hot stove is painful...
And food mistakes do burn indeed...
But if you're a human being who's still breathing, you've got a miraculously strong ability to recover and leave that mistake in the past.
Cage the Pig and watch it squirm!
Chapter 14
### "Unconscious" Bingeing
The Pig always prefers us to remain 100% unaware of its activities because it knows that if we were fully aware of what it was up to, we would have to be crazy to give it ANY control! For this reason, most people report feeling somewhat "unconscious" during a Binge, almost as if another entity had "taken over." Some people even suggest this went on for weeks or even months, and they simply "woke up" having gained a lot of weight and feeling miserable...
But it's more accurate and helpful to say we consciously decided not to think about what we were doing during a Binge. We turned a blind eye so the Pig could have its Slop. We did NOT go into a temporary coma while the Pig did its thing!
Here's what I mean...
If I were to interview you immediately after a Binge, the odds are very good you'd be able to recount virtually everything which happened. We could reconstruct exactly what you ate, what brands you bought, what the bags and boxes looked like, about how much you paid for them, where you got them, what the cashier looked like, what else was in the isles where you picked up the junk, how you decided what to buy, about how much you put in your cart _(or arms)_... and if we tried hard enough you could even remember the stream of thoughts which led you to the store.
The video recorder in your mind was running the whole time you were bingeing... you just chose not to look through the lens while it was making the tape.
While it's only natural to behave like this because it's too uncomfortable for a rational, conscious person to accept they are allowing themselves to be out of control, it's still a critically important distinction.
The notion of being unconscious may provide a safe haven from the guilt and shame we feel about the Binge, but it does so at a very steep price...
To believe the Pig has the ability to knock you unconscious so it can do as it pleases is to relinquish your free will and responsibility. To believe the Pig can put you in a coma removes all your power and ability to keep your own word...
And it's your word that allows you to set and achieve goals...
To accomplish the things you want to in this life...
To be true to the people you love...
To be exactly the kind of person you want to be.
Remember, you can and should let go of the guilt and shame associated with Bingeing once you've analyzed the Squeals, corrected your Food Plan _(if necessary,)_ and re-committed 100%...
So you really don't need the cover of a weird "psychological anesthesia" for your past Binge behaviors. You are never going to binge again, so you can and should claim responsibility for every last choice you made in the past.
This way the Pig will know you're always watching...
And are prepared to dominate it if it even _thinks_ about getting out of line.
Chapter 15
### Your Personal Pig Squeal Journal
As discussed above, all that's necessary to stop Bingeing is to stop Bingeing...
Define a Food Plan, commit to it with a 100% certain resolution, and then go about the rest of your life.
You don't have to practice using any particular tools, meditations, chants, or rituals. All you need to do is comply with your Food Plan, and utterly ignore any thought _(Pig Squeal)_ which suggests you do otherwise.
Journaling is therefore NOT a requirement of the Never Binge Again program.
That said, you can only ignore Pig Squeal if you recognize it. And _—especially in the beginning—_ the Pig will be busy dreaming up NEW ways to disguise its Squeals. After all, the Pig doesn't want to be locked in a cage forever. It will passionately work to find loopholes.
Ultimately all the Pig's reasons boil down to "because it tastes good" or "because I want the Food High"...and it will eventually stop bothering you when it realizes you know this. Like all wild animals in captivity it realizes there's no use continuing to bang on the inside of a permanently locked door.
But because the Pig lives inside you and has access to your native thinking, every person will hear different types of Pig Squeal during the adjustment phase...so it's impossible to list every last possibility in this book.
For this reason journaling can be very helpful.
Journaling sensitizes you to how the Pig sounds when it attempts a new Squeal. Wait, what's that? I can hear your Pig now:
"Glenn says you've got to journal or else you won't hear my super-creative NEW reasons for Bingeing. This means the first day you forget and/or don't have the time to journal we can go off to the races and Binge our little faces off. Yippeee!!!"
Pig Squeal!
You've unambiguously defined a Food Plan which draws clear lines in the sand...
You've solemnly sworn an oath to hold to it forever...
You CAN do this regardless of whether you journal or not.
But journaling makes it less stressful because you'll recognize the Squeals sooner. That's all.
Anyway, a simple way to go about this is to challenge your Pig each morning before you've eaten anything. Say "Go ahead Pig. I'll give you control over my fingers to type/write any reason you can think of to convince me to feed you some Slop. Let's see if you can come up with a good one!"
It's OK. They're your fingers and you can take back control whenever you like. And because you will NEVER Binge again no matter what the Pig says, you can let the Pig have at it.
Once the Pig's Squeals are in black and white it takes less energy to recognize and ignore them.
Now, you'd think the Pig would catch on to this game and just stop playing after it realizes you're only baiting it to reveal its hand. But the Pig is so impulse driven it can't help but lunge at the opportunity. Again and again, no matter what the results were last time, the time before that, or the forty two million times before _that!_
It's kind of like dangling roast beef in front of a Doberman Pincher. The chance to get the meat, however slim, is too alluring. Its primitive instincts will take over, no matter what happened before.
Just like the Doberman, your Pig will always give you its best shot if you dangle a Bingeing opportunity in front of it.
Stupid Pig.
Make it suffer!
Chapter 16
### Binge Anxiety
Many people say they feel frightened a Binge is imminent and/or inevitable "someday soon" shortly after resolving to Never Binge Again. These people aren't consciously lying, they just don't realize it's the Pig talking, not them.
What's underneath "I'm afraid I might Binge" is just the Pig saying "I really, really want to Binge!"
Always.
100% of the time.
It's that simple.
Binge Anxiety is a big hairy lie which starts and ends with the Pig's plan to Binge...
Any and all doubt in your ability to Never Binge Again is Pig Squeal.
Any and all insecurity comes from the Pig.
But you will Never Binge Again, so you can just put this to rest.
WHAT TO DO WITH BINGE ANXIETY?
I've prepared a simple Binge Anxiety audio and wallet-cheat-card you can download and carry around with you in your smart phone. Get it at www.NeverBingeAgain.com
Chapter 17
### What to Do When It's Not Working
"What if it doesn't work?"
This question _itself_ is Pig Squeal.
By definition, the Never Binge Again approach isolates and starves any and all Binge-related impulses so you can once again exercise free will with food. How you use that innate human capacity is entirely up to you.
If you choose to deploy free will to work for you, it WILL work for you. You literally can't fail, because all you're doing is letting go of an illusion and stepping squarely into the way things are.
But there's one ploy your Pig may use in a last-ditch attempt to trick you:
"You can't stop Bingeing using free will because free will doesn't really exist."
Here the Pig is trying to draw you into an unresolvable debate so you will keep Bingeing until a definitive answer is found.
Now, although I'm not intellectually equipped with decades of philosophical study to prove it, I emphatically believe free will exists. But even if it didn't and our fate was entirely predetermined, what evidence would we have to conclude we were fated to exercise the Pig's desires vs. our own?
See, the Pig is hiding the second half of its argument in the anti-free-will ploy. What it's really saying is because there's no free will you must _choose_ to let it keep Bingeing. But if there were no free will, you couldn't choose anything at all.
Stupid Pig!
In any case, the answer is to let the philosophers debate the free will issue until they're blue in the face...
And besides, even if free will didn't exist we'd still have to act as if it did or we couldn't have a society at all _—because nobody would be responsible for anything, and anyone could do whatever they wanted without justifiable consequence or punishment!_
Because until someone has had a scientifically demonstrable and repeatable talk with God _(whatever that means)_ we will probably never know. In the meantime, we'll just relentlessly continue to dominate the Pig...
Why?
Because we can.
And because the alternative is too ugly to consider.
Chapter 18
### Alcohol Pigs, Drug Pigs, and Other Pigs Worth Dominating
By now, if you've implemented even just a little of what we've talked about I'm sure your brain is exploding with ideas for applying the Never Binge Again philosophy to other areas of your life.
The truth is, I didn't invent the idea of aggressively separating your thin-thinking-self from your fat-thinking-alter-ego, then carefully watching for the latter so you could ignore it with contempt. The "devil vs. angel on your shoulder" has been man's way of wrestling with constructive vs. destructive impulses since time immemorial.
But while others have been hard at work for decades perfecting its application to black-and-white addictions like drugs, alcohol, and cigarettes, I found serious modifications were necessary to apply this thinking to complex behavioral systems like overeating.
Most significantly it was necessary to develop a more appropriate before-vs. after-the-Binge mindset. This was necessary to address the multitude of attempts most people seem to require in order to _"confidently peddle to the top the Never Binge Again hill"_ without becoming distracted by the possibility of failure and/or the destructive use of guilt and shame for mistakes.
It was also critical to identify an appropriate analogy— _society's reliance on a body of law—_ for complex behavioral systems as compared to simple yes/no addictions.
And finally, it was necessary to develop a set of core principles for defining an individual's Food Plan without usurping their autonomy.
Now, if you DO struggle with drugs, alcohol, or other black-and-white addictions, I can't recommend anyone's work more highly than Jack Trimpey's at Rational Recovery Systems. _(_www.Rational.org _)_ Rather than trying to define an "Alcohol Pig" or "Drug Pig", please just use his methodology, which you'll find very compatible with the philosophy you've learned in this book.
While there is some overlap, these black and white addictions will NOT succumb to the Never Binge Again philosophy I've outlined in this book in the same way that food will. I've also never seriously struggled with drugs, alcohol, or cigarettes on a personal level. More importantly, I haven't studied those addictions in the same comprehensive way I've studied food.
For these reasons, you're MUCH better off with Mr. Trimpey's body of work if these particular substances have you caught in the Venus Fly Trap of toxic pleasure.
On the other hand, if you're thinking Never Binge Again can be effectively applied to _other_ complex behavioral systems in the same way it works for overeating—you're right!
For example, perhaps you'd like to Never Procrastinate Again™ so you can comply 100% with your exercise routine, finish your book, and/or do anything else you know you'd be capable of if it weren't for the self-sabotaging voice inside you which always says "later." Just define a reasonable schedule with 100% clarity, then summarily ignore your Procrastination Pig when it suggests you deviate for any reason whatsoever.
Better yet, read my next book "The End of Failure™" so you can assure yourself of success across every important area of your life going forward and...Never Fail Again. I'm just saying! _(When you download the free bonus materials for Never Binge Again you'll also be sure to be notified when the new book is released._ www.NeverBingeAgain.com _)_
Chapter 19
### My Personal Food Plan
What do I eat? None of your Pig's business!
But I will tell you what I will NEVER eat again...
Pig Slop!
Chapter 20
### Taking the Next Step
You have everything you need to Never Binge Again right here in this book. You don't have to talk to a shrink, attend a recovery group, smack yourself in the head with a spatula to atone for your mistakes, or go sit by the river for months to contemplate your navel.
You only need to define a healthy Food Plan, commit to it 100%, and remember that Pig Slop is anything even 0.0000001% outside your plan.
Then just ignore the Pig when it Squeals for Slop. Every last time!
Do this and your last Binge _—whether it was 5 seconds, 5 minutes, or 5 months ago—_ really can be your LAST.
Notwithstanding the above, some people find it helpful to talk this over in person, absorb the information in a more customized manner in a LIVE environment, and/or see how I help other people with their own Pigs. And some people simply do better when they absorb information in a multitude of formats.
I therefore offer:
• **The Never Binge Again Success Club:** Each month, I work with another person struggling with their Pig's cravings in an in-depth, recorded session you can listen to, study, and discuss with other members in our online forum.
• **Personal Consultations** : Get powerful, personalized guidance to stop bingeing right away. Available from myself personally as well as a handful of trained Never Binge Again coaches
• **Weekend Immersions** : Make Never Bingeing Again your first priority this month by attending one of our Intensive Food Plan Confidence weekends.
**Please visit** www.NeverBingeAgain.com **for the latest options. And be sure to download the special FREE book upgrade which contains ALL of the following:**
• **Pig Damage Calculator:** Take the short, free test and see how much impact has the Pig has had on your life. A great way to get motivated and get started.
• **Free Starter Food Plan Templates** : No matter what your nutritional philosophy you'll find a pre-filled starter template to help fill in your own Food Plan with NEVERS, ALWAYS, UNCONDITIONALS, and CONDITIONALS
• **Custom Food Plan Creation Worksheet** : A set of detailed questions to help you identify and customize your own plan.
• **Craving Defeater Set:** Quickly defeat ANY craving with this simple cheat-card you can carry around in your wallet AND and MP3 audio you can play on your smart phone
• **Binge Recovery Set** : This MP3 and Workbook will help you put the Pig back in its cage for good no matter how painful a Binge you've experienced
• **How to Change Your Food Plan Cheat Sheet** : A simple one-pager with a detailed set of criteria to help ensure it's YOU and not your Pig suggesting the changes!
• **Avoiding the Deprivation Trap Workbook:** Struggling with whether to set a particular Food Rule or move a conditional to a NEVER? Who will be deprived, you or your Pig? Fill out this workbook and find out so you can make the decision more easily.
• **The Four Most Common Food Industry Lies and How to Defeat Them** _(Audio Interview + Transcript):_ Our society is set up to feed your Pig. Here are some tricky ways they do it, and simple strategies for winning the game regardless!
• **Unusual Ways to Neutralize Other People's Pigs** _(Audio Interview + Transcript):_ Troubled by what other people say, do, or tempt you with in an eating environment? Stop that! Just listen to this educational audio and arm yourself with a simple way to immediately neutralize their power
• **12 Sneaky Pig Squeals and How to Defeat Them** _(Audio Interview + Transcript):_ Taken directly from people's sneakiest Pigs, this interview will strengthen your ability to recognize Pig Squeal in all its sneaky forms
• **The "No Regrets" Worksheet:** How to see the road not taken – the two different paths and where they may lead
• **Binge Anxiety Killer:** I've prepared a simple Binge Anxiety audio and wallet-sized-cheat-card you can download and carry around with you in your smart phone to help eliminate Binge Anxiety whenever it strikes.
### **Download All of the Above
in the FREE Book Upgrade at
**www.NeverBingeAgain.com
Last, I LOVE to hear your stories. It's particularly helpful if you can share sneaky Pig Squeals you've learned to identify. Please post them on our Facebook Page and/or upload them to YouTube and send us the link. Instructions are on the website.
Now, YOU...
Cage the Pig, let it suffer and...
Never Binge Again!
Notes
[1] IMPORTANT: Your Food Plan is a very private and personal matter. Other people's Food Plans are not really any of your business unless you're invited to discuss them. Telling someone else they're eating Pig Slop is a great way to ruin a perfectly good relationship. Everyone gets to decide what goes in their Pig's trough vs what goes on their personal human plate. In fact, everyone gets to decide for themselves whether they want to separate their fat thinking self (the Pig) from their thin-thinking-self at all. You've therefore got NO real way of knowing how to define Pig Slop for anyone but yourself! More on this in the chapter on dealing with other people's Pigs.
[2] This philosophy was first quoted in the 1949 movie "Knock on Any Door" by actor John Derek. The full quote was "Live fast, die young, and leave a good looking corpse"
[3] The real name of my friend and the details of his company have been disguised to protect the innocent.
[4] I should know since, sadly, I used to be one of them! My companies have earned tens of millions of dollars consulting for Fortune 500 firms.
[5] Hell is Other People" comes from Jean Paul Sartre's existentialist play "No Exit" where the characters are forced to spend eternity in one room fruitlessly seeking themselves in each other.
[6] In fact, when you do it right, dominating the Pig actually improves your reasoning ability!!
[7] Note: They do NOT have to "hit bottom"...but they do have to have sufficient motivation. (Waiting to "hit bottom" is a type of Pig Squeal in and of itself. The Pig says "I guess you haven't hit bottom yet. Let's just keep Bingeing until you do. Yummy!!!")
[8] Can you have a "red light running disease", for example? Could you be a compulsive bowler?
[9] My Pig calls me Bubba. I don't really know why.
[10] While I promptly removed the "Eat with Your Head" book from the market once I realized how wrongheaded my original notions about psychology and food addiction were, I was unable to do the same with the EmotionalEatingSecrets.com website because it is intricately bound up with other projects and partners to whom I have legal commitments.
|
{
"redpajama_set_name": "RedPajamaBook"
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| 5,875
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{"url":"https:\/\/deepai.org\/publication\/synthetic-topology-in-homotopy-type-theory-for-probabilistic-programming","text":"# Synthetic topology in Homotopy Type Theory for probabilistic programming\n\nThe ALEA Coq library formalizes measure theory based on a variant of the Giry monad on the category of sets. This enables the interpretation of a probabilistic programming language with primitives for sampling from discrete distributions. However, continuous distributions have to be discretized because the corresponding measures cannot be defined on all subsets of their carriers. This paper proposes the use of synthetic topology to model continuous distributions for probabilistic computations in type theory. We study the initial \u03c3-frame and the corresponding induced topology on arbitrary sets. Based on these intrinsic topologies we define valuations and lower integrals on sets, and prove versions of the Riesz and Fubini theorems. We then show how the Lebesgue valuation, and hence continuous distributions, can be constructed.\n\n## Authors\n\n\u2022 2 publications\n\u2022 2 publications\n\u2022 12 publications\n\u2022 ### Measurable Cones and Stable, Measurable Functions\n\nWe define a notion of stable and measurable map between cones endowed wi...\n11\/27\/2017 \u2219 by Thomas Ehrhard, et al. \u2219 0\n\n\u2022 ### Sharp Elements and the Scott Topology of Continuous Dcpos\n\nWorking constructively, we study continuous directed complete posets (dc...\n06\/09\/2021 \u2219 by Tom de Jong, et al. \u2219 0\n\n\u2022 ### Generative Datalog with Continuous Distributions\n\nArguing for the need to combine declarative and probabilistic programmin...\n01\/17\/2020 \u2219 by Martin Grohe, et al. \u2219 0\n\n\u2022 ### Applied Measure Theory for Probabilistic Modeling\n\nProbabilistic programming and statistical computing are vibrant areas in...\n10\/01\/2021 \u2219 by Chad Scherrer, et al. \u2219 0\n\n\u2022 ### Separating minimal valuations, point-continuous valuations and continuous valuations\n\nWe give two concrete examples of continuous valuations on dcpo's to sepa...\n09\/01\/2021 \u2219 by Jean Goubault-Larrecq, et al. \u2219 0\n\n\u2022 ### Measure Transformer Semantics for Bayesian Machine Learning\n\nThe Bayesian approach to machine learning amounts to computing posterior...\n08\/03\/2013 \u2219 by Johannes Borgstr\u00f6m, et al. \u2219 0\n\n\u2022 ### Modalities, Cohesion, and Information Flow\n\nIt is informally understood that the purpose of modal type constructors ...\n09\/21\/2018 \u2219 by G. A. Kavvos, et al. \u2219 0\n\n##### This week in AI\n\nGet the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.\n\n## 1 Introduction\n\nMonads on Cartesian closed categories are a semantics for a large class of effectful functional programming languages (Moggi, 1991). The ALEA Coq library (Audebaud and Paulin-Mohring, 2006) provides an interpretation of ml, a functional programming language with primitives for random choice, by constructing a version of the Giry monad\u00a0(Giry, 1982) on the category of Coq\u2019s types. Giry monads generally assign to a suitable class of spaces their spaces of valuations, and in ALEA\u2019s case it is the class of discrete spaces. This monad is suitable for embedding programming languages with discrete sampling constructs into the ambient logic of Coq, as for example in applications to cryptography (B\u00e9guelin, 2010)\n\n. But continuous distributions are essential in statistics, machine learning and differential privacy, and these distributions have to be discretized in ALEA because they cannot be defined on discrete spaces. For example, the Lebesgue measure is only defined on Borel sets, and hence is not directly definable in ALEA.\n\nWe propose the use of synthetic topology as a principled way to deal with the problem of continuous distributions. In synthetic topology, one works with a set of open truth values, from which a notion of intrinsic topology on any set can be derived. Working internally in a model of synthetic topology, we develop a theory of valuations and lower integrals on sets which takes the intrinsic topologies into account. We show that a version of the Riesz theorem holds in this setting: Valuations are in one-to-one correspondence with lower integrals. This is then used to define a Giry monad on the category of sets in terms of the continuation monad, and we prove a version of the Fubini theorem. Assuming the metrizability of the real numbers , which asserts that the intrinsic topology on the set agrees with the metric topology, we then define the Lebesgue valuation as an element of .\n\nIn non-classical measure theory (which is required because the metrizability of is contradictory with classical logic), the Dedekind or Cauchy real numbers have to be replaced by the lower reals because the former are not closed under enumerable suprema. A lower real is a lower closed rounded inhabited subset of , and in synthetic topology it is natural to require that this subset is furthermore an open subset. An analogous construction for Dedekind reals in synthetic topology is studied by Le\u0161nik (2010) in great generality. The Homotopy Type Theory (HoTT) book (Univalent Foundations Program, 2013) also proposes this in the special case of equal to the initial -frame, and a formalization on top of Coq\u2019s Math Classes (Spitters and Van\u00a0der Weegen, 2011) and the HoTT library (Bauer et\u00a0al., 2017) has been carried out by Gilbert (2016). We develop the theory of lower reals valued in the initial -frame and construct an isomorphism with the -cpo completion of the rationals .\n\nThe initial -frame is itself the -cpo completion of the partial order of the booleans or equivalently the pointed -cpo completion of the unit set . Pointed -cpo completions of sets are studied by Altenkirch et\u00a0al. (2017) in HoTT using quotient inductive inductive types (Altenkirch et\u00a0al., 2018). We explain how their construction can be adapted to -cpo completions of preorders with respect to covers. This generality is needed to define -cpo completions of the rationals and the definition of a formal -frame of opens in the Dedekind reals .\n\nSome of the results presented in this paper have been formalized in Coq on top of the HoTT library, and an exposition of the formalization has appeared in French (Faissole and Spitters, 2018). Homotopy type theory has a number of advantages over standard Coq, even when one is only interested in sets, i.e. types with trivial higher structure. ALEA can only prove its version of the Giry monad to adhere to the monad laws pointwise and resorts to setoids because neither function extensionality nor quotients are part of standard Coq. This is not a problem in homotopy type theory, where function extensionality is provable and quotients of sets can be constructed as a special case of higher inductive types. Sets in HoTT form a -pretopos with a (externally) countable hierarchy universes; that is, it is a model predicative constructive mathematics including quotients and universes (Rijke and Spitters, 2014). As we are working predicatively, the set has to be understood as set of truth values in a fixed but implicit universe . We adopt the convention of the HoTT book and say that a fact holds merely to mean mean a proof irrelevant statement, and otherwise mean a proof relevant one.\n\nThis is the logical foundation throughout the paper, with two exceptions: First, we assume the existence of free -cpo completions (assumption 1), and it is to our knowledge unknown whether these can be constructed in our foundations. However, we identify three reasoning principles, all of which are generally considered constructive, and which each separately implies the existence of free -completions. Secondly, the metrizability of the Dedekind reals is assumed in section 8 in order to construct the Lebesgue valuation. This assumption is perhaps more limiting as it contradicts classical logic. Nevertheless, Brouwerian intuitionistic mathematics proves it (Le\u0161nik, 2010), and so our results can be interpreted in models such as the big topos of topological spaces (Fourman, 2013; Le\u0161nik, 2010) or K2-realizability topos (Bauer, 2005; Kleene and Vesley, 1965; Weihrauch, 2012). It is worth observing that we do not assume the axiom of countable choice.\n\nThe topos used in Fourman (1984, 2013) and the topos of continuous -actions for the localic monoid of endomorphisms of Baire space used in Van Der\u00a0Hoeven and Moerdijk (1984) are equivalent by the Comparison Lemma (Johnstone, 2002, Theorem C.2.2.3) because the topological monoid is dense in the site of separable locales, all of which can be covered by Baire space. Thus sheaves in the latter topos can be seen as a uni-typed versions of sheaves in the former topos. Both of these works provide a constructive elaboration of Brouwer\u2019s continuity principles.\n\nIt was proved by Shulman (2019) that most of HoTT as presented in the HoTT book can be interpreted in all Grothendieck -toposes (Lurie, 2009). Shulman\u2019s -topos models can also interpret propositional resizing (impredicativity), and so assumption 1 holds in these models, too. Every Grothendieck -topos is equivalent to the category of -truncated objects in the corresponding -topos. Thus the -topos models over the sites of Fourman (1984) and Van Der\u00a0Hoeven and Moerdijk (1984) also interpret our second assumption.\n\nIn concurrent work with our initial work on this topic (Faissole and Spitters, 2018), Huang (2017) developed the semantics of a probabilistic programming language targeted at machine learning with semantics in topological domains. Meanwhile, Huang et\u00a0al. (2020) have connected the two approaches by showing that the interpretation of a valuation in the internal logic of the K2-realizability topos indeed gives the notion of valuation on topological domains as defined in Huang (2017).\n\nThe paper is structured as follows. Section 2 contains some of the order-theoretic preliminaries and notation used throughout the paper. Section 3 discusses the construction and properties of -cpo completions. Section 4 studies the initial -frame as a set of truth values in synthetic topology. Section 5 constructs the lower reals and contains a proof of their universal property (theorem 2). Section 6 defines valuations and integrals and proves their equivalence (the Riesz theorem 3). Section 7 constructs the Giry monad and proves a Fubini theorem 4. Section 8 discusses the metrizability of and constructs the Lebesgue measure. Section 9 provides an interpretation of ml based on the Giry monad, which can be extended to continuous distributions. Section 10 concludes.\n\n## 2 Preliminaries\n\nA preorder consists of a carrier set and a transitive and reflexive relation on . We generally identify a preorder with its carrier set , leaving the order relation implicit. A map of preorders is monotone if implies for all . A partial order is a preorder whose ordering relation is antisymmetric. A suborder of a preorder is a monotone map with a partial order such that implies . Suborders of may be identified with subsets of .\n\nLet and be preorders and let be a monotone map. The join of is a least element such that for all . Dually, a meet is a greatest element such that for all . If is a partial order, joins and meets are unique if they merely exist. Identifying subsets with suborders of , we write for the join over the corresponding inclusion map. A monotone map of preorders and is final if for each there merely exists such that . If is a monotone map into a partial order and is final, then the two joins and exist and agree if either one exists.\n\nA preorder is directed if is inhabited and there is a function (not necessarily monotone) such that for all we have and . The partial order has for its carrier set the natural numbers with its natural order (which is generated by for all ). If is enumerable (i.e. there exists a surjection ) and directed, then there exists a final map . Thus enumerable directed joins in can be reduced to joins over maps , i.e. chains in .\n\nBottom and top elements are joins respectively meets over the empty set. A lattice is a partial order which as all binary joins and binary meets for . It is distributive if holds for all . An -complete partial order (-cpo) is a partial order which has all enumerable directed joins. A monotone map of -cpos and is -(Scott-)continuous if preserves enumerable directed joins. A -frame is a partial order with bottom and top elements, binary meets and enumerable joins which satisfy the distributivity law . A partial order is a -frame if and only if it has top and bottom elements and is both a distributive lattice and an -cpo: Arbitrary enumerable joins can be computed as using just the lattice and -cpo structure.\n\nSets of truth values are partially ordered by implication. They are stable under joins (disjunctions) and meets (conjunctions) over small indexing sets.\n\n## 3 Presentations of \u03c9-cpos\n\nIn this section we adapt the notion of dcpo presentation described in Jung et\u00a0al. (2008) for -cpo presentations. We discuss three proofs of the existence of free -cpo completions, and construct presentations of product -cpos.\n\n###### Definition 1.\n\nAn -cpo presentation consists of a preorder and a cover relation such that ( is covered by ) holds only if is an enumerable directed suborder of (thus is given by a map with directed image). We generally leave the covering relation implicit and refer to the -cpo presentation as just . A morphism of -cpo presentations is a monotone map preserving covers, in the sense that if holds in , then holds in for all and .\n\nEvery -cpo can be regarded as an -cpo presentation with cover relation\n\n c\u25c3U\u27fac\u2264\u22c1U (1)\n\nfor directed and enumerable. -continuous maps of -cpos may be identified with their morphisms when considered as -cpo presentations.\n\n###### Assumption 1.\n\nLet be an -cpo presentation. Then there is a free -cpo over , i.e. there is a morphism of -cpo presentations with an -cpo such that for any given morphism with an -cpo there is a unique -continuous map such that .\n\nIt appears that assumption 1 is independent of constructive predicative mathematics. However, it follows from rather weak additional mathematical principles, all of which are generally considered constructive.\n\nAs a first option, one can work with propositional resizing (impredicativity) (Univalent Foundations Program, 2013), i.e. assume that the inclusions are equalities. Working impredicatively, Jung et\u00a0al. (2008) construct free dcpos over dcpo presentations. We sketch a straightforward adaptation of their proof for -cpos. Say a lower subset is an ideal if from and it follows that , and let be the partial order of all ideals. Ideals are closed under arbitrary intersections, so every subset is contained in the least ideal containing it:\n\n \u27e8M\u27e9=\u22c2{a\u2208Idl(P)\u2223M\u2286a}. (2)\n\nIt follows that has all joins and that they can be computed as . Assigning to each the principle ideal gives a monotone map from to which preserves covers. It exhibits as the free suplattice over , i.e. the free partial order with all joins subject to the cover relations. Now can be defined as the least subset of which contains the principle ideals that is closed under joins of enumerable directed families.\n\nNext, can be constructed as a quotient inductive inductive type (QIIT) (Altenkirch et\u00a0al., 2018) in homotopy type theory. The special case of the free -cpo with bottom element over a set (i.e. discrete partial order without covers) is worked out in Altenkirch et\u00a0al. (2017). Given a set , they define and a dependent predicate mutually recursive as a QIIT. Elements of and their equalities are generated by the constructors \u03b7: A \u2192A_\u22a5: (\u2211_x : N \u2192A_\u22a5 \u220f_n : N x_n \u2264x_n + 1) \u2192A_\u22a5\n\u22a5: A_\u22a5\u03b1: \u220f_x, y : A_\u22a5 x \u2264y \u2192y \u2264x \u2192x = y. has constructors corresponding to reflexivity, transitivity and the universal properties of and . The recursion principle for as QIIT is the universal property of the free domain over . This argument can easily be adapted for our purpose: To construct given an -cpo presentation , one omits from the scheme defining the constructor and adds constructors corresponding to monotonicity of and\n\n \u220fp:P\u220fU\u2208P(P)p\u25c3U\u2192\u03b7(p)\u2264\u22c1cU (3)\n\nwhere is a monotone and final map into . The semantics of QIITs are not entirely understood, but it is proved in Lumsdaine and Shulman (2017) that all Grothendieck -topos models validate the existence of many HITs. Work on reducing QIITs to such simpler inductive constructions is ongoing; see (Altenkirch et\u00a0al., 2018).\n\nAs a third alternative, can be constructed as a quotient of the set of monotone sequences in if one is willing to assume the axiom of countable choice, at least in the important special case where the covering relation is such that holds only if for all , which is true in all our applications. A similar construction for is worked out in Altenkirch et\u00a0al. (2017), with the general idea going back to Rosolini (1986). Let be the preorder on the set of monotone functions which is generated from if for all there merely exists such that , and whenever , where denotes the constant sequence with value and is a final sequence in . If are monotone and , then it can be shown by induction over transitivity of that for all there merely exist either or such that respectively is an upper bound for both and . It follows that the image of the set-theoretic transpose of a monotone function ( need not be monotone with respect to the product order) is directed: The mere existence of binary upper bounds implies the existence of a function assigning upper bounds because of the bijection and countable choice. We obtain a final sequence , which can be shown to be a join of . Let be the quotient partial order of the preorder . By countable choice, every sequence can be lifted to one in , where its join can be computed and mapped back to . Thus is an -cpo, and the verification of its universal property is straightforward.\n\n###### Proposition 1.\n\nThe free -cpo completion is monotone on functions: If , then .\n\n###### Proof.\n\nThe subset contains for all and is closed under directed enumerable joins. \u220e\n\nJung et\u00a0al. (2008, proposition 2.8) construct presentations of product dcpos based on presentations of their factors, and an analogous result holds for -cpos. Our proof differs slightly from the theirs because we do not assume that -completions are constructed as set of ideals and instead rely solely on the universal property.\n\n###### Proposition 2.\n\nLet and be -cpo presentations. Define a cover relation on the product partial order by if in and if in . Then the canonical map is an order isomorphism.\n\n###### Proof.\n\nLet be the function assigning to each the function . is an -cpo with joins computed pointwise. If and , then by definition of the cover relation on . Thus preserves covers and induces an -continuous map . Let be its transpose; it is valued in -continuous functions. Suppose and let us prove that for each we have\n\n g2(q)(x)\u2264\u22c1v\u2208Vg2(v)(x). (4)\n\nIf for some , then this holds because in . If (4) holds for every element for a directed enumerable family , then\n\n g2(q)(\u22c1W)=\u22c1x\u2208Wg2(q)(x)\u2264\u22c1x\u2208W\u22c1v\u2208Vg2(v)(x)=\u22c1v\u2208Vg2(v)(\u22c1W) (5)\n\nbecause and for all commute with joins and joins commute among each other. Thus preserves covers and induces an -continuous map . Let be its transpose.\n\nis -continuous in each argument. Thus if and are monotone maps with enumerable and directed, then\n\n g(\u22c1i\u2208I(pi,qi))=\u22c1i\u2208I\u22c1j\u2208Ig(pi,qj)=\u22c1k\u2208Ig(pk,qk) (6)\n\nbecause, being directed, the diagonal is final. It follows that is -continuous. Thus is the identity by the universal property of the -cpo completion, and holds by the universal property of products. \u220e\n\n###### Corollary 1.\n\nLet be an -cpo presentation. If has a bottom element , then is a bottom element, and likewise for top elements. If has all binary joins which are compatible with covers in the sense that preserves the covers on defined in proposition 2, then has all binary joins and preserves them. The same is true for binary meets.\n\n###### Proof.\n\nWithout loss of generality, we may assume that for all we have because adding these covers to does not change the generated -cpo . Endow the terminal partial order with the covering relation , where is the unique element of the unit set. Then the map is a map of -cpo presentations, and so are its right or left adjoints if they exists. Because and the -cpo completion is monotone (proposition 1), it follows that is a right (left) adjoint if is. Thus has a bottom (top) element if has one.\n\nSuppose in . Then\n\n (\u03b7(p),\u03b7(p))\u2264\u22c1u\u2208U\u22c1v\u2208U(\u03b7(u),\u03b7(v))=\u22c1w\u2208U(\u03b7(w),\u03b7(w)) (7)\n\nbecause is directed. We may thus add the diagonal covers\n\n (p,p)\u25c3{(u,u)\u2223u\u2208U} (8)\n\nto the covers of without changing the generated -cpo. Because presents the product , the diagonal is obtained by -cpo completion of the diagonal of . Now suppose has binary joins which preserve the covers defined in proposition 2. Binary joins will always preserve diagonal covers as in (8). Thus the binary join map can be extended to a left adjoint to the diagonal of , i.e. has binary joins. Similarly, if has a cover preserving binary meet map, then its extension to will be right adjoint to the diagonal. \u220e\n\n## 4 Synthetic topology and the initial \u03c3-frame\n\nIn synthetic topology (Hyland, 1991; Escard\u00f3, 2004; Le\u0161nik, 2010) one works with sets and functions as if they behave like topological spaces and continuous maps. For this analogy to have any value, the very least one would expect is a notion of open subset of a given set (i.e. space). The set of (small) subsets of a given set is given by the set of functions . It is thus natural to expect a subset\n\nthat classifies the\n\nopen subsets, in the sense that a function is the indicator function of an open subset if and only if it factors via . may be thought of as set of open truth values. We obtain sets of open subsets for every set (space) , and it can indeed be verified that the preimage of an open subset under every function is again open. Thus all functions are continuous.\n\nIn traditional (analytic) topology, corresponds to the Sierpinsky space: The space with carrier whose only nontrivial open is the singleton set . Indicator functions with a topological space (in the usual sense) are continuous if and only if the preimage of is open; in other words if and only if corresponds to an open subset.\n\nWithout imposing any further requirements on , there is not much we can say about the sets . For example, might be empty, in which case only the empty subset has any open subsets at all. If , then for all . For the booleans, the opens are precisely the decidable subsets. In this case, is closed under finite conjunctions and disjunction, corresponding to open subsets being closed under finite intersections and unions. But in constructive models, the booleans are usually not closed under infinite conjunction, so we may not assume that any infinite unions of opens are open. Arguably the most interesting case is where is a proper subset of (so that the topology is not discrete), contains the boolean truth values and and is closed under enumerable disjunction. This makes it possible to study limits and first-countable spaces such as the real numbers, which are at the heart of integration theory. Following the HoTT book and Gilbert (2016), we take for the least subset of satisfying these constraints: The initial -frame.\n\n###### Definition and Proposition 1 (Gilbert (2016)).\n\nThe Sierpinsky space is the free -cpo over the partial order of decidable truth values. admits the structure of a -frame, and it is the initial one. The map given by exhibits as suborder of and preserves all -frame structure.\n\nThus is a suborder of , and we freely identify elements with their image in . The preservation of enumerable joins by the inclusion means that if holds for an enumerable family of elements , then there merely exists such that .\n\nAs explained in section 3, in the presence of countable choice may be identified with monotone binary sequences where distinguish sequences only by whether they eventually reach . This set is also known as the Rosolini dominance (Rosolini, 1986) and denoted by . When , open subsets can be understood as the semi-decidable subsets. Let and let be an increasing binary sequence representing . If for some , then , but we can never conclude by checking only a finite prefix of . Under a realizability interpretation, corresponds to a computation producing an infinite stream of digits which will eventually contain if and only if . If furthermore itself is enumerable, we obtain an enumeration of . The Rosolini dominance is not well-behaved without countable choice. For example, it is not closed under enumerable disjunction. We circumvent this issue by using the initial -frame instead, which is closed under enumerable disjunction by definition.\n\nAn important requirement imposed on the set of open truth values is the dominance axiom. Consider inclusions of spaces such that is open in and is open in . In analytic topology, this implies that is open in . This is not automatic in synthetic topology, but holds if is a dominance (Rosolini, 1986):\n\n###### Definition 2.\n\nA subset is a dominance if for all and it holds that\n\n (s\u27f9(p\u2208S))\u27f9(s\u2227p)\u2208S. (9)\n\nRosolini (1986) proved that is a dominance under the assumption of countable choice. It follows that is a dominance if countable choice holds. But being a dominance can be proved directly, and even without assuming countable choice:\n\n###### Theorem 1.\n\nThe Sierpinsky space is a dominance.\n\n###### Proof.\n\nWe prove (9) for fixed using the induction principle of as free -cpo completion of . If and , then in particular and thus is in . If , then , which is an element of . Now let for an ascending chain in . Suppose that and that (9) with in place of holds for all . Combining this with and it follows that is in for all . But then\n\n s\u2227p=(\u22c1nsn)\u2227p=\u22c1n(sn\u2227p) (10)\n\nby the distributive law, which is in . \u220e\n\nGiven a dominance and a set , Rosolini constructs a partial map classifier of , which is an object representing partial maps whose domains of definition are open with respect to . Following Escard\u00f3 and Knapp (2017), the partial map classifier can be defined as\n\n LSA={(s,v)\u2223s\u2208S,v:s\u2192A}. (11)\n\nHere is identified with the subsingleton set . They refer to elements as partial elements. is the value, its extent. Under a realizability interpretation and , maps can be thought of as partial functions from to , in the sense that their interpretations yield potentially non-terminating computations producing results in . The interpretation of constructive logic in the effective topos even validates the axiom that for every function\n\nthere merely exists a Turing machine which computes it\n\n(Bridges and Richman, 1987, chapter 3).\n\nAltenkirch et\u00a0al. (2017) propose defining the partial map classifier of as the QIIT described in section 3. In our terminology, is the -cpo completion , where we consider as the partial order obtained by freely adjoining a bottom element to the discrete partial order . Escard\u00f3 and Knapp (2017) mention that can be understood in terms of Rosolini\u2019s lifting construction.\n\nIndeed, has the structure of an -cpo with bottom element under : The structure map is defined by assigning to each element the unique map with value . For and in let\n\n (s,v)\u2264(s\u2032,v\u2032)\u27fa((s\u27f9s\u2032)\u2227v\u2032|s=v:s\u2192A; (12)\n\nthis defines a partial order on . Its bottom element is the unique map . The join of an enumerable directed set is given by , where is defined by whenever is in . Thus there is a unique -continuous map which is compatible with the structure maps and preserves the bottom element. We can then show the following:\n\n###### Proposition 3.\n\nThe map is an order isomorphism.\n\n###### Proof.\n\nFirst note that the projection that sends a partial element to its extent is -continuous and preserves the bottom element. The unique map induces a map , which can equivalently be described as assigning to the truth value by proposition 1. (A direct proof of this can also be found in Gilbert (2016).) By the universal property of , these maps commute with , so if , then .\n\nNow let us show that exhibits as suborder of . Suppose and such that in . We show by induction over . If , then trivially . If for some , then , hence . From this it follows by our initial remark that there merely exists such that . In particular, , where is the unique element of the unit set, hence . Now let be the join of a directed enumerable subset . We may assume that for all , if , then . Thus because for all . But then by definition of least upper bound.\n\nIt remains to show that is surjective and hence an order isomorphism. For this we must construct for each partial element an element such that . We proceed by induction over . We can set if and if . Now let be a directed enumerable join in . We may assume that for partial elements of the form with there merely exists such that . Because was already proved to be the inclusion of a suborder,\n\n V={x\u2208A\u22a5\u2223f(x)=(u,v|u)\u00a0for some\u00a0u\u2208U} (13)\n\nembeds into . By the induction hypothesis it is isomorphic to , hence directed and enumerable. Now . \u220e\n\n## 5 The lower reals\n\nA Dedekind cut is pair of sets of rational numbers of the form and for some real number . The condition that is of this form can be stated purely in terms of rational numbers without referring to the real numbers, so the (Dedekind) real numbers can be defined as the set of all pairs satisfying these requirements; see e.g. Johnstone (2002). Constructively, even a bounded set of does not necessarily have a supremum. This is problematic in integration theory as integrals of functions on non-compact spaces are constructed by approximating them from below.\n\nA lower real is given only by the lower part . Note that, constructively, cannot be reconstructed from just or vice-versa. In the setting of synthetic topology, it is natural to ask that the subsets (and ) are valued in the Sierpinsky space , so that they correspond to open subsets of . For Dedekind reals, this has been studied extensively by Le\u0161nik (2010). The usage of the initial -frame in the definition of Dedekind real numbers is also proposed in the HoTT book (section 11.2) and has been formalized by Gilbert (2016). For us is the Sierpinsky space, so real numbers given by open Dedekind cuts can be understood as those for which the predicates and on rational numbers are semi-decidable. If is a lower real, then only the predicate will be semi-decidable. We use the symbol to refer to the Dedekind reals valued in and likewise .\n\n###### Definition 3.\n\nA lower real is an open subset of satisfying the following axioms:\n\n\u2022 There merely exists such that ,\n\n\u2022 for all , if then there merely exists such that , and\n\n\u2022 for all , if , then .\n\nThe set of all lower reals is denoted by . For let\n\n q\u2013={p\u2208Q\u2223p\n\nThe subset of non-negative lower reals is given by\n\n R+l={L\u2208Rl\u2223\u2200q\u2208Q(q<0\u27f9L(q))}. (15)\n\nIn predicative foundations, the Dedekind or lower reals usually have to be parameterized by a universe level , corresponding to the size of the set of truth values the lower (and upper) cuts are valued in. The resulting set of reals will only be an element of the th universe. Using the set of open truth values , we avoid this nuisance and obtain just one set of Dedekind and lower reals, respectively.\n\nCrucial for the use of lower reals in integration theory is their order-theoretic structure:\n\n###### Proposition 4.\n\nThe lower reals endowed with the relation\n\n L1\u2264L2\u27fa\u2200q\u2208Q(q\u2208L1\u27f9q\u2208L2) (16)\n\nfor are a partial order. Finite meets and enumerable joins in are computed pointwise and satisfy the distributivity law . The suborder of non-negative lower reals is a -frame. The map exhibits as suborder of . \u220e\n\nIn view of proposition 4, it is natural to wonder whether is obtained by a completion process of . This is indeed the case. Define a cover relation by for enumerable directed such that exists and is equal to . The embedding preserves enumerable joins and thus induces an -continuous map . Similarly we have , where is understood as -cpo presentation with the restricted cover relation of .\n\n###### Theorem 2.\n\nThe unique -continuous maps and under respectively are order isomorphisms.\n\nNoting that the two operations preserve covers, we conclude with 2 the following:\n\n###### Corollary 2.\n\nAddition on and multiplication on extend uniquely to -continuous operations on and , respectively.\n\nMultiplication cannot be (constructively) extended to an operation on all lower reals because it is not monotone. In terms of lower cuts, we have if and only if there merely exist and such that , and similarly for multiplication.\n\nThe statement analogous to theorem 2 for the usual lower reals (which are not required to be valued in ) and completion under arbitrary directed joins can be shown as follows. The proposed inverse to maps a lower real to the union in the completion of under arbitrary directed joins. This defines a continuous map which is compatible with the inclusions of , hence by the universal property of the completion. On the other hand, because for all . Unfortunately, this proof does not directly transfer to our situation because lower reals are not necessarily enumerable in the sense that there is a surjection , at least not in the absence of countable choice.\n\n###### Proof of theorem 2..\n\nFor brevity, we only prove the statement about , the proof for being similar. Note that the covers of are stable under binary joins, thus has binary joins and hence arbitrary enumerable joins. This allows us to construct a map as follows. Let and pick . For each , let be the unique -continuous map which sends to and to . Now set\n\n g(L)=\u22c1p\u2208QpL(p). (17)\n\nIf , then by definition, and so . Thus is well-defined as it does not depend on the choice of .\n\nis defined as composition of -continuous maps, so is -continuous itself. It is compatible with the structure maps and because\n\n g(q\u2013)=\u22c1p\u2208Qpq\u2013(p)=\u22c1p\n\nby definition of the cover relation on . It follows that by the universal property of .\n\nNote that preserves arbitrary enumerable joins (not necessarily directed) because the map preserves binary joins. Let . It can be shown by induction over that for all . Thus\n\n f(g(L))=f(\u22c1p\u2208QpL(p))=\u22c1p\u2208Qf(pL(p))\u2264L. (19)\n\nOn the other hand, suppose and let us show that , i.e. that . Because is a rounded lower subset of , there merely exists such that . Then , hence . \u220e\n\n## 6 Integrals and Valuations\n\nIn this section we define valuations, which play the role of measures but are defined only on opens, and integrals. We then prove a version of the Riesz theorem, which states that there is a one-to-one correspondence between valuations and integrals. Valuations are often preferred over measures in constructive mathematics because measures would have to be valued in the hyperreals (Coquand and Palmgren, 2002). They have a long tradition in the domain-theoretic semantics of probabilistic computations, see e.g. Jones and Plotkin (1989). It is observed there that classically, valuations on compact Hausdorff spaces are in bijective correspondence with regular measures. Our proof of the Riesz theorem is inspired by Coquand and Spitters (2009) and Vickers (2011), who prove similar results in the setting of locales.\n\nFix a set . Recall that , the set of open subsets of , is defined as the set of functions . The -frame structures of and induce -frame structures on the sets of functions and , with all structure defined pointwise.\n\n###### Definition 4.\n\nA (-continuous) valuation on a set is an -continuous map preserving the bottom element that satisfies the modularity law\n\n \u03bc(U)+\u03bc(V)=\u03bc(U\u222aV)+\u03bc(U\u2229V). (20)\n\nfor all opens . is a sub-probability valuation if . The set of all valuations on is denoted by\n\nand the set of sub-probability valuations by\n\n.\n\nLet be the unique -continuous map such that and . By postcomposition we obtain a map that assigns to each its (real) indicator function . This map is an order embedding, and so we can equivalently think of a valuation as assigning lower reals to a class of functions . The Riesz theorem states that every valuation can be extended to a lower integral, which is a function defined on all maps , and that every lower integral is determined by its restriction to indicator functions.\n\n###### Definition 5.\n\nA lower integral on is an -continuous map preserving the bottom element that is furthermore additive, i.e. satisfies\n\n I(f+g)=I(f)+I(g). (21)\n\nfor all . is a sub-probability lower integral if . The set of all lower integrals on is denoted by and the set of sub-probability lower integrals by .\n\nThe reader might wonder at this point why we need the generality of sub-probability valuations and integrals, as opposed to probability valuations and integrals, which would assign to (the indicator function of) the whole space the value 1. Valuations and integrals on some set form partial orders, with ordering defined pointwise. Now if we restrict to proper probability valuations and integrals, these orders will usually not have least elements (consider, for example, valuations on the set of two elements). On the other hand, for their sub-probabilistic versions we have the following, which will be crucial for the interpretation of fixpoint operators in section 9:\n\n###### Proposition 5.\n\nThe inclusions and are embeddings of -cpos with bottom elements. \u220e\n\n###### Proposition 6.\n\nEvery lower integral is compatible with multiplication by scalars from , in the sense that for all and . In particular, lower integrals are linear over .\n\n###### Proof.\n\nIf , then because is additive. Thus if is a positive rational, then , hence . If is a directed enumerable set of lower reals such that for each we have for all , then\n\n I((\u22c1U)f)=I(\u22c1a\u2208U(af))=(\u22c1U)I(f) (22)\n\nby -continuity of and multiplication, so is compatible with multiplication by . Because is the -cpo completion of (theorem 2), it follows that is compatible with scalar multiplication by arbitrary non-negative lower reals . \u220e\n\nWe are now ready to state the central result of this section.\n\n###### Theorem 3 (Riesz).\n\nThe assignment\n\n I\u21a6(U\u21a6I(1U)) (23)\n\ndefines map that restricts to a map . Both maps are order isomorphisms.\n\nWe begin the proof by showing that restrictions of lower integrals to indicator functions are valuations.\n\n###### Lemma 1.\n\nLet be an integral on . Then is a valuation on . If is a sub-probability integral, then is a sub-probability valuation.\n\n###### Proof.\n\nRecall that is obtained by postcomposing with the unique -continuous map that satisfies and . Thus is -continuous, too, hence -continuity of follows from -continuity of . By definition , so if the latter is , then so is the former.\n\nWhat remains to be shown is that satisfies the modularity law, i.e. that\n\n I(1U\u222aV)+I(1U\u2229V)=I(1U)+I(1V). (24)\n\nholds for all . By linearity of and the definition of indicator functions, it will suffice to show that for all it holds that\n\n r(s\u2228t)+r(s\u2227t)=r(s)+r(t), (25)\n\nand we will do so by induction over . If , both sides are equal to , and if , then both sides are equal to . Now let for an enumerable directed subset , and suppose that equation (25) holds with in place of for all . Using the fact that the involved operations binary meet and join with , addition and are all -continuous, we compute\n\n r(s\u2228t)+r(s\u2227t)= \u22c1u\u2208U(r(u\u2228t)+r(u\u2227t)) (26) = \u22c1u\u2208U(r(u)+r(t)) (27) = r(s)+r(t). (28)\n\nNext we construct the extension of a valuation to an integral. Fix .\n\n###### Definition 6.\n\nLet . The lower -integral is defined as follows. For let\n\n [f>q]={x\u2208A\u2223q\n\nit is an open subset of . Let\n\n sf,m,n=mn\u2211i=11m\u03bc([f>im]) (30)\n\nfor . Now\n\n \u222bfd\u03bc=\u22c1n,m\u2208Nsf,m,n. (31)\n\nThe main difficulty in showing that is indeed a lower integral is the verification of linearity. Our main tool will be the generalized modularity lemma, originally due to Horn and Tarski (1948, corollary 1.3) in the special case of boolean algebras. More recent references are Coquand and Spitters (2009) and Vickers (2011); the latter also contains a proof of the version that will be used here. Generalized modularity is phrased in terms of the following construction, which in the special case can be understood as the submonoid of functions generated by the indicator functions for .\n\n###### Definition 7.\n\nLet be a distributive lattice with bottom element. The modular monoid is the commutative monoid generated by the carrier of subject to\n\n a+b=(a\u2227b)+(a\u2228b) (32)\n\nfor all , and .\n\nNote that the modularity law and the preservation of bottom elements guarantee precisely that valuations factor uniquely as monoid homomorphism .\n\n###### Lemma 2 (Generalized Modularity Lemma).\n\nLet be a distributive lattice and . Then in we have\n\n n\u2211i=1xi=n\u2211k=1\u22c1{xI\u2223I\u2286{1,\u2026,n},|I|=k} (33)\n\nwhere for decidable .\n\nLet and . Define to be if and equal to if .\n\nLet . 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Home Africa Live Cyclone Batsirai weakens after hitting Madagascar, floods feared
Cyclone Batsirai weakens after hitting Madagascar, floods feared
In this image supplied by EUMETSAT from satellite Meteosat 8 taken at 09.15 UTC on Wednesday, Feb. 2, 2022, Cyclone Batsirai is seen to the east of Madagascar(EUMETSAT via AP)
In this image supplied by EUMETSAT from satellite Meteosat 8 taken at 09.15 UTC on Wednesday, Feb. 2, 2022, Cyclone Batsirai is seen to the east of Madagascar. (EUMETSAT via AP)
Cyclone Batsirai weakened overnight but floods were still expected due to heavy rain after it hit eastern Madagascar with strong winds, the island's meteorological office said Sunday.
"Batsirai has weakened," Meteo Madagascar said, adding that the cyclone's average wind speed had almost halved to 80 kilometers per hour (50 miles per hour), while the strongest gusts had scaled back to 110 km/h from the 235 km/h recorded when it made landfall on Saturday evening.
The cyclone, the second storm to hit the large Indian Ocean island nation in just a few weeks, was moving westwards at a rate of 19 km/h, the meteorological services said.
But "localized or generalized floods are still feared following the heavy rains," it said, adding that Batsirai should emerge at sea in the Mozambique Channel later Sunday.
Batsirai made landfall in Mananjary district, more than 530 kilometers (310 miles) southeast of the capital Antananarivo, around 8 pm local time (1700 GMT) Saturday.
It reached the island as an "intense tropical cyclone", packing winds of 165 kilometers per hour (102 miles per hour), Faly Aritiana Fabien of the country's disaster management agency told AFP.
The national meteorological office has said it fears "significant and widespread damage".
Just an hour and a half after it first hit land, nearly 27,000 people had been counted as displaced from their homes, Fabien said.
He said his office has accommodation sites, food and medical care ready for victims, as well as search and rescue plans already in place.
– 'Very serious threat' –
The Meteo-France weather service had earlier predicted Batsirai would present "a very serious threat" to Madagascar, after passing Mauritius and drenching the French island of La Reunion with torrential rain for two days.
In the hours before the cyclone hit, residents hunkered down in the impoverished country, still recovering from the deadly Tropical Storm Ana late last month.
In the eastern coastal town of Vatomandry, more than 200 people were crammed in one room in a Chinese-owned concrete building.
Families slept on mats or mattresses.
Community leader Thierry Louison Leaby lamented the lack of clean water after the water utility company turned off supplies ahead of the cyclone.
"People are cooking with dirty water," he said, amid fears of a diarrhoea outbreak.
Outside plastic dishes and buckets were placed in a line to catch rainwater dripping from the corrugated roofing sheets.
"The government must absolutely help us. We have not been given anything," he said.
Residents who chose to remain in their homes used sandbags and yellow jerrycans to buttress their roofs.
– Cyclone still 'dangerous' –
Other residents of Vatomandry were stockpiling supplies in preparation for the storm.
"We have been stocking up for a week, rice but also grains because with the electricity cuts we cannot keep meat or fish," said Odette Nirina, a 65-year-old hotelier in Vatomandry.
"I have also stocked up on coal. Here we are used to cyclones," she told AFP.
Winds of more than 50 kilometers per hour (30 miles per hour) pummelled Vatomandry on Saturday morning, accompanied by intermittent rain.
The disaster agency said the cyclone was expected to remain "dangerous" as it swept across the large island overnight and in the morning.
Flooding is expected due to excessive rainfall in the east, southeast and central regions of the country, it warned.
The United Nations was ramping up its preparedness with aid agencies, placing rescue aircraft on standby and stockpiling humanitarian supplies.
At least 131,000 people were affected by Ana across Madagascar in late January. Close to 60 people were killed, mostly in the capital Antananarivo.
That storm also hit Malawi, Mozambique and Zimbabwe, causing dozens of deaths.
The UN's World Food Programme pointed to estimates from national authorities that some 595,000 people could be directly affected by Batsirai, and 150,000 more might be displaced due to new landslides and flooding.
The storm poses a risk to at least 4.4 million people in one way or another, the International Federation of Red Cross and Red Crescent Societies said.
Cyclone Batsirai strengthening, threatening Madagascar
Cyclone Batsirai blows across Indian Ocean toward Madagascar
More than 4 million people at risk as Cyclone Batsirai bears down on Madagascar
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Maxime Vandelannoitte (born 23 January 2002) is a Belgian footballer who currently plays as a defender for K.S.V. Roeselare.
Career statistics
Club
Notes
References
2002 births
Living people
Belgian footballers
Association football defenders
Challenger Pro League players
K.S.V. Roeselare players
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,730
|
'use strict'
const fetch = require('node-fetch')
const https = require('https')
const { kgcerts } = require('../lib/kgcerts')
function getEnvAuth () {
console.log('Running under node.js')
const [jira, username, password] = [
process.argv[2] || 'https://atlassian-test.hq.k.grp/jira',
process.argv[3] || process.env.USERNAME,
process.argv[4] || process.env.pw
]
const credentials = (username !== undefined && password !== undefined)
? 'Basic ' + base64Encode(username + ':' + password)
: undefined
const agent = getAgent(jira, kgcerts)
return {getFetch, jira, credentials, agent}
}
function getFetch () {
return fetch
}
function base64Encode (string) {
return Buffer.from(string, 'binary').toString('base64')
}
function getAgent (url, ca) {
return !url.match(/^https:/)
? undefined
: ca !== undefined
? new https.Agent({ ca, rejectUnauthorized: true })
: new https.Agent({ rejectUnauthorized: false })
}
module.exports = { getEnvAuth }
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 8,033
|
19039 Bandra Muzaffarpur Avadh Express train from Bandra to Muzaffarpur runs on Monday, Thursday, Saturday, covering 2160 kms in 47 hours & 10 minutes, running at a speed of 50.7 km/hr, making 80 stoppages of 274 minutes in total.
Returning train number 19040. Bandra Muzaffarpur Avadh Express commences from Muzaffarpur Jn at 22:40 and reaches Bandra Terminus at 21:50. It runs on monday, thursday, saturday.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 381
|
Q: Какой принцип работы стандартной библиотеки? Уважаемые пользователи, нужна помощь новичку в С++. Возможно я ставлю вопросы некорректно, в свете моей "зелёности" в этом деле, но тягу к знаниям не отнять. Долго я искал в интернете какой принцип работы у стандартной библиотеки, к примеру у той же iostream, но так и не нашел(может плохо искал). Можете пожалуйста объяснить как она устроена изнутри и какие процессы обеспечивают работоспособность? Либо где можно посмотреть ее реализацию.
С ув.
A: Ничего там нет необычного. Но сможете ли разобраться, посмотрев внутрь - я не знаю. Поэтому, надо делать план по другому.
Для начала стоит почитать базового по плюсам, к примеру, Программирование. Принципы и практика с использованием C++ | Страуструп Бьерн. В этой книге, к примеру, рассказывается как сделать свой вектор с аллокатором. Без этого смотреть стандартную библиотеку даже нет смысла.
Потом книгу по стандартной библиотеке Стандартная библиотека C++: справочное руководство
А потом открыть собственно код библиотеки и посмотреть. Например от gcc или Майкрософт. Но там не все так очевидно.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 9,447
|
I live in the beautiful community of White House, Tennessee and offer a loving, calm, safe, and FUN alternative to kennel boarding.
I've loved dogs since I was a little girl. I lived in England during the 80's and my favorite pastime was watching a working sheepdog move an entire herd of sheep from the pasture to the farm. The interaction and trust between the dog and his owner was an amazing sight-"whistles" meant different things, and the dog understood. I wanted to be that Farmer!
Through the years, dogs have taught me unconditional love, selflessness, and loyalty, They are such blessings, and deserve to be loved and pampered.
Your dog will have the run of my house and encouraged to relax and make himself/herself at home. If they normally sleep with you, that's allowed here too. I live on the 2nd floor so your pet will need to be comfortable with one flight of stairs.
I would be honored to host your pet, either at your home or my own. Just bring their food, blanket, toys...anything to make them feel at home.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 2,447
|
Nummer-et hits i Danmark i 1994 er en liste over de singler der lå nummer et på den danske singlehitliste i 1994. Den var udarbejdet af International Federation of the Phonographic Industry og Nielsen Soundscan, og udgivet af Billboard i "Hits of the World"-sektionen.
Historie
Referencer
Se også
Musik i 1994
1994
Musik i 1994
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 3,399
|
import time
import zipfile
from django.http import JsonResponse, Http404, HttpResponse, HttpResponseBadRequest
from django.shortcuts import render
from django.views.decorators.http import require_POST
from . import forms, utils
from .auth import staff_required
@staff_required
def index(request):
return render(request, 'filem/index.html')
@staff_required
def dir_info(request, path=''):
'''
Returns a list of entries in the given directory.
'''
try:
full_path = utils.safe_join(utils.ROOT, path)
except (FileNotFoundError, ValueError):
raise Http404
return JsonResponse({
'path': str(full_path.relative_to(utils.ROOT)),
'files': [
utils.file_details(path)
for path in sorted(full_path.iterdir())
]
})
@staff_required
def tree(request):
'''
Returns a full directory tree as a map of paths -> [list of children]
'''
return JsonResponse({
'tree': utils.dir_tree(utils.ROOT),
})
@staff_required
@require_POST
def dir_action(request):
form = forms.DirActionForm(request.POST)
if not form.is_valid():
return HttpResponseBadRequest(form.errors.as_json(), content_type='application/json')
action = form.cleaned_data['action']
target = form.cleaned_data['target']
if action == 'rename':
name = form.cleaned_data['name']
target.rename(name)
elif action == 'create':
name = form.cleaned_data['name']
p = target / name
p.mkdir()
elif action == 'delete':
target.unlink()
elif action == 'download':
response = HttpResponse()
filename = str(target.relative_to(utils.ROOT)).replace('/', '_')
response['Content-Disposition'] = 'attachment; filename={}_{}.zip'.format(filename, int(time.time()))
with zipfile.ZipFile(response, compression=zipfile.ZIP_DEFLATED) as zf:
for path in target.glob('**/*'):
if path.is_dir():
continue
zf.write(str(path), arcname=str(path.relative_to(utils.ROOT)))
return response
return JsonResponse({})
@staff_required
@require_POST
def file_action(request):
pass
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 8,360
|
Die römisch-katholische Pfarrkirche Mogersdorf am östlichen Ende des Dorfangers von Mogersdorf (ungarisch: Nagyfalva) im Bezirk Jennersdorf im Burgenland ist dem heiligen Josef geweiht und gehört zum Dekanat Jennersdorf.
Geschichte
Die Kirche wurde bereits vor 1664 zur Pfarrkirche erhoben – in einer Urkunde aus dem 17. Jahrhundert ist von einer St. Martinskirche die Rede.
Der heutige Bau wurde 1775 errichtet. In den Jahren 1948 und 1975 wurde sie einer Renovierung unterzogen, bei letzterer entdeckte man eine Gruft.
Architektur und Ausstattung
Die Kirche ist ein einschiffiger Saalbau. Über der hohen Westfassade befindet sich ein Turm mit Spitzhelm. Das Gotteshaus hat einen eingezogenen Polygonalchor.
Die Decke ist dreijochig mit schmalen Platzlgewölben. Über der halbrunden Apsis befindet sich eine Halbkuppel.
Die Wandmalerei am Triumphbogen zeigt die "Schlacht bei Mogersdorf" vom 1. August 1664 gegen die Osmanen. Sie wurde 1912 von Josef Rösch gemalt. Sie zeigt ein schlossähnliches Gebäude auf dem Schlößlberg. Bei dem Reiter auf dem weißen Pferd soll es sich um General Sporck handeln. Am Himmel steht Maria mit dem Kind. Als Symbol für den Sieg der Christen über die Osmanen erstrahlt ein Kreuz.
Der neoromanische Hauptaltar und Seitenaltar entstanden um 1900.
Die Kanzel entstand in der zweiten Hälfte des 18. Jahrhunderts. Sie ist mit vergoldetem Rokokodekor an Korb und Schalldeckel verziert.
Bemerkenswert sind die neobarocken Luster.
Die 1739 geschaffene Madonna aus Holz neben dem Hochaltar stammt ursprünglich aus der Schlösslberg-Kapelle.
Im Untergeschoss des Turmes befinden sich eine Pietà und eine Figurengruppe aus der Mitte des 18. Jahrhunderts.
Literatur
Dehio Burgenland 1976, Dobersdorf, Kath. Pfarrkirche Mariae Heimsuchung, S. 55.
Mogersdorf
Mogersdorf
Mogersdorf
Mogersdorf
Mogersdorf
Mogersdorf
Kirchengebäude in Europa
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 3,651
|
{"url":"https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/multivariate-random-variables\/state-and-apply-the-central-limit-theorem\/","text":"Limited Time Offer: Save 10% on all 2022 Premium Study Packages with promo code: BLOG10\n\n# State and apply the Central Limit Theorem\n\nFor this learning objective, a certain knowledge of the normal distribution and knowing how to use the Z-table is assumed.\n\nThe central limit theorem is of the most important results in the probability theory. It states that the sum of a large number of independent random variables has an approximately normal distribution. It provides a simple method for computing approximate probabilities for sums of independent random variables and helps explain the remarkable fact that the empirical frequencies of so many natural populations exhibit bell-shaped (or normal) curves.\n\nAfter analyzing the moment generating technique, we have found that the mean $$\\bar{X}$$ of a random sample size n from a distribution with mean $$\\mu$$ and variance $$\\sigma^2 > 0$$ is a random variable with the properties:\n\n$$E(\\bar{X}) = \\mu \\quad\\text{and}\\quad Var(\\bar{X}) = \\frac{\\sigma^2}{n}$$\n\nAs n increases, the variance of $$\\bar{X}$$ decreases. Consequently, the distribution of $$\\bar{X}$$ clearly depends on n, and we see that we are dealing with sequences of distributions.\n\nIf we consider n mutually independent normal variables with n means and n variances, each one belong to its n sub-indexes, then the linear function:\n\n$$Y = \\sum_{i=1}^{n}c_iX_i$$\n\nhas the normal distribution:\n\n$$N\\bigg(\\sum_{i=1}^{n}c_i\\mu_i,\\sum_{i=1}^{n}c_{i}^2\\sigma_{i}^2\\bigg)$$\n\nThis can be proved by applying the moment generating technique to the linear function.\n\nHaving applied this we can note that as n increases, the probability becomes concentrated in a small interval centered at $$\\mu$$. This means, as n increases, $$\\bar{X}$$ tends to converge to $$\\mu$$ or ($$\\bar{X} \u2013 \\mu$$) tends to converge to 0 in a probability sense.\n\nFor most cases, if we assume:\n\n$$W=\\frac{\\sqrt n}{\\sigma}\\left(\\ \\bar{X}-\\mu\\right)=\\frac{\\ \\bar{X}-\\mu}{\\sigma\/\\sqrt n}=\\frac{Y-n\\mu}{\\sqrt n\\sigma}$$\n\nwhere $$Y$$ is the sum of a random sample of size n from some distribution with mean $$\\mu$$ and variance $$\\sigma^2$$, then, for each positive integer n,\n\n$$E(W) = E\\bigg[\\frac{\\bar{X}-\\mu}{\\sigma\/\\sqrt{n}} \\bigg]= \\frac{E(\\bar{X})-\\mu}{\\sigma\/\\sqrt{n}}=\\frac{\\mu \u2013 \\mu}{\\sqrt{n}\\sigma}=0$$\n\nand\n\n$$Var(W)= E(W^2) = E\\bigg[\\frac{(\\bar{X}-\\mu)^2}{\\sigma^2\/n} \\bigg]= \\frac{E\\big[(\\bar{X}-\\mu)^2\\big]}{\\sigma^2\/n}=\\frac{\\sigma^2\/n}{\\sigma^2\/n}=1$$\n\nThen, when $$\\bar{X}-\\mu$$ tends to \u201creduce\u201d to 0, the factor $$\\sqrt{n}\/\\sigma$$ in $$\\sqrt{n}(\\bar{X}-\\mu)\/\\sigma$$ starts making the probability enough to prevent this \u201creduction.\u201d\n\nBut what happens to $$W$$ when n increases? If this sample comes from a normal distribution, then we know that $$\\bar{X}$$ is $$N(\\mu,\\sigma^2\/n)$$, and hence $$W$$ is $$N(0,1)$$ for each positive n. So in this limit, the distribution of $$W$$ necessarily will be $$N(0,1)$$. Circling back to the original question: if this does not depend on the underlying distribution, the answer must be $$N(0,1)$$.\n\nNow, we can state the following theorem:\n\n## The Central Limit Theorem\n\nIf $$\\bar{X}$$ is the mean of a random sample $$X_1,X_2,\\cdots,X_n$$ of size n from a distribution with a finite mean $$\\mu$$ and a finite positive variance $$\\sigma^2$$, then the distribution of:\n\n$$W = \\frac{\\bar{X} \u2013 \\mu}{\\sigma\/\\sqrt{n}} = \\frac{\\sum_{i=1}^{n}X_i \u2013 n\\mu}{\\sqrt{n}\\sigma}$$\n\nis $$N(0,1)$$ in the limit as $$n \\to \\infty$$. When n is \u201csufficiently large\u201d, a practical use of the central limit theorem is approximating the cdf of $$W$$:\n\n$$P(W \\leq w) \\approx \\int_{-\\infty}^{w}\\frac{1}{\\sqrt{2\\pi}}e^{-z^{2}\/2}dz = \\Phi(w).$$\n\nAn interesting thing about the Central Limit Theorem is that it does not matter what the distribution of the $$X_i\\prime s$$ is; $$X_i\\prime s$$ can be discrete, continuous, or mixed random variables.\n\nFor example, assume that $$X_i\\prime s$$ are Bernoulli (p) random variables, then $$E[X_i]=p,\\ Var\\left(X_i\\right)=p(1-p)$$.\u00a0 Also, $$Y_n=X_1+X_2+\\ldots+X_n$$ has a Binomial (n,p) distribution. Thus,\n\n$$Z_n=\\frac{Y-np}{\\sqrt{np\\left(1-p\\right)}}$$\n\nWhere $$Y_n\\sim Binomial\\ \\left(n,p\\right)$$.\n\nIn the example, $$Z_n$$ is a discrete random variable; thus, mathematically, we refer to it as having a PMF and not a PDF. This is the reason why the Central Limit Theorem states that the CDF and not the PDF of $$Z_n$$ converge to the standard normal CDF.\n\nA common question asked is how large n should be so that the normal approximation can be used. Using the normal approximation will generally depend on $$X_i$$\u2019s distribution. However, a rule of thumb is often stated that if $$n\\geq30$$, then a normal approximation applies.\n\n### Steps on How to Apply the Central Limit Theorem (CLT)\n\nStep 1:\u00a0Write the random variable of interest, $$Y$$, as the sum of n independent random variables $$X_j^\\prime s$$:\n\n$$Y=X_1+X_2+\\ldots+X_n$$\n\nStep 2: Compute $$E(Y)$$ and $$Var(Y)$$ by noting that:\n\n$$E\\left(Y\\right)=n\\mu, \\text{ and } Var\\left(Y\\right)=n\\sigma^2$$\n\nWhere $$\\mu=E(X_i)$$ and $$\\sigma^2=Var(X_i)$$.\n\nStep 3: As per the Central Limit Theorem, conclude that $$\\frac{Y-E(Y)}{\\sqrt{Var\\left(Y\\right)}}=\\frac{Y-n\\mu}{\\sqrt n\\sigma}$$ is approximately standard normal.\n\nHence, to find $$P\\left(y_1\\le Y\\le y_2\\right)$$, we can write,\n\n$$P\\left(y_1\\le Y\\le y_2\\right)=P\\left(\\frac{y_1-n\\mu}{\\sqrt n\\sigma}\\le\\frac{Y-n\\mu}{\\sqrt n\\sigma}\\le\\frac{y_2-n\\mu}{\\sqrt n\\sigma}\\right)$$\n\nWhich is given by:\n\n$$P\\left(y_1\\le Y\\le y_2\\right)=\\Phi\\left(\\frac{y_2-n\\mu}{\\sqrt n\\sigma}\\right)-\\Phi\\left(\\frac{y_1-n\\mu}{\\sqrt n\\sigma}\\right)$$\n\n#### Example: Central Limit Theorem #1\n\nLet $$\\bar{X} = 18$$ and $$Var(X) = 3$$ for a random sample of $$n = 30$$. Approximate $$P(17.4 < \\bar{X} < 18.5$$.\n\nSolution\n\nFrom the information given, $$\\bar{X}$$ has an approximate $$N(18,3\/30)$$ distribution. We can compute probabilities such as:\n\n\\begin{align} P(17.4 < \\bar{X} < 18.5) & = P\\bigg(\\frac{17.4-18}{\\sqrt{3\/30}} < \\frac{\\bar{X}-18}{\\sqrt{3\/30}} < \\frac{18.5-18}{\\sqrt{3\/30}}\\bigg)\\\\ & \\approx \\Phi(0.158) \u2013 \\Phi(-0.189) = 0.94295-0.02872 = 0.9142 \\end{align}\n\n#### Example: Central Limit Theorem #2\n\nLet $$X_1,X_2,\\cdots, X_{15}$$ be a random sample of size 15 from a joint random distribution. Let $$E(X_i) =\\frac{1}{4}$$ and $$Var(X_i) = \\frac{1}{24}$$ for $$i=1,2,\\cdots, 20$$.\n\nIf $$Y$$ is a transformation $$Y = X_1 + X_2 + \\cdots X_{15}$$, approximate $$P(Y \\leq 4.11)$$.\n\nSolution\n\n\\begin{align} P(Y \\leq 4.11) & = P\\bigg(\\frac{Y \u2013 15(1\/4)}{\\sqrt{15\/24}}\\leq \\frac{4.11 \u2013 3.75}{\\sqrt{15\/24}}\\bigg) = P(W \\leq 0.455)\\\\ & \\approx \\Phi(0.455) = 0.676 \\end{align}\n\nNotice how the formula in Example 1 is different from the formula in Example 2. In example 1, we are using a single variable with a single sample, so we are using the left side of the expression, whereas, in example 2, we are using a random sample from a random distribution with $$X_n$$ data points, so we need to weight the distribution, and we end up using the right side of the formula.\n\n#### Example: Central Limit Theorem #3\n\nA company offers payment for its employees; the amount paid is 10,000 for its 200 employees if they survive a set criterion. The probability of survival for each employee is 1.1%. The person who built this fund says there is a 99%\u00a0 probability that the fund will handle the payouts.\n\nCalculate the smallest amount of money that the company should put into the fund.\n\nSolution\n\nLet $$P$$ be the payments and $$X$$ the number of deaths, $$P = 10,000X$$, where $$X \\sim Bin(200,0.011)$$.\n\n$$E(P) = E(10,000X)= n\\cdot p =10,000(200)(0.011)=22000$$\n\n$$Var(P) = Var(10,000X) = n\\cdot p \\cdot (1-p)= 10,000^2(200)(0.011)(1-0.011)=217,580,000$$\n\n$$Sd(P)=\\sqrt{Var(P)}= 14,750.60$$\n\nSince there is a probability of at least 0.99 that the fund will be able to handle the payout, then:\n\n$$Pr\\left(Z\\le\\frac{P-22,000}{14,750.60}\\right)=0.99$$\n\nThus,\n\n$$\\Rightarrow\\Phi\\left(\\frac{P-22,000}{14,750.60}\\right)=0.99$$\n\nIntuitively,\n\n$$\\frac{P-22,000}{14,750.60}=\\Phi^{-1}(0.99)$$\n\n$$\\therefore P=22,000+14,750.60\\left(2.326\\right)=56,309.90$$\n\nThe value $$2.326$$ is nothing more than our application of the Central Limit Theorem ($$\\Phi(0.99)$$).\n\nLearning Outcome\n\nTopic 3.i:\u00a0Multivariate Random Variables \u2013\u00a0State and apply the Central Limit Theorem.\n\nShop CFA\u00ae Exam Prep\n\nOffered by AnalystPrep\n\nFeatured Shop FRM\u00ae Exam Prep Learn with Us\n\nSubscribe to our newsletter and keep up with the latest and greatest tips for success\nShop Actuarial Exams Prep Shop GMAT\u00ae Exam Prep\n\nDaniel Glyn\n2021-03-24\nI have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!\nmichael walshe\n2021-03-18\nProfessor James' videos are excellent for understanding the underlying theories behind financial engineering \/ financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.\nNyka Smith\n2021-02-18\nEvery concept is very well explained by Nilay Arun. kudos to you man!","date":"2022-08-07 22:05:24","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 2, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 2, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8290240168571472, \"perplexity\": 391.7710439651909}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-33\/segments\/1659882570730.59\/warc\/CC-MAIN-20220807211157-20220808001157-00558.warc.gz\"}"}
| null | null |
package org.jetbrains.plugins.dotty.lang.parser.parsing.statements
import org.jetbrains.plugins.dotty.lang.parser.parsing.expressions.Expr
import org.jetbrains.plugins.dotty.lang.parser.parsing.patterns.Pattern2
import org.jetbrains.plugins.dotty.lang.parser.parsing.types.Type
/**
* @author adkozlov
*/
object PatDef extends org.jetbrains.plugins.scala.lang.parser.parsing.statements.PatDef {
override protected val expr = Expr
override protected val `type` = Type
override protected val pattern2 = Pattern2
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,118
|
Q: TCP Socket connection between android and windows application I am developing an MFC dialog application in VS2019 c++. Application requires multiple android devices to be connected as client to a windows application server through USB. Connecting multiple devices one by one at the starting of the windows application is working fine. But once an device is disconnected from USB, and reconnected again, the server is not accepting the client.
I tried using a thread detach() only to accept() clients in background.
UINT CCheckDlg::bindAndListen(LPVOID Param)
{
while (true)
{
ClientSocket = accept(ListenSocket, NULL, NULL);
}
return 0;
}
But this loop breaks out after 2 iterations, and while this loop runs, other UI operations of the Application are blocked also.
For the android client side, as soon as the android application catches socketExceptions, it tries to reconnect to server. When the USB is connected again, the try continues.
How can i have a thread in windows application which is runs in background accepting clients, without blocking the UI operations?
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 5,419
|
Q: How to share picture or post via PHP SDK similar to a facebook share button? I want to Share Photos on my profile when I post photo on my facebook page.
how can I do this with php sdk ?
Similar to the share link shown in this picture
http://g1303.hizliresim.com/17/8/kusyg.png
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 513
|
function Basecamp(hudson) {
this.BASECAMP_URL = 'loadBasecampInfos.php';
this.BASECAMP_DOM = $('#projects');
this.BASECAMP_TIMER = null;
this.BASECAMP_BUG_TIMER = null;
this.BASECAMP_BUG_CLASSNAME = 'bug';
this.OPTIONS = {
timeToTick: 5 * 60 * 1000
};
this.init = function() {
var $this = this;
$this.loadInformations();
$this.BASECAMP_TIMER = setInterval(function() {$this.loadInformations()}, this.OPTIONS.timeToTick);
};
this.loadInformations = function() {
var $this = this;
$.ajax({
url: $this.BASECAMP_URL,
success: function(html) {
hudson.loadInformations();
$this.BASECAMP_DOM.html(html);
if($this.BASECAMP_BUG_TIMER == null) {
$this.BASECAMP_BUG_TIMER = setInterval(function() { $this.flashBugs() }, 3000);
}
}
});
};
this.flashBugs = function() {
$('.' + this.BASECAMP_BUG_CLASSNAME + " img")
.animate({opacity: 0.25}, 1000, function() {
$(this).animate({opacity: 1}, 1000)
});
};
}
//$.fx.step.textShadowBlur = function(fx) {
// $(fx.elem).css({textShadow: Math.floor(fx.now) + 'px ' + '0px ' + Math.floor(fx.now) + 'px red'});
//};
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 33
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The renovated club house has a full-service restaurant along with an upper lounge overlooking the 18th hole. This room is perfect for groups up to about 60. Great for birthday parties, anniversaries, small business meetings & luncheons, family functions etc.
We feel your catering needs are as unique and individual as you are. Please contact our Food and Beverage Manager for personal services. Menus available for all occasions.
For all Food and Beverage information, please call (705) 743-3812.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 8,556
|
#
## contents
introduction
cherished
vespa 90
mother's
silver
lambretta grand prix
heinkel tourist
the unknown vespa
bond p3
nsu prima
ednetta
honda spacy
il mio amore
lambretta li 150
lambretta 150d
start me up
lilly
lucy in the sky
new originals
unknown pleasures
the in-crowd scooter club
london fields rideout
broomstick
reincarnation
the rabbit
warhorse
lambretta turismo veloce
harlow
double denim
vespa cosa 200
wally
his and hers
greyhound 240
hotel navarra
form and function
loggy
copper
hotwheels scooter club
roller coaster
m'lord
authentic
lambretta li 125
100 per cent
lambretta tv175
triumph tigress 175
patience
goggo roller
r. agius scooters
precious
zündapp bella
eel and pie rideout
pretty green
lambretta sx225
waterloo sunset
clacton
iwl pitty
lui
moto rumi
the heirloom
sourcebook
credits
acknowledgements
#
## introduction
The scooter: so much more than a stopgap between owning a bicycle, motorcycle or car. Instead it was a form of mobility born out of necessity in a Europe ravaged by war. The scooter picked the best elements of existing transport and bundled them with flair into an agile, low-cost package – ideal for narrow, rutted and congested roads. More importantly it gave the majority, not just the well-off few, the mobility they'd craved for so long. What unfolded was nothing short of a phenomenon, surpassing the envisaged form of transport for the masses and becoming far more. Riding a scooter became synonymous with freedom and a symbol of a positive lifestyle in what were harsh times. Inevitably such a romance made its presence felt in cinema and print, further cementing its place in social history. The scooter, without question, takes its place among the most significant icons of the 20th century. Of course scooters existed, in various guises, before the austerity of post-war Europe. However, these first-generation pioneers were scarce and the scooters were often floored by high purchase prices and unwieldy designs. It was left to the second generation of scooter designers to pencil the familiar form we see today.
The question of what exactly makes a scooter a scooter is one that is much debated – is it the step-through chassis, the rear-mounted engine, the small wheels? But wherever you draw the line, the classic Italian scooter is unmistakeable. And the catalyst for what so many admire today was steel-tubing manufacturer Ferdinando Innocenti and his foresight in seeing the burgeoning market beckon for a cheap motor scooter. He approached Corradino D'Ascanio (an Italian aeronautics engineer), who found himself unemployable after the Second World War due to Italy's restrictions on researching or manufacturing military or aerospace technology. D'Ascanio tasked himself with the job of designing a simple, economical, robust, unisex, easy to ride, affordable scooter with partial weather-protection and a space for a passenger riding pillion. And all the ugly mechanics hidden away for the majority who cared not how it worked – just that it did.
However, when D'Ascanio and Innocenti's company fell out over Ferdinando's canny insistence on utilising steel tubing in the construction of the frame (thereby boosting his fledgling pre-war company), D'Ascanio took his preferred aeronautical-inspired spar frame to the more sympathetic ear of Enrico Piaggio. The new allegiance helped Piaggio take the lead in the scooter race by developing and manufacturing D'Ascanio's original concept in the form of the Vespa 98 ( _vespa_ being Italian for wasp), launched in 1946. The Innocenti Lambretta Model A, designed by Giuseppe Lauro and named after the Lambrate district of Milan where it was first produced, followed one year later. Thus started the rivalry between marques that exists, albeit good-naturedly, between loyal followers even today. However, one advantage shared by both manufacturers was the edge they had on their soon-to-emerge rivals.
Italy's seemingly overnight adoration for the scooter left the world looking on with wide-eyed wonder. Potential customers reacted to this new form of imported social mobility with curiosity, while manufacturing entrepreneurs were all too eager to have their slice of the booming scooter market. The far corners of the globe began turning their hands (often eccentrically) to scooter design. Some succeeded, many failed – most eventually fell prey to the automobile as it became more affordable. By the early 1970s road users had fallen out of love with scooters, and they were afforded a level of respect that those of a sensitive nature choose not to dwell upon.
Although scooters can be pinned to other youth movements, the predominant one remains that of the mod era, and the pages that follow naturally reference both the mod explosion of the 60s and its revival in the late 70s, and the influences that music, fashion and scooters had on people's lives. Impressionable teenagers on both occasions, when mod culture was in full stride, were deliberately and wholeheartedly swept along with it, absorbing the forward-thinking modernist vibe. Thus began the constant teenage battle to keep one step ahead when expressing themselves via the appearance of their scooters as well as their own. Despite the decades that have passed, little has changed; even now an owner's personality is projected onto their scooter with an array of lights, mirrors, emblems or even sign-writing – all with the aim of being distinct.
Researching this book has not only been an opportunity for Lyndon and myself to develop an appreciation for the aroma of two-stroke engines (not a welcome addition to everyone else's nasal passages, as Lyndon was told in no uncertain terms more than once), but yet again a welcome chance to explore a subject by way of research, photography and narratives. All of this has been made an even greater pleasure by the enthusiastic demeanour of the scooter owners. It's been a joy listening to their varied and fascinating anecdotes about how they came to own their scooter and, at times, about how it's changed and enriched their life. I hope their passion is suitably reflected in the personal commentaries that accompany their photographs.
It's often the case that the best design is the first design – and it's hard to argue that isn't the case with the scooter. However, with the few machines featured that don't herald from Italy, I hope to enlighten existing or aspiring scooter owners to these often unsung heroes, who are fully deserving of their moment in the limelight. I hope you will concur that this book covers a sympathetic mix of scooter marques and styles, and in part will help dispel the stereotypical opinion that anyone with a classic scooter is from the 'lights and mirrors' brigade. To everyone involved, thank you – it's been a blast.
#
## cherished
#
In what has become an expensive pastime, it's refreshing to have been given the opportunity to explore why the owners within this chapter hold their scooters in such high esteem, and to explore their reasons for purposely avoiding the temptation to profit financially from the demand for these sought-after design icons. The same praise can be attributed to the majority of owners within the book, but these individuals deserve to be singled out for their steadfast loyalty to the cause.
These are 'cherished' scooters for many varied reasons. On occasions it's the already lengthy term of ownership that has secured the scooter's future – fond memories from the owner's life or that of a loved one. Or maybe it's something else: how they came to possess their scooter – through a lucky find or by gaining the trust of the previous owner before a sale could take place; how scooters steered one owner from trouble and brought a semblance of order into his life, which resulted from a chance encounter; or perhaps the many years of observation and waiting before a bond between owner and scooter was established. Family heirlooms, extreme levels of workmanship and more will be found within this chapter.
There's often much more than meets the eye when it comes to owning a scooter – external appearance is just a part of it. Seldom will two owners share the same reasons for cherished ownership, and my intention is to show just how it came to pass. I hope you enjoy this chapter's selection of sometimes inspiring stories as well as beautiful scooters.
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### vespa 90
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'People from a certain generation get very nostalgic about small-frame 90cc scooters such as mine, many having probably experienced their first taste of true independence on something similar,' comments fine art lecturer Adam, who shares an appreciation for mid-century design with his partner Louise. 'We don't attract the same attention that showcase scooters command, but there is a minority that is overwhelmed by our scooter's originality – especially these days when time capsules like our Douglas Vespa 90 are becoming far less common. It was sheer beginner's luck in acquiring this scooter; it started with what can only be described as a modest mid-life crisis. In unison we decided to just get on with the things we talked about – as the stars seldom align to create the perfect moment in life when everything is harmonious.'
Adam continues: 'We began to browse scooter outlets and swooned over the models on display. However, since this was the first time we'd dipped our toes into the world of classic mobility (unless you count an old hand-me-down Skoda as a classic), we decided to take a smaller entry-level step into scooter ownership, broadening our search to a hopeful online bargain. We succeeded when I spotted a classified advert moments after it was posted online. The owner explained that the scooter had been in her family since it was bought new in 1966 by her father, recollecting the day he bought it and how it had been her task to choose the colour. Her father rode it for several months before the scooter became surplus to requirements and was stored in an outbuilding for 10 years or more.
'It was then her husband's chance to use it for a short while, before he too returned the scooter to its resting place for another 10 years. It saw the light of day again only when their son used it while at university in the 80s. Then it didn't get an airing for a further 25 years, before reluctantly being offered for sale – necessitated by a move to Scotland.
'Since the Vespa was in London, I asked Niall at Retrospective Scooters to give me his opinion, which was: "You've found a good one!" That was all the reassurance we needed and soon after the scooter, along with original paperwork – log book, etc. – was ours. The scooter is very desirable, with a traceable provenance. Apart from a bit of polishing, we've done, need to, or plan to do little else – it would be sacrilege to restore it. We're rather attracted to its sedate pace, allowing us to fully appreciate the experience. Like myself, it has its cranky moments, probably due to the fact it's not accustomed to being used so much. It's about ready for another hibernation, which it won't be getting any time soon.'
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### mother's
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'The scooter was purely a practical form of mobility, as opposed to a fashion statement or craze. I followed few trends; even a certain four-piece band from Liverpool eluded my recognition. Scooting at the time was very much encouraged as a lifestyle choice,' explains Audrey, who purchased her Lambretta Li 150 new in 1960. 'My new-found freedom was exciting yet overwhelming at the same time – certainly a step up from my bicycle. It enabled me to spread my wings, even, along with a friend, touring northern France and Holland.
'I also used it to commute to work in Sloane Street, London, where I worked as a dental nurse – which, incidentally, is where I met my late husband, Michael. He was a patient and I was captivated by this fascinating man. I even took it upon myself to check his notes, and found he was educated at Cambridge University. A Sloane Ranger he wasn't. He'd arrive on his trusty and rusty motorcycle in a jacket so covered in grease that it would stand up by itself. He was a maverick, some might say eccentric, lawyer with very high morals – few escaped his judgement. However, his disillusionment with the legal system led him to author a revolutionary how-to book about bypassing a solicitor when conveyancing.
'Our relationship blossomed and the scooter served us well on many a long-distance trip. Once we were married, Michael commandeered the scooter in order to commute into London. The scooter received little more than lackadaisical maintenance, was never cleaned or pampered. To him it was a practical, incognito form of transport, but to us all (including Michael) it evoked a curious form of love. Legal associates grew accustomed to seeing him on the Lambretta, often laden with books and paperwork bungeed to the scooter rack. On one occasion, while his fellow graduates arrived in Porsches and Jaguars to a reunion in Cambridge, he arrived on the Lambretta. He used it daily until the day he died, by which point the scooter was rather ratty-looking. Passing ownership on to my son Guy, who was heavily involved in the scooter scene, was the best action to take.'
Guy continues: 'I set about restoring the scooter to its former glory. Scooters are in my DNA and this one is an intrinsic part of the Joseph family. I'm the current custodian; but it will eventually be handed down to my eldest daughter. However, it has always been – and always will be – referred to as "Mother's scooter".'
#
### silver
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'I'm comfortable being deemed a hoarder. Hard to deny it when at one stage owning 26 scooters!' explains Simon, who started scootering on a 125 Vespa at the age of 17. Maybe his father was trying to relive his own youth upon a scooter – who knows? – but whatever his motivation for bringing home a sorry-looking Lambretta in need of renovation, he did not have to do much to persuade Simon to join him in a father–son restoration project.
'Every penny earned from my part-time job went towards finishing the Lambretta. Saturday was payday and the ritual, which continued for twelve months, was to visit the scooter shop for the next part on my list. Once finished, I used it for several months before the untimely death of my father. This changed my perspective towards the scooter, as it was a tangible connection to my father. Such is the sentimentality assigned to the scooter that since 1986 it has resided in my lounge, never to be used again.
'It's not the rarest, nor the most attractive scooter I own, but another with a sentimental label is my 1959 Lambretta Li 150, due to the part it played on the first date with my girlfriend, a romantic yet high-revving Sunday afternoon ride through the countryside.
'As with many of my scooters, this acquisition was the result of an online auction. I bid, won and soon after made the journey to collect it. Now, like many, I'm up for a bit of haggling – especially if something has inadvertently been missed from the seller's description. This was not such an occasion. I was greeted by a shaven-headed goliath of a man. Filling every inch of the door void, he turned sideways, stooped his head and shoulders beneath the frame and made fleeting eye contact with me. He ushered me towards the garage and muttered, "There it is. You won it for a good price – no haggling!"
'I graciously accepted his offer of a test ride. However, instead of the characteristic nippy acceleration, the scooter limped forward as if tethered to a bungee cord. The seller yelled, "Give it some revs!" Sure enough, after seemingly revving the hell out of it, the lacklustre performance gave way to lightning acceleration! Upon my return I timidly questioned the iffy start. He explained that the scooter's gearing had been modified so it was capable of pulling away with him and the missus. This left me mulling about what this poor scooter had been enduring, especially when his wife made an appearance. The scooter most likely gave a huge sigh of relief the day I rode it away. I've done little to it since. The gearing and even the heavily worn springs in the front saddle, which offer little or no comfort, remain – all testament to its previous valiant service.'
#
### lambretta grand prix
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'In 1984 I was a highly strung, angry, teenage tearaway. Luckily I left all my teenage angst and demons behind at this statue in the market square and now I'm fortunate to have a great life. Although I don't often dwell upon my past, it has to be acknowledged that it was a pivotal day that shaped me into who I am today,' explains Guy Busfield, who realises that were it not for a chance observation his life may not have turned out quite so well.
'I lacked direction in life. It was all too easy to sway into trouble that is, until I not only physically but metaphorically turned a corner. There, like a cinematic cliché, was a scooter with its seemingly illuminated distinctive turquoise body panels. I'd seen scooters before, but this one captivated me – it felt like fate. Instantly I knew it was what I'd been looking for in life – box ticked! I took a departure from the norm and diverted home via the library; I gathered as much information as I could muster, including a well-timed newspaper article about the mod revival.
'Soon after, despite being only 13, I went out and bought myself a Lambretta. Occasionally, over the next eight years, I'd see this particular scooter around town but I was never in a suitable position to flag down the owner. It then went off radar and despite having my own I couldn't get this mystery Lambretta out of my mind. Although never knowing its fate, I still kept a hopeful eye out for it, especially at countless scooter rallies. For all I knew, it could have been scrapped.
'Ten years on and many scooters had passed through my hands. I received a call, from a friend of a friend, saying that one had been obtained during a local house clearance. Was I interested? Never wanting to miss an opportunity, I went over to take a look. As I pulled up to the seller's drive, my blood froze and my jaw dropped. Facing me was a Lambretta scooter. Not just any Lambretta but the same turquoise Grand Prix I'd seen all those years previously. I snapped out of my self-imposed daze, went for a closer inspection, involuntarily swung my leg over and sat on it, the reason being that after years admiring it I'd never had this opportunity. By this stage, the price was irrelevant – I had to have it.
'It's hard apportioning credit to a scooter which had such a positive bearing on my life – but that's what happened, it spun my life around. It's the first time the scooter has been back in this spot since 1984. Thinking back, was it chance or fate that the scooter was parked there? Either way, who knows what I might be doing now if it hadn't been?'
#
### heinkel tourist
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'Wanted. Old scooters. Any make considered.' It seems a simple enough request. 'They were the words used in my classified advert to fuel my obsession for diverse scooters, which all stems from the time I spent cheffing with a lad of German heritage. Like mye, he was into the whole northern soul scene of the mid-70s onwards. Like ham and eggs, northern soul went hand in hand with scooters. I already had my Lambretta, but he was looking for something from his fatherland – a Heinkel Tourist.
'He'd yet to obtain his licence, so I collected his scooter for him. I knew nothing about German scooters before, but after the 90-minute journey home I knew I wanted one too. Sure, it wasn't as fast as its Italian counterparts – you don't accelerate, you accumulate speed – but it was comfortable, rock solid and economical,' explains Graham, who in 1982 purchased this UK import 1956 Heinkel Tourist. Excelsior motorcycles, based in the city of Coventry, did not want to miss out on the scooter boom and so imported Heinkel scooters and added their own marque to them.
Often referred to as 'the Rolls-Royce of Scooters' in England and 'the Cadillac of Scooters' in the USA, the high-end Heinkel Tourist was the vision of Ernst Heinkel, founder of Heinkel Flugzeugwerke, the German aircraft manufacturing company. The four-stroke chain-driven scooter was available with a speedometer, steering lock, clock, luggage rack and spare wheel. Its tubular steel frame to which pressed-steel body panels were mounted, and four-stroke engine, meant it was noticeably heavier than its counterparts, resulting in a more stable and pleasurable ride – ideal for travelling long distances. Between 1953 and 1965 more than 100,000 were built.
Graham continues: 'Responses to my advert started to build, with most conversations starting along the lines of "I've got this horrible scooter, don't know what it is – are you interested?" Zero respect was afforded to them. As far as most people were concerned, if it wasn't a Vespa or Lambretta it was useless. In a 10-year period I bought around 50 weird and wonderful machines, on average paying little more than £20 a scooter. Although they still don't command the same values as the iconic Italian scooters, it's fair to say that the 30 or so ones I've retained were a mighty good investment.'
#
### the unknown vespa
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'I was 18 when I bought my first scooter: a 1980 Vespa 90cc. Even now it sits among my modest collection of Vespa scooters. Prior to that, unable to own a scooter and not wanting to be left out, I made do the only way I could – a mountain of mirrors resembling Archimedes' death ray attached to a Raleigh Grifter,' remembers Warren.
'Each Christmas my wife Hayley and I go backpacking. In 2011 Vietnam was our chosen destination. The cacophony of noise from the urban bustle of Vietnamese towns and cities, would be pleasantly interrupted by the familiar ding, da-da, ding-ding of an ageing scooter appearing from one alleyway and disappearing down another! The choice of holiday destination wasn't a clever ruse to surreptitiously obtain another scooter right under my wife's nose, yet seeing them everywhere really made me curious.
'On a trip from Nha Trang to Hanoi I showed our guide a photo of the type of scooter I "might" be interested in. He'd call ahead so that, over a bowl of chicken and rice, I'd be treated to a pageant of scooters and hopeful owners. The ingenuity of the locals to keep their scooters running was amazing, yet troubling for a speculative buyer like myself when confronted by weld lines and random patchworks of metal. Only when we got as far north as Hoi An did I find a suitable machine. It was a far cry from what you see now, but beneath the kaleidoscope of paint colours appeared to be a solid scooter. I knew it wasn't an original low-light Vespa, but nor could I confirm exactly what it was, even when cross-referencing it against photographs. The clincher for me was its lovely curves, reminiscent of early 50s scooters, which to me are near perfect,' explains Warren, now the proud owner of this mystery Vespa scooter.
'That evening I joined the Veteran Vespa Club and sought further clarification. The following morning my inbox was full of well-meaning "Steer clear!" comments and reasons why I shouldn't buy it. The problem was that I'd already bought it. It handled well and looked fairly honest – what could go wrong? A month later, a wooden crate containing my scooter arrived at my door – all for the remarkable delivery cost of 100 dollars!
'Since then it's been put through a sympathetic but thorough restoration with a few tasteful, moderately blingy additions. I'm still no nearer confirming exactly what the scooter is. It's obviously much earlier, probably 1950s, but to satisfy the authorities the safest bet was to register my hybrid scooter of mixed parentage as a 1971 Vespa Sprint 125cc.'
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### bond p3
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'In the mid-80s, when I was 15, to satisfy my motorised urges, my parents bought me a 1973 Spanish smallframe Vespa (retrofitted with an 80s 50cc engine). Scooter popularity had dwindled significantly by the time I reached 16 [the legal age for driving a scooter in the UK], but regardless I scooted around sporting the standard-issue parka coat. A job and regular wage meant I could splash out on a motorbike, but still keeping one foot in the scooter scene, knowing one day I'd return. That day came in 1999, when I purchased a nearly new Vespa ET4.
'I joined a scooter club and began using my Vespa more for leisure than for commuting. By now I fancied riding something of an earlier vintage; fortuitously, I'd kept my first Vespa tucked away in the back of my parents' shed. The Vespa hadn't fared too well, but by 2000 it was back on the road. But something else had happened; either the scooter had got smaller, or I'd got bigger! The scooter to rider algorithms were out of kilter – the solution was a more ample Vespa PX200.'
'Then, I discovered that my grandmother had a couple of 60s scooters tucked away in garden outbuildings. They'd belonged to my granddad, a shrewd man into all kinds of stuff,' explains Shaun, remembering his Normandy veteran grandfather who passed away in 1996. He continues: 'Upon passing his driving test he tucked them away, but not before taking the time to properly prepare them for long-term storage. After searching excitedly, I discovered a Bond scooter. Coming from Preston, I knew the marque immediately; Bond was a local company famous for their three-wheeled mini-cars. The scooter was an ideal restoration project, not forgetting the other Bond P3 I managed to find in another shed.
'I learned that the first new old stock (NOS) Bond P3 was purchased in 1966, after my grandfather traded in his Lambretta. After several years inevitably something failed on the scooter, so my grandfather went out to source a new part, only to return with another NOS Bond P3.'
The fibreglass Bond scooter was never successful, hence the availability of NOS in 1968, when manufacturing concluded in 1961. Despite slick styling and engineering, it was overpriced at almost £200, the same as a Lambretta TV or Vespa GS.
Shaun continues: 'Riding Nellie (a name adopted years ago when my daughter called the scooter Smelly Nellie) is unlike anything else – horrendous but in a really good way. The three-speed gearbox and 150cc engine needs thrashing within an inch of its life to obtain any performance. Factor in the muddled pedal configuration and it's like performing _Riverdance_ when travelling through traffic. However, it fares much better on open roads and is used regularly on club trips, rain or shine. I'm not precious about it – it's got scuffs and tarnished chrome, but it's mechanically well looked after and that's the way I prefer it. The bulky scooter is unlikely to be suitable for my daughter, Phoebe, so when the time is right it will be loaned to a museum for others to appreciate.'
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### nsu prima
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'If I hadn't looked over the shoulder of a lad restoring his Lambretta in the body shop I ran in the early 90s, I might never have owned a scooter myself,' explains Johnny from Lancashire. 'The end result made me envious, yet it took a further decade before I found what I was looking for. An internet auction item, for what I naively assumed was a Lambretta, caught my eye. It looked the perfect project; the starting bid was low and no one had yet bid on it. A more detailed inspection, from the poorly listed item, revealed it was in fact a 1960 NSU Prima V. Still, for all intents and purposes it was exactly what I needed. I placed a bid, the only one it received. I eagerly phoned the seller to arrange collection, hoping that I'd be dealing with a scooter enthusiast who'd take me under his wing and mentor me in all things scooter. Sadly, my cheerful demeanour was greeted with quite the opposite: "It's here, come and pick it up!" The collection address was the epitome of a northern terraced street; I could have been on the set of 'Coronation Street'. I'd clearly timed my visit poorly: it was teatime. Tonight was fry-up night and the house smelled like a café!
'I passed through the grease-filled haze of cooking to the backyard. Hospitality wasn't his forte, and tea was obviously paramount, so I made the rest of the journey alone. Sure enough, wedged up against a load of other stuff was the scooter in just the condition I expected to find it. On closer inspection I noticed the odometer registered only 680 miles – not even close to being fully run-in at 1000 miles. I enquired as to the seemingly impossibly low mileage. I was obviously being a nuisance, because he just looked up from his armchair, at the same time as biting into his egg butty, and said (with a mouthful of yolk dripping down his chin), "Do you want it or not?" I replied, "Yeah," and with that was instructed to leave the £204 on the mantel.
'Just as I'd finished loading the scooter into my car, the seller emerged, somewhat more communicative, having eaten. It transpired that it was originally his uncle's scooter, but his aunt (recently deceased) couldn't bear to part with it after he died in 1961. All the scooter needed was a sympathetic restoration and respray to bring it back to glory. The engine didn't need touching, it started after a few attempts – much to the disbelief of scooter mechanics who couldn't believe it wasn't seized. I've never had to change as much as a bulb – just perished rubber items. Testament to what, at the time, was an expensive scooter: £465 would've bought you a Mini, £159 a Lambretta 150LD – the NSU was £214, but the engineering justifies it. I'm happy to report it's nothing short of perfect and a joy to ride. It feels like it would go for ever and ever!'
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### ednetta
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'It's not uncommon to look overseas for inspiration, especially when growing up in a small Peruvian village. The romanticism of owning a scooter, especially an Italian Lambretta, always appealed to me – but sadly at that time of my life it was unachievable. I can't even recall the make of my first scooter. It was rough, possibly Japanese...to be honest, somewhat of a bitser. Nevertheless, from the age of 16 onwards myself and that scooter clocked up some serious miles that instilled fond memories into my memory bank,' comments Renzo, who became sidetracked and upon moving to the city subsequently moved out of the scooter scene for a decade or more.
'Only when I moved to London did I hanker after owning a scooter once again. I guess subconsciously, through all the times I didn't have a scooter, I missed having one. I knew exactly what I was looking for and it took a while to track one down. So when this one-owner 1957 150LD, with its chic styling, exposed handlebars and cabling, appeared online, I didn't hesitate.
'I bought it for what, at the time, was a surprisingly cheap price. A bargain-basement price it might have been, but reliability wasn't the compromise. In fact, I rode it all the way home from Nottingham without even a murmur. Mechanically, Ednetta (named after a friend who donated my scooter a parking space) is first class. The bodywork, with its wonderful patina, is to be preserved and not revived. Changing the exterior would be akin to changing its personality. Neither has anything been added to the scooter, only sympathetically replaced – apart from the wooden crate!
'I adopted a puppy, Moncho, three years ago and from that day forth he's followed me everywhere. The logical progression (logical for me, anyhow) was for Moncho to accompany me on the Lambretta. The first time he ventured out, thankfully at low speed, he tried to launch himself out of the crate! However, that was the first and last time he tried that trick – now he loves it. I'm no attention-seeker and it wasn't the goal, but riding about with a dog on the back of the scooter certainly attracts the odd double-take!'
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### honda spacy
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'It's fair to say that there's a collector in all of us. However, just how fast 'n' vast a collection grows is down to the passion you possess for your chosen subject. My vice for British scooters didn't materialise until many years after I purchased my first scooter, a British-made Dayton Albatross, in 1960. The gap between 1960 and 1999, when I bought another scooter, was filled with the usual series of motorcycles and everyday cars. In 1999, to complement my jukebox in a newly built home extension, I convinced my wife a classic Lambretta would make a rather nice decorative feature – and that it did.
'However, this sparked the collector in me. So soon after, I joined the Vintage Motor Scooter Club and eagerly awaited their quarterly club magazine. I'd enthusiastically scan through the "for sale" section and snap up vintage scooters that caught my eye. Before long my collection tallied 35 scooters, of which 20 were of British origin. The scope for my collection further narrowed when it became my aim to obtain all 42 production British models of scooters from 25 manufacturers between a set period – something no one had ever done,' explains Robin, who over a 15-year period amassed an impressive collection of scooters. This led him to author his own book: _British Motor Scooters 1946–1970_.
'As you'd expect, it was difficult to keep the lid on a collection like mine – and I relished others seeing it. So when the British Motorcycle Charitable Trust enquired as to whether I would be interested in displaying my scooters at a temporary exhibition at the Coventry Transport Museum, I leapt at the chance.
'Owning 42 scooters brought me a lot of pleasure, yet it was somewhat of a burden when every spare space was occupied by a scooter. So after much dilemma I enquired as to whether the Trust would be interested in purchasing my collection. The idea appealed to them, but finding a permanent museum big enough proved tricky. That is, until the Haynes Museum stepped forward and set aside space in their museum near Yeovil. Even though putting the scooters piecemeal into an auction would have given me a greater financial return, it was important that a collection which had taken me so long to put together stayed together.
'Even with the collection of British scooters off my hands, I was still obsessed with scooters. However, I wanted something which would start on the button and that was effortless to ride. One such range of scooters that ticked all those boxes was the radical futuristic Honda Spacy series, which was first introduced in 1983. This set me off on yet another (but this time low-key) collection, starting with the wonderful 1987 125cc model you see here, a 250cc model and then the big daddy Helix. All very much retro statements these days and, I feel sure, future design icons. A stark contrast to my obsession for British scooters, but with that collection ticked off, no one surely expected me to stop collecting? But I had to be a tad more realistic this time round!'
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### il mio amore
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'I was given this 1956 Lambretta 150D in 1969 from a friend who had no use for a scooter that he'd been given by a client. Initially I took the scooter to my house in the mountains but treated it with little respect, working it hard in the woods and over the rugged countryside. I shudder when I think back to what she went through.'
'Fortuitously I passed a scooter just like mine, but this 150D was in pristine condition – unlike mine. In that moment, the fate of what I now refer to as _il mio amore_ (my love) changed for the better. She deserved more than her harsh life in the mountains; I wanted her to be just as stunning and turn heads. Therefore, as recompense, she went through a total restoration,' says Giuliano, owner of this Lambretta 150D, of which 54,593 were built between 1954 and 1956. It inherited much of its appearance from earlier Lambretta scooters and was to be the last of the bare-boned Lambrettas.
Giuliano continues: 'We are now inseparable. Much like when I was 20, riding the scooter makes me feel cool and years younger – it does nothing but good for the soul and spirit. I'm also lucky to be a member of the Lambretta Club of Lucca, a wonderful group of scooter owners, many of whom are half my age! They recently showed me great respect by appointing me as honorary club president. On sunny days, I take her for a spin in the mountains and more often than not stop at my favourite bench for a leisurely read of my newspaper. The Italian scooter scene is once again alive, which is helping to unearth scooters that have remained dormant in garages and barns for many years. But it doesn't help that many scooters have been sent abroad. However, as compensation, it's a pleasure to go abroad and see our beautiful scooters whizzing around – it fills me with Italian pride.'
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### lambretta li 150
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'If you look long and hard at a scooter, as I've done while behind the shop counter, you begin to look beyond what most take for granted. In the late 70s I'd observe all manner of scooters, critiquing them and forming my opinions, while their owners loitered outside my family's Noted Eel and Pie shop in Leytonstone. At that time, East London was a hotbed of scooter activity. As the scooters gathered, I'd be mesmerised only to be snapped out of my trance, ladle in hand dripping with liquor, by a customer chasing up his pie 'n' mash order.
'For me there has always been one standout winner – a Series 3 Lambretta. They've almost cartoon-like proportions: a stance that's seemingly moving forward, even when they're not. Yet at the same time they're majestic, from the curvaceous tail through to the graceful sweep at the front, like that of a swan lifting its head – to me the shape is utter perfection.
'The mod revival started when I was 16 and too young for a proper scooter, besides the fact that my father never wanted me to own one, as in his opinion they were far too dangerous. At the age of 17 I was the only one, within my circle of mates, who owned a car – a Mk1 Ford Cortina. I was the envy of them and, to be fair, along with my two-tone tonic suit, a car was more impressive to the opposite sex – as opposed to my friends' mopeds and scooters. However, I still had a thing for scooters and occasionally we'd swap vehicles so I could get my scooter fix,' explains Pieter. 'One thing led to another: sports cars; a bit of cheap motor-racing; sports bikes, and more. Then came the moment most wives dread, a space in the garage! In a split second, it came to me: I've got to get a Lambretta! I looked long and hard for over a year. I thought seriously about a couple of fully restored scooters, but in the end I wanted more of a project.
'Eventually I bought a 1964 Lambretta Li 150 that had just arrived from Italy. It was a 100 per cent bona fide project scooter that I ended up spending three years' worth of evenings and weekends restoring, relishing in the finer details, to end up with a scooter as it would have been, apart from the splash of blue paint, when it left the factory.
'This Lambretta is gonna stay with me till the day I die. My eldest son is in line to own it when I'm gone, as he knows how I feel about the scooter. So I'm safe in the knowledge that he'll cherish it and won't sell it. I've seen the whole world and his dog going past my window, yet my day is still made when occasionally an old scooter parks up outside.'
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### lambretta 150d
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'Despite 14 being the legal age to ride a 50cc scooter in Italy, it wasn't nearly early enough for me. With approval, I commandeered my father's unloved Ciao moped and on the fields, within the confines of my childhood home, I soon mastered its mighty power. As my confidence grew, so did my eagerness to perform death-defying acts of stupidity – for years my knees and arms were barely graze-free.
'My grandfather was a farmer and on market day he'd trundle into town on his trusty 1956 Lambretta 150D with the Stabil cart heavily laden with his fine organic produce. On summer weekends, when travelling to the beach, the crops would be replaced by a wife, children and other family members precariously hanging on to the cart. You wouldn't have thought it possible to generate enough momentum to eject my aunt from the cart – yet my grandfather managed it on one memorable trip when taking a corner too tightly! This story and countless others resulted in the scooter overflowing with family memories since he purchased it from new,' explains Alberto, who due to the scooter's rarity and sentimental value set about restoring the combo when it was retired after years of faithful service.
'Although I own other scooters, my grandfather's Lambretta is reserved for attending the Lucca Scooter Club meetings, such as in 2014 when our club helped support the cars taking part in the historic Mille Miglia. We led the way as the priceless sports cars meandered their way through the narrow picturesque streets of Lucca. As ever, the Lambretta came up trumps when I returned with several demijohns of wine, cheeses, salamis and bread. What better way to round off a glorious day?'
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### start me up
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'After a lengthy spell of not owning a scooter, I felt the urge to get back on the saddle. Not with just any scooter, though – the 1971 Lambretta GP200 "Start Me Up" I'd sold 10 years earlier, when family life rightly took precedence. The word went out within the scooter community and I learned that the scooter was still in possession of the chap to whom I'd sold it on the Isle of Wight, and we made contact. He was fifty-fifty about parting with it, and eventually a price that was way more than I was willing to pay was put forward. For me, that was the end of it. But my wife Vicki knew that not owning it would eat me up inside, so she convinced me to proceed with the purchase,' explains Mark, who while at Clacton in 1985 had succumbed to the lure of custom scooters when he saw one called Dazzle (based on the Siouxsie and the Banshees song). Its customisation was head and shoulders above anything else that had been done and even now is spoken about with high regard.
'While waiting for the scooter to arrive on the Isle of Wight ferry, we knew we'd paid a premium price for it. Yet what rode off the ferry wasn't the same premium scooter I'd cherished years earlier – my heart sank. It was the same scooter, but with tarnished chrome and paint in far from show quality. After a few family photos with the scooter, I began stripping it down – I never even started it up. The paint and gold leaf was blasted back to bare metal and the engraving polished out. Why do this to a scooter that had, during its show days, won 50 pieces of silverware? Because I wanted to outdo its previous incarnation.
'A scooter like mine isn't really planned; it evolves. Nothing on the scooter was to be an off-the-shelf item, right down to the custom-engraved valve caps. There were trips back and forth to the artists (Ty Lawer paintwork and Adi Clark engraving) with Rolling Stones imagery, bouncing ideas to and fro until a decision was made. It was tricky to visualise exactly how the finished article would look, but I needn't have worried; both artists put their heart and soul into the project. Excluding the preparation work, 300 hours alone went into the airbrushed artwork, with the engraving topping out at nearly 123 hours. As finished parts arrived, all I could do was admire them, because I couldn't fit anything to the scooter until everything was received. They were rewrapped and put away like a gift you couldn't use. The job of assembly was mine, and a nerve-wracking one at that. If something didn't quite fit – often the case with a custom scooter – I'd stop, mop my sweaty brow and calm down over a cuppa; one careless slip of the screwdriver, over fresh paint, would have been disastrous. Slowly, piece by piece, my vision emerged.
'My scooter's different in another way. Despite what you might expect, it gets thoroughly used. Often with Vicki, who also rides a custom 1979 GP200 named It's All About Me, we travel the UK to attend and display at scooter rallies. It's recognition of a dream. I built something that I love and am passionate about – built to the best of my ability. People have commented that it's the best custom scooter since Dazzle and the best paint job they've ever seen. I'm chuffed.'
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### lilly
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'I was having a casual chat in the pub with a chap from the village when the conversation veered towards vehicles and Jeff enquired after my weakness for motors,' explains Richard. 'I confessed that I was into scooters and had been for many years and that I was looking to tick a Lambretta off my wish list. His eyes tightened, as if racking his brain for information, then he mentioned he possibly knew someone who had an old Lambretta that had been in a garage untouched for years. Year and model he was unclear about and he wasn't sure if the owner would even sell it, but he would ask. The following evening he returned with a scrap of paper with "Li 150" scrawled on it. Better still, the owner, John, was willing for me to take a look, but on the understanding that it wasn't technically for sale.
'With my area of expertise being Vespas, I took a local Lambretta guru along for his opinion. We arrived and along with the owner made our way to the back of his garage towards a scooter draped in protective sheets. Our anxiety was palpable and when the scooter was uncovered we both gasped in admiration. There stood a carefully mothballed 1959 Lambretta Li 150 Series 1 with only 7000 miles on the clock, the tax disc confirming its dormant state since 1965. Despite our state of wonderment, the fact remained that the scooter technically wasn't for sale. The worst thing would be knowing of its existence but unable to own it.
'Over tea I chatted to John, once an engineer at Longbridge, and learned that he'd bought it new and stopped using it only when a company car was made available to him. For 45 years he'd safeguarded his beloved Lambretta because he didn't want to part with it – in the same breath admitting that he's very much owned by his possessions. We were both getting on really well, so I chanced my luck and respectfully enquired as to his intentions for the scooter, and without any pressure on my part John agreed to sell it to me. Hallelujah! I'm sure he could see in my eyes just how much I loved the Lambretta and that I wouldn't just flip it for the sake of a quick buck,' says Richard, the lucky new owner who was left with the dilemma of what to do now. Being a plasterer by trade, he prides himself on delivering smooth mirror-like finishes. However, that was a no-no with this scooter. With everything being original, preserving and not restoring was in order.
'John and I keep in touch regularly. It's my way of ensuring that he gets to know that the scooter is still being looked after.'
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### lucy in the sky
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'The scooter saved me from unemployment during the years when I was trying hard to get my magic career off the ground. It was the only real asset I had and, more so in those preinternet days, London was buzzing with companies shuttling packages hither, thither and yon. So I joined the ranks of a despatch rider, carrying an often seriously overloaded cargo of cardboard tubes, documents and undefined packages bungee-corded to any free section of the scooter.
'By the time I'd delivered my last package, after four years' service, not only was I sick of boxes but no amount of magic could revive my battle-scarred Lambretta – it was looking very much the worse for wear,' explains self-taught magician Fay Presto, who during those years as a courier honed her skills as a close-up magician.
'However, it wasn't the first time my 200SX (nicknamed Lucy In The Sky – after my love of the Beatles) had been used for such purposes since I purchased it from new in 1967. My father was a tailor, so I'd help him out as and when required by delivering freshly tailored clothing to his clientele. It was the least I could do: after all, with me being only 17 he kindly signed the scooter's finance agreement. However, it was down to me to jolly well keep up the repayments. Which were enough of a financial stretch without finding out, when it was too late, that the scooter dealer had pulled a fast one on me by charging me an additional £18 (a month's wages) for a Lambretta in supposedly special-order white, only for me to find out years later that they were imported from Italy in white anyway!
'Ironically, shortly before I finished as a courier, I'd deliver packages to the same TV studio, with little gratitude shown to me, where a few years later I was being whisked through the VIP entrance and wooed by TV executives. As I started to earn an income from TV appearances and stage shows, I decided it was only fitting, as a way of returning the favour to a very trusty scooter, to have it restored back to its former glory.
## new originals
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This chapter focuses on those individuals or collectives who often draw a line in the sand of conventional scooter ownership – choosing not to conform to a stereotypical demographic. Instead they pluck the elements of original and current scooter trends that work for them and then instil their own personality traits and taste. On occasions these new twists within scootering develop into their own subcultures. People of this mindset are as important as those who stem from the first historic chapter of scootering in the 1950s and 60s – as well as those from the scooter revival of the late 70s. Without new generations stepping forth and exploring new avenues of the scene, it could all too easily become stagnant – therefore confirming the incorrect one-sided perception of scootering to the masses.
The accessories, styling and choices of scooter are rightly and selfishly (in a positive way) that of the owner. Deliberate or original patina and material choices come into play, often going beyond what is original or period to the scooter in terms of mechanical components and exterior styling.
Many of the scooterists within this chapter credit their family lineage for inspiring them, often from an early age, about the positive aspects of scootering as well as the music and fashions that go hand in hand with it. While some within this chapter don't consider themselves as stemming from a mod background, they still possess the typical mod ethos of looking ahead for their inspiration with the aim of being different. As a result of this nonconformist way of life, like-minded individuals are often brought together via the strong camaraderie and social aspect that surrounds scootering.
Those featured within this chapter are faithful to scootering's original spirit, but new in appearance – new originals.
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### unknown pleasures
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'I moved from up north to London circa 2004, and public transport soon got the better of me. A scooter seemed ideal, but being afflicted with a sense of style – a tough cross to bear – a modern one was out of the question. A slice of iconic Italian design was more to my liking. I consequently bought a supposedly top-notch 1961 Vespa VBB. Subsequent bills of £1500 just to get it through its MOT proved otherwise – bewildering when the scooter cost only £900. I wasn't really seeking any social aspect from owning a scooter, it was purely something that served its purpose with style. I quickly learned that a pristine scooter on the sometimes abusive streets of London isn't ideal. In quick succession my scooter was first torched and then stolen. A lesson had been learned, so I used the insurance payout to buy a battered old Italian Lambretta. Proper Italian stock with tatty paintwork, and there was no shying away from the fact it needed work,' explains Andrew, owner of Bolt, a new scooter/motorcycle lifestyle brand.
'I then started mixing with a developing scene of scooter owners from around Hackney, a crowd that exists slightly outside of the "proper" scooter scene, who prefer doing their own thing. Neither mods nor scooter boys, just somewhere in the middle. It sounds as if we're a mysterious bunch that comes out only at night and lurks in the shadows. Far from it, we're a confident lot with creative leanings who share the ethos that you can't fully live life retrospectively as a mod – times have changed. We're in it for the love of scooters and our take on fashion.
'My scooter stayed in its battered state for a couple of years before I'd pretty much ridden it into the ground. I'd already daubed the scooter with the words "Unknown Pleasures", an album by post-punk band Joy Division. I always wanted it professionally sign-written, and with the scooter in need of TLC there was no better time than the present. I'd been following the work of artist Nicolai Sclater aka Ornamental Conifer, known for his contemporary, pop-style typography. He'd been sign-writing petrol tanks, but the chance to paint a whole scooter proved too inspiring to turn down. I'm a firm believer in giving the artist as much freedom as possible and the result didn't disappoint. Various others have followed, some of a similar style by Nico, but mine was the forerunner. Everyone recognises the scooter before they know me. I'm tending to introduce myself as "I'm Andrew, the guy who owns Unknown Pleasures!"'
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### the in-crowd scooter club
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It's par for the course that spare time in a capital city is a precious commodity. With this in mind, and whenever commitments allow, a certain collective of youthful London-based scooter owners and friends regularly meet up at cafés and coffee bars, before departing on a well-earned rideout via the landmarks of their city. It's a relaxed gathering, no official club name exists or is required – they prefer instead to keep things informal and thus avoid problems that often follow in the wake of official clubs. Turn up or don't turn up. Yet, for those who do, it's an ideal opportunity to catch up with one another and temporarily leave their stresses behind on the streets of London, with each rider travelling as far as they wish (or time permits) before they go their separate ways until the next time.
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### london fields rideout
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Sunday morning is their time. Whether it's over a cholesterol-rich full English or something more continental, the In-crowd (a name afforded to them in jest) meet while others have barely awoken from their slumber. They escape domestic chores and DIY in exchange for scooter banter with their like-minded mates, before heading out into the Cambridgeshire countryside on their distinctive scooters. At home, for many of the In-crowd, their passion for scooters is mainly a solitary one – many of their respective partners fail to share in their enthusiasm. For these gentlemen this is their hobby, their 'me' time. Which to some may come across as selfish, yet they strongly believe that it's healthy, in a relationship, for each party to have their own pursuits. Although many of these individuals belong to various scooter clubs, this weekly rendezvous in their busy lives is an important ritual.
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### broomstick
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'I'm pretty new to the world of scooter ownership – five years, to be precise – but it was very much a case of when, not if, I got a scooter. While I was living in my flat, scooters were put right under my nose when a bunch of neighbours moved into the flat beneath me. The unmistakeable smell and noise of two-stroke engines belching from their scooters got my attention. But far from me yelling "keep it down" from my upstairs window, I felt compelled to introduce myself, thus becoming good friends with them. They'd wax lyrical about how much fun scooters were and in no time wore me down into wanting one myself,' says Cath, a graphic designer and photographer.
'Ownership was accelerated by a lucky find at a junk shop. I spotted a random piece of second-hand sound equipment bearing the Glensound label for £7 – the brand resonated with me and a quick call to a good friend who was a sound engineer confirmed it was a bargain. I snapped it up and put it for sale online. My modest reserve was soon reached and it ultimately sold for £780! Soon after I found this 1982 Vespa Douglas V100 advertised for £800. Taking into account my lucky junk shop find, I had to shell out only £20 for the scooter. What a result!' explains Cath, who is originally from Manchester but who made a new life in London after studying at Saint Martin's School of Art.
'Once I'd fetched the scooter home, I toyed with the idea of respraying it in one shade of blue, rather than its myriad tones. However, after a minor prang resulted in me having to source a new headset (with only green being available), I received favourable comments on the new colour combination. This despite the old adage of "blue and green should never be seen" – but I guess I'm the something in-between?
'I was tagged with the nickname "Window Witch" after an evening out with one of my scooter mates, Grubby. I used to jokingly intimidate him while gliding past the window of the fried-chicken shop. With time it just evolved into plain and simple "Witch", so when I got the chance to meet artist and sign-writer Steve Millington I requested he applied his talent to my leather jacket. And, with no witch being complete without her broomstick, he later added sign-writing to my scooter's side panel, in the process carefully obscuring an area that I'd stained with petrol.
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### reincarnation
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'Scootering for me started when I was 15, certainly before I was old enough to ride one – and all without the knowledge of my mother who, when I broached the subject of buying a scooter, was adamant it wasn't going to happen! I was chatting to a family friend who lived over the road, about my wanting a scooter and my mother's unfaltering disapproval. To which he replied, "Your mother doesn't have to know, keep it in my garage." So that I did and bought a Vespa from a mate who had a few that we'd knock around the fields on. In all I squirrelled it away for the best part of 18 months, evading my mother's eagle eyes – she hadn't a clue,' explains Matthew Thompson.
'On one occasion I was out learning to ride the scooter a few streets away from my home when I spotted a blue Mini coming out of a side junction. My mother drove a blue Mini! I panicked, lost control of the scooter and careered across four front gardens! Despite myself and scooter being covered in hedge, I managed to stay upright. The irony, to my mate's amusement, was that it wasn't even my mother.
'Like many, I had a break from the scene lasting for over a decade – that is, until my girlfriend Louise and I were holidaying in Greece. While walking to a restaurant, I spotted a dilapidated Vespa abandoned and tangled in a bush. To her embarrassment, I dragged it free and elatedly announced that I could restore it! At the time she knew little about my scootering past, so my notion was hilarious to her. Reluctantly, I put the scooter back in its resting place and continued forlornly with our walk. Soon after we returned home, a scootering magazine dropped through the letterbox. Without my knowledge Louise had taken out a subscription as a joke. However, the last laugh was on her when a week later I brought home a Lambretta.'
Turning to what was originally a 1959 Lambretta Li 150 Series 1, Matthew continues: 'I purchased this particular scooter as a legally running rusty wreck. After a few years of use, like an ageing pit pony, it had had enough – the time had arrived for it to be reborn. Now there's a mod scooter and then there's a _mod_ 'ified scooter. Its reincarnation fits squarely into the latter classification. It broke the mould in terms of taking an early scooter and making it into a customised scooter. Neither is it a sheep in wolf's clothing, with performance matching its lively exterior. The engine is a 240cc TS1 with upgraded crankshaft, clutch and brakes, but retaining all the original '59 bodywork.
'For me an enjoyable part of owning a scooter is working on it. Every nut, bolt, washer and everything in between is my own handiwork – including a rear light from a Vincent motorcycle and paintwork with its hotrod-inspired scallops.'
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### the rabbit
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The roots of the Fuji Rabbit can be traced back to the Nakajima Aircraft Company. At the end of the Second World War, peace treaties forbade Japanese companies from manufacturing aircraft. Therefore the company re-formed as Fuji Sangyo Co., with the aim to fulfil the demand for civil transportation. The enormously successful Fuji Rabbit S-1 was Japan's first production scooter – introduced in June 1946, a full six months before the Vespa. The marque's scooters evolved into a formidable range, with scooter technology way ahead of its rivals – electric start, automatic transmissions and pneumatic suspension systems. Inevitably the demand for scooters went into a decline as the Japanese economy grew. The company's client base were now seeking four-wheeled transport – thus came the introduction of the Subaru range of automobiles. The scooter production line ceased in June 1968, but even to this day the Fuji Rabbit is held in high regard by appreciators of Japanese popular culture.
The technology didn't go unnoticed by Niall, owner of Retrospective Scooters, one of London's leading specialists in vintage scooters. His contagious appreciation for classic scooters was formed back in his late teens, when he was a mod in Northern Ireland, where, before turning his deep-seated passion for scooters into a business he was, for many years, a scooter courier.
Niall comments: 'When a scooter that differs from our usual staple diet of Italian scooters rolls into the workshop, I'm keen to explore how other countries fulfilled their demand for scooters by way of design and engineering. When the 1968 Fuji Rabbit was up on the ramp, I was soon struck by its styling, ingenuity and build quality when compared to some aspects of classic Italian scooters. Seeing that it's an especially rare scooter in the UK, I saw no harm in asking the owner if he would consider selling it – which, to my delight, he agreed to do.
'In no way am I turning my back on selling vintage Italian scooters. However, every once in a while it's good to step outside your comfort zone – if only to see things from a different viewpoint and further appreciate what the experience of owning a scooter offers.'
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### warhorse
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'I don't do lights and mirrors. My scooter's for serious mileage. So far this year I've clocked up 3000 miles with five months still to go. Trust me, you feel every mile – even more so now I've reached the milestone of 50. And as it's unlikely I'll see another 50 years, I'm making the best use of every moment. I bought my first scooter in 1993 and, putting it mildly, it was a nightmare. I spent a fortune on it, yet it was nothing more than unreliable. At the time it was a lonely period to be a scooter owner, with experts few and far between. In the end I got the hump with it and sold it to someone with more patience than me. Irrespective of not actually owning one, I still followed scootering through magazines. I suppose I was annoyed that I'd had such a bad innings – once bitten, twice shy.
'To fill the void I went with both feet into the VW scene and then classic cars, moving on to the next pastime only when each became too costly. By 2005 I was ready to give scooters another stab. This time with better luck – it was great to be back again!' explains Tornado Trev, who purchased this Spanish 1958 Series 1 Lambretta, named Warhorse, three years ago. The 125cc being of no use to Trev on the lengthy journeys he undertakes, Warhorse was tuned to a more adequate 200cc, with all its original bodywork benefitting from only a few choice stickers and gold-leaf sign-writing by a fairground sign-writer.
'I'm a member of and ride for the Wisemen Scooter Club of Yorkshire. Even though I'm on the south coast, it's my preferred choice of club – they're a great bunch of scooterists. Members travel from all over the country, pushing to the limit machines only ever intended as glorified shopping trolleys. The club have taken this southern softie under their wing and great friendships have formed. We're not into picking holes in each other's scooters – just enjoying life, drinking a few beers and talking scooters.
'Regardless of the inclement weather, the points championship event takes place. During the Land's End to John O'Groats Rally, it rained for three days solid, made worse when there's three sharing a room in a B&B with one radiator; our clothing never drying out. Forty-five started and only 33 musty-smelling riders finished. Over 900 miles on A roads – it was a challenge of mechanical and human endurance. And no matter what precautions were taken, the rain always works its way up and settles into your crotch area – 950 miles on a scooter is tough enough without that discomfort.
'It's a lot of commitment campaigning, but every point counts and they quickly mount up. In all, I've not spent huge sums of money on the scooter, but I get great enjoyment from it. For pounds invested, the return has been amazing!'
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### lambretta turismo veloce
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'I need to be able to observe the inner workings of commonplace machinery – in short, I'm mechanically minded to the core. I need to know _how_ something works. As a kid I steered away from mainstream toys, instead choosing those that involved a modicum of construction. For me, Christmas was the pinnacle of the year with bestowed gifts reverse-engineered before I saw in the New Year, such as a model steam train that initially emitted a steady stream of smoke. After my meddling, it produced choking levels of smoke. I feel I was born in the wrong era, and more in line with the pre-80s decades, when things could be repaired with just a socket set and screwdriver.
'I inherited my love for scooters from parents who've a deep affection for these masterpieces of utilitarian transport. When I was a kid I tagged along on the back of my father's Vespa P200E when he visited the local scooter shop. At 15 I was fortunate enough to obtain work experience at Gran Sport (a renowned scooter workshop), which turned into a Saturday job and then full-time employment,' explains 25-year-old Ashley, a self-employed classic vehicle mechanic from Birmingham.
'I've had this Lambretta TV175 scooter since I was 17. However, when I say "scooter", it was basically a set of leg shields peppered with 32 holes, a frame and a few ancillary items that may or may not have actually belonged to the scooter. Unfazed, I confidently set out to source the parts needed to get my scooter roadworthy. Once again Christmas worked its magic, with a timely arrival of a boxful of scooter parts – my boss's idea of a festive bonus. The end result is my black and gold race-inspired scooter with the 63 decal denoting the year of manufacture. Despite the deep sentimental and cold hard cash value my scooter holds, I built it to ride it. In my opinion, going to a rally with your scooter ratchet strapped to the inside of a van is pointless. Half the fun of going, or sometimes only partially making it, to a rally is the journey itself.
'My aim was for a subtle-looking exterior, but this scooter, as you would expect from me, is certainly tuned. It still possesses the standard TV 175 gearing, but with the addition of a reed-valved GT 186 kit, 25mm Dellorto carburettor, 12v electronic timing and an expansion pipe, which acts like a turbo on a two-stroke engine by pushing any unburned fuel into the barrel for another chance at combustion. So it has a fantastic power band, to the surprise of many – including the V8 hotrod I was once pitted against and dominated on a quarter-mile drag strip.'
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### harlow
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'My brother Jared was a couple of years older than me and very much into the whole ska and rocksteady music scene. As I idolised him, so I immersed myself in the whole subculture – including scooters. I was 20 when I purchased my first scooter, which I still own to this day and will never part with,' explains Janel, an interior designer from the Bay Area of San Francisco who holds a passion for mid-century design. She lists her priorities: 'Fashion, cocktails, lipstick, shoes and then scooters – said in jest, as scooters are what bring the club together, the club being the Secret Servix, a female-only scooter club founded in Denver, Colorado, circa 1995, established as an alternative to the male-driven, macho scooter clubs. We're like one big extended family and, as one of the founding members recently commented, "It's far cheaper than therapy!" The name is a humorous sideswipe at a male-only San Diego scooter club called the Secret Society.
'This scooter, named Harlow, is the same model my brother had when he was 16. It is a Sears Blue Badge Sprint, which is basically a rebadged Vespa 150 Sprint. It stems from the era when Sears was the go-to place for everything from socks to even a whole house. Mine is a 1966 model, the final year of a seven-year sales run. In my opinion it's the best vintage, because during the earlier years the imported scooters had pared-down specifications to increase Sears' bottom-line profits. Everything on the scooter is original to how it would have appeared in the showroom, even down to the affectionately named Mickey Mouse tail-light.
'My loving husband was a souvenir from my coast-to-coast trip across the USA aboard my Airstream motorhome. We met at a scooter rally and have been inseparable ever since. He comes down on me for wearing heels when I ride the scooter, but if I'm feeling rebellious I wear them regardless. Because, as I maintain, the higher the heel, the closer you are to God.'
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### double denim
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'Two wheels run heavily through my family, especially with my father, who was a ton-up boy. My mother topped 100mph on the back of my father's Triumph 110 – a fact they kept quiet about until recently!' explains Kelly, who with partner Scott founded the successful British clothing brand Dawson Denim. 'Dad had a Vespa to get to work and Scott's parents were mods. Therefore it's no surprise that we're both deeply passionate, some would say fanatical, about the late 50s and 60s, with all it encompasses. It even extends to the machinery that we produce our denim workwear on. To some the notion of working on machines older than both our ages combined is laughable, but it's the experience that matters to us and especially to our customers, with some able to identify the machine used by stitch pattern alone.'
Scott continues: 'Being a youth in a small town with an appreciation of old stuff was seen by many to be an embarrassment. It really wasn't a cool thing back then in the early 90s. Luckily I could easily see past what others couldn't – and it was well worth the ridicule I sometimes endured. So much that was made in the 50s and 60s is still in existence, often because it was built with pride and with longevity in mind – as opposed to the disposable generation from which I descend, which is something to be genuinely embarrassed about. I lived a very authentic 60s lifestyle for many years. At one stage, everything I owned was pre-1970...I mean everything! I purchased my first Lambretta Series 2 scooter when I was 19, having previously been into the vintage VW scene. Then followed a Vespa Sprint, Vespa GL, Lambretta LD Mk2 and now our 1959 Lambretta Li 150 Series 2. To me it's all in the design and what it signifies – a scooter being an extremely important part of post-war Europe.'
Kelly concludes: 'Many of the qualities that we relish are being lost in the wake of consumer demands for ever-cheaper products. The experience of using a 1950s sewing machine is akin to the joy we get from riding our old scooters. We've both taken tests on modern twist 'n' go scooters, but with just a push-button start you might as well be sitting on a lawnmower – zero experience. However, when you jump on a classic Lambretta or Vespa and click the gear into place, or it gets stuck, there's that element of momentary panic – as to whether you're gonna drop it into third or second! Each scooter has its own personality and quirks, all of which keeps you on your toes and enriches the experience. Cheaper and characterless modern scooters do the same job as an authentic Italian scooter, yet I guarantee at the end of the journey the latter has been undeniably more rewarding.'
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### vespa cosa 200
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'I try to avoid the clichéd preconceptions of what makes a typical scooter owner. I own and have a passion for something frowned upon by scooter snobs because of its unconventional angular design, a departure from its stablemates, and the financial stresses it put upon Piaggio during its development. Yet the more it offends, the more I love it. Many quizzical observers (I can't say admirers) ask if it's a prototype. The Cosa really is a "love it or hate it" scooter. I acknowledge the poor design judgements: a belly pan made from plastic, which shatters on sight of gravel and a glovebox rendered useless when it's occupied by the central column, deeming the remaining space useful only for storing spaghetti.
'Period accessories need not apply to my Cosa. Anything goes – the uglier, the better. My journey to the dark side of scootering was assured by adding a motorbike flyscreen that was crudely adapted for a Lambretta and then fettled to fit my Vespa! My status is underlined by being a follower of the Darkside scooter club; I applaud their progressive approach to all aspects of the scooter scene, both autos and "classic" geared scooters. My machine's current nickname is "The Nun", thanks to its forward-facing resemblance to a nun's cornette – an improvement on the previous "flying wheelie bin".
'Although I sprayed it black to cover its previous awful green incarnation, it still shows through in places like scooter acne. However, none of the problems and haters will turn me against my Cosa – I just feel sorry for it and then love it more. My route to ownership was because I needed something cheap and reliable,' explains Stuart, who studied fine art at university. His work is permanently on display at the Royal Academy – on the floor, that is. He insists a prerequisite to becoming a floor layer is to have a fine art degree.
The Cosa was the creation of designer Paolo Martin, introduced in the late 80s in an attempt to modernise the Piaggio brand and compete with the futuristic designs coming out of Japan. Seeing as Paolo was attuned to contemporary angular designs, in vogue in the 80s, he was seen as the obvious choice. Millions of lire were spent, with huge additional sums squandered on design compromises in order for the Cosa to be road-legal in Britain. The scooter flopped, with around 10,000 built, and nearly put an end to Piaggio.
'I've paid my dues by owning many classic scooters over the years, since my first Britpop-inspired Vespa at the age of 17. Now I plan to have the Cosa properly painted with a Second World War RAF shark-mouth motif – a nod to my late father, a Lancaster Bomber gunner.'
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### wally
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'My father was an original mod, who turned 16 in 1964 – the heyday of the mod era. He recounts fun-filled times, full of scooting (to him it has been and always will be Vespa), mohair suits, fantastic music and dancing – but no drugs or fighting, he assures me. I grew up listening to these anecdotes relayed by my father. At that time it wasn't of great interest to me; adolescent crazes and rap music were far more to my taste. However, as I matured I developed a distinct sense of nostalgia about my parents' lives and wanted to know more. I started off listening to the music from the era, paid more attention to his stories and even asked the odd question or two. When scooters came back into the spotlight I bought a Vespa PX, as it was manual and deemed acceptable by the scooter fraternity. My transition was complete. I know you can't influence a bygone era and I'm not trying to be something I'm not. I'm doing my own thing – to me it's about being unique and having a sense of pride. The Vespa, although great, was never my dream scooter, though,' explains Tom, a model maker, paper artist and double-cross, in his father's eyes, for owning a Lambretta.
'I caused a humorous family rift by purchasing this barn-find Italian import. He put the phone down on me when I told him I'd sold the Vespa in order to buy a Lambretta. The 1964 Li 125, named Wally after my grandfather (a Desert Rat who rode motorcycles), was a standing seizure decorated with household paint and accessorised with a thick layer of dust, feathers and snail shells.
'I set about practically rebuilding the scooter through trial and error, referencing information in books and online, but the scooter community is a huge knowledge portal – it's all about helping each other stay on the road. The whole process enables you to get to know the scooter really well, so much so that you know from the sound of the carbs if something is up. In all, I find it a great tonic for the mind – you can really lose yourself in the process.
'My father now owns a scooter again (Vespa, of course), which is most likely off the back of me. I'm sure he gets a kick from the fact that his passion is now living on through me.'
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### his and hers
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'We both approached scooter ownership from different directions: Tim developing a keen interest in Motown and northern soul via the scooter scene, and me appreciating and then owning a scooter via the same niche of music; with us ultimately meeting somewhere in the middle and being a couple ever since,' explains Amy, who egged her father on, an original mod, to once again own a scooter.
She continues: 'Dad was an instrumental figure in introducing me to the music of his youth, and with that grounding, my sense of style developed. When he got his Lambretta TV175, it made up my mind that I wanted to follow suit – a scooter was the missing link I'd been searching for and when I moved to London I decided to get one. Dad was so pleased, he insisted that we both went together to collect my 1968 Vespa Sprint so that he could teach me the basics, as I'd never ridden a scooter before. I looked around for other scooter owners and ended up at Bar Italia in Soho, London – a popular hang-out for scooter owners for many decades. I then found a like-minded group of twenty-somethings all heavily into their scooters. My scooter had its fair share of breakdowns, so often, like a damsel in distress, I'd throw my hand to my brow and seek help from within my circle of scooter friends. One knight in shining armour, who was all too eager to help, stepped forward – namely Tim. He'd then keep popping up at soul nights and with uncanny (more likely planned) accuracy our paths would cross. When I saw him on a scooter, I didn't need any more convincing.'
Tim continues: 'Amy's spot-on with her assumption that our paths crossing wasn't by chance. Amy, with her Vespa and distinct sense of style, immediately caught my eye – especially in what is a very male-dominated scene. I'd love to say I grew up with the same influences as Amy, but despite my father having been a mod and owning a scooter, I didn't. He left it all behind when he became a hippy in the 70s, before settling down and becoming a family man.
'I purchased my first scooter by way of a friend – a characterful chap who'd spend money like water. On one occasion he rocked up on a Vespa PX200 with a sidecar equipped with a 12-disc multi-changer and subwoofer! We tore around the roads of Norfolk and I loved it! I had to get some of this fun for myself. Just a few weeks later I'd bought a scooter and two weeks later I was at the Great Yarmouth Scooter Rally – with a row of scooters stretching as far as the eye could see. This 1971 Vespa 150 Super is my second scooter and I'm also proud to say that my father has overcome his fears and since bought himself a scooter.'
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### greyhound 240
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'Kids are devious and I was no exception. Aged 13 I was a wannabe mod, who was slightly on the wrong side of fully enjoying the late 70s' revival. My mum, being a nurse, vowed never to allow one of those wretched scooters under her roof. And my dad, a police officer, toed the party line and agreed with her – hypocritical of him, especially as he'd owned one in the 60s! Yet I managed to con them into letting me have a scooter by signing myself up for the Duke of Edinburgh's Award scheme, where it was conditional that you restored something old. I'd already earmarked a perfect resto project: a Lambretta Li 150 Series 2 from a neighbour. To be honest, the scooter didn't need restoring, but at least I'd got myself a scooter, which I'd ride round the garden while my parents were out,' explains Nathan, whose mischievous deed had a happy ending – he's worked for a company repairing and restoring scooters for the last 20 years.
'I got this 1968 SX150 about five years ago, but I've known of its existence for 20 years or more. It was among a friend's mighty collection of scooters. However, as much as I tried, he just wouldn't part with it. Regardless, I kept on at him. Then, with the prompt of a collapsing roof where the scooter was stored, he eventually buckled and sold it to me.
'As well as fitting a tuned and bored-out 200cc motor, I changed a lot to get the look you see now. The aim was for something a bit different from the rest, influences stemming from racing scooters of the 60s – yet appearing, by carefully added patina, as if just found forlorn in a disused workshop. Ancillotti, a 1960s racing-scooter tuner, based their logo around a jumping panther, and similarly Wildcat featured a jumping tiger – my take on the theme was a racing greyhound at full extension. I sourced greyhound emblems from vintage bicycles and one from a 1920s brooch and added them to prominent areas of the scooter. Why greyhounds? Well, I own two ex-racing greyhounds myself, so it made sense – after all, they're the fastest dogs in the world.
'I've other scooters, but this has sentimental value to me. Partly because, more than most I've restored, I've added my personality and loves to this scooter, building an imaginary image of the scooter's possible history and styling it accordingly.'
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### hotel navarra
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'My attention span is short. Not short enough to bypass hobbies, but just a need to seek out new avenues of a pastime and move with the times – and the same principle applies to my scooters. I've owned a scooter since the age of 16 and in that time I've pretty much sampled all the diversity the hobby offers. I dabbled with being mod, with an impeccably restored scooter, but it never really gelled for me. Choppers, cutdowns, scooter-boy look with my camouflage green scooter, mad-coloured stuff. However, the current ratty style that's in vogue is much more in keeping with where I am at the moment. I'm not frightened of committing to one genre. Instead, I'm not choosing to be blinkered to one thing – just keeping my options open in case I'm missing out on something better.
'A few years ago, in my characteristic style, I was getting a bit bored of my spec'd-up Vespa T5. While driving to Coventry with a co-worker, I mentioned my predicament and asked him to have a quick flick through my scooter magazine to see if, on the off-chance, anyone was looking to do a trade. There, lo and behold, was a classified for a Lambretta Series 2 Spanish import – in Coventry, no less! It was clearly a sign. I rang the number, explained I was in the area and asked if we could call round. So with that we sloped off work to check out the scooter. With nothing more than photos of my T5, a swappsy was agreed,' explains Gary, owner of this Lambretta TV175 who, instead of just doing a standard rebuild, wanted to celebrate the fact it was from Spain.
'Inspiration came from an old photograph I'd seen years earlier of a scooter outside a hotel adorned with the resort name on the side panels. I wasted no time in replicating the aged sign-written look – just in case I changed my mind. Which I'm very glad I didn't, because I'm enamoured with the end result and it attracts a lot of attention in my social network of like-minded friends.'
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### form and function
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'It started with the realisation that my money could be put to better use, because sitting in a barn for 50 weeks of the year, was umpteen thousands of pounds' worth of concourse-condition VW campervan. With the bus now someone else's pride and joy, I was able to allot money to a more usable 1959 Westfalia caravan and still have plenty set aside for a rainy day. It wasn't a case of money burning a hole in my pocket – I'd always wanted an Italian scooter and with funds now in place, I set the ball rolling. However, I took my time and diligently carried out my homework, repeatedly visiting my local scooter workshop to have a browse. Eventually I bought a 1963 Series 3 Li 125. It was much loved, as all first-time scooters surely are, but I had a penchant for a Series 2 with its slightly wider stance and rounder front,' explains Nick, a designer by trade who stresses the importance of attention to detail and being able to add your own stamp of identity.
'During a visit to the scooter workshop that I'd bought my Series 3 from, I was chatting with one of the staff who owned a stunning Series 2. He commented how he loved my Series 3 and regretted the day he'd sold his; I jokingly mentioned that maybe we should swap. This obviously resonated with him, because after a few chats that's exactly what happened. We swapped scooters and agreed to keep back a few prized accessories for our new respective scooters. No money changed hands – I even got a few extra accessories to boot.
'Form and function – where practicality meets aesthetics – is to me what defines a winning design. The scooter is cheap to run, practical and yet looks fantastic! There's something special in taking a stock scooter and giving it an identity of its own. I've added original tartan and back rack, front embellisher, granny basket, "cock of the walk" illuminated cockerel, and there's the flyscreen. Although from a Series 1 Lambretta, I think it works, but for the real purists it's a tricky dilemma – it's about personal taste and whether it's aesthetical and functional.
'When I got my first scooter an old school friend introduced me to some like-minded scooter enthusiasts, an aesthetically pleasing bunch (hey, Mr Parr) who'd informally meet on a Sunday morning for a fry-up followed by a relaxed scooter ride through the Cambridgeshire fenlands to burn off the calories (I wish). The wonderful thing about this kind of group is that you can have ten offbeat scooterists and ten completely different-looking scooters, each with their own characteristics.'
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### loggy
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'In life I'd consider myself a moderately lucky chap. I have good health; I play hard; I've good friends and I work damn hard and have obtained the modest trappings of life as a result. I've been around many scenes in my life, taking elements of each that make me who I am. However, the only scene anyone really needs to be comfy in is their own skin. I've been in the VW scene for many years, and as a result I became on first-name terms with a charismatic scouser named Brian, organiser of many VW shows throughout the UK. For many years my wife Estelle and myself would visit his place and admire and often dream about his vast collection of classic VWs and Porsches. Collectors seldom stop at their initial obsession – sure enough, Brian had a scooter. He now has in the order of 100, but that solitary scooter, a 1965 Li 150 Series 3 Lambretta, really attracted my attention and Brian found it amusing that I'd always make a beeline for it. I was captivated by its simple beauty – it was also a longstanding intention for us to own one as a project. However, sadly a shortfall of money stood between us and making it a reality – and short of winning the lottery, that's how it would probably remain,' explains Loggy, who while at a swap meet was talking with Brian about, among others things, scooters.
'At that time Brian was in the envious position of relocating to France and, unbeknown to us, as a result of his good fortune, was spreading his luck by way of random acts of kindness. I thought he was joking when, with a glint in his eyes, he said, "Shake my hand, you've got yourself a scooter." To my amazement this wasn't a joke, he was deadly serious – he'd gifted me a beautifully original-looking 1965 Li 150! I was overcome with shock and needed to sit down, it was like winning the lottery. Sure enough, a few weeks later, Brian arrived with the Lammy on a trailer. Never before had I experienced, nor am I likely to again, such generosity and luck!'
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### copper
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'Copper is the base coat before the chrome plating is added. It's basically forgoing the final process and thus a cheaper option and, based on what I've been told, was fairly commonplace in the 60s – though I've yet to find any visual evidence to back up the claim. Not that I'm worried, because often the best ideas come from a sideways look at a design from yesteryear. Therefore, at this point in time, I'm the originator and proud owner of something rather different,' explains Scott, who when looking for his first set of wheels while at college knew from the start that new would not do. Instead he chose an 80s retro-inspired 50cc Vespa.
'I was smitten with the experience of owning and riding a classic scooter. I keenly worked my way through several scooters and began hanging around with a scooter club in Brighton, resulting in my embrace of the whole ethos that surrounds scooters. In the process I learned so much about scooter mechanics from knowledgeable owners, thereby taking away the mysticism that surrounds a scooter malfunction – leaving me to just enjoy using them. With my new-found knowledge, I bought more scooters and even dabbled with buying, restoring and selling. The trouble was that I just wanted to keep the scooters, having injected so much of my personality into them – yet I had to sell in order to earn a crust. It took the meaning away from why I loved scooters, namely the enjoyment of owning and riding one. Eventually I vowed to keep it personal and not about business.
'The decision to facelift my 1965 Lambretta Li 150 Special occurred around the same time as did my obsession for copper. I'd introduced copper into accessories for my clothing label, as I adored the fact that, given time, freshly formed copper changes from a rosy pink to a russet brown colour – or even blue-green. I'd also grown weary of watching guys (and at one stage you would have found me in the same boat) chasing each other's tails to buy the same overpriced scooter accessory, in order to mimic a style someone else had previously done. So off came the 17 lights and accessories and gone was the graphite-grey paintwork, and eventually, after respraying 25 parts, came the new colour scheme of dark blue and off-white. The end result, with the copper detailing and cashmere seat, is a restrained classy look – rather than a really showy-offy "look at me" statement.'
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### hotwheels scooter club
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In 2001, released from the drudgery of work, good friends Ukkio and Corbe planned (with trepidation) a trip to Isola d'Elba for their first scooter rally. Neither owned the requisite scooter, so Corbe borrowed his father's Vespa, and with that hurdle overcome, nothing now stood in their way. Upon arrival they were exposed to the alien world of scooterists – and it fascinated them. They quickly forged friendships and a liking for the eclectic mix of northern soul, ska, reggae and garage music. Upon their return home to Siena after four days away, they excitedly explained to friends what an unforgettable experience the rally was. They vowed to return the following year and so they did, this time with their own scooters and two other friends. They soon met up with old friends and so the party began – a year on, their enthusiasm hadn't dwindled.
All too soon it was over for another year. Once back in Siena they approached several scooter clubs, but the atmosphere wasn't to their liking when compared to their Elba experiences. They sought kindred spirits who were happy to customise their vintage scooters in any way they saw fit. Eventually they found solace among the Green Onions, a progressive scooter club based in Siena. That lasted until 2006, when they founded Hotwheels Scooter Club – with their clubhouse no more than a garage.
What started as just two friends with a garage and dreams had grown to 37 members by the time the club returned to Elba in 2011. It now tops 80 members and the garage has been replaced with an ample clubhouse. Scootering is their way of life, whether it's going to work or travelling around the world participating in endurance races. Above all, it's the camaraderie and freedom a scooter offers that ultimately makes them happy.
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### roller coaster
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'I feel less is more with this scooter. TV200s were the bee's knees, the preserve of well-off London types. The badge says it all and how I've styled it is true to the look it would likely have had. I prefer the eye to be drawn to distinct areas, so the big-ticket accessories I've worked so hard to find can be fully appreciated without other paraphernalia detracting from them. I could have bought a finished TV200, probably cheaper in the long run, but certainly not as much fun because to a degree it's never truly your scooter. Sure, the logbook states your name, but the look of the scooter is the vision of someone else. Owning a TV200 wasn't on a whim – I'd always wanted one. Besides, apart from my daughter, I don't spend my money on much else. You more often than not recoup what you spend out and certain models hold their value nowadays – scooters are my weakness,' explains Lee, owner of what in its day was the top-of-the-line scooter. The Lambretta TV200 filled the gap in the 1960s British market for a more powerful racing scooter, in order to compete with the likes of the Vespa GS.
Lee continues: 'My father was an original Brighton mod, yet never owned a scooter, being too young. However, it didn't stop him witnessing first-hand mods flocking to Brighton and the troubles between them and the rockers – some of which were certainly exaggerated by the press at the time.
'Owing to my father's jukebox, I've grown up listening to Motown. Apart from, that is, a heady decade listening to acid house. Once I left the rave scene (worse for wear), I realised what I'd been missing. I saw a 1965 Li 125 Special for sale in the classifieds, the result being that I bought my first scooter. Although I'd always wanted one, the realisation of owning a scooter (let alone riding it) was daunting and for several months it remained unused until a mate pushed me into using it. And once I'd rode it down the road I've never looked back.
'After a very tough time in my life, I came close to selling my scooter, an intention thwarted only by support from my new partner and soulmate Tina. It was a real roller-coaster time. However, I've since acquired another scooter, a 1961 TV175 Series 2. The two scooters haven't met yet – not sure how I'm going to divide my attention between them, and not forgetting Tina. I could've had a hellishly busy day, but the moment I'm in the presence of my scooters the day's worries are out the window – that's my relaxing time. My father has certainly heavily influenced my life and he's chuffed to bits that I'm owning the scooters he never had the chance to.'
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### m'lord
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'Originally I hail from the king of all backwater colonies – Perth, Western Australia. With a mother obsessed with Motown and a great-uncle obsessed with Vespas, I was exposed from an early age to strong musical and style influences. On moving to London I decided to buy my first scooter, a 1979 Vespa ET3 smallframe. After spending some great times with the New Originals Scooter Club, I gravitated towards central London, and Soho in particular. I was soon welcomed by the Bar Italia Scooter Club and got hooked on their timeless style, bad jokes and laid-back attitude,' says Nick Robins, owner of this 1966 Li 150 Lambretta. Established in 1949 by the Polledri family, Soho's Bar Italia flourished in what were austere times. The late 50s saw the bar establish itself as the place to be for smartly dressed, hip-cat, scooter-riding teenagers with money in their pockets. With the blessing of the Polledris, 2002 saw the forming of the Bar Italia Scooter Club, bringing together like-minded individuals who'd regularly meet at the bar on their classic scooters. Nick is now 'El Presidente' and continues to ensure the club respects the 60s vibe as well as organising club rides around London's iconic locations and beyond.
He continues: 'Since my trusty ET3, I've been through a number of scooters: a Vespa GTR with more lights than a Christmas tree; a custom restoration Vespa VBB with a modern engine, perfect for rallies around the south-east; followed by my dream scooter – an original condition GS160 MK1 with some "tasteful" period accessories. A desire to own a rideable scooter led me to sell the GS and pursue a lovely Lambretta Series 3 Li 150 that I'd had my eye on for a few months. The Li 150 is totally reliable and – apart from a few carefully selected accessories – remains as unmolested as it was when purchased. "M'lord" is my workhorse that I can rely on in any situation – I wouldn't change it for anything.'
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Many owners featured in this book choose not to class themselves as true mods any more. Yet there's one residual factor that remains with them throughout life regardless – a sense of pride in not only their own appearance but their scooter's, too. Those that do confess to pay homage to the much-loved mod style often authenticate this through fashion and sought-after scooter accoutrements, displaying a fastidious attention to detail when replicating the appearance of a scooter from a bygone era – regardless of time, effort and money.
Scootering for many has been a key part of their life, with pivotal moments revolving around scooters. Never more so than when the film 'Quadrophenia' came out in September 1979, with the ensuing formations of kids in parkas lining the pavements. This chapter will also feature several owners who took advantage of opportunities that arose via their passion for scooters.
Yes, you'll find an abundance of lights, mirrors and chrome in the following pages – of which I'm confident there will be lovers as well as haters. There are scooters very original in appearance, hardly deviating from factory standard, as well as exemplary machines that differ from the more familiar Italian models.
However, all those featured are here due to their high levels of passion and scooter authenticity and low levels of personal arrogance – for which they should be afforded the upmost respect. To these individuals their style of scooter is the epitome of a short-lived era, which some of them didn't have the opportunity to be part of first-hand.
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### lambretta li 125
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'The late 70s were ripe for the mod revival – disillusioning, fractious times made even more so for me living in a provincial border town north of Dublin,' says Patrick. 'I, like many, bought a scooter off the back of the film 'Quadrophenia'. In those days scooters in Ireland were plentiful. A mate told me that he'd seen one of those motorised bikes "that looks like an upside-down toilet" in a garden on his estate. Sure enough, it was a 1966 Cento Starstream Lambretta. I duly bought it and it provided me with my first experience of 1960s scooter riding. My progress on the scooter ladder continued in the same vein with a GP200, a great purchase and my first proper mod scooter. One aspect that needed addressing was the tricolour circle in red, white and blue – known as the "mod target". For obvious reasons, the colour scheme needed tweaking to (at that time) a more favourable green, white and gold insignia.
'My cousin, who'd moved to London, was also a mod. It was like all my birthdays and Christmases rolled into one when a box arrived filled with his outgrown mod clothes – Sta Prest suits and more. Overnight I became the best-dressed mod in town,' explains Patrick. His degree in fashion wasn't getting him anywhere in Ireland, so he made the move to London and thus began the search for another scooter.
'I bought this '64 Li 125 from an Italian gentleman. I didn't want to be precious about it – a quick spruce-up would suffice. From Day One it's been pure enjoyment, whether on trips round Europe or the everyday commute. With lengthy ownership and steadfast service comes an emotional attachment. A restoration had always been in the back of my mind and so had iconic images of 60s street-racer scooters – typified as a scooter ridden to the track, raced, and ridden home again. And nothing capitalised on this more than the Arthur Francis S-Type, probably the most well known of all the sales-enhancing dealer specials. It was no good asking Arthur Francis, based in Watford, for a scooter that just looked fast – the performance had to match: race-tuned engine, Smiths motorcycle clock (more accurate for racing), spotlights for night racing, unique paint scheme and more. It took me and my good friend Marcus Standen well over a year to complete my homage to AF. For years I was a fully dedicated mod, accurate in every detail to the cause. But the advantage of living in a cosmopolitan city like London is that pretty much everything is accepted. However, there's only so long you can live your life aligned with six months of 1964, so I took a step out of the scene. Now I'm floating around the edge and picking the best of all worlds. But the attention to detail and perfection will always remain.'
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### 100 per cent
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'I was 14 and the whistle had just blown on a gruelling game of football. While walking back to my bicycle, wishing there was an easier way home than pedalling, I noticed my father had arrived on his Piaggio Bravo – the cousin of the top-selling Ciao moped from the 80s. He gestured towards the moped and invited me to ride it home while he rode my bicycle. Up until this point the closest I'd come to riding the moped was standing on the footboard while my father rode it. The surprises didn't finish there: once I'd reached home he presented the moped to me as a gift for my 14th birthday! At that age the freedom to ride with friends and leave my slow and boring bike at home was intoxicating,' explains Paolo Angelini, from the Lambretta Club Lucca, who was lucky to live in Italy, where you can ride a scooter from the age of 14.
'I purchased this 1962 Lambretta Li 150 three years ago from a friend who, although having painstakingly restored it, failed to utilise it. In my opinion it was a pity to let such a beautiful scooter languish unused in a garage. Even more so when it had been awarded the 'golden plate' from ASI (Automotoclub Storico Italiano) – the maximum award attributed to scooters of 100 per cent originality. My relentless expressions of verbal dismay with regard to the scooter's lack of use eventually paid off when, to my delight, Andrea (the owner) let me ride it as often as I wished. This became such a regular occurrence that I began to believe it was actually mine, and after some persuasion he agreed to sell it to me.
'What do I get from owning a Lambretta? It has to be freedom and the chance to relax. A trusty companion that without fail is ready at a moment's notice, when an opportunity arises for me to escape daily routines and thoughts of work. Freedom made all the more pleasurable while surveying the stunning vistas from the hills that surround my home town of Lucca.
'I'm in two minds when it comes to how I feel about the mass exporting of our vintage scooters. Yes, I wish more had been retained. Yet at the same time, I'm appreciative and proud of the fact that these Italian design icons have amassed such global appreciation.'
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### lambretta tv175
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'I'm every advertiser's dream. All it took was a well-conceived promotional poster for the Vespa PX – tanned Italian man accompanied by a stunning-looking girl riding pillion along the Amalfi coast – and I was ready to ditch a moped in favour of the aspirational Vespa. I was taken in hook, line and sinker. After the Vespa I knocked about on a few Lambrettas, until having a break from scooters in 1983 – after the Jam split up. When I went to see a Jam tribute band in 1994, the memories flooded back and once again everything just clicked into place, though prices had sky-rocketed in the intervening decade. Second time round, my aim was to be more authentic and pay closer attention to the small details that matter, especially the clothing – Bass Weejuns loafers, Levi vintage and Fred Perry. As for the scooter, well, it had to be Italian-registered and adorned with the correct period accessories.
'The fact I own this scooter is a stroke of luck. Around 12 years ago I'd just parted with my Lambretta Li 125 and was £1300 richer. My wife, in her mind, had spent the money several times over. However, she had to forgo the city break and shopping trip when I saw a classified for a TV175 being sold for the princely sum of £2200,' explains Simon, salesman for British menswear brand Gibson and owner of this 1964 Lambretta TV175, one of the ultimate mod scooters. He continues: 'I'd always wanted one – in the 60s all the "faces" (the top mods and fashionistas) wanted a TV175. However, me becoming a modern-day face looked like it would remain a dream, as I fell a long way short of the money required. But nothing ventured, nothing gained, so I phoned the seller, expressed my interest and delivered my cheeky offer of £1500. My opening salvo was rejected, but I still left my number just in case he didn't sell it. Eventually it was mine for £1700. I'd bagged myself a bargain, so I hot-footed it down to Bognor Regis and returned with my prize possession.
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### triumph tigress 175
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'I don't often admit defeat, but I met my match in a Triumph Tigress. While many were getting rid of their scooters, I was buying them, doing them up and selling them on – a nice little earner for a 17-year-old. When I acquired the Tigress, I was instantly captivated by its design. Despite its streamlined space-age looks, it never got further than my driveway. The more I fought to get it running, the more it retaliated. I finally surrendered and got shot of it.
'Years later, it was time to own a scooter again. This was 2004 and a Lambretta was just too expensive. I remembered the Triumph Tigress and the small matter of unfinished business. It took over a year to find the one I wanted; it was being sold by a couple of Merseyside scallies. I offered a fair cash price, which they rejected. So I entered my maximum £1000 bid, confident I'd win, because who in their right mind would pay that for a Triumph when a Lambretta was only slightly more?' explains Bob, who was gutted when the machine – the creation of British motorcycle designer Edward Turner, and more expensive in its day than an equivalent Lambretta – went for £1200! He continues: 'Several months later it reappeared for sale by the chap who'd outbid me. I was curious and, since I hadn't found anything else, I arranged to go and take a look. Either he subsequently had second thoughts or he knew what a lemon it was. Being a true gent, he agreed to sell it for the £1000 I'd originally bid. But now the Tigress came with history he'd dug up. He had tracked down the original lady owner from 1959, who had used it for a year before having a minor accident, which put her off riding it again – at which point the odometer registered just 1300 miles, and there it remained until 2004. Considering the length of time it had stood unused, the condition is remarkable.
'Second time round I was wiser, but, as with my first Tigress, this was not going to be an easy scooter to tame. One problem is that it's so over-engineered. You have to question the judgement of an engineer who not only designs a side panel to be secured with nine bolts, but three different-sized bolts – which each required me to purchase a new spanner because in their infinite wisdom they'd used Whitworth bolts, a thread invented in the 1840s and now hardly used! I remained resolute that I would get it going, and ultimately I did. Now it's running so well – it's a joy to ride, being that it's so well balanced, picks up quite a pace and is so beautiful to look at.'
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### patience
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'They say good things come to those that wait, but I had to wait until my forties before I got my first scooter. By the time I'd amassed what I thought was enough money to buy a scooter, in the late 70s, the prices – fuelled by the mod revival – had increased beyond my reach. The only option was to bide my time until the opportune moment, when the kids had grown up and life's expenses were taken care of. Only then could I indulge myself in the purchase of a scooter,' explains Jeff, born and raised in Bethnal Green, London. Jeff credits his appreciation for 60s culture and scooters to his older siblings, in particular his Lambretta-owning brother who knew Marc Bolan; they were already filling Jeff's mind with the sights, sounds and smells of scooters during the mod era.
'When the wait was over, I knew exactly what I was looking for: a 1963 Li 150 Series 3, with what to me has the most stylish lines of any scooter. The Li wasn't known for its reliability, but as the saying goes, "We'd rather push our Lambretta than own a Vespa." When I found my beloved Li Series 3, it was far from ready-to-use. The £750 Italian import was as rusty as a nail. Many months and several thousands of pounds later, it was restored to all its glory, the only additions being a 200cc GP engine and a modest assortment of lights and chrome – achieving a pared-down "middle of the road" look.
'Since completing the restoration I've been lucky enough to appear, along with my scooter and several hundred other scooterists, as a 'background artist' – posh word for "extra" – in the 2010 film 'Brighton Rock'. Yet the pinnacle for me has to be the part I played in the closing ceremony for the London 2012 Olympics. A colossal amount of rehearsal went into memorising the routine, learning to maintain the right pace in order to intersect the Union Jack just a split second before another group of scooter riders did the same – all while a dancer was jiggling around on the back of my scooter. With our engines running, we waited patiently for the command "Go" to come through on our earpieces. I took my position in the lead group of scooters and rode out into a stadium of sound and light, while the Kaiser Chiefs belted out the song "Pinball Wizard". To take your scooter out in front of a world audience of billions is a once-in-a-lifetime experience – it still gives me goosebumps now just thinking about it. So yes, it was worth the wait and good things have indeed come my way.'
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### goggo roller
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A slump in the need for certain types of agricultural machinery in the late 1940s saw Bavarian company Hans Glas GmbH re-orient into a new thriving business sector – scooters. The prototypes for the Goggo scooter emerged in early 1951 and later that year, in new production facilities at their factory in Dingolfing, scooters began to roll off the assembly line. In the following five years of production, more than 46,000 iconic and curvaceous Goggo scooters were built, before the factory set its sights on microcars and the equally iconic Goggomobil. Despite the high build quality and sizeable production run, few remain. Beyond Germany, the Goggo never really commanded the kudos of its Italian cousins, which makes this recently restored 1955 example, by Mark Battye, a very rare scooter indeed.
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### r. agius scooters
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'My father, Richard, was French, but he was brought over to England during the war by the British Army Intelligence Corps because he was fluent in five languages. After the war, my father's business (selling bicycles) blossomed and he soon spotted a further opportunity to expand with Vespa scooters. Piaggio weren't exporting and Douglas Motorcycles (Bristol) was licensed to start making Vespa scooters for the UK market. In 1951 R. Agius Scooters Ltd became one of the first authorised dealers and we're now the longest established Piaggio Vespa dealers in the UK – looking after the scooter needs of second- and even third-generation owners,' explains Claude Agius. 'My shop duties as tea-maker and sweeper-upper started when I was ten. Apart from a brief stint as an office clerk and a course at Saint Martin's School of Art, Fashion and Design, I've been working at the shop ever since. During the mid-60s the shop was a popular hang-out for mods, myself included. I got this Vespa GS160 in 1963, when it was just a year old.
'My Vespa was an instrumental factor in the courting of and eventual marriage to my lovely wife Barbara. My scooter is still adorned with furry tiger-print seat cover and accoutrements I had all those years ago. Not forgetting the Spirit of Ecstasy bonnet ornament from a Rolls-Royce – which, I hasten to add, wasn't stolen by myself; just unbolted from a scooter that came in as part exchange!'
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### precious
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'All it took was emerging bleary-eyed into the daylight, after a northern soul all-nighter, to see rows of meticulously parked gleaming scooters like soldiers on duty. There and then I knew I wanted to be part of the scooter scene. I was 15; it was the first time I'd been involved in some sort of radical youth movement and it felt good. A year later I was 16 so it was time for my first scooter – a trusty Vespa 50 Special, a scooter on which many have earned their stripes. Armed with increased riding confidence, I bought a 90cc conversion kit – resulting in a seized engine and me vaulting the handlebars into a ditch,' confesses Simon Thompson, who in later years managed to combine his love of scooters and other passions, 50s Americana and 40s USAF.
'I continued undeterred with life, loves, one thing and another, and then meeting my wonderful wife Tina. After many years together, she was getting weary of looking at countless scooters in my quest to find a Vespa GS. In a bid to bring the ordeal to an end, she bought me a 1958 GS150 VS4. Then began its transformation into this Cadillac-esque scooter, with flamboyant colour scheme and paint style matching that of a late-50s Baldet of Northampton Arc en Ciel special.'
Baldet (MotoBaldet) was a Northampton scooter dealership owned by Andre Baldet, a salesman and showman unmatched among his rivals and renowned for his unorthodox marketing. Dispensing with traditional techniques, he embarked on a 3620-mile 10-day tour of Europe aboard his Vespa and then completed 3775 miles of the Isle of Man mountain circuit in under 100 hours. Gratifyingly, and surely to the relief of Andre, the stunts had the desired effect in boosting sales figures.
'Only those with a scooter will understand the process involved in getting that yearned-for accessory. It's hard enough finding parts that are 50 years old, but if you're lucky enough to find the part, then the real fun and games begin. Convincing the owner to part with it is seldom easy, especially if they're anything like me. Basically, we're a bunch of collectomaniacs!
'My GS is shockingly unreliable – hence its name Precious. If it didn't look so damn good, I would've ditched it long ago. I put up with it because after 18 years you can't help but love it. I was feeling brave and decided to take Precious over to the Isle of Wight scooter rally. En route, while going through a tunnel, I switched on the lights, only for the engine to cut out, a problem quickly resolved by switching _off_ the lights. I always carry a selection of spare parts, as you never know what you'll need – with the most important being the AA card.
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### zündapp bella
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'In a blast of nostalgia my father bought an Austrian 1950s Puch Alpine scooter. He impressed on me that, in the post-war era, everyone and his dog had a go at making a scooter. I scoured the classifieds to see what was available that didn't originate from behind the gates of Piaggio or Innocenti. However, whatever I found, I kept obsessing over a Zündapp Bella,' explains Marc, owner of this 1953 R150 Series 2.
As with many German companies after the Second World War, Zündapp transitioned into the manufacture of alternative machines. They ceased production of their bulky motorcycles and focused resources into the development of several prototype scooters, tapping into the scooter craze sweeping through Italy. Despite fewer curves, when compared to a Lambretta or Vespa of the era, the whimsically named Zündapp Bella still attracted acclaim for its elegant design when unveiled at the 1953 Frankfurt Show. Initially it was sold with a two-stroke 146cc engine (later 198cc), 12-inch wheels and an undamped telescopic fork. Its large front wheel arch and petite rear end, on a tubular frame more similar to that of a Norton motorcycle than a scooter, gave it an attractive stance. The Bella scooter was manufactured between 1953 and 1964 and approximately 130,000 were sold.
Marc continues: 'It started with one, as most collections do, but currently I've six Bellas – with good reason, though. Parts are rare, so you inevitably end up buying whole scooters for parts to replenish the spares cupboard. This R150, the prize of my collection, was bought from a German collector of all things Zündapp – everything from lawnmowers to sewing machines were stored in his basement.
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### eel and pie rideout
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From the regular scooterist haunt of the Noted Eel and Pie House, this line-up of scooters gathered. Depending on the occasion, either many dozens or just a handful will meet and discuss their scooters before devouring portions of pie, mash and liquor – a firm favourite for many of the scooter owners whose roots are in the East End. Once these have been digested the owners embark on a rideout from the streets of Leytonstone to a location of their choosing. On this occasion, with special permission, it was to be London's Olympic Park, a location where one featured scooter owner had appeared when involved in the 2012 Olympic Games closing ceremony (see here).
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### pretty green
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'In 1978 £300 was an amount not to be sniffed at, yet it did mean saying goodbye to my beloved scooter for three months. I've had a scooter since 1972 – way before I was old enough to legally ride it on the road. On private land I was guilty of destroying many Lambrettas, by scrambling on terrain even motocross riders would think twice about. When one failed I simply went out and bought another for a fiver – game on again! When I turned 16 (in 1974) it was time to spend a little more wisely, so I bought a Lambretta SX150 for £95.
'The £300 all started when a few hundred of us gathered at a scooter rally in Southend. A chap, looking very out of place, rolled up and explained that he was making a film. We all thought he was spinning a yarn. He explained that those interested in appearing in the film, as extras and having their scooters hired, should meet up the following week at our local pub. We still didn't believe him, but curiosity got the better of us, so we went along. Much to our surprise he turned up, explained a little more about the film and started issuing cheques to those being hired, including me. We knew it involved the 'Quadrophenia' album by the Who, but that was all,' explains Robin, who didn't earn the nickname 'Yob' without having been through a few scrapes.
Through no real fault of his own, trouble had followed him around and the public's perception of scooter owners was becoming negative, resulting in many of his fellow scooter friends falling by the wayside – but he remained undeterred. In 1976 he founded the Modrapheniacs Scooter Club – quickly becoming a support group, if you like, for fellow scooter-obsessed individuals.
'When filming commenced, I was mainly an extra in the background. Comically, some of the fight scenes featured extras who'd no prior acting experience, so when the director called "Action!" some of the brawling got rather overzealous, with the occasional swinging fist making face contact, inadvertently adding to the realism. During some scenes I was instructed to run alongside superstar Sting so any stray punches would strike me first – as I was deemed replaceable. It was a great experience and a case of being in the right place at the right time.
'The scooter gave me a chance to travel with friends to the mythical scooter scene up north where it was vibrant and delectable. A disorganised bunch of kids taking numerous wrong turns, resulting in journey times quadrupling! But the camaraderie was infectious and I wouldn't swap those times for anything. In 1978 I was given a wreck of a 1972 Spanish Lambretta Jet 200. I'd already accumulated a garage full of scooter parts and accessories, so by 1980 "Pretty Green", with its bright VW Beetle paint colour was born – no mistaking me around town! It may not be the most valuable scooter, but to me it's irreplaceable – with every facet of the scooter handled by me in the 36 years we've been together.'
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### lambretta sx225
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'It was before my time, but family recollections of scooter adventures in the 60s probably inspired me to follow suit. My father owned a Lambretta TV200 scooter and sidecar. He, Mother and my elder brother would ride it on trips between Southampton and Blandford. Owing to my mother's embarrassment at being seen in the sidecar, my brother was designated this space. However, he didn't provide the requisite ballast, so my father added strategically placed breeze blocks in order to stop it tipping over,' explains David, a designer from the south coast town of Hastings, who's flying the flag for 10-inch wheels with an unparalleled attention to detail.
'After the failure of my friend's attempt to get his Lambretta SX150 working (by washing the carburettor with hot water and washing up liquid), it was pretty easy to pry it away from his clean but unknowledgeable hands. Once it was in my more mechanically adept hands, I stripped it down, fixed the issues in the correct manner, rebuilt it and resprayed it black and ivory with rattle cans. My allegiance to scootering was now well and truly affirmed.
'One of my early dalliances with scooter culture was inspired by the style of an Italian youth culture called the _Paninaro_ , Italian slang in the 80s for young men known for their fashionable clothes, Timberland boots and fondness for large _panini_ sandwiches. Being young Italian kids, it's a safe bet scooters played a major part. A _panini_ at that time, on the streets of Southampton, would have been met with blank faces, so with indomitable spirit I made do with fish and chips!
'I'm passionate about the historical aspects of scooter racing. I love poring over reference books and period photos, observing scooter details in their minutiae. My current scooter was purchased 10 years ago. Originally it was a fairly nondescript Li 125 Special in duck-egg blue and pistachio, before I decided to S-Type it. I then decided to Supertune it and, with the help of Ron Moss, stripped and rebuilt it, adding considered elements in a methodical way to its striking black and white Supertune colour scheme. I drive myself crazy with the details, making sure everything is aligned millimetre perfect, specially commissioned replica badges with customised typefaces – details which to many would go unnoticed, but to me they'd be glaring.
'At present I have a foot in both the scooter and motorcycle camps, each offering me something different. The essence harboured by both, apart from two wheels, is the freedom: liberty and control of your own destiny and destination.'
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### waterloo sunset
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'I owned a Lambretta back in the early 70s, missing the height of the mod era. Despite cherishing it, scooters were unfashionable by then and rarely seen on the road. Those who could afford it upgraded to a car and a running scooter could be snapped up for ten pounds. To this day I wish I could recall what I did with my Lambretta. We moved house and one explanation is that I left it behind for the new owner to dispose of. It's now a sought-after model,' explains John, owner of this mod-inspired scooter, who discovered that the smell of two-stroke had never left him.
'Wife, children, then grandchildren ensued and in what seemed like no time at all it was the August bank holiday weekend, 1989, on the Isle of Wight. The family were settling down for a day on the beach, when we were surrounded by scooters, like a swarm of bees. My wife asked if we should move. I replied with a casual, "No, we'll be just fine here." I then spent the rest of the day browsing the fantastic line-up. It blew me away just how alive the scooter scene still was. By that October I'd bought a scooter and I've never looked back.
'I bought this 1961 TV175 in 2007 without my wife's knowledge. It wasn't that she didn't want me to own a scooter – owning two was the problem. It was delivered by courier and I just managed to hide it with moments to spare before my wife arrived home; it was my guilty secret.
'Project Waterloo Sunset was already in place. Aided by several iconic photos from the 60s, which served as my benchmark, I spent two years putting it together. I couldn't obtain all the parts at once; it involved months of research to locate rare accessories from around the globe. Then I had to wait patiently until parts were sourced in the order they needed to be added. My securely bolted-on "smiley" flyscreen is as rare as hen's teeth. Often they'd just fly off and were never recovered – or were crushed by the following vehicle.
'For many it's assumed that a scooter laden with lights and mirrors is synonymous with and was prolific through the mod era. In reality the era was short-lived and mod trends changed overnight. At the time the sin was being the same as everyone else. So a bloke would turn up on his scooter with 20 mirrors, which everyone would then emulate. Next it was 20 lights and aerials, then as quick as it first happened it reverted back to lesser-dressed scooters – it was as quick as that. I get some flak from scooterists who trek the length of Britain. "Chrome doesn't get you home," and similar comments are bantered around. Yet, unlike some, I ride this scooter. Yes, I cherish it, but it's to be ridden – otherwise what's the point in owning it?
'I had to confess to the wife when the scooter featured in a magazine. To my relief, the beauty of the scooter diminished her anger and I was forgiven. She often enquires what it cost to build. I've honestly never totted up the cost myself and nor do I want to! The saying is, "If I die today, tell my wife not to sell the scooter for the price I told her I'd paid for it!"'
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### clacton
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In March 1964, two groups, the mods and rockers, descended on the seaside town of Clacton, Essex. It was more than chance that both groups chose that particular weekend; it was the culmination of tensions that erupted in a headline-grabbing, deckchair-wielding riot. The thousands of scooters in attendance in 2014 pledged to mark the 50th anniversary rather than celebrate it.
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### iwl pitty
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In 1936, just south of Berlin, Industriewerke Ludwigsfelde (IWL) was formed by Daimler-Benz to construct aircraft engines. Being of military purpose, the factory was heavily bombed during the Second World War and by 1950 IWL was little more than damaged and empty assembly halls.
After the war various manufacturers diversified, many choosing to build scooters. East Germany was no different and was also struggling to keep up with a growing demand in the early 50s for cheap mass transport. The East German government, after earlier commandeering the factory, ceased production of agricultural machinery so IWL could develop a range of scooters – this 1955 Pitty being one of them. As well as mimicking the design of the West German Goggo Roller, IWL adopted the practice of mounting the engine in front of the rear wheel – resulting in a long wheelbase and somewhat awkward handling. With a hand clutch and foot gear-change, what lay beneath the scooter's exterior had more in common with a motorcycle. A 5hp, 123cc, two-stroke engine seldom achieved the advertised 70kph. Regardless, the Pitty was deemed a good cruiser, and 11,293 scooters were built before production ceased in 1956.
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### lui
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'In the late 80s, I travelled from the Midlands to London on my Lambretta, in search of work. I had one specific goal in mind – to join a ballet company – and the scooter was indispensable when I had to hot-foot it across London to auditions at short notice. I'd grown up through the era when northern soul became more up-tempo – the dancing was intense! Guys, having worked hard all week, would go out at the weekend with the sole intention to dance – for me the spins, flips and backdrops came somewhat easier. So it was never an issue being a wannabe ballet dancer; if anything, my moves were treated with green-eyed envy. Scooters came into my life long before my aptitude for dancing and ballet was honed. I must have been 12 when I got my scooter and since then I've primarily stuck with Lambrettas,' explains Patrick, who in his heyday was a principal dancer with the Vienna Festival Ballet, including 97 Swan Lake performances in an almost continuous run. But after 10 years of touring, the wear and tear was taking its toll on his body, and it was time to take a step back and focus on his other passion – scooters.
'Scooter mechanics and restoration seemed a logical decision; especially when, in the late 90s, no one was really taking on such projects. I was active in the scooter scene while dancing and I'd built a reputation for knowing a thing or two about the fine art of scooter mechanics. When I'd return from tour, after three- to six-month stints, people would be on my doorstep asking me to fix their scooters – so a ready supply of customers was in place. It wasn't long before I established the Scooter Surgery.
'The somewhat forgotten Lambretta Lui came into my life 15 years ago. Although visually, with its delicate looks, it ticked all the boxes, its performance was woefully inadequate. Seeing that I was the UK agent for Casa Lambretta, I installed their upgrade kit, which boosted its 50cc to 75cc like its big brother the Vega. It immediately transformed the scooter into a really suitable commuter ride. It's a proper city scooter: thin enough to get through tight spaces and, being as light as a feather, it turns on a sixpence. It's true to say that good design can stand the test of time, when nearly 50 years on it could be mistaken for a modern scooter. It's my unsung hero of the Lambretta fleet.' Patrick has a point. It was conceived by the Bertone design house as the race was on to reach the moon, and the space-age era was certainly reflected in the radical forward-thinking design. The tubular-steel front section and the rear frame formed with monocoque steel give an appearance mimicking that of the early 'D' types. However, timing is critical with any new product, and when the Lui launched scooter sales were already on the decline. Production ceased after just two years, in 1969.
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### moto rumi
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As has been illustrated throughout this book, many marques had previous experience manufacturing products other than scooters – never more so than with the Italian Moto Rumi company which specialised in cast components for textile machinery prior to the Second World War. With the onset of war they turned their hand to armaments, miniature submarines and torpedoes. Then in 1950, on the back of the European demand, they developed and began the manufacture of lightweight motorcycles – the Formichino scooter, the 'Little Ant'. The scooter's form was meticulously sculpted in clay before being cast in aluminium by artist and sculptor Donnino Rumi, the son of the company founder. With a horizontal, two-cylinder, two-stroke 125cc engine, it was, at the time, reputed to be the fastest scooter in production, with a top speed of 50mph, which might not sound a lot today, but combined with its noise and size made for a thrilling experience.
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### the heirloom
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'I couldn't have been more excited when, shortly after my 14th birthday, my father led me out to a rickety outbuilding and gifted me his old rusty and dusty 1964 Vespa 50cc. I wasted no time in dragging the scooter free and soon set about the lengthy restoration. The Vespa served me well for many years, during which time I gleaned great practical experience for my future scooter escapades,' says Omar Betti.
'My current Lambretta originally belonged to my grandfather. Over the years it has been passed down as a family heirloom, first to my father and then to myself. In his day my grandfather used the Lambretta during his hunting trips in the countryside that surrounded his home in Porcari. With his dog, rifle and provisions in the sidecar, he'd head out into the countryside and return late in the day as the sun hung low in the sky, the sidecar brimming with dead birds and a very weary dog. Nowadays I'm pleased to say it carries a more precious cargo – my girlfriend Valentina,' explains Omar, long-standing member of the Lambretta Club Lucca and owner of this 1963 Li 125 Series 2 scooter and Longhi sidecar.
'At the end of my first lengthy ride in it, my arms were in physical torment! I'd somewhat underestimated the additional effort required when cornering with a sidecar. Nonetheless, I love the scooter with a passion and feel privileged for it to be entrusted to my care – until one day I too pass it down to the next generation. The rewards from owning such a beautiful scooter are immense. As well as the lively social scene that surrounds vintage scooters in Italy, it also gives Valentina and I the chance to unwind and take time out for ourselves at a somewhat sedate pace.'
## sourcebook
**owners clubs**
**Bond Owners Club**
www.bondownersclub.co.uk
**British Motor Scooters**
www.britishscooters.com
**Darkside Scooter Club**
www.darkside-sc.net
**Heinkel**
www.heinkel-trojan-club.co.uk
**Hotwheels Scooter Club Siena**
www.hotwheelsclub.it
**Lambretta Club of Great Britain**
www.ilambretta.co.uk
**Lambretta Club Italy**
www.lambrettaclubitalia.it
**Lambretta Club Lucca**
www.lambrettaclublucca.it
**Lambretta Club USA**
www.lambretta.org
**Moto Rumi Club**
www.motorumiclub.co.uk
**NSU**
www.nsuoc.co.uk
**Triumph Scooters**
www.triumphscooters.co.uk
**Vespa Club of Britain**
www.vespaclubofbritain.co.uk
**Vespa Club Italy**
www.vespaclubditalia.it
**Vespa Club USA**
www.vespaclubusa.com
**Veteran Vespa Club**
www.veteranvespaclub.com
**Vintage Motor Scooter Club**
www.vmsc.co.uk
**Zundapp Bella Enthusiast Club**
www.zundappbella.co.uk
**clothing and apparel**
**Belstaff**
www.belstaff.co.uk
**Ben Sherman**
www.bensherman.com
**Biltwell Inc.**
www.biltwellinc.com
**Bolt London**
www.boltlondon.com
**Dawson Denim**
www.dawsondenim.com
**Fred Perry**
www.fredperry.com
**Gibson London**
www.gibsonlondon.com
**Holden**
www.holden.co.uk
**Maple Moto**
www.maplemoto.com
**Scott Fraser Collection**
www.scottfrasercollection.com
**reference and inspiration**
**Bar Italia Soho**
www.baritaliasoho.co.uk
**Classic Scooterist**
www.scooteristscene.com
**New Untouchables**
www.newuntouchables.com
**Pageant Paintwork**
www.pageantpaintwork.com
**Scooter Geek**
www.scootergeek.co.uk
**Scootering**
www.scootering.com
**The Distinguished Gentleman's Ride**
www.gentlemansride.com
**scooter sales, restoration, service and parts**
**A.F. Rayspeed**
www.afrayspeed.co.uk
**Agius Scooter**
www.agiusscooters.com
**Allstyles Scooters**
www.allstyles-scooters.com
**Cambridge Lambretta Workshops**
www.lambretta.co.uk
**Casa Lambretta**
www.casalambretta.it
**Gran Sport Scooters**
www.gransportscooters.com
**Jahspeed Scooters**
www.jahspeedscooters.com
**Medway Scooters**
www.medwayscootersltd.moonfruit.com
**Retrospective Scooters**
www.retrospectivescooters.com
**Rimini Lambretta Centre**
www.riminilambrettacentre.com
**San Francisco Scooter Centre**
www.sfscootercentre.com
**Scooter Emporium**
www.scooteremporium.com
**Scooter Moda**
www.scootermoda.com
**Scooter Restorations**
www.scooterrestorations.com
**Scooter Surgery**
www.scootersurgery.co.uk
**Scooter Trader**
www.scootertrader.com
**Scooter Works**
www.scooterworks-uk.com
**Scooters Originali**
www.scootersoriginali.com
**Scootopia (Casa Lambretta UK)**
www.scootopia.co.uk
**Soul Scooter**
www.soulscooter.com
**Supertune**
www.supertune.co
**Vintage Scooter Service**
www.vintagescooter.com
**museums**
**Lambretta Museum**
www.lambrettamuseum.com
**The Piaggio Museum**
www.museopiaggio.it
#
## credits
**All photography by Lyndon McNeil unless otherwise stated.www.lyndonmcneil.com**
**cherished**
Pages 12–13 | Vespa 90, Adam Gillam and Louise Howlett, London
---|---
Pages 14–16 | Mother's, Guy Joseph, London
Pages 17–19 | Silver, Simon Flint, Cambridgeshire
Pages 20–21 | Lambretta Grand Prix, Guy Busfield, Cambridgeshire
Pages 22–23 | Heinkel Tourist, Graham Fisher, Cambridgeshire
Pages 24–26 | The unknown Vespa, Warren Jopson, Essex
Pages 27–29 | Bond P3, Shaun Ackroyd, Preston
Pages 30–33 | NSU Prima, Johnny McLaughlin, Manchester
Pages 34–36 | Ednetta, Renzo Mejia, London
Pages 37–39 | Honda Spacy, Robin Spalding, Surrey
Pages 40–41 | Il mio amore, Giuliano Casali, Lucca, Italy
Pages 42–43 | Lambretta Li 150, Pieter Hak, Essex
Pages 44–45 | Lambretta 150D, Alberto Della Maggiore, Lucca, Italy
Pages 46–48 | Start me up, Mark and Vicki Swinge, Essex
Pages 49–51 | Lilly, Richard Holian, Warwickshire
**new originals**
Pages 52–53 | Lucy in the sky, Fay Presto, London
---|---
Pages 56–58 | Unknown pleasures, Andrew Almond, London
Page 59 | The In-Crowd Scooter Club, Cambridgeshire
Pages 60–61 | London Fields Rideout
Pages 62–64 | Broomstick, Cath Birch, London
Pages 65–67 | Reincarnation, Matthew Thompson, London
Pages 68–69 | The Rabbit, Niall McCart, London
Pages 70–72 | Warhorse, Tornado Trev, Dorset
Pages 73–75 | Lambretta turismo veloce, Ashley Phipps, Birmingham
Pages 76–77 | Harlow, Janel Holiday Huff, San Francisco, CA, USA (Photography by Chris Haddon)
Pages 78–79 | Double Denim, Kelly and Scott Dawson, East Sussex
Pages 80–81 | Vespa Cosa 200, Stuart Hanny, London
Pages 82–84 | Wally, Tom Ashton-Booth, London
Pages 85–87 | His and hers, Tim Fielding and Amy Ireland, London
Pages 88–90 | Greyhound 240, Nathan Warriner, West Midlands
Pages 91–93 | Hotel Navarra, Gary Brown, Essex
Pages 94–96 | Form and function, Nick Welsh, Cambridgeshire
Pages 97–99 | Loggy, Loggy Bilson-Booker, Bedfordshire
Pages 100–102 | Copper, Scott Fraser Simpson, London
Pages 103–105 | Hotwheels Scooter Club, Siena
Pages 106–109 | Roller coaster, Lee Maxey, West Sussex
Pages 110–111 | M'lord, Nick Robins, London
**authentic**
Pages 114–116 | Lambretta Li 125, Patrick Lee, London
---|---
Pages 117–119 | 100 per cent, Paolo Angelini, Lucca, Italy
Pages 120–121 | Lambretta TV175, Simon Parr, Cambridgeshire
Pages 122–123 | Triumph Tigress 175, Bob Morris, London
Pages 124–125 | Patience, Jeff Fairman, Essex
Pages 126–127 | Goggo Roller, Mark Battye, Hampshire
Page 128 | R. Agius Scooters, Claude Agius, London
Pages 129–131 | Precious, Simon Thompson, Cambridgeshire
Pages 132–133 | Zündapp Bella, Marc Spurrell, Essex
Pages 134–135 | Eel and pie rideout
Pages 136–138 | Pretty Green, Robin Williams, Dorset
Pages 139–141 | Lambretta SX225, David Hardy, East Sussex
Pages 142–145 | Waterloo Sunset, John Hill, Essex
Page 149 | IWL Pitty, Marc Spurrell, Essex
Pages 150–151 | Lui, Patrick Hood, London
Pages 152–153 | Moto Rumi, Graham Fisher, Cambridgeshire
Pages 154–155 | The heirloom, Omar Betti, Lucca, Italy
**Additional captions:page 1 unknown pleasures; pages 2–3 lambretta sx225; page 4 waterloo sunset; page 6 roller coaster; page 9 clacton; page 10 silver; page 54 vespa cosa 200; page 112 100 per cent; page 159 (top) ednetta; (centre) hotel navarra (below) clacton; page 160 nsu prima**
## acknowledgements
I feel proud at having been part of the original team for the 'my cool' series, which continues to grow. _My cool scooter_ is the sixth title in which I have been involved and I would like to thank those who continue to support the series by purchasing the books and spreading the word about your enjoyment of them.
One of the tasks I enjoy most, after the research and photography is done and having sent the material off to the publishers, is to think back over the last few months of work and give praise to all those who have assisted in the production of the book. As before I would like to thank Pavilion Books and to single out special thanks to my commissioning editor Fiona Holman. I'd like to acknowledge my appreciation to Nick Welsh, Ashley Phipps, Andrew Almond, Paolo Angelini, Stuart Hannay and Sarah Bradley – your help was invaluable and I'm truly grateful.
A big thank you, also, to all the scooter owners who are featured in the book. You all went to such great lengths in order for us to realize _my cool scooter_ – as with the previous books, Lyndon and I have met some wonderful people along the way.
I would like to dedicate this book to Maureen Hunt, my wonderful (yes, wonderful) mother-in-law. Not only does she tolerate my harebrained ideas and eclectic vehicular purchases, but she has also been of huge assistance to me with this and previous book titles.
I hope you enjoy this book as much as Lyndon and I enjoyed bringing it before you.
**chris haddon**
Chris Haddon is a designer with more than 20 years' experience. He has a huge passion for all things retro and vintage. Among his collection is a converted 1960s Airstream, which he uses as the studio for his design agency.
**lyndon mcneil**
Even during his school years, a camera was never far from Lyndon McNeil's reach. Since then he has found a photographic niche for all things wheeled and his work has graced the pages of the world's top motoring magazines. His keen eye for the perfect picture has been a true asset to the 'my cool' series.
First published as Hardback and eBook in the United Kingdom in 2015 by Pavilion
1 Gower Street
London WC1E 6HD
Copyright © 2015 Pavilion Books Company Ltd
Text copyright © 2015 Chris Haddon
Editorial director Fiona Holman
Photography by Lyndon McNeil
Styling by Chris Haddon
Editor Ian Allen
eISBN 978-1-910904-02-2
All rights reserved. No part of this book may be copied, displayed, extracted, reproduced, utilised, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical or otherwise, including but not limited to photocopying, recording or scanning without the prior written permission of the publishers.
This book can be ordered direct from the publisher at
www.pavilionbooks.com
|
{
"redpajama_set_name": "RedPajamaBook"
}
| 8,664
|
\section{Introduction}
In a recent communication \cite{kkp5}, we have reported the results of pseudoscalar decay constants of heavy-light mesons in a QCD potential model with linear part of the potential as perturbation. The technique used was the quantum mechanical perturbation theory with plausible relativistic correction.
\\
In this paper, we extend the QCD Potential Model with its input parameters towards the semeleptonic decays to study the Isgur-Wise function. Exclusive semileptonic decays of hadrons containing a bottom quark provide a path to measure the Cabibbo-Kobayashi-Maskawa(CKM) matrix elements $V_{cb}$,an important parameter to test the Standard Model. It is well-known in the literature that in case of heavy to heavy transitions like $b\rightarrow c$ decays, all heavy quark bilinear current matrix elements are described in terms of only one form factor, which is called the Isgur-Wise(IW) function in leading order. The IW function, particularly its slope ($\xi^{\prime}(1)$)at the zero recoil point is important since it allows a model independent way to determine the CKM element $|V_{cb}|$ for the semileptonic decay of $\left(B^{0}\rightarrow{D^{*}l\nu}\right)$ and $\left(B^{0}\rightarrow{Dl\nu}\right)$. This method of obtaining the CKM element within the framework of Heavy Quark Effective Theory (HQET) was proposed by Neubert\cite{neubert1}. He observed that the zero recoil point is suitable for the extraction of CKM element $|V_{cb}|$. The method basically relies on the existence of one universal form factor(Isgur-Wise function) and the fact that the form factor is unaffected from $1/m_{Q}$ $(Q = b, c)$ corrections at zero recoil.\\
Here, we compute the slope $\rho^{2}$ and curvature $C$ of the Isgur-Wise funcion for $B$ meson and then obtain the CKM element $V_{cb}$.
In section 2, we discuss the formalism and summarise the results and conclusion in section 3.\\
\section{Formalism}
\subsection{Wave function in the model}
The wavefunction obtained by using the Dalgarno method of perturbation with linear part of the Cornell Potential as perturbation is being discussed in ref.\cite{kkp5,kkp2,NSB2000}. For completeness we write the wavefunction here again.
\begin{equation}
\label{eqn:ch5,1}
\psi_{rel+conf}\left(r\right)=\frac{N^{\prime}}{\sqrt{\pi a_{0}^{3}}} e^{\frac{-r}{a_{0}}}\left( C^{\prime}-\frac{\mu b a_{0} r^{2}}{2}\right)\left(\frac{r}{a_{0}}\right)^{-\epsilon}
\end{equation}
\begin{equation}
\label{eqn:ch5,2}
N^{\prime}=\frac{2^{\frac{1}{2}}}{\sqrt{\left(2^{2\epsilon} \Gamma\left(3-2\epsilon\right) C^{\prime 2}-\frac{1}{4}\mu b a_{0}^{3}\Gamma\left(5-2\epsilon\right)C^{\prime}+\frac{1}{64}\mu^{2} b^{2} a_{0}^{6}\Gamma\left(7-2\epsilon\right)\right)}}
\end{equation}
\begin{equation}
\label{eqn:ch5,3}
C^{\prime}=1+cA_{0}\sqrt{\pi a_{0}^{3}}
\end{equation}
\begin{equation}
\label{eqn:ch5,4}
\mu=\frac{m_{i}m_{j}}{m_{i}+m_{j}}
\end{equation}
\begin{equation}
\label{eqn:ch5,5}
a_{0}=\left(\frac{4}{3}\mu \alpha_{s}\right)^{-1}
\end{equation}
\begin{equation}
\label{eqn:ch5,6}
\epsilon=1-\sqrt{1-\left(\frac{4}{3}\alpha_{s}\right)^{2}}.
\end{equation}
The QCD potential is taken as
\begin{equation}
\label{eqn:ch5,7}
V\left(r\right)=-\frac{4}{3r}\alpha_{s}+br+c
\end{equation}
Here $A_{0}$ is the undetermined factor appearing in the series solution of the Schr\"odinger equation.However with $A_{0}$=0 the effect of c vanishes entirely from the solution. \\
The corresponding normalised wavefunction in momentum space is\cite{kkp5}:
\begin{equation}
\label{eqn:ch5,8}
\psi_{rel+conf}\left(p\right)=\frac{N^{\prime}\sqrt{2}\left(2-\epsilon\right)\Gamma\left(2-\epsilon\right)}{\pi\left(1+ a_{0}^{2}p^{2}\right)^{\frac{3-\epsilon}{2}}}\left[C^{\prime}-\frac{\left(4-\epsilon\right)\left(3-\epsilon\right)\mu b a_{0}^{3}}{2\left(1+a_{0}^{2}p^{2}\right)}\right].
\end{equation}
\subsection{The Isgur-Wise function and Semileptonic decay}
In case of weak decay like the semileptonic $B\rightarrow Dl\nu$ decay, the amplitude is a product of two matrix elements, the hadronic weak current$H_{\mu}$ and the leptonic weak current$L_{\mu}$ with its vector $V^{\mu}$ and axial vector $A^{\mu}$ i.e
\begin{equation}
A=\frac{G_{F}}{\sqrt{2}}V_{cb}\langle l^{-}(k_{1}),\overline{\nu_{l}}(k_{2})|L_{\mu}|0\rangle \times \langle D(P^{\prime})|H^{\mu}|\overline{B}(p)\rangle
\end{equation}
where $H_{\mu}=\overline{c}\gamma^{\mu}(1-\gamma_{5})b$ and $L_{\mu}=\overline{l}\gamma^{\mu}(1-\gamma_{5})\nu_{l}$.
Since both the $B$ and $D$ mesons are pseudoscalar $(J^{p}=0^{-})$, so from the consideration of lorentz covariance and parity one has $ \langle D(P^{\prime})|A^{\mu}|\overline{B}(p)\rangle =0$ and there remains the vector part
\begin{equation}\label{eq.p}
\langle D(p^{\prime})|V^\mu|B(p)\rangle=f_+(q^2)(p+p^{\prime})_\mu+f_-(q^2)(p-p^{\prime})_\mu.
\end{equation}
where $f_+(q^2) $ and$ f_-(q^2) $ are two form factors.\\%in contrast to a single form factor $F_{\pi}(q^{2})$ as in pion case since the weak vector current $V^{\mu}=\overline{c}\gamma^{\mu}b$ is not cnserved here[$q_{\mu}V^{\mu}\propto(m_{b}-m_{c})\neq 0$].\\
Similarly for $B\rightarrow D^{*}l\nu$, we get another four independent form factors
\begin{eqnarray}\label{eq.v}
\langle D^{*}(p^{\prime},\epsilon)|\bar u\gamma^\mu b|B(p)\rangle&=&2i\epsilon^{\mu\nu\alpha\beta}\frac{\epsilon_\nu p^{\prime}_\alpha p_\beta}{M_{B}+M_{D^{*}}}V(q^2)\\
\langle D^{*}(p^{\prime},\epsilon)|\bar u\gamma^\mu\gamma_5b|B(p)\rangle&=&(M_{B}+M_{D^{*}})\left[\epsilon^\mu-\frac{\epsilon\cdot qq^\mu}{q^2}\right]A_1(q^2)\nonumber\\
&&-\epsilon\cdot q\left[\frac{(p+p^{\prime})^\mu}{M_{B}+M_{D^{*}}}-\frac{(M_{B}-M_{D^{*}})q^\mu}{q^2}\right]A_2(q^2)\nonumber\\
&&2M_{D^{*}}\frac{\epsilon\cdot q q^\mu}{q^2}A_0(q^2)
\end{eqnarray}
Unlike the case of electromagnetic interaction here the normalisation of weak form factors are in general unknown.\\
However, in the limit of infinitely heavy quark masses $M_{B}\rightarrow\infty$, a new heavy flavour symmetry appears in the effective Lagrangian of the standard model which provides the model independent normalisation of the weak form factors in the framework of HQET. \\
In the heavy-quark limit the masses of the heavy quarks and consequently, the masses of the heavy hadrons are taken to be infinite. This leads to an additional symmetry which is known as the heavy flavour symmetry. With the hadron masses their momenta also go to infinity but the hadron four velocities remain finite in this symmetry. One is then interested in the dependence of form factors on the (finite) velocity product $v.v^{\prime}$ . Moreover, the heavy quark symmetry is an approximate symmetry and correction arises since the quark masses are not infinite. This correction may be studied systematically in the framework of HQET. The leading symmetry-breaking corrections are from the terms of the order of $\frac{1}{m_{Q^{*}}}$
Although the relative corrections can be calculated using perturbative QCD, the $m_{Q^{*}}$ corrections produce new uncalculable functions. For $B\rightarrow D^{*}l\nu$ decay there are found to be four such uncalculable functions. Hence the predictive power of the theory is reduced. Isgur, Wise, Georgi and others\cite{neubert1,Neubert,Isgur} showed that in case of weak semileptonic decays of $B\rightarrow Dl\nu$ or $B\rightarrow D^{*}l\nu$, all the form factors are expressible in terms of a single universal function of velocity transfer, which is normalized to unity at zero recoil. This universal function is known as the Isgur-Wise function, which measures the overlap of the wave functions of the light degrees of freedom in the initial and final mesons moving with velocities $v$ and $v^{\prime}$ respectively.\\
\subsection{Isgur-Wise function in the model}
In the heavy quark limit close to $y=1$, the Isgur-Wise function is written as :
\begin{eqnarray}
\label{eqn:ch5,IW}
\xi\left(v_{\mu}.v^{\prime}_{\mu}\right)\nonumber&=&\xi\left(y\right)\\&=&1-\rho^{2}\left(y-1\right)+ C\left(y-1\right)^{2}+...
\end{eqnarray}
where
\begin{equation}
y= v_{\mu}.v^{\prime}_{\mu}
\end{equation}
and $v_{\mu}$ and $v^{\prime}_{\mu}$ being the four velocity of the heavy meson before and after the decay.The quantity $\rho^{2}$ is the slope of I-W function at $y=1$ and known as charge radius :\\
\begin{equation}
\rho^{2}= \left. \frac{\partial \xi}{\partial y}\right.|_{y=1}
\end{equation}
The second order derivative is the curvature of the I-W function known as convexity parameter :\\
\begin{equation}
C=\left .\frac{1}{2}\right. \left(\frac{\partial^2 \xi}{\partial y^{2}}\right)|_{y=1}
\end{equation}
For the heavy-light flavor mesons the I-W function can also be written as \cite{NSB2000,close} :\\
\begin{equation}
\label{eqn:ch5,IW2}
\xi\left(y\right)=\int_{0}^{+\infty} 4\pi r^{2}\left|\psi\left(r\right)\right|^{2}\cos pr dr
\end{equation}
where\\
\begin{equation}
p^{2}=2\mu^{2}\left(y-1\right)
\end{equation}
Upon integration of eqn.\ref{eqn:ch5,IW2} one obtains\cite{NSB2000,NSB2009}
\begin{eqnarray}
\label{eqn:ch5,IW1}
\xi\left( y \right)= 1-\frac{N^{\prime2}a_{0}^{2}\mu^{2}\left(y-1 \right)}{2}\left[\frac{4\Gamma\left(5-2\epsilon\right)}{2^{4-2\epsilon}}-\frac{4\mu b a_{0}^{3}\Gamma\left(7-2\epsilon\right)}{2^{6-2\epsilon}}+\frac{\mu^{2} b^{2} a_{0}^{6}\Gamma\left(9-2\epsilon\right)}{2^{8-2\epsilon}}\right] \nonumber\\ + \frac{4N^{\prime2}a_{0}^{4}\mu^{4}\left(y-1 \right)^{2}}{2^{5-2\epsilon}}
\left[ \Gamma\left(4-2\epsilon\right)\left\{\frac{5-2\epsilon}{8} + \frac{3-2\epsilon}{3}+ \frac{\left(3-2\epsilon \right)^{2}}{4} + \frac{\left(3-2\epsilon\right)^{3}}{24} \right\}\right. \nonumber\\ \left.- \frac{\mu b a_{0}^{3}\Gamma\left(6-2\epsilon\right)}{4}\left\{\frac{7-2\epsilon}{8} + \frac{5-2\epsilon}{3}+ \frac{\left(5-2\epsilon \right)^{2}}{4} + \frac{\left(5-2\epsilon\right)^{3}}{24} \right\}\right. \nonumber \\ \left. +\frac{\mu^{2} b^{2} a_{0}^{6}\Gamma\left(8-2\epsilon\right)}{64}\left\{\frac{9-2\epsilon}{8} + \frac{7-2\epsilon}{3}+ \frac{\left(7-2\epsilon \right)^{2}}{4} + \frac{\left(7-2\epsilon\right)^{3}}{24} \right\}\right].
\end{eqnarray}
The normalized wave function naturally follows the zero recoil condition of the IW function $\xi(1)=1$ in the model. \\
\subsection{The strong coupling constant $\alpha_{s}$ in the Model}
In the perturbation procedure, the convergence point of view demands from the eqn.\ref{eqn:ch5,8} that
\begin{equation}
\label{eqn:ch5,9}
\frac{(4-\epsilon)(3-\epsilon)\mu b a^{3}_{0}}{2(1+a^{2}_{0}p^{2})}<<C^{\prime}.
\end{equation}
This condition provides a lower limit of $\alpha_{s}\geq 0.38$ in the model to incorporate a small value of $p_{0}^{2}$($p_{0}^{2}\leq \Lambda^{2}$). Again the reality condition of $\epsilon$ provides an upper limit of $\alpha_{s} \leq \frac{3}{4}$. Hence the condition of equation.(\ref{eqn:ch5,9}) allows a range of $0.38\leq \alpha_{s}\leq 0.75$ in the model to treat the linear part of the Potential as perturbation with its model parameters.\\
Instead of using a free strong coupling constant $\alpha_{s}$ within this range, we therefore consider
the strong running coupling constant appeared in the potential $V(r)$, is related to the quark mass parameter as\cite{kkp5,kkp2,badalianalpha,Faustovalpha}
\begin{equation}
\label{eqn:Faustovalpha}
\alpha_{s}\left(\mu^{2}\right)=\frac{4\pi}{\left(11-\frac{2n_{f}}{3}\right)ln\left(\frac{\mu^{2}+M^{2}_{B}}{\Lambda^{2}}\right)}
\end{equation}
where, $n_{f}$ is the number of flavours, $\mu$ is the renormalisation scale related to the constituent quark masses as $\mu=2\frac{m_{i}m_{j}}{m_{i}+m_{j}}$ and $M_{B}$ is the background mass. The background mass is not an arbitrary parameter and can be calculated in the frame work of lattice QCD. The apperance of mass $M_{B}$ in eqn.\ref{eqn:Faustovalpha} is similar to the case of QED where $\alpha$ has the mass of $e^{+}e^{-}$ pair under logarithm \cite{badalianalpha}. Here we relate the background mass to the confinement term of the potential as $M_{B}=2.24 \times b^{1/2}=0.95 GeV$ \cite{Faustovalpha,kkp5}.\\
In studying leptonic decay \cite{kkp5}, the value of $\Lambda_{QCD}=200 MeV$ was fixed in the eqn.\ref{eqn:Faustovalpha} to obtain the value of running background coupling $\alpha_{s}$. In the case of leptonic decay of charged mesons, the quark and antiquark annihilate to produce a virtual $W^{\pm}$ boson such that $q^{2}=M^{2}$ and hence we get only one form factor, the decay constant $f_{p}$ which absorb all the strong interaction effects. In the case of semileptonic decay, however the case is different since $q^{2}$ is different for event to event and hence more than one form factor appears. This decrease of $q^{2}$ in semileptonic decay leads us to consider a larger value of $\Lambda_{QCD}$ in compared to that of the leptonic decay which effectively increases the strong coupling constant $\alpha_{s}(\mu)$. The physically plaussible range of effective $\Lambda_{QCD}$ should in principle be deduced from the allowed bands of the slope and curvature of the I-W function. Considering the theoretical bounds on slope $3/4\le\rho^{2}<1.51 $\cite{Jugeau,younac} and curvature $C\ge\frac{5\rho^{2}}{4}$\cite{younac}, we draw a curve for the variation of I-W function for $B$ meson and is shown in fig.1. The allowed range of $\rho^{2}$ provides a range of $\Lambda_{QCD}$ in the model as $382 MeV\le\Lambda_{QCD}\le430 MeV$.\\
\begin{figure}[htb]
\begin{center}
\includegraphics[scale=0.8]{iw.eps}\label{fig:ch5,iw}
\caption {Variation of I-W function with Y for different scales of $\Lambda$.}
\end{center}
\end{figure}
In ref.\cite{badalianalpha}, it was analysed in studying the freezing of QCD coupling effects that for running background coupling in $V$ scheme, one can choose $\Lambda_{V}(n_{f}=3)=410 MeV$(eqn.30 of ref.\cite{badalianalpha}) and this value of $\Lambda_{V}$ does not contradict with those which are commonly used in $\overline{MS}$ renormalisation scheme and give rise to $\alpha_{s}(M_{Z})=0.118\pm0.001$. Hence we justify ourself to choose $\Lambda_{QCD}=0.410GeV$ in this work.
The input parameters used in the numerical calculation are the same as is used in our previous works\cite{kkp5} $n_{f}=3$, $m_{d}=0.336 GeV$, $m_{c}=1.55 GeV$, $m_{b}=4.97 GeV$ with $b=0.183$ $GeV^{2}$ and $cA_{0}$=1$GeV^{2/3}$ with $c=-0.4 GeV$\\
\section{Results}
\subsection{Determination of CKM element $V_{cb}$}
Using eqn.\ref{eqn:ch5,IW} and eqn.\ref{eqn:ch5,IW1}, we compute the slope and curvature of the I-W function for $B$ meson.
It is also added that the result with $\Lambda_{QCD}=410$ MeV is found to be improved than our previous work with $V$ Scheme\cite{NSB2009}.
\begin{table}[h]
\begin{center}
\caption{Slope and curvature of I-W function for $B$ and $D$ mesons.}\label{tab:ch5,1}
\vspace{0.2cm}
\begin{tabular}{|c|c|c|}
\hline Slope and Curvature & With $\Lambda_{QCD}=200 MeV$ & With $\Lambda_{QCD}=410 MeV$ \\ \hline
$\rho^{2}_{B}$ & 28.42 & 1.11\\
$C_{B}$ & 420.68 & 0.99 \\
\hline
\end{tabular}
\end{center}
\end{table}
From the table.\ref{tab:ch5,1}, we see that with $\Lambda_{QCD}=200$ MeV, the results overshoots all other theoretical upper bounds $3/4\le\rho^{2}<1.51 $\cite{Jugeau,younac} and hence for determination of $V_{cb}$ we consider the value of $\rho^{2}_{B}$ and $C_{B}$ with $\Lambda_{QCD}=410 MeV$.
\begin{table}
\begin{center}
\caption{ Comparison of slope and curvature of $B$ mesons with other works.}\label{tab:ch5,2}
\vspace{0.2cm}
\begin{tabular}{|c|c|c|}\hline
work & $\rho^{2}_{B}$ & $C_{B}$ \\\hline
Present & 0.993 & 1.114 \\
Faustov etal;\cite{Faustovnewanalysis}& 1.04&1.36\\
Lattice QCD\cite{Bowler}&$0.83^{+15+24}_{-11-22}$&..\\
ALEPH\cite{ALEPH}&$0.92\pm0.98\pm0.36$&..\\
Belle\cite{Belle}&$1.12\pm0.22\pm0.14$&..\\
Le Youanc et al \cite{younac} &$\ge 0.75$&$\ge 0.47$\\
QCD Sum Rule \cite{BDAI}&0.65&0.47\\
Relativistic Three Quark Model \cite{IVANOV}&1.35&1.75\\
Neubert \cite{NEUBERT}&0.82$\pm$0.09&..\\\hline
\end{tabular}
\end{center}
\end{table}
The differential semileptonic decay rate $B\to D\,l\,\bar{\nu}$ for
the massless leptons is given by\cite{neubert1,Qkim}
\begin{equation}
\frac{d\Gamma}{d y}=\frac{G_F^2}{48\pi^3}\,|V_{cb}|^2\,M_D^3\,
(y^2-1)^{3/2}(M_B+M_D)^2\ \xi^{2}\left( y \right),
\end{equation}
where $y$ lies in the range $1\le y\le \frac{M^{2}_{B}+M_{D}^{2}-m^{2}_{l}}{2M_{B}M_{D}}$.\\
The differential semileptonic decay rate $B\to
D^*\,l\,\bar{\nu}$ is defined by
\begin{eqnarray}
\frac{d\Gamma}{d y}&=&\frac{G_F^2}{48\pi^3}\,|V_{cb}|^2\,(M_B-M_{D^*})^2\,M_{D^*}^3\,
\sqrt{(y^2-1)}\,(y+1)^2\cr
&&\times\bigg[
1+\frac{4y}{y+1}\ \frac{q^{2}\left(y\right)}{(M_{B}-M_{D^{*}})^2}
\bigg]\ \xi^{2}\left( y \right),
\end{eqnarray}
where $q^{2}(y)=M^{2}_{B}+M^{2}_{D^{*}}-2 y M_{D^{*}}M_{B}$.
By integrating the expressions for the differential decay rates
\begin{equation}
\Gamma=\int\frac{G_F^2}{48\pi^3}\,|V_{cb}|^2\,M_D^3\,
(y^2-1)^{3/2}(M_B+M_D)^2\ \xi^{2}\left( y \right)d y\\
\end{equation}
and
\begin{eqnarray}
\Gamma&=&\int\frac{G_F^2}{48\pi^3}\,|V_{cb}|^2\,(M_B-M_{D^*})^2\,M_{D^*}^3\,
\sqrt{(y^2-1)}\,(y+1)^2\cr
&&\times\bigg[
1+\frac{4y}{y+1}\ \frac{q^{2}\left(y\right)}{(M_{B}-M_{D^{*}})^2}
\bigg]\ \xi^{2}\left( y \right)dy,
\end{eqnarray}
we get the predictions for the total decay rates in our model as
\begin{eqnarray}
\Gamma(B\to D l\nu)&= &6.82|V_{cb}|^2\ {\rm ps}^{-1},\\
\Gamma(B\to D^* l\nu)&=&28.40|V_{cb}|^2\ {\rm ps}^{-1}.
\end{eqnarray}
Taking mean values of lifetimes from PDG2012:
$\tau_{B^0}=1.519\times 10^{-12}$~s and $\tau_{B^+}=1.641\times
10^{-12}$~s, and also using the experimental masses for the eq.24 and eq.25, we compute the semileptonic branching ratio by using the relation $BR=\Gamma\times \tau$ and find
\begin{eqnarray}
BR(B^0\to D^+ l^-\nu)&=&10.401|V_{cb}|^2,\cr
BR(B^+\to D^0 l^+\nu)&=&11.10|V_{cb}|^2,\cr
BR(B^0\to D^{*+} l^-\nu)&=&43.31|V_{cb}|^2,\cr
BR(B^+\to D^{*0} l^+\nu)&=&46.78|V_{cb}|^2.
\end{eqnarray}
The comparison of these theoretical results with the experimental branching ratios from the lattest PDG \cite{pdg2012}
gives us following values of the CKM matrix element $|V_{cb}|$:
\begin{eqnarray}
BR(B^0\to D^+ l^-\nu)^{\rm exp}=0.0218&\qquad& |V_{cb}|=0.046,\cr
BR(B^+\to D^0 l^+\nu)^{\rm exp}=0.0229&\qquad& |V_{cb}|=0.045,\cr
BR(B^0\to D^{*+} l^-\nu)^{\rm exp}=0.0509 &\qquad& |V_{cb}|=0.034,\cr
BR(B^+\to D^{*0} l^+\nu)^{\rm exp}=0.0558&\qquad& |V_{cb}|=0.035.
\end{eqnarray}
Thus the averaged $|V_{cb}|$ over all presented
measurements of semileptonic decays $B\to De\nu$ and $B\to D^*e\nu$ is
equal to
\begin{equation}
\label{eq:bdavvcb}
|V_{cb}|=0.040
\end{equation}
and is in good agreement with the experimental result \cite{pdg2012}.
\[|V_{cb}|=0.0396\pm0.0009\quad ({\rm exclusive}). \]
\section{Conclusion}
In this work, we have studied the renormalisation scale dependance of Isgur-wise function by using a wavefunction with linear part of the Cornell Potential as perturbation. Considering the exclusive semileptonic decay of $B\to De\nu$ and $B\to D^*e\nu$, we then compute the CKM element$|V_{cb}|$ in this approach. The result of the CKM element is found to be within the error limits of other results. The following features are observed in this work:
\begin{itemize}
\item The renormalization scale of the model was set to be $\Lambda_{QCD}=410\;MeV$ as is used in ref.\cite{badalianalpha}
\item The slope and curvature of the Isgur wise function are found to lie within the range of limits found in the literature.
\item The computed value of the CKM element from the exlusive semileptonic decay of $B$ meson is obtained as $|V_{cb}|=0.040$. The result is to be well consistent with the lattice result $|V_{cb}|=0.0409\pm0.0015\pm0.0007$\cite{Divitis}.
\item It becomes an worthy comment to note that the result with $\Lambda_{QCD}=200$(as is done in our previous work)is found to be very poor to study the branching ratio and $|V_{cb}|$
\end{itemize}
From a phenomenological point of view, the present theoretical framework is a considerably useful tool to investigate various physical quantities for the heavy-light quark systems. Further work on the renormalisation schemes and scale dependance of strong coupling $\alpha_{s}$ is under study
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}
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Maria Dragoni née à Procida (Campanie] le est une soprano italienne active dans les grands opéras internationaux à partir de 1984.
Biographie
Maria Bianca Anna Dragoni est née à Procida, et s'est formée au conservatoire de musique de Frosinone Licinio Refice. Elle a étudié le chant avec Maria Alòs, épouse du pianiste Arnaldo Graziosi. En 1979, elle rejoint le chœur de la RAI à Rome. Dans cette ville, elle étudie le chant avec la Duchesse Melina Pignatelli della Leonessa, puis elle poursuit ses études à Naples avec Rodolfo Celletti et Gina Cigna. En 1981, elle remporte le prix Maria Callas au concours international Vincenzo Bellini à Caltanissetta et en 1983, elle remporte de nouveau le prix Maria Callas au Foro Italico à Rome.
Maria Dragoni a fait ses débuts à l'opéra en 1984 dans Imogene dans l'opéra Il pirata de Vincenzo Bellini et au Théâtre Pergolesi à Jesi, puis cette même année, elle fait ses débuts au Teatro San Carlo à Naples, dans le rôle principal de Il Flaminio de Giovanni Battista Pergolesi rarement présenté à l' opéra. Elle réinterprète ce rôle l'année suivante à l' Internationale Maifestspiele Wiesbaden. En 1986, elle interprète encore Imogene au Teatro Massimo de Palerme, et de nouveau en 1987 à Naples. Elle a également interprété Adalgisa dans Norma de Bellini.
En 1988 Maria Dragoni fait ses débuts à La Scala chantant Fenena dans Nabucco de Giuseppe Verdi, puis à l'Opéra national de Lorraine et le Festival de Ravenne dans le rôle principal de Turandot de Giacomo Puccini. En 1989, elle interprète le rôle principal de Aida de Verdi au Macerata Festival d'Opéra, puis la même année au Théâtre des Champs-Élysées elle joue Mathilde dans Guillaume Tell de Gioachino Rossini.
Depuis, Maria Dragoni maintient une présence active dans les grands théâtres d'opéra internationaux.
Références
Liens externes
Intervista a Maria Dragoni (consulté le ).
Naissance à Procida
Naissance en décembre 1958
Personnalité italienne du XXe siècle
Personnalité italienne du XXIe siècle
Soprano italienne
Chanteuse italienne d'opéra
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\section{Introduction}
$\delta$ meson is an isovector scalar meson, its contribution is
expected to be neglectable in nuclei with small isospin asymmetry
and in nuclear matter at saturation density. However, for strongly
isospin-asymmetric matter at high densities in neutron stars the
contribution of the $\delta$ field should be considered
\cite{Kubis}. In the last decade, the effects of coupling to the
$\delta$ meson like field on nuclear structure properties of the
drip-line nuclei, on the dynamic situations of heavy ion collisions
and on asymmetric nuclear matter are investigated
\cite{Hofmann,Gaitanos,Liu1,magnetic}. Recently, the density
dependent coupling constants are introduced additionally to
reexamine the $\delta$ meson effects on properties of finite nuclei
and asymmetric nuclear matter in the Quantum Hadron Dynamics (QHD)
model \cite{Haddad,Liu2}. The $\delta$ meson effects are also
investigated in other models, such as a chiral SU(3) model
\cite{chiral}, a relativistic point coupling model \cite{RMFPC},
relativistic transport model \cite{RTM} and so on. But there is no
similar work in the quark-meson coupling (QMC) model yet, so we will
investigate the $\delta$ meson effects by using this model in this
paper.
The quark-meson coupling model was proposed by Guichon in 1988
\cite{Guichon1} where nuclear matter is described as nonoverlapping
MIT bags interacting through the exchange of mesons in the
mean-field approximation. The effective nucleon masses in the QMC
model are obtained self-consistently at the quark level, which is an
important difference from QHD model. The model is refined by
including nucleon Fermi motion and center of mass corrections to the
bag energy by Fleck \cite{Fleck}. Jin and Jennings introduced the
density-dependent bag constant, which is called modified quark-meson
coupling (MQMC) model, to get larger scalar and vector potentials
compatible with experiments \cite{Jin}. Furthermore, the MQMC model
possibly includes the effects of quark-quark correlations associated
with overlapping bags which was missing in the original QMC model,
therefore it is applicable at the densities appropriate to neutron
stars. The $(\sigma^*,\phi)$ meson fields are incorporated to
account for the strong attractive $\Lambda\Lambda$ interaction
observed in hypernuclei which cannot be reproduced by the
$(\sigma,\omega,\rho)$ only in MQMC model \cite{Pal}. The MQMC model
gives a satisfactory description of finite nuclei
\cite{finite_nuclei} and nuclear matter \cite{nuclear_matter}, and
it is widely used in nuclear physics. For example, the temperature
effects of nuclear matter \cite{temperature}, $K$ condensation
\cite{K_condensation1,K_condensation2,Ma}, trapped neutrinos
\cite{trapped_neutrinos}, strong magnetic field
\cite{magnetic_field} and deconfined phenomena \cite{deconfined} in
neutron stars are all investigated in the MQMC model.
In this paper, we extend MQMC model to incorporate $\delta$ meson
field, in which the density-dependent couplings between baryons and
scalar mesons are calculated self-consistently. The model parameters
are determined by the properties of symmetric nuclear matter and
pure neutron matter. Then the influences of leptons, baryons and
$(\sigma^*,\phi)$ mesons on the $\delta$ meson effects are
discussed.
\section{The model}\label{sect2}
The modified quark-meson coupling model is extended to include the
$\delta$ meson field. $\delta$ meson couples only to $u$ and $d$
quarks, because it is built out of nonstrange quarks. $\sigma^*$ and
$\phi$ mesons are also incorporated which couple only to the $s$
quark in a hyperon bag. So there are isoscalar scalar mesons
$\sigma$ and $\sigma^*$, isoscalar vector mesons $\omega$ and
$\phi$, isovector scalar meson $\delta$ and isovector vector meson
$\rho$ in our present model.
In the mean field approximation the Dirac equation for a quark field
of flavor $q\equiv(u,\ d,\ s)$ in the bag for the hadron species
$B\equiv(p,\ n,\ \Lambda,\ \Sigma^+,\ \Sigma^0,\ \Sigma^-,\ \Xi^0,\
\Xi^-)$ is then given by
\begin{equation}
\left[{\rm i}\gamma\cdot\partial-\left(m_
q-g_\sigma^q\sigma-g_{\sigma^*}^q\sigma^*
-g_\delta^qI_{3q}\delta_3\right) -\gamma^0\left(g_{\omega}^q\omega_0
+g_{\phi}^q\phi_0+g_{\rho}^qI_{3q}\rho_{03}
\right)\right]\psi_{qB}(\vec{r},t)=0.
\end{equation}
Here $I_{3q}$ is the isospin projection of quark $q$; $g_\delta^q$
is the coupling constant between quark $q$ and $\delta$ meson,
$\delta_3$ denotes expectation value of the isospin 3rd-component of
$\delta$ meson field, and the other symbols are the same as in
\cite{Ma}. The normalized ground state is solved as
\begin{equation}\psi_{qB}=\mathcal{N}_{qB}\exp\left(\frac{-{\rm i}\epsilon_{qB}t}{R_B}\right)
\left(
\begin{array}{c}
j_0\left(\displaystyle\frac{x_{qB}r}{R_B}\right) \\
\displaystyle{\rm i}\beta_{qB}\vec{\sigma}\cdot\hat{r}j_1
\left(\displaystyle\frac{x_{qB}r}{R_B}\right)
\end{array}
\right)\frac{\chi_{qB}}{\sqrt{4\pi}}
\end{equation}
where
\begin{eqnarray}
\epsilon_{qB}&=&\Omega_{qB}{\pm}R_B\left(g_{\omega}^q\omega_0
+g_{\rho}^qI_{3q}\rho_{03}+g_{\phi}^q\phi_0\right),\label{3}\\
\beta_{qB}&=&\sqrt{\frac{\Omega_{qB}-R_Bm_q^*}{\Omega_{qB}+R_Bm_q^*}},\\
\Omega_{qB}&=&\sqrt{x_{qB}^{2}+\left(R_Bm_q^*\right)^{2}},
\end{eqnarray}
with $R_B$ is the bag radius of baryon $B$ and $x_{qB}$ is the
dimensionless quark momentum which can be determined by the linear
boundary condition
\begin{equation}j_0(x_{qB})=\beta_{qB}j_{1}(x_{qB})\end{equation} The effective
quark mass is
\begin{equation}m_q^*=m_q-g_\sigma^q\sigma
-g_{\sigma^*}^q\sigma^*-g_\delta^qI_{3q}\delta_3\end{equation} The
energy of a MIT bag for baryon $B$ is then given by
\begin{equation}
E_B^{\rm
bag}=\frac{\displaystyle\sum_qn_{qB}\Omega_{qB}-z_B}{R_B}+\frac{4}{3}\pi
R_B^{3}B_B\left(\sigma,\sigma^*,\delta_3\right)
\end{equation}
where $n_{qB}$ is the number of constituent quark $q$ in baryon $B$,
$z_B$ is the zero-point motion parameter and $B_B$ is the medium
dependent bag parameter. The ansatz for the coupling of bag
parameter to the scalar fields $\sigma$, $\sigma^*$ \cite{zj} is
extended to $\delta_3$
\begin{equation}
B_B\left(\sigma,\sigma^*,\delta_3\right)=B_0\exp\left\{-\frac{4}{M_B}
\left[n_{sB}g_{\sigma^*}^{\rm
bag}\sigma^*+\sum_{q=u,d}n_{qB}\left(g_\sigma^{\rm
bag}\sigma+g_\delta^{\rm bag}I_{3q}\delta_3\right)\right]\right\}
\end{equation}
where $B_0$ is the bag constant in free space, $M_B$ is the bare
mass of the baryon $B$, and $g_\sigma^{\rm bag}$, $g_{\sigma^*}^{\rm
bag}$ and $g_\delta^{\rm bag}$ are real parameters.
After the corrections of spurious center of mass motion, the
effective baryon mass is given by
\begin{equation}\label{eq:mstar}
M_B^*=\sqrt{\left(E_B^{\rm bag}\right)^{2}-\left<p_{\rm
c.m.}^{2}\right>_B}
\end{equation}
where
\begin{equation}
\left<p_{\rm
c.m.}^{2}\right>_B=\frac1{R_B^{2}}\sum_qn_{qB}x_{qB}^{2}
\end{equation}
The bag radius $R_B$ could be obtained through the minimization of
the baryon mass with respect to the bag radius
\begin{equation}\label{minimization}
\frac{\partial M_B^*}{\partial R_B}=0
\end{equation}
Consider an many-particle system consisting of the full baryon octet
which interact via $\sigma, \sigma^*, \omega, \phi, \delta, \rho$
meson fields. The Lagrangian density
is\begin{eqnarray}\mathcal{L}&=&\sum_{B}\bar{\Psi}_{B}\left[{\rm
i}\gamma_\mu\partial^\mu-M_{B}^{*}\left(\sigma,\sigma^*,\delta_3\right)
-\left(g_{\omega B}\omega_\mu\gamma^\mu+g_{\rho
B}\frac{\vec{\tau}_B}{2}\cdot{\vec{\rho}}_\mu\gamma^\mu +g_{\phi
B}\phi_\mu\gamma^\mu\right)\right]\Psi_{B}
+\frac12\left(\partial_\mu\sigma\partial^\mu\sigma\right.\nonumber\\
&&\left.+\partial_\mu\vec{\delta}\cdot\partial^\mu\vec{\delta}
+\partial_\mu\sigma^*\partial^\mu\sigma^*\right)
-\frac{1}{2}\left(m_{\sigma}^{2}\sigma^{2}
+m_\delta^2\vec{\delta}\cdot\vec{\delta}+m_{\sigma^{*}}^{2}\sigma^{*2}
-m_{\omega}^{2}\omega_\mu\omega^\mu
-m_{\rho}^{2}{\vec{\rho}}_\mu\cdot{\vec{\rho}}^\mu
-m_{\phi}^{2}\phi_\mu\phi^\mu\right)\nonumber\\
&&-\frac14\left(W_{\mu\nu}W^{\mu\nu}
+\vec{G}_{\mu\nu}\cdot\vec{G}^{\mu\nu}+F_{\mu\nu}F^{\mu\nu}\right)+\sum_{l}\bar{\Psi}_{l}\left({\rm
i}\gamma_{\mu}\partial^{\mu}-m_{l}\right)\Psi_{l}\label{eq:L}
\end{eqnarray}
where $l\equiv(e,\mu)$. Then from Eq. (\ref{eq:mstar}) and
(\ref{eq:L}), we can derive the equations of the motion for the
meson fields in uniform static matter:
\begin{eqnarray}
\label{fields}m_\sigma^{2}\sigma&=&\frac1{\pi^{2}}\sum_Bg_{\sigma
B}C_B(\sigma)\int_0^{k_B}\frac{M_B^*}
{\left[k^{2}+M_B^{*2}\right]^{1/2}}k^{2}{\rm d}k,\\
\label{fieldss}m_{\sigma^*}^{2}\sigma^*&=&
\frac1{\pi^{2}}\sum_Bg_{\sigma^* B}C_B\left(\sigma^*\right)
\int_0^{k_B}\frac{M_B^*}
{\left[k^{2}+M_B^{*2}\right]^{1/2}}k^{2}{\rm d}k,\\
\label{fieldd}m_\delta^{2}\delta_3&=&\frac1{\pi^{2}}\sum_Bg_{\delta
B} C_B(\delta_3)\int_0^{k_B}\frac{M_B^*}
{\left[k^{2}+M_B^{*2}\right]^{1/2}}k^{2}{\rm d}k,\\
\label{fieldo}m_{\omega}^{2}\omega_0&=&
\frac1{3\pi^{2}}\sum_Bg_{\omega B}k_B^{3},\\
\label{fieldp}m_{\phi}^{2}\phi_0&=&\frac1{3\pi^{2}}\sum_Bg_{\phi B}k_B^{3},\\
\label{fieldr}m_{\rho}^{2}\rho_{03}&=&\frac1{3\pi^{2}}\sum_Bg_{\rho
B}I_{3B}k_B^{3}.
\end{eqnarray}
Here $k_B$ is the Fermi momentum of the baryon species $B$. The
factors $C_B(\sigma), C_B(\sigma^*), C_B(\delta_3)$ are:
$$g_{\phi B}C_B(\phi)=-\frac{\partial
M_B^*}{\partial\phi},\hskip1cm\phi=\sigma,\ \sigma^*,\
\delta_3$$
\begin{eqnarray} -\frac{\partial M_B^*}{\partial\sigma}
&=&\frac{E_B^{\rm
bag}}{M_B^*}\sum_{q=u,d}n_{qB}\left\{g_\sigma^q\left[S_{qB}\left(1-\frac{\Omega_{qB}}{E_B^{\rm
bag}R_B}\right)+\frac{m_q^*}{E_B^{\rm bag}}\right]+\frac{16\pi
g_\sigma^{\rm
bag}B_BR_B^{3}}{3M_B}\right\}\label{g1}\\
-\frac{\partial M_B^*}{\partial\sigma^*} &=&\frac{E_B^{\rm
bag}}{M_B^*}n_{sB}\left\{g_{\sigma^*}^q
\left[S_{sB}\left(1-\frac{\Omega_{sB}}{E_B^{\rm
bag}R_B}\right)+\frac{m_s^*}{E_B^{\rm bag}}\right]+\frac{16\pi
g_{\sigma^*}^{\rm
bag}B_BR_B^{3}}{3M_B}\right\}\label{g2}\\
-\frac{\partial M_B^*}{\partial\delta_3} &=&\frac{E_B^{\rm
bag}}{M_B^*}\sum_{q=u,d}n_{qB}I_{3q}\left\{g_\delta^q
\left[S_{qB}\left(1-\frac{\Omega_{qB}}{E_B^{\rm
bag}R_B}\right)+\frac{m_q^*}{E_B^{\rm bag}}\right]+\frac{16\pi
g_\delta^{\rm bag}B_BR_B^{3}}{3M_B}\right\}\label{g3}
\end{eqnarray}
The scalar density of quark $q$ in the bag $B$ are
\begin{equation}\label{S}
S_{qB}=\frac{\Omega_{qB}/2+R_Bm_q^*(\Omega_{qB}-1)}{\Omega_{qB}(\Omega_{qB}-1)
+R_Bm_q^*/2},\quad q\equiv(u,d,s),
\end{equation}
At last, there are two conditions left:
\begin{eqnarray}
\label{neutrality}&&\textrm{charge
neutrality:}\,\sum_Bq_Bk_B^{3}=\sum_lk_l^{3};\\
\label{betaequ}&&\textrm{$\beta$
equilibrium:}\,\mu_B=\mu_n-q_B\mu_e,\quad \mu_{\mu}=\mu_e.
\end{eqnarray}
where $q_B$ and $\mu_B$ correspond to the electric charge and
chemical potential of baryon $B$, respectively. The energy
eigenvalue of Dirac equation for baryon $B$ and lepton $l$ are:
\begin{eqnarray}
\epsilon_B&=&\sqrt{k_B^{2}+M_B^{*2}}+g_{\omega
B}\omega_0+g_{\phi B}\phi_0+g_{\rho B}I_{3B}\rho_{03},\label{eB}\\
\epsilon_l&=&\sqrt{k_l^{2}+m_l^{2}}\label{el}
\end{eqnarray}
Then the Fermi momentum can be obtained from the equations
\begin{eqnarray}\epsilon_B(k_B)&=&\mu_B\label{BaryonFermi}\\
\epsilon_l(k_l)&=&\mu_l\label{LeptonFermi}\end{eqnarray}
After the meson fields ($\sigma, \sigma^*, \omega, \phi, \delta_3,
\rho_{03}$), Fermi momenta ($k_B, k_l$) and effective masses $M_B^*$
are obtained by solving the Eqs. (\ref{fields})--(\ref{fieldr}),
(\ref{BaryonFermi})--(\ref{LeptonFermi}) and (\ref{minimization})
self-consistently at a given baryon number density
\begin{equation}\rho=\frac1{3\pi^{2}}\sum_Bb_Bk_B^{3}\label{totaldensity}\end{equation}
where $b_B$ is the baryon number of baryon $B$, we can obtain the
total energy density and pressure:
\begin{eqnarray}
\varepsilon&=&\frac{1}{2}\left(m_\sigma^{2}\sigma^{2}
+m_{\sigma^*}^{2}\sigma^{*2}+m_{\omega}^{2}
\omega_0^{2}+m_{\phi}^{2}\phi_0^{2}
+m_\delta^{2}\delta_3^2+m_{\rho}^{2}\rho_{03}^{2}\right)\nonumber\\
&&+\frac1{\pi^{2}}\sum_B\int_0^{k_B}\left[k^{2}
+M_B^{*2}\right]^{1/2}k^{2}{\rm
d}k+\frac{1}{\pi^{2}}\sum_l\int_0^{k_l}\left[k^{2}+m_l^{*2}\right]^{1/2}k^{2}{\rm
d}k
\label{energydensity}\\
P&=&\frac{1}{2}\left(m_{\omega}^{2}\omega_0^{2}
+m_{\phi}^{2}\phi_0^{2}+m_{\rho}^{2}\rho_{03}^{2}
-m_\sigma^{2}\sigma^{2}
-m_{\sigma^*}^{2}\sigma^{*2}-m_\delta^{2}\delta_3^{2}\right)\nonumber\\
&&+\frac1{3\pi^{2}}\sum_B \int_0^{k_B}\frac{k^{4}{\rm
d}k}{\left[k^{2}+M_B^{*2}\right]^{1/2}}+\frac{1}{3\pi^{2}}\sum_l\int_0^{k_l}\frac{k^{4}{\rm
d}k}{\left[k^{2}+m_l^{*2}\right]^{1/2}}\label{pressure}
\end{eqnarray}
\section{Parameters and calculation details}\label{sect3}
Take the current quark mass to be $m_u=m_d=0$ and $m_s=150$ MeV.
Small current quark mass for the non-strange flavors or other values
for the strange flavor lead only to small numerical refinements
\cite{K_condensation2}. The meson masses are $m_\sigma=550$ MeV,
$m_\sigma^*=980$ MeV, $m_{\rho}=775$ MeV, $m_\delta=985$ MeV,
$m_{\omega}=783$ MeV, $m_{\phi}=1020$ MeV, respectively.
Assume $\sigma, \omega, \rho, \delta$ mesons couple only to the $u$,
$d$ quarks and $\sigma^*, \phi$ mesons couple only to the $s$ quark,
we have
\begin{equation}
g_\sigma^s=g_{\omega}^s=g_\delta^s=g_{\rho}^s
=g_{\sigma^*}^u=g_{\sigma^*}^d=g_{\phi}^u=g_{\phi}^d=0
\end{equation}
By assuming the SU(6) symmetry of the simple quark model\cite{Pal}
\begin{equation}\begin{array}{llllllll}&g_\sigma^d=g_\sigma^u,&
g_{\sigma^*}^s=\sqrt2g_{\sigma}^u, &g_\delta^d=g_\delta^u;
&g_\omega^d=g_\omega^u,& g_{\phi}^{s}=\sqrt2g_{\omega}^u,
&g_\rho^d=g_\rho^u& \end{array}\end{equation} we can get the
relations
\begin{eqnarray}
&&\frac{1}{3}g_{\omega
N}=\frac{1}{2}g_{\omega\Lambda}=\frac{1}{2}g_{\omega\Sigma}=g_{\omega\Xi}=g_\omega
^u\\
&&g_{\phi\Lambda}=g_{\phi\Sigma}=\frac{1}{2}g_{\phi\Xi}=\sqrt2g_{\omega}^u,\hskip5mm
g_{\phi N}=0\\
&&g_{\rho N}=g_{\rho\Lambda}=g_{\rho\Sigma}=g_{\rho\Xi}=g_\rho^u
\end{eqnarray}
To reduce parameters we set\begin{equation}\frac{g_{\delta}^{\rm
bag}}{g_{\delta}^u}=\frac{g_{\sigma^*}^{\rm
bag}}{g_{\sigma^*}^s}=\frac{g_{\sigma}^{\rm
bag}}{g_{\sigma}^u}\end{equation}
The free nucleon zero-point motion parameter $z_{N0}$ and the free
bag constant $B_0$ are fixed to reproduce the free mass of nucleon
$m_{N}=939$ MeV with the minimization condition (\ref{minimization})
at a free bag radius $R_{N0}=0.6$fm. Then the free zero-point motion
parameters $z_{B0}$ and free radii $R_{B0}$ of other baryons are
obtained by reproducing the free baryon mass $M_B$ with the
minimization condition (\ref{minimization}). They are all listed in
the Table \ref{tb1}.
\begin{table}
\begin{center}
\caption{The zero-point motion parameters $z_{B0}$ and bag radii
$R_{B0}$ in free space are obtained to reproduce the free space mass
spectrum after the parameters $B_0^{1/4}=188.102$ MeV and
$z_{N0}=2.030$ have been fixed by the properties of
nucleon.}\begin{tabular} {c|ccc}\hline\hline
&$M_B$(MeV) &$z_{B0}$ &$R_{B0}$(fm) \\
\hline
$\Lambda$ &1115.68 &1.815 &0.643\\
$\Sigma^+$ &1189.37 &1.638 &0.669\\
$\Sigma^0$ &1192.64 &1.630 &0.670\\
$\Sigma^-$ &1197.45 &1.612 &0.672\\
$\Xi^0$ &1314.83 &1.501 &0.689\\
$\Xi^-$ &1321.31 &1.483 &0.689\\
\hline \hline
\end{tabular}\label{tb1}
\end{center}
\end{table}
Four independent coupling constants $g_\sigma^u, g_{\omega}^u,
g_{\rho}^u$ and $g_\sigma^{\rm bag}$ can be adjusted by reproducing
the symmetric nuclear matter binding energy $B/A$=16 MeV, symmetry
energy $a_{\rm sym}$=32.5 MeV and compressibility $K=289$ MeV at
saturation density $\rho_0=0.17$ ${\rm fm}^{-3}$, as listed in Table
\ref{tb2}. The $\delta$ meson-quark coupling constant is constrained
in an range of $0\le g_\delta^u\le4.2$ so that the pure neutron
matter EOS is consistent with the experimental flow data in
heavy-ion collision \cite{g_delta}, which is shown in the upper
panel of Figure. \ref{gdelta}, the EOS for symmetric nuclear matter
is also shown in the lower panel and we can see that it is also
consistent with the experimental flow data in heavy-ion collision.
\begin{table}
\begin{center}
\caption{Four independent coupling constants are fixed to reproduce
the symmetric nuclear matter binding energy $B/A=16$ MeV, symmetry
energy $a_{\rm sym}=32.5$ MeV and compressibility $K=289$ MeV at
saturation density $\rho_0$=0.17 fm$^{-3}$. $\delta$ meson coupling
constant is set 0 and 4.2.}\begin{tabular}{c|cccc}\hline\hline \ \
$g_\delta^u$\ \ &\ \ $g_\sigma^u$\ \ &\ \ $g_{\omega}^u$\ \ &\ \
$g_{\rho}^u$\ \ &\ \ $g_\sigma^{\rm
bag}$\ \ \\
\hline
0 &0.980 &2.705 &7.948 &2.278\\
4.2 &0.980 &2.705 &10.217 &2.278\\
\hline \hline
\end{tabular}\label{tb2}
\end{center}
\end{table}
\begin{figure}
\begin{center}
\includegraphics[width=6.5cm]{g_delta}
\caption{(Color online) The EOSes obtained in MQMC model for pure
neutron matter and symmetric nuclear matter. The upper magenta
hatched area and the lower orange hatched area correspond to the
pressure regions for neutron matter after inclusion of the pressure
from asymmetry term with strong density dependence and for symmetric
nuclear matter consistent with the experimental flow data,
respectively \cite{g_delta}.} \label{gdelta}
\end{center}
\end{figure}
The equilibrium properties of neutron stars are obtained by solving
Tolman-Oppenheimer-Volkoff (TOV)\cite{TOV} equations\begin{eqnarray}
\frac{{\rm d}P(r)}{{\rm
d}r}&=&-\frac{G\left[\varepsilon(r)+P(r)\right]\left[M(r)+4\pi
r^{3}P(r)\right]}{r^{2}\left[1-2GM(r)/r\right]}\\ \frac{{\rm
d}M(r)}{{\rm d}r}&=&4\pi r^{2}\varepsilon(r).
\end{eqnarray}
The Baym-Pethick-Sutherland model \cite{BPS} is used to describe the
EOS at subnuclear densities.
\section{Results and discussions}\label{sect4}
Four cases in Table \ref{tb3} are investigated: (1) pure neutron
matter denoted by $nn$; (2) $\beta$-equilibrium nucleonic matter
denoted by $np$; (3) $\beta$-equilibrium hadronic matter composed of
baryon octet without $(\sigma^*, \phi)$ meson fields, denoted by
$npH$; (4) The same as in Case (3) with two additional meson fields
$(\sigma^*, \phi)$, denoted by $npH^*$.
\begin{table}
\begin{center}
\caption{The cases we study in the paper. $H$ represents hyperons
$(\Lambda, \Sigma^+, \Sigma^0, \Sigma^-, \Xi^0,
\Xi^-)$.}\begin{tabular} {c|c|c|c|c}\hline\hline
notation &$nn$ &$np$ &$npH$ &$npH^*$\\
\hline
baryons &$n$ &$n, p$ &$n, p, H$ &$n, p, H$\\
\hline
leptons & &$e$ &$e$, $\mu$ &$e, \mu$\\
\hline mesons &$\sigma, \omega, \rho(, \delta)$ &$\sigma, \omega,
\rho(, \delta)$ &$\sigma, \omega,
\rho(, \delta)$ &$\sigma, \omega, \rho(, \delta), \sigma^*, \phi$\\
\hline \hline
\end{tabular}\label{tb3}
\end{center}
\end{table}
The meson fields for $npH^*$ are shown in the left panel of Figure.
\ref{field}. We can see that $\delta$ meson field decreases
$(\sigma, \omega)$ fields while increases $(\sigma^*, \phi)$ fields.
This is because the $\delta$ meson increases the strange number in
nuclear matter, which is shown in the right panel of Figure.
\ref{field}, and $(\sigma^*,\phi)$ couple only to $s$ quark. The
$\delta$ meson increases $\rho_{03}$ meson field, and the effect
becomes smaller when the $\delta$ meson field decreases as baryon
density increases.
\begin{figure}
\begin{center}
\includegraphics[width=7cm]{field}
\includegraphics[width=7.3cm]{strangenum}
\caption{(Color online) The left panel are meson fields as functions
of baryon density for $npH^*$. The right panel is the ratio of $s$
quark to total quark in nuclear matter versus baryon density. The
upper two curves are for $npH$ and the lower two are for
$npH^*$.}\label{field}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width=7cm]{composition}
\caption{The compositions of neutron stars in $npH^*$ as a function
of baryon density and the vertical lines represent the central
baryon densities of neutron stars with maximum
mass.}\label{composition}
\end{center}
\end{figure}
Let's look at the compositions of nuclear matter for $npH^*$ in
Figure. \ref{composition}. $\delta$ meson decreases the neutron
fraction while increases the proton and lepton fractions when
$\rho\gtrsim\rho_0$. From the right panel of Figure. \ref{mu} we see
that $\delta$ meson decreases the effective mass of neutron, which
makes the neutron fraction fall when the density exceed some
critical density which is approximately nuclear matter density
$\rho_0$ as shown in Figure. \ref{composition}. The proton fraction
goes up because the similar reason, and the charge neutrality
condition requires larger lepton fractions.
\begin{figure*}
\begin{center}
\includegraphics[width=14cm]{mu}
\caption{(Color online) The left panel is the changes of chemical
potentials of neutron and lepton and the quark-meson exchange
potentials versus the baryon density $\rho$ when the $\delta$ meson
are included. The right panel is the differences of baryon effective
masses. Both are for $npH^*$.}\label{mu}
\end{center}
\end{figure*}
$\Sigma^{-}, \Xi^{-}$ (negative isospin projection) and $\Lambda,
\Sigma^{0}$ (zero isospin projection) appear earlier when $\delta$
meson are included, but the appearance of $\Sigma^{+}$ (positive
isospin projection) is postponed. From equations (\ref{betaequ}),
(\ref{eB}) and (\ref{BaryonFermi}), we know that the fraction for
baryon $B$ is determined by $(\mu_n-q_B\mu_e)$, $(g_{\omega
B}\omega_0+g_{\phi B}\phi_0+g_{\rho B}I_{3B}\rho_{03})$ and $M_B^*$,
which are all shown in the Figure. \ref{mu}. We see that the changes
of $g_{\omega}^{q} \omega_0$ and $g_{\phi}^{q}\phi$ are proximately
offseted; $ M_B^*$ and $g_{\rho}^u\rho_{03}$ (Compare Figure.
\ref{mu} with Figure. \ref{field}, we can see that the change of
$g_{\rho}^u\rho_{03}$ mainly origins in the large change of
quark-$\rho$ meson coupling constant $g_{\rho}^u$) change obviously.
The changes of $ g_{\rho B}I_{3B}\rho_{03}$ and $M_B^*$ are
isospin-dependent, so whether the hyperon appears earlier is
determined by its isospin projection. The critical density of its
appearance only shifts a little except $\Xi^-$, since the changes of
$ g_{\rho B}I_{3B}\rho_{03}$ and $M_B^*$ are almost the same.
The $\Sigma^-$ population with $\delta$ meson is larger than that
without $\delta$ meson at the beginning, but it becomes smaller than
that without $\delta$ meson because of the appearance of $\Xi^-$.
The reasons are that charge neutrality can be kept more economically
by the larger mass particles with the same charge, and the $\delta$
meson decreases $M_{\Sigma^{-}}^{*}$ more than $M_{\Xi^{-}}^{*}$
(right panel of Figure.\ref{mu}) since the isospin projection of
$\Xi^-$ is $-1/2$ and $\Sigma^-$ is $-1$. $\delta$ meson increases
$\Xi^-$ population obviously larger than other hyperons since it
decreases $\Sigma^-$ population. The appearance of $\Sigma^-$ makes
the lepton fraction begins to fall, which can also be explained by
charge neutrality condition. There is another interesting phenomenon
that the $\Sigma^{+}$ may not appear in neutron stars with $\delta$
meson while its fraction could exceed 1\% for neutron stars at the
maximum masses without $\delta$ meson.
\begin{figure}
\begin{center}
\includegraphics[width=7cm]{EOS}
\caption{(Color online) The equation of state, pressure $P$ versus
energy density $\varepsilon$ for all cases we study in this paper.
The causual limit ($P=\varepsilon$) is also shown.}\label{EOS}
\end{center}
\end{figure}
The EOSes for $nn, np, npH, npH^*$ are plotted in Figure. \ref{EOS}.
The effects of $\delta$ meson can be seen clearly from this figure:
The $\delta$ meson makes the EOS of $nn$ stiffer similar as in QHD
model \cite{EOSH}. For $np$, the $\delta$ meson stiffens the EOS at
low density while softens at high density. The density-dependent
coupling constants are introduced additionally in QHD model
\cite{Liu2} to get the similar results, but the density-dependence
of couplings between scalar mesons and baryons are obtained
self-consistently in our paper. If hyperons are taken into account,
the EOSes with $\delta$ meson suffer a transition to nucleon-hyperon
phase at some density and become softer, this can be seen from the
EOSes of $npH$ and $npH^*$ in Figure. \ref{EOS} clearly. $(\sigma^*,
\phi)$ mesons obviously stiffen the EOSes as in Ref.\cite{Pal}, but
their influences on the $\delta$ meson effect could be neglected.
Since $(\sigma^*,\phi)$ meson fields couple only to $s$ quark and
$\delta$ meson couple only to ($u$, $d$) quarks, $\delta$ meson has
no direct influence on $(\sigma^*,\phi)$ meson fields, which can
also be seen from the lower panel in Figure. \ref{field} as
mentioned above.
We find that no matter whether hyperons are positive, negative or
neutral, their inclusions can make the EOSes with $\delta$ meson
become softer. This result probably reveals that it is the strange
quark makes the EOSes with $\delta$ meson become softer. That is to
say that it is the strange quarks in hyperons results in reversed
direction changes of EOSes if compared with a nucleonic star.
\begin{figure}
\begin{center}
\includegraphics[width=8cm]{mr}
\caption{(color online) The mass-radius relation for neutron stars
in $nn$, $np$, $npH^*$, $npH$. The filled triangles, inverted
triangles, squares and circles represent the positions of maximum
masses for $nn$, $np$, $npH^*$, $npH$ EOSes, respectively. A
gravitational redshift of 0.35 \cite{redshift} (observed from EXO
0748-676) is shown in this figure. Mass-radius constraints from
thermal radiation of isolated NS RX J1856.5-3754 \cite{RXJ1856}
(cyan hatched area) and from QPOs in the LMXBs 4U 0614+09
\cite{4U0614} (magenta hatched area) and 4U 1636-536 \cite{4U1636}
(orange hatched area) shall be regarded as separate constraints to
the EOSes. The mass of PSR 1913+16 \cite{PSR1913} is also shown in
this figure.}\label{mr}
\end{center}
\end{figure}
The mass-radius relation of neutron stars are shown in Figure.
\ref{mr}. We see that the $\delta$ meson increases the maximum
masses of neutron stars for all cases we studied in this paper. This
is different from QHD model in which the maximum mass decreases for
$np$ with density-dependent couplings \cite{Liu2} and $npH$ when
$\delta$ meson are included \cite{EOSH}. The $\delta$ meson enlarge
the radii of neutron stars about 0.5 km for stars with $M>M_{s}$,
this is an obvious change considering the same EOS at low density
are used for all cases. Another conclusion is that the central
density of neutron star becomes about 0.5 $\rho_0$ smaller when
$\delta$ meson is included. These can be seen from Table \ref{tb4}
clearly. Some observation values are also displayed in Figure.
\ref{mr}. We can see that all cases are compatible with the
observations from PSR 1913+16 \cite{PSR1913} and 4U 0614+09
\cite{4U0614}, but $npH^*$ and $npH$ neutron stars might be ruled
out by neutron star 4U 1636-536 \cite{4U1636} or EXO 0748-676
\cite{redshift}. To show quantitatively the $\delta$ meson effects
on neutron stars properties, the maximum mass $M_{\rm max}$ and the
corresponding radii $R_{M_{\rm max}}$, central baryon density
$\rho_c$, central energy density $\varepsilon_{c}$, central pressure
$P_{c}$ are listed in Table \ref{tb4} for all cases.
\begin{table}
\begin{center}
\caption{The maximum masses of neutron stars and the corresponding
radii $R_{M_{\rm max}}$, central baryon density $\rho_c$, central
energy density $\varepsilon_{c}$, central pressure $P_{c}$ for
different EOSes.}\begin{tabular} {ccccccc}\hline\hline
&$g_\delta^u$&$M_{\rm max}/M_{s}$ &$R_{M_{\rm max}}$ &$\rho_c/\rho_0$ &$\varepsilon_c$ &$P_c$\\
&& &(km) & &(MeV\ fm$^{-3}$) &(MeV\ fm$^{-3}$)\\
\hline
$nn$&4.2 &2.275 &12.07 &5.1 &1093 &418\\
$nn$&0 &2.147 &11.50 &5.6 &1213 &459\\
$np$&4.2 &2.045 &11.30 &6.0 &1274 &446\\
$np$&0 &2.012 &10.95 &6.3 &1352 &493\\
$npH^*$&4.2 &1.556 &11.56 &6.0 &1157 &201\\
$npH^*$&0 &1.543 &11.10 &6.5 &1274 &236\\
$npH$&4.2 &1.509 &12.03 &5.2 &986 &140\\
$npH$&0 &1.491 &11.54 &5.8 &1106 &166\\
\hline \hline
\end{tabular}\label{tb4}
\end{center}
\end{table}
\section{Conclusions}\label{sect5}
We have investigated the $\delta$ meson effects on neutron star
proporties within the modified quark-meson coupling model. We sum up
the conclusions in four aspects:
(1)$\delta\leftrightarrow$strangeness: the $\delta$ meson can make
the pure nucleonic matter EOSes stiffer, while make the hyperon
matter EOSes softer and this could be explained by the appearance of
strange quarks in hyperons.
(2)$\delta\leftrightarrow$leptons: the $\delta$ meson results in
opposite effects on the EOSes of $\beta$-equilibrium nuclear matter
such as $np$, $npH$ and $npH^*$ compared with the EOS of $nn$, which
is similar to the influence of hyperons, but the effect is smaller.
This is because of density-dependence of the couplings between
baryons and scalar mesons.
(3)$\delta\leftrightarrow(\sigma^*, \phi)$: $\delta$ meson has no
direct influence on $s$ quark, so it has little effect on
$(\sigma^*,\phi)$ meson fields. As a result, $(\sigma^*,\phi)$
mesons have no obvious influence to the $\delta$ meson effect on
EOSes, although ($\sigma^*, \phi$) stiffen the EOSes obviously.
(4)$\delta\leftrightarrow$ neutron star properties: the $\delta$
meson can increase the maximum masses of neutron stars, decrease the
corresponding both baryon density and energy density. The radii
become about 0.5 km larger for stars with $M>M_{s}$. It changes
compositions of neutron stars: decrease the neutron fraction and
increase the proton and leptons fractions when $\rho\gtrsim\rho_0$;
make the abundance of $\Xi^{-}, \Xi^{0}$ and $\Sigma^{+}$ larger,
while the abundance of $\Sigma^{-}$ smaller; and increase the
strange number of neutron stars. It can also make the isospin
dependent physical quantities splitting, such as effective baryons
masses.
\section*{Acknowledgments}
One of the authors Chun-Yuan Gao acknowledges the financial support
from the National Natural Science Foundation of China under grants
10305001, 10475002 \& 10435080. The authors are grateful to
Professor Pawel Danielewicz for providing the data for pressure-
density relationship consistent with the experimental flow data
which is indicated by the shaded region in Figure. \ref{gdelta}. We
thank to the useful guidance of Professor Jie Meng and the inspiring
discussions with Chang-Qun Ma and Bao-Yuan Sun.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 4,193
|
Who were the Ancient Egyptians? Where did they live?
What was everyday life like for an Ancient Egyptian?
Who was Howard Carter and why is he famous?
Why was the River Nile so important?
Literacy: Journalistic writing – watching Pigeon Impossible and writing a recount of the events that took place. Explanation texts – explaining how to mummify a body!
The Y4 Spelling page has our spelling lists for Autumn 1.
Maths: Counting, reading, writing and ordering numbers to at least 9,999, counting forwards and backwards in steps of different sizes, calculating and solving problems using addition and subtraction, rounding numbers to the nearest whole number, 10, 100 or 1000. Tables facts- knowing all tables facts to 12 x 12 from memory and using these to work out division facts e.g. if 7x8=56, then 56÷8=7. Number – addition and subtraction working towards using formal methods.
'MyMaths' is used for some set homework tasks but also has many useful games for online home learning.
Science: We will be investigating how electricity works and what is required to make a successful circuit. We'll then use this knowledge to illuminate a pyramid.
IT: We'll be revising how to search the Internet safely and effectively, and learning more about the Egyptians using an archaeological simulation.
Music: In music, we'll be learning songs with an Egyptian theme.
DT: We'll be learning how the Ancient Egyptians used shadufs to help irrigate the land; we'll then design and make our own.
RE: We be thinking about Egyptian death rituals/ceremonies and then comparing them with Christian ceremonies.
PE: Indoor PE will be on Monday afternoons. Outdoor PE will be on Thursday afternoons, but please make sure that PE kit is in school at all times in case things change. We will also be continuing to do the Golden Mile so trainers will be needed in school every day.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 8,564
|
In this article the temperament of psychiatric conditions will be fully explained.
Therefore all lifestyle tips for warm and dry Mizaj (temperament) would apply to anger and excitement as two psychiatric conditions. Eating spicy, sweat, salty, deep fried and roasted food stuff especially in warm seasons would trigger anger and excitement.
These people should cut back on dairy products, watery and sour fruits and other food stuff of the kind. Instead they had better use food and hot drinks with warm temperament. Kebabs, spices, salty and spicy food, cinnamon tea, saffron tea, mint tea, or ginger tea suits such people as the fear and the sadness they feel caused by cold Mizaj of their brain or body would go away and they feel more courageous and fear less.
It is worth mentioning that one should not necessarily experience the fear or anger, even imagining such psychiatric conditions would produce the same result.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 4,004
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
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<head>
<title>Description of spsvd</title>
<meta name="keywords" content="spsvd">
<meta name="description" content="Space frequency SVD of input data - continuous processes">
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<!-- ../../menu.html chronux_2_10 --><!-- ../menu.html spectral_analysis --><!-- menu.html continuous -->
<h1>spsvd
</h1>
<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../../../up.png"></a></h2>
<div class="box"><strong>Space frequency SVD of input data - continuous processes</strong></div>
<h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../../../up.png"></a></h2>
<div class="box"><strong>function [sv,sp,fm] = spsvd(data,params,mdkp) </strong></div>
<h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../../../up.png"></a></h2>
<div class="fragment"><pre class="comment"> Space frequency SVD of input data - continuous processes
Usage: [sv,sp,fm] = spsvd(data,params,mdkp)
Inputs:
data (data matrix in timexchannels form)-required
params structure containing parameters - params has the
following fields: tapers, Fs, fpass, pad
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Fs (sampling frequency) -- optional. Defaults to 1.
fpass (frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
pad (padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
mdkp (number of dimensions to be kept)-optional. Default is the
maximum possible modes determined by taper parameters
Outputs:
sv sp fm : singular values, space modes, frequency modes</pre></div>
<!-- crossreference -->
<h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../../../up.png"></a></h2>
This function calls:
<ul style="list-style-image:url(../../../matlabicon.gif)">
<li><a href="../../../chronux_2_10/spectral_analysis/helper/dpsschk.html" class="code" title="function [tapers,eigs]=dpsschk(tapers,N,Fs)">dpsschk</a> Helper function to calculate tapers and, if precalculated tapers are supplied,</li><li><a href="../../../chronux_2_10/spectral_analysis/helper/getfgrid.html" class="code" title="function [f,findx]=getfgrid(Fs,nfft,fpass)">getfgrid</a> Helper function that gets the frequency grid associated with a given fft based computation</li><li><a href="../../../chronux_2_10/spectral_analysis/helper/getparams.html" class="code" title="function [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params)">getparams</a> Helper function to convert structure params to variables used by the</li></ul>
This function is called by:
<ul style="list-style-image:url(../../../matlabicon.gif)">
</ul>
<!-- crossreference -->
<h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../../../up.png"></a></h2>
<div class="fragment"><pre>0001 <a name="_sub0" href="#_subfunctions" class="code">function [sv,sp,fm] = spsvd(data,params,mdkp)</a>
0002 <span class="comment">% Space frequency SVD of input data - continuous processes</span>
0003 <span class="comment">% Usage: [sv,sp,fm] = spsvd(data,params,mdkp)</span>
0004 <span class="comment">% Inputs:</span>
0005 <span class="comment">% data (data matrix in timexchannels form)-required</span>
0006 <span class="comment">% params structure containing parameters - params has the</span>
0007 <span class="comment">% following fields: tapers, Fs, fpass, pad</span>
0008 <span class="comment">% tapers : precalculated tapers from dpss or in the one of the following</span>
0009 <span class="comment">% forms:</span>
0010 <span class="comment">% (1) A numeric vector [TW K] where TW is the</span>
0011 <span class="comment">% time-bandwidth product and K is the number of</span>
0012 <span class="comment">% tapers to be used (less than or equal to</span>
0013 <span class="comment">% 2TW-1).</span>
0014 <span class="comment">% (2) A numeric vector [W T p] where W is the</span>
0015 <span class="comment">% bandwidth, T is the duration of the data and p</span>
0016 <span class="comment">% is an integer such that 2TW-p tapers are used. In</span>
0017 <span class="comment">% this form there is no default i.e. to specify</span>
0018 <span class="comment">% the bandwidth, you have to specify T and p as</span>
0019 <span class="comment">% well. Note that the units of W and T have to be</span>
0020 <span class="comment">% consistent: if W is in Hz, T must be in seconds</span>
0021 <span class="comment">% and vice versa. Note that these units must also</span>
0022 <span class="comment">% be consistent with the units of params.Fs: W can</span>
0023 <span class="comment">% be in Hz if and only if params.Fs is in Hz.</span>
0024 <span class="comment">% The default is to use form 1 with TW=3 and K=5</span>
0025 <span class="comment">%</span>
0026 <span class="comment">% Fs (sampling frequency) -- optional. Defaults to 1.</span>
0027 <span class="comment">% fpass (frequency band to be used in the calculation in the form</span>
0028 <span class="comment">% [fmin fmax])- optional.</span>
0029 <span class="comment">% Default all frequencies between 0 and Fs/2</span>
0030 <span class="comment">% pad (padding factor for the FFT) - optional (can take values -1,0,1,2...).</span>
0031 <span class="comment">% -1 corresponds to no padding, 0 corresponds to padding</span>
0032 <span class="comment">% to the next highest power of 2 etc.</span>
0033 <span class="comment">% e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT</span>
0034 <span class="comment">% to 512 points, if pad=1, we pad to 1024 points etc.</span>
0035 <span class="comment">% Defaults to 0.</span>
0036 <span class="comment">% mdkp (number of dimensions to be kept)-optional. Default is the</span>
0037 <span class="comment">% maximum possible modes determined by taper parameters</span>
0038 <span class="comment">%</span>
0039 <span class="comment">% Outputs:</span>
0040 <span class="comment">% sv sp fm : singular values, space modes, frequency modes</span>
0041
0042
0043 <span class="keyword">if</span> nargin < 1; error(<span class="string">'Need data'</span>); <span class="keyword">end</span>;
0044 <span class="keyword">if</span> nargin < 2 || isempty(params); params=[]; <span class="keyword">end</span>;
0045 [tapers,pad,Fs,fpass,err,trialave,params]=<a href="../../../chronux_2_10/spectral_analysis/helper/getparams.html" class="code" title="function [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params)">getparams</a>(params);
0046 clear err trialave params
0047 [N,NCHAN]=size(data);
0048 tapers=<a href="../../../chronux_2_10/spectral_analysis/helper/dpsschk.html" class="code" title="function [tapers,eigs]=dpsschk(tapers,N,Fs)">dpsschk</a>(tapers,N,Fs);
0049 nfft=max(2^(nextpow2(N)+pad),N);<span class="comment">% number of points in fft</span>
0050 [N,K]=size(tapers);
0051 <span class="keyword">if</span> nargin<3 || isempty(mdkp); mdkp=min(K,NCHAN);
0052 <span class="keyword">elseif</span> mdkp > min(K,NCHAN); error(<span class="string">'mdkp has to be less than both K and NCHAN'</span>);<span class="keyword">end</span>;
0053
0054 tvec=(1:N)';
0055 tvec=repmat(tvec,[1 K]);
0056 tvec=tvec*2*pi*i;
0057 f=<a href="../../../chronux_2_10/spectral_analysis/helper/getfgrid.html" class="code" title="function [f,findx]=getfgrid(Fs,nfft,fpass)">getfgrid</a>(Fs,nfft,fpass);
0058 nf=length(f);
0059 sp=zeros(NCHAN,nf,mdkp);
0060 sp=sp+i*sp;
0061 fm=zeros(K,nf,mdkp);
0062 fm=fm+i*fm;
0063 sv=zeros(nf,min([K,NCHAN]));
0064 <span class="keyword">for</span> j=1:nf
0065 <span class="comment">% for k=1:K</span>
0066 <span class="comment">% proj(:,k)=tapers(:,k).*exp(-f0*tvec');</span>
0067 <span class="comment">% end</span>
0068 proj=tapers.*exp(-f(j)*tvec);
0069 tmp=data'*proj; <span class="comment">% projected data</span>
0070 [u,s,v]= svd(tmp,0); <span class="comment">% svd</span>
0071 <span class="keyword">for</span> mk=1:mdkp,
0072 sp(:,j,mk)=u(:,mk)';
0073 fm(:,j,mk)=v(:,mk)';
0074 <span class="keyword">end</span>
0075 sv(j,:)=diag(s);
0076 <span class="keyword">end</span>;</pre></div>
<hr><address>Generated on Fri 12-Aug-2011 11:36:15 by <strong><a href="http://www.artefact.tk/software/matlab/m2html/" target="_parent">m2html</a></strong> © 2005</address>
</body>
</html>
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3
|
<?php
namespace Circuit\Middleware;
use Circuit\Interfaces\Middleware;
use Circuit\Interfaces\Delegate;
use Symfony\Component\HttpFoundation\Request;
use Symfony\Component\HttpFoundation\Response;
/**
* Parameter Matcher
*
* A middleware that reorders controller method parameters so that named parameters in the method signature
* match to named parameters in the router definition. Any unmatched parameters will be called in their original
* order
*
* @author Nik Barham <nik@brokencube.co.uk>
*/
class ParameterMatcher implements Middleware
{
/**
* Run Middleware for a particular request
*
* @param Request $request HTTP Foundation Request object
* @param Delegate $delegate Either the Router or HandlerContainer, depending on whether this is run pre or post
* routing
* @return Response
*/
public function process(Request $request, Delegate $delegate) : Response
{
$params = $request->attributes->get('controller');
$args = $params->args;
$parameters = (new \ReflectionClass($params->className))->getMethod($params->method)->getParameters();
if ($parameters[0]->name == 'request') {
array_shift($parameters);
}
$count = count($parameters);
$newparams = [];
// Slot matched params in proper order
foreach ($parameters as $var => $p) {
foreach ($args as $key => $value) {
if ($key == $p->name) {
$newparams[$var] = $value;
unset($args[$key]);
}
}
}
// Fill in any unmatched gap based on original order (minus tracks)
for ($i = 0; $i < $count; $i++) {
if (!array_key_exists($i, $newparams)) {
$newparams[$i] = array_shift($args);
}
}
ksort($newparams);
$param->args = $newparams;
return $delegate->process($request);
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 4,568
|
IRC 0 =1.030 or greater.
Series scored using the High Scoring System, the more difficult races are weighted with a factor of 1.3 for cross channel Races over 100 miles. 1.2 for cross channel races less than 100 miles. 1.0 for the Night Race and 0.9 for day races.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 799
|
orbitbooks.net
orbitshortfiction.com
**Begin Reading**
Table of Contents
Orbit Newsletter
Copyright Page
In accordance with the U.S. Copyright Act of 1976, the scanning, uploading, and electronic sharing of any part of this book without the permission of the publisher constitute unlawful piracy and theft of the author's intellectual property. If you would like to use material from the book (other than for review purposes), prior written permission must be obtained by contacting the publisher at permissions@hbgusa.com. Thank you for your support of the author's rights.
_For All My Fellow Barbarians_
# PART I
# OF MORTAL WISHES
Friendship is the daughter of virtue. Villains may be accomplices but not friends.
—Francisco Goya, subtitle to _¡Quién lo creyera!_ , in _Los Caprichos_ (1799)
# [CHAPTER
1](toc.xhtml#toc-chapter001)
It was all going so nicely, right up until the massacre.
Sir Hjortt's cavalry of two hundred spears fanned out through the small village, taking up positions between half-timbered houses in the uneven lanes that only the most charitable of surveyors would refer to as "roads." The warhorses slowed and then stopped in a decent approximation of unison, their riders sitting as stiff and straight in their saddles as the lances they braced against their stirrups. It was an unseasonably warm afternoon in the autumn, and after their long approach up the steep valley, soldier and steed alike dripped sweat, yet not a one of them removed their brass skullcap. Weapons, armor, and tack glowing in the fierce alpine sunlight, the faded crimson of their cloaks covering up the inevitable stains, the cavalry appeared to have ridden straight out of a tale, or galloped down off one of the tapestries in the mayor's house.
So they must have seemed to the villagers who peeked through their shutters, anyway. To their colonel, Sir Hjortt, they looked like hired killers on horseback barely possessed of sense to do as they were told most of the time. Had the knight been able to train wardogs to ride he should have preferred them to the Fifteenth Cavalry, given the amount of faith he placed in this lot. Not much, in other words, not very much at all.
He didn't care for dogs, either, but a dog you could trust, even if it was only to lick his balls.
The hamlet sprawled across the last stretch of grassy meadow before the collision of two steep, bald-peaked mountains. Murky forest edged in on all sides, like a snare the wilderness had set for the unwary traveler. A typical mountain town here in the Kutumban range, then, with only a low reinforced stone wall to keep out the wolves and what piddling avalanches the encircling slopes must bowl down at the settlement when the snows melted.
Sir Hjortt had led his troops straight through the open gate in the wall and up the main track to the largest house in the village... which wasn't saying a whole lot for the building. Fenced in by shedding rosebushes and standing a scant two and a half stories tall, its windowless redbrick face was broken into a grid by the black timbers that supported it. The mossy thatched roof rose up into a witch's hat, and set squarely in the center like a mouth were a great pair of doors tall and wide enough for two riders to pass through abreast without removing their helmets. As he reached the break in the hedge at the front of the house, Sir Hjortt saw that one of these oaken doors was ajar, but just as he noticed this detail the door eased shut.
Sir Hjortt smiled to himself, and, reining his horse in front of the rosebushes, called out in his deepest baritone, "I am Sir Efrain Hjortt of Azgaroth, Fifteenth Colonel of the Crimson Empire, come to counsel with the mayor's wife. I have met your lord mayor upon the road, and while he reposes at my camp—"
Someone behind him snickered at that, but when Sir Hjortt turned in his saddle he could not locate which of his troops was the culprit. It might have even come from one of his two personal Chainite guards, who had stopped their horses at the border of the thorny hedge. He gave both his guards and the riders nearest them the sort of withering scowl his father was overly fond of doling out. This was no laughing matter, as should have been perfectly obvious from the way Sir Hjortt had dealt with the hillbilly mayor of this shitburg.
"Ahem." Sir Hjortt turned back to the building and tried again. "Whilst your lord mayor reposes at my camp, I bring tidings of great import. I must speak with the mayor's wife at once."
Anything? Nothing. The whole town was silently, fearfully watching him from hiding, he could feel it in his aching thighs, but not a one braved the daylight either to confront or assist him. Peasants—what a sorry lot they were.
"I say again!" Sir Hjortt called, goading his stallion into the mayor's yard and advancing on the double doors. "As a colonel of the Crimson Empire and a knight of Azgaroth, I shall be welcomed by the family of your mayor, or—"
Both sets of doors burst open, and a wave of hulking, shaggy beasts flooded out into the sunlight—they were on top of the Azgarothian before he could wheel away or draw his sword. He heard muted bells, obviously to signal that the ambush was under way, and the hungry grunting of the pack, and—
The cattle milled about him, snuffling his horse with their broad, slimy noses, but now that they had escaped the confines of the building they betrayed no intention toward further excitement.
"Very sorry, sir," came a hillfolk-accented voice from somewhere nearby, and then a small, pale hand appeared amid the cattle, rising from between the bovine waves like the last, desperate attempt of a drowning man to catch a piece of driftwood. Then the hand seized a black coat and a blond boy of perhaps ten or twelve vaulted himself nimbly into sight, landing on the wide back of a mountain cow and twisting the creature around to face Sir Hjortt as effortlessly as the Azgarothian controlled his warhorse. Despite this manifest skill and agility at play before him, the knight remained unimpressed.
"The mayor's wife," said Sir Hjortt. "I am to meet with her. Now. Is she in?"
"I expect so," said the boy, glancing over his shoulder—checking the position of the sun against the lee of the mountains towering over the village, no doubt. "Sorry again 'bout my cows. They're feisty, sir; had to bring 'em down early on account of a horned wolf being seen a few vales over. And I, uh, didn't have the barn door locked as I should have."
"Spying on us, eh?" said Sir Hjortt. The boy grinned. "Perhaps I'll let it slide this once, if you go and fetch your mistress from inside."
"Mayoress is probably up in her house, sir, but I'm not allowed 'round there anymore, on account of my wretched behavior," said the boy with obvious pride.
"This isn't her home?" Hjortt eyed the building warily.
"No, sir. This is the barn."
Another chuckle from one of his faithless troops, but Sir Hjortt didn't give whoever it was the satisfaction of turning in his saddle a second time. He'd find the culprit after the day's business was done, and then they'd see what came of having a laugh at their commander's expense. Like the rest of the Fifteenth Regiment, the cavalry apparently thought their new colonel was green because he wasn't yet twenty, but he would soon show them that being young and being green weren't the same thing at all.
Now that their cowherd champion had engaged the invaders, gaily painted doors began to open and the braver citizenry slunk out onto their stoops, clearly awestruck at the Imperial soldiers in their midst. Sir Hjortt grunted in satisfaction—it had been so quiet in the hamlet that he had begun to wonder if the villagers had somehow been tipped off to his approach and scampered away into the mountains.
"Where's the mayor's house, then?" he said, reins squeaking in his gauntlets as he glared at the boy.
"See the trail there?" said the boy, pointing to the east. Following the lad's finger down a lane beside a longhouse, Sir Hjortt saw a small gate set in the village wall, and beyond that a faint trail leading up the grassy foot of the steepest peak in the valley.
"My glass, Portolés," said Sir Hjortt, and his bodyguard walked her horse over beside his. Sir Hjortt knew that if he carried the priceless item in his own saddlebag one of his thuggish soldiers would likely find a way of stealing it, but not a one of them would dare try that shit with the burly war nun. She handed it over and Sir Hjortt withdrew the heavy brass hawkglass from its sheath; it was the only gift his father had ever given him that wasn't a weapon of some sort, and he relished any excuse to use it. Finding the magnified trail through the instrument, he tracked it up the meadow to where the path entered the surrounding forest. A copse of yellowing aspen interrupted the pines and fir, and, scanning the hawkglass upward, he saw that this vein of gold continued up the otherwise evergreen-covered mountain.
"See it?" the cowherd said. "They live back up in there. Not far."
Sir Hjortt gained a false summit and leaned against one of the trees. The thin trunk bowed under his weight, its copper leaves hissing at his touch, its white bark leaving dust on his cape. The series of switchbacks carved into the increasingly sheer mountainside had become too treacherous for the horses, and so Sir Hjortt and his two guards, Brother Iqbal and Sister Portolés, had proceeded up the scarps of exposed granite on foot. The possibility of a trap had not left the knight, but nothing more hostile than a hummingbird had showed itself on the hike, and now that his eyes had adjusted to the strangely diffuse light of this latest grove, he saw a modest, freshly whitewashed house perched on the lip of the next rock shelf.
Several hundred feet above them. Brother Iqbal laughed and Sister Portolés cursed, yet her outburst carried more humor in it than his. Through the trees they went, and then made the final ascent.
"Why..." puffed Iqbal, the repurposed grain satchel slung over one meaty shoulder retarding his already sluggish pace, "in all the... devils of Emeritus... would a mayor... live... so far... from his town?"
"I can think of a reason or three," said Portolés, setting the head of her weighty maul in the path and resting against its long shaft. "Take a look behind us."
Sir Hjortt paused, amenable to a break himself—even with only his comparatively light riding armor on, it was a real asshole of a hike. Turning, he let out an appreciative whistle. They had climbed quickly, and spread out below them was the painting-perfect hamlet nestled at the base of the mountains. Beyond the thin line of its walls, the lush valley fell away into the distance, a meandering brook dividing east ridge from west. Sir Hjortt was hardly a single-minded, bloodthirsty brute, and he could certainly appreciate the allure of living high above one's vassals, surrounded by the breathtaking beauty of creation. Perhaps when this unfortunate errand was over he would convert the mayor's house into a hunting lodge, wiling away his summers with sport and relaxation in the clean highland air.
"Best vantage in the valley," said Portolés. "Gives the headperson plenty of time to decide how to greet any guests."
"Do you think she's put on a kettle for us?" said Iqbal hopefully. "I could do with a spot of hunter's tea."
"About this mission, Colonel..." Portolés was looking at Sir Hjortt but not meeting his eyes. She'd been poorly covering up her discomfort with phony bravado ever since he'd informed her what needed to be done here, and the knight could well imagine what would come next. "I wonder if the order—"
"And I wonder if your church superiors gave me the use of you two anathemas so that you might hem and haw and question me at every pass, instead of respecting my command as an Imperial colonel," said Sir Hjortt, which brought bruise-hued blushes to the big woman's cheeks. "Azgaroth has been a proud and faithful servant of the Kings and Queens of Samoth for near on a century, whereas your popes seem to revolt every other feast day, so remind me again, what use have I for your counsel?"
Portolés muttered an apology, and Iqbal fidgeted with the damp sack he carried.
"Do you think I relish what we have to do? Do you think I would put my soldiers through it, if I had a choice? Why would I give such a command, if it was at all avoidable? Why—" Sir Hjortt was just warming to his lecture when a fissure of pain opened up his skull. Intense and unpleasant as the sensation was, it fled in moments, leaving him to nervously consider the witchborn pair. Had one of them somehow brought on the headache with their devilish ways? Probably not; he'd had a touch of a headache for much of the ride up, come to think of it, and he hadn't even mentioned the plan to them then.
"Come on," he said, deciding it would be best to drop the matter without further pontification. Even if his bodyguards did have reservations, this mission would prove an object lesson that it is always better to rush through any necessary unpleasantness, rather than drag your feet and overanalyze every ugly detail. "Let's be done with this. I want to be down the valley by dark, bad as that road is."
They edged around a hairpin bend in the steep trail, and then the track's crudely hewn stair delivered them to another plateau, and the mayor's house. It was similar in design to those in the hamlet, but with a porch overhanging the edge of the mild cliff and a low white fence. Pleasant enough, thought Sir Hjortt, except that the fence was made of bone, with each outwardly bowed moose-rib picket topped with the skull of a different animal. Owlbat skulls sat between those of marmot and hill fox, and above the door of the cabin rested an enormous one that had to be a horned wolf; when the cowherd had mentioned such a beast being spied in the area, Sir Hjortt had assumed the boy full of what his cows deposited, but maybe a few still prowled these lonely mountains. What a thrill it would be, to mount a hunting party for such rare game! Then the door beneath the skull creaked, and a figure stood framed in the doorway.
"Well met, friends, you've come a long way," the woman greeted them. She was brawny, though not so big as Portolés, with features as hard as the trek up to her house. She might have been fit enough once, in a country sort of way, when her long, silvery hair was blond or black or red and tied back in pigtails the way Hjortt liked... but now she was just an old woman, same as any other, fifty winters young at a minimum. Judging from the tangled bone fetishes hanging from the limbs of the sole tree that grew inside the fence's perimeter—a tall, black-barked aspen with leaves as hoary as her locks—she might be a sorceress, to boot.
Iqbal returned her welcome, calling, "Well met, Mum, well met indeed. I present to you Sir Hjortt of Azgaroth, Fifteenth Colonel of the Crimson Empire." The anathema glanced to his superior, but when Sir Hjortt didn't fall all over himself to charge ahead and meet a potential witch, Iqbal murmured, "She's just an old bird, sir, nothing to fret about."
"Old bird or fledgling, I wouldn't blindly stick my hand in an owlbat's nest," Portolés said, stepping past Sir Hjortt and Iqbal to address the old woman in the Crimson tongue. "In the names of the Pontiff of the West and the Queen of the Rest, I order you out here into the light, woman."
"Queen of the Rest?" The woman obliged Portolés, stepping down the creaking steps of her porch and approaching the fence. For a mayor's wife, her checked dirndl was as plain as any village girl's. "And Pontiff of the West, is it? Last peddler we had through here brought tidings that Pope Shanatu's war wasn't going so well, but I gather much has changed. Is this sovereign of the Rest, blessed whoever she be, still Queen Indsorith? And does this mean peace has once again been brokered?"
"This bird hears a lot from her tree," muttered Sir Hjortt, then asked the woman, "Are you indeed the mayor's wife?"
"I am Mayoress Vivi, wife of Leib," said she. "And I ask again, respectfully, to whom shall I direct my prayers when next I—"
"The righteous reign of Queen Indsorith continues, blessed be her name," said Sir Hjortt. "Pope Shanatu, blessed be _his_ name, received word from on high that his time as Shepherd of Samoth has come to an end, and so the war is over. His niece Jirella, blessed be _her_ name, has ascended to her rightful place behind the Onyx Pulpit, and taken on the title of Pope Y'Homa III, Mother of Midnight, Shepherdess of the Lost."
"I see," said the mayoress. "And in addition to accepting a rebel pope's resignation and the promotion of his kin to the same lofty post, our beloved Indsorith, long may her glory persist, has also swapped out her noble title? 'Queen of Samoth, Heart of the Star, Jewel of Diadem, Keeper of the Crimson Empire' for, ah, 'Queen of the Rest'?" The woman's faintly lined face wrinkled further as she smiled, and Portolés slyly returned it.
"Do not mistake my subordinate's peculiar sense of humor for a shift in policy—the queen's honorifics remain unchanged," said Sir Hjortt, thinking of how best to discipline Portolés. If she thought that sort of thing flew with her commanding colonel just because there were no higher-ranked clerical witnesses to her dishonorable talk, the witchborn freak had another thing coming. He almost wished she would refuse to carry out his command, so he'd have an excuse to get rid of her altogether. In High Azgarothian, he said, "Portolés, return to the village and give the order. In the time it will take you to make it down I'll have made myself clear enough."
Portolés stiffened and gave Sir Hjortt a pathetic frown that told him she'd been holding out hope that he would change his mind. Not bloody likely. Also in Azgarothian, the war nun said, "I'm... I'm just going to have a look inside before I do. Make sure it's safe, Colonel Hjortt."
"By all means, Sister Portolés, welcome, welcome," said the older woman, also in that ancient and honorable tongue of Sir Hjortt's ancestors. Unexpected, that, but then the Star had been a different place when this biddy was in her prime, and perhaps she had seen more of it than just her remote mountain. Now that she was closer he saw that her cheeks were more scarred than wrinkled, a rather gnarly one on her chin, and for the first time since their arrival, a shadow of worry played across the weathered landscape of her face. Good. "I have an old hound sleeping in the kitchen whom I should prefer you left to his dreams, but am otherwise alone. But, good Colonel, Leib was to have been at the crossroads this morning..."
Sir Hjortt ignored the mayor's wife, following Portolés through the gate onto the walkway of flat, colorful stones that crossed the yard. They were artlessly arranged; the first order of business would be to hire the mason who had done the bathrooms at his family estate in Cockspar, or maybe the woman's apprentice, if the hoity-toity artisan wasn't willing to journey a hundred leagues into the wilds to retile a walk. A mosaic of miniature animals would be nice, or maybe indigo shingles could be used to make it resemble a creek. But then they had forded a rill on their way up from the village, so why not have somebody trace it to its source and divert it this way, have an actual stream flow through the yard? It couldn't be that hard to have it come down through the trees there and then run over the cliff beside the deck, creating a miniature waterfall that—
"Empty," said Portolés, coming back outside. Sir Hjortt had lost track of himself—it had been a steep march up, and a long ride before that. Portolés silently moved behind the older woman, who stood on the walk between Sir Hjortt and her house. The matron looked nervous now, all right.
"My husband Leib, Colonel Hjortt. Did you meet him at the crossroads?" Her voice was weaker now, barely louder than the quaking aspens. That must be something to hear as one lay in bed after a hard day's hunt, the rustling of those golden leaves just outside your window.
"New plan," said Sir Hjortt, not bothering with the more formal Azgarothian, since she spoke it anyway. "Well, it's the same as the original, mostly, but instead of riding down before dark we'll bivouac here for the night." Smiling at the old woman, he said, "Do not fret, Missus Mayor, do not fret, I won't be garrisoning my soldiers in your town, I assure you. Camp them outside the wall, when they're done. We'll ride out at first"—the thought of sleeping in on a proper bed occurred to him—"noon. We ride at noon tomorrow. Report back to me when it's done."
"Whatever you're planning, sir, let us parley before you commit yourself," said the old woman, seeming to awaken from the anxious spell their presence had cast upon her. She had a stern bearing he wasn't at all sure he liked. "Your officer can surely tarry a few minutes before delivering your orders, especially if we are to have you as our guests for the night. Let us speak, you and I, and no matter what orders you may have, no matter how pressing your need, I shall make it worth your while to have listened."
Portolés's puppy-dog eyes from over the woman's shoulder turned Sir Hjortt's stomach. At least Iqbal had the decency to keep his smug gaze on the old woman.
"Whether or not she is capable of doing so, Sister Portolés will _not_ wait," said Sir Hjortt shortly. "You and I are talking, and directly, make no mistake, but I see no reason to delay my subordinate."
The old woman looked back past Portolés, frowning at the open door of her cabin, and then shrugged. As if she had any say at all in how this would transpire. Flashing a patently false smile at Sir Hjortt, she said, "As you will, fine sir. I merely thought you might have use for the sister as we spoke, for we may be talking for some time."
Fallen Mother have mercy, did every single person have a better idea of how Sir Hjortt should conduct himself than he did? This would not stand.
"My good woman," he said, "it seems that we have even more to parley than I previously suspected. Sister Portolés's business is pressing, however, and so she must away before we embark on this long conversation you so desire. Fear not, however, for the terms of supplication your husband laid out to us at the crossroads shall be honored, reasonable as they undeniably are. Off with you, Portolés."
Portolés offered him one of her sardonic salutes from over the older woman's shoulder, and then stalked out of the yard, looking as petulant as he'd ever seen her. Iqbal whispered something to her as he moved out of her way by the gate, and wasn't fast enough in his retreat when she lashed out at him. The war nun flicked the malformed ear that emerged from Iqbal's pale tonsure like the outermost leaf of an overripe cabbage, rage rendering her face even less appealing, if such a thing was possible. Iqbal swung his heavy satchel at her in response, and although Portolés dodged the blow, the dark bottom of the sackcloth misted her with red droplets as it whizzed past her face. If the sister noticed the blood on her face, she didn't seem to care, dragging her feet down the precarious trail, her maul slung over one hunched shoulder.
"My husband," the matron whispered, and, turning back to her, Sir Hjortt saw that her wide eyes were fixed on Iqbal's dripping sack.
"Best if we talk inside," said Sir Hjortt, winking at Iqbal and ushering the woman toward her door. "Come, come, I have an absolutely brilliant idea about how you and your people might help with the war effort, and I'd rather discuss it over tea."
"You said the war was over," the woman said numbly, still staring at the satchel.
"So it is, so it is," said Sir Hjortt. "But the _effort_ needs to be made to ensure it doesn't start up again, what? Now, what do you have to slake the thirst of servants of the Empire, home from the front?"
She balked, but there was nowhere to go, and so she led Sir Hjortt and Brother Iqbal inside. It was quiet in the yard, save for the trees and the clacking of the bone fetishes when the wind ran its palm down the mountain's stubbly cheek. The screaming didn't start until after Sister Portolés had returned to the village, and down there they were doing enough of their own to miss the echoes resonating from the mayor's house.
# [CHAPTER
2](toc.xhtml#toc-chapter002)
Everything was dull dull _dull_ , until the princess snuck away from the interminable Equinox Ceremony taking place in the Autumn Palace and went in search of spirits in the pumpkin fields surrounding the Temple of Pentacles.
Ji-hyeon Bong wasn't really _the_ princess, only _a_ princess. At home in her familial castle at Hwabun she was one of three, and the middle one at that. And here, in the capital, with all the court gathered, there must be more princesses than there were stars in the sky, all crammed into a multiplicity of ballrooms. Even without being the sole princess in the palace, however, getting away had proven difficult, since Princess Ji-hyeon was here in part to formally meet her fiancé for the very first time. Prince Byeong-gu of Othean, fourth son of Empress Ryuki, Keeper of the Immaculate Isles, seemed every bit as stuck-up as his title had implied, and so Ji-hyeon set herself to escape at all costs, but she never would have managed it without the help of her three guards (especially her Spirit Guard, Brother Mikal, much as he had protested the plan initially). Now the fifteen-year-old woman traipsed through tangled vines under a moon as fat as the gourds at her feet, the hubbub inside the palace walls reduced to a drone much softer than the rasping of fuzzy leaves against silk skirts.
"Your Highness," Brother Mikal called from where he and Keun-ju, the princess's Virtue Guard, strolled along one of the straight paths that cut through the field. "I wonder if you might favor to walk with us here, between the rows rather than across them? Keun-ju is concerned for your gown."
"If Keun-ju would prefer to carry my dress for safeguarding, I have no objections to walking naked on such a pleasant eve," said Ji-hyeon, happy to hear the reserved boy splutter by way of response. He hardly minded such joking when they were alone in her chambers, but in front of Brother Mikal and Choi was another matter.
"In all seriousness, Princess, I wonder if he might have a point—" Mikal began, but Ji-hyeon cut him off.
"Wonder no longer, then, for I favor my own approach," she said, but the wit of her riposte was spoiled as she tripped over a pumpkin. She would have gone down if Choi hadn't been there to catch her arm; Ji-hyeon grinned at her Martial Guard, and Choi warmly flashed her shark teeth in response. Stitched up in her own slick black gown at the ceremony, Choi could have passed for human, a princess even, if not for her petite horns. She had also looked about as comfortable as a lobster sitting on the edge of a pot, and no more talkative. Ji-hyeon preferred her wildborn guard when the woman was relaxed enough to open her deceptively small, fang-filled mouth; apparently guests to her home at Hwabun sometimes assumed the woman was mute, so rarely was she at her ease.
"Do you think we'll find one?" Ji-hyeon asked eagerly.
"The moon's full and the equinox is near," said Choi in her gruff, quiet voice. "I'll be surprised if you don't, this near to a hungry mouth."
Ji-hyeon liked Choi's sharp teeth, and her ebony horns, and her sometimes frightening speed, and even her sword lessons, exhausting though they were, but most of all the princess liked the way Choi would use the wrong words for things. It was never an error in vocabulary, Ji-hyeon knew, but rather that the wildborn thought the Immaculate tongue was often misused even by native speakers—every cat was actually a trouble, every sword a tusk, every arrow a disgrace... and every Gate a hungry mouth. Looking at the tall pearl walls of the Temple of Pentacles shining ahead of them like a lighthouse across a vegetal sea, Ji-hyeon shivered with delight. She liked being scared, a little, which was part of why she loved Choi so much.
She loved _all_ of them so much, the three complementing one another every bit as much as they complemented their ward: Choi was serious, but Mikal was very funny and charming and handsome for an older foreign man, and Keun-ju, well, Keun-ju was Keun-ju, her best friend since forever, pretty much. Her Virtue Guard was almost as comely as Mikal and almost as good at swordplay as Choi, plus Keun-ju was better at dressmaking than either, which Ji-hyeon enjoyed just as much as fencing.
And once she was married to Prince Boring, she would have to leave them all behind and accept whatever new guards her husband provided for her. It made her heartsick, and she turned her mind from it, hard though it was to do when she had just met the man who would take her closest friends away from her. None of the others mentioned it, either, their numbered days the proverbial whale in the carp pond.
"Is there anything else we can do?" she asked. "Other than walk around, hoping we get lucky?"
"Luck is an excuse," said Choi. "If you kept a better vigil you would have already succeeded. I've seen three so far."
"Nuh-uh!" cried Ji-hyeon, imitating her younger sister's imitation of some yet younger cousin. "Choi! Why didn't you show me?"
Choi's eyes flashed like rubies even in the colorless pall of the moon, and she gestured to the plants at their feet. "Keep a better vigil."
"Mikal!" Ji-hyeon called a good deal louder than was necessary, knowing how much Choi despised an excess of volume... or an excess of anything, really. Other than vigilance. "Mikal, can you do something to make them appear?"
"Ji-hyeon, the brother's function is the very opposite of _that_ , as you well know," said Keun-ju huffily. "Stop trying to get him in trouble."
"If my parents find out he bribed the palace guards to spirit me away from the festival, I think that will cause a lot more embarrassment than if he fulfills the dearest wish of a darling daughter," said Ji-hyeon. "Don't you think?"
"Princess, do you believe I am making sport with you when I profess my ignorance of the spirits of your land?" The path Mikal and Keun-ju followed was taking them away from Ji-hyeon and Choi, and so the pair began tramping over to their noble ward. "I would be reluctant to make any assumptions as to their character or, for that matter, their humor at being addressed by a foreigner. Why not return to the palace and ask one of your priestesses if—"
"If I wanted to talk to the nuns I would have stayed at the party," said Ji-hyeon, wishing every night could be this perfect, just she and her guards questing beneath a full moon. "I want to see a harvest devil."
"Then hush your mouth and be vigilant," said Choi.
"I am being vigilant, I just—oh!" Ji-hyeon froze, her heart plunging into ice water as if she had noticed a snake underfoot, her muddy silk shoe suspended in the air above a twisting coil of black vines. The round pumpkin at its center rolled backward in its nest, revealing the triangular eyes and jagged mouth of its face—a faint yellow glow emanated from within the gourd, pouring from maw and eyes to illuminate the gilt hem of Ji-hyeon's jet gown, shining off the silver buckle of her shoe and the abalone inlay of her dress sword's scabbard. Then, fast as she'd seen it, the saffron light faded, the eyes and mouth closed over, and it was just a pumpkin again.
Ji-hyeon squealed in delight, looked up to see if the others had seen... and then gasped, stumbled back, dumbstruck by what reared up in front of her, twenty feet tall, rasping, churning, spiraling. Maddening.
"Back to the palace, Princess," Choi hissed as she put herself between Ji-hyeon and the cobra-swaying monolith of vines and leering jack-o'-lanterns that had erupted from the fertile soil of the temple fields. "Now!"
# [CHAPTER
3](toc.xhtml#toc-chapter003)
While the copper kettle came to a boil, Sir Hjortt insisted on a tour of the house. Not bad. The interior wouldn't need too much work beyond redecorating (the tacky old tapestries had to go, and fast). The wall between the kitchen and the living room ought to be punched out, though, to make the ground floor more of a hall. The mayor and mayoress had a surprisingly impressive library, no fewer than fifty tomes crammed onto a beautifully turned fir shelf, so it wasn't all doilies and bric-a-brac, although there was certainly a bit of that, too. The mantel was cluttered with wooden tubāq pipes and horsehair pottery. He would have to pick out a nice pipe for Aunt Lupitera and a vase for his father. The rest could be trashed.
Once the herbs or roots or whatever had steeped and been deemed safe for consumption by Brother Iqbal, the witchborn fatass took his tea on the deck overlooking the valley while Sir Hjortt and the mayoress convened at her kitchen table. Under the heavy walnut board dozed a lean mutt that looked as old as the woman and bore more resemblance to a coyote or bearded jackal than it did to a hound. Through the open shutters the aspens gossiped away, their inscrutable whispers as relaxing as strong fingers kneading the knots out of Sir Hjortt's saddle-cursed buttocks.
"I wish that you would speak plainly with me, sir," said the matron, all business now that the tea was poured and she was back in her domestic element. Not even the bloody satchel sitting next to the plate of scones she had put out could shake her up, the hard old cow. "All this stalling is beginning to grate."
"Is it?" said Sir Hjortt, frowning into his tea and returning the terra-cotta cup to its saucer. It smelled bitter, whatever she'd put in the pot disagreeing with his nostrils. No tea, then. Bother.
"Is that... is my husband in that bag?"
"No, not your husband," said Sir Hjortt, annoyed that she was leaping to such conclusions, stealing his show. The best he could come up with to reassert his dominance of the situation was to abruptly stand, grab the satchel, and upend its contents onto the table in front of her. It dropped out and, even better than he'd expected, bounced off the table into her lap. "Just his head."
Rather than screaming as the knight had hoped, or at least pitching it away in understandable disgust, the woman shrunk her broad shoulders inward as her callused fingers went to the severed head, turning it over to look at her husband's face. That was a cold draught, it was, seeing this grey hen gently stroke the disgusting, matted hair and gaze lovingly into the wide, horror-frozen eyes of a dead man. The smell was strong from the warm ride, and it turned Sir Hjortt's stomach.
"Go ahead and cry if you need to," said the knight, hoping to prod a more appropriate reaction from the biddy. "Perfectly understandable, given... well, obviously."
She looked up at him, and he was satisfied to see her pallid blue eyes shine with emotion. Hatred, maybe, but it was better than nothing. So quietly he barely heard her, she said, "Tears enough in time, Colonel."
The woman set the head back on the table, nesting it in the discarded satchel to keep it from rolling off again, and slowly stood. She was half a foot shorter than the knight, and more than twice his age at a minimum, but Sir Hjortt nevertheless shivered to see the wrath on her face.
A loud bark at groin level made Sir Hjortt start, but rather than attacking his codpiece the mutt shoved its muzzle out from under the table and nosed it against the knight's bare palm—he had taken off his gauntlet for tea, naturally. He was far more of a cat person, but there's only so much one can do when confronted with the pleading, rheumy eyes of an ancient dog in desperate need of a petting. He dug his fingers in behind a floppy ear, drawing forth a contented whine, but as he did he kept an eye on the mayor's widow lest she try something stupid with teapot or butter knife.
It seemed the enormity of the situation had finally sunk in, for her face fell as she watched him scratch the dog, all her rage replaced with bald terror. Sir Hjortt made no attempt to hide his smirk, and only ceased giving the beast his attention when it licked his fingers and happily tottered away of its own accord. He watched it go to the old woman, but she made no move to pet it, looking back and forth between the animal and the knight with features so wracked that Sir Hjortt wondered if she was having a heart attack right there in front of him.
Then the dog looked back over its shoulder and _smiled_ at him, its chops curling back to reveal black, rotting teeth and a grub-white tongue. The ugly expression on the mutt's snout gave Sir Hjortt the chills, and then the dog circled behind the trembling woman and hobbled through the kitchen doorway, wagging its tail as it went. Wiping its now-cold slobber off his hand as he heard it nose the front door open, the knight silently repledged his allegiance to the far less disquieting feline race and decided that prolonging this affair wasn't so enjoyable after all.
"As we told your husband," he began, gesturing to the mayor's head, "the terms of—"
"What have you done?" the old woman whispered, her eyes fixed on the open kitchen door with such intensity that Sir Hjortt glanced over to make sure there wasn't someone creeping up on him. "You stupid, wretched, idiot boy, what have you done?"
"I'm not a boy," said Sir Hjortt, hating her for forcing the sulky words to leave his mouth. "I am a knight of the realm, and I—"
"To the village," she said, the fear scoured off her face by something much, much worse as she directed a ferocious stare at her guest. "By the six devils I bound, what order did you give your Chainwitch, boy? What did you tell her to do to my people?"
"Sisters of the Burnished Chain are _not_ witches," Sir Hjortt huffed, all this _boy_ talk putting him in a ratty mood. This old bird was about to learn a very hard lesson about respecting one's betters. "As for my orders, they involve the two hundred lances I positioned in your town before climbing up to this dump."
A distant scream rode in on the breeze just then, so perfectly timed that Sir Hjortt wondered if Brother Iqbal was eavesdropping on their conversation and had somehow given Sister Portolés a signal. Commendations all around, if so!
Sir Hjortt realized with disappointment that he had forgotten to get his hawkglass back from Portolés before sending her down to the village; how was he supposed to see anything from up here without it? She should have known he'd want it and reminded him to hold on to it. It wouldn't surprise him if she had taken it with her just to spite him. Well, even if he couldn't see the action down in the town, he could still have some fun with this old coot.
Rather than upsetting the matron, the distant scream had brought an evil grin to her chapped lips, twisting her already woodsy features into the grimace of an especially gnarled knothole. She turned to the open door leading onto the deck, where Sir Hjortt could see the chain-encircled-crown crest of the newly reunited Crimson Empire emblazoned on the back of Brother Iqbal's cloak. The witchborn was looking down over the rail at the hamlet far below, and the mayor's widow stepped out onto the deck to join him, her legs the only part of her not shivering like a plucked fiddle string.
"As I told your husband before I had him executed..." began Sir Hjortt, thinking for sure this would regain her attention. It didn't, but he went on anyway, following her to the door as she walked slowly to the railing. "I believe the terms your husband so _generously_ offered our army are identical to those he brokered with Pope Shanatu's troops when this territory fell under his dominion during the civil war. On an appointed day your mayor shall deliver to the crossroads below your valley approximately one-fifth of your yearly root wines, cheeses, and marmot oil in peacetime, and one-half in times of war. In exchange your citizens shall not be pressed into service, your children shall not be enslaved, and your borders shall be defended. Did I miss anything?"
"No." Her voice was no louder than the zephyr passing through the trees as she set her hands on the thin wooden balustrade and gazed down. Brother Iqbal glanced over at the woman beside him, offering her a sympathetic grimace.
"Fair terms, Mum," said Iqbal. "Most fair."
"Why?" she asked, still not looking away, although from up here she couldn't possibly see much of the action. The distant screams and clangor had grown louder, though. "In the name of the six devils I bound, _why_?"
That weird oath of hers seemed to befuddle Iqbal, the man's perpetually snowmead-whitened lips silently repeating it as he stared at the woman. Sir Hjortt had heard stranger curses on a slow day at court. Following her as far as the doorway, he called after her, "I don't owe you any answers, woman. Besides, I'm sure that smart mouth of yours can supply one of its own."
"Maybe so," she said quietly, hands gripping the railing.
"Really, though, we're spoiled for choice, aren't we?" said Sir Hjortt. "Maybe it's because the fealty due the pontiff and queen shall _not_ be decided by the hill-creatures who pay it. Maybe it's because by your husband's own admission, the citizenry of this village traded supplies to Pope Shanatu's rebel army, which makes your people traitors to the Crown. And maybe an example has to be made, for all the other backwater towns who took up arms against the rightful ruler of the Crimson Empire—bad luck on your husband's part, to be waiting at the crossroads with tribute for the losing team when our scouts spotted him."
"Before this last war we always delivered our annual tithe to agents of the queen. We trade food to those who demand it, regardless of what banners they fly—to do otherwise would provoke an assault we could never withstand. And so you're sacking a village guilty of no greater crime than common sense, and... and... _bad luck_?" She looked back at Sir Hjortt, her cobalt eyes wild as the Bitter Sea. "You're destroying everything these innocents have as _an example_?"
"That's about the shape of it," said Sir Hjortt, leaning against the doorframe. Another headache had been fomenting behind his temples ever since this nanny goat had started bleating _why-why-why_ at him, and it was only growing worse. "But fret not, woman, fret not, the letter of the terms is being honored—your borders are quite secure, and my soldiers have it on my strictest orders not to flirt with a single villager, no matter how tempting, nor shackle even one of your plump little moppets, rich a price as they might fetch in Her Grace's markets."
"No?" There was the most delicious tinge of hope in her voice.
"No," said Sir Hjortt, pleased that she had given him the setup he so dearly desired. Now for the punch line. "Every single one of your townies is being put to the steel. No exceptions. Other than you, of course. You we let live."
"Is that so?" She didn't flinch—cold as the Queen of Samoth, this one.
"You are charged with a task of the utmost importance to Crown and Chain," said Sir Hjortt, a rumble in his belly turning up to keep his headache company. One of those scones might settle his stomach. "Fill her in, Iqbal."
"Good Colonel Hjortt and I discussed your future on our promenade up to your lovely home," Iqbal said genially as Sir Hjortt returned to the kitchen table. "And we came to terms that I think will be most agreeable to Chain, Crown, and, of course, yourself."
The woman muttered something Sir Hjortt couldn't quite make out, but it must have been fresh, for Brother Iqbal faked a laugh before continuing.
"Our pontiff loves you, Mum, just as she loves all those worthy martyrs below. As her sole representative on this charming veranda, I offer you, nay, _honor_ you with the charge of becoming one of her apostles. You shall be a mendicant witness, traveling from burg to burg to testify of your experience here today, and—"
Sir Hjortt bit into a fluffy apple scone just as Iqbal let out a squeal, and the knight looked up from his snack in time to see the witchborn go toppling over the railing. Iqbal plummeted out of sight, and then his high-pitched wail abruptly cut off. The old woman straightened up from the half-crouch she had dropped into in order to launch the brother. Sir Hjortt laughed in surprise, crumbs flying—had that fat fool actually been murdered by a widow old enough to be his mother? This would make quite the story back in Cockspar!
What a day, Sir Hjortt thought as he drew his sword and strode back onto the deck with more enthusiasm than he had felt all campaign, scone still trapped in his teeth; what an absurd, marvelous day!
# [CHAPTER
4](toc.xhtml#toc-chapter004)
The elders of Sullen's clan blew a lot of smoke about how you never forgot your first devil. They claimed a Horned Wolf's life was split between the nameless pup that sat at a storyteller's knee, enraptured by tales, and the adult who lived legends instead of dreaming them. The turning point from whelp to worthy member of the clan was not your first battle, your first kill, or even your naming, but the first devil you saw watching you from the darkness, the first time you looked at a beast and _knew_ it was something more than mundane. Until you had squared off against a devil and stared it down, you had no right to call yourself a member of the Horned Wolf Clan.
That rite of passage had been a lot easier back when the Star teemed with devils, of course, but nowadays they were almost as rare as the clan's totem animal. Used to be folk could earn their place at the fire either way, by finding a devil or fighting a horned wolf, but such great deeds seemed near impossible in the modern age. Being as there were hardly any of the monsters left in the world—all praise the true goddess—proving your teeth to your people involved a whole lot of dicking around in the misty tundra outside of the village. Invariably the young ones went loopy from exposure or starvation, and stumbled back into town claiming to have seen all manner of bat-winged fiends perching in the boughs of what few bur oaks remained on the Frozen Savannahs. They were flogged by their parents for telling tales, and that was about it—most everyone under the age of fifty grumbled that the elders put a primacy of honor on devil sightings as a means of preventing younger members of the tribe from joining the ruling council.
Sullen couldn't recall his first devil, because for as long as he could remember they had been there, watching him. Not the corporeal ones— _the ones that counted_ , according to the elders—but vague, phantasmal creatures that sometimes flitted around the edge of his vision, brightening into focus only as he was drifting off to sleep. In the Immaculate tongue his mother insisted he learn to deal with the foreign traders, these immaterial monsters were called _spirits_ , but Sullen knew they were the same devils from all the songs, only ones that hadn't yet claimed a living body. Grandfather said Sullen could see the devils that nobody else could because he'd been born with the eyes of a snow lion, and the one time Sullen had broken the clan's laws about not looking at your own reflection lest one of your evil ancestors possess you, he had seen that the old man was right. Unlike the rest of his clan, whose uniformally human peepers came in various shades of brown and green, Sullen's pupils were slits in eyes the rich blue of the glaciers bordering the nearby coast where the Immaculates landed their ships. It had scared him, seeing a monster looking back at him from the still pool where he had stolen a peek at himself, and from that day on he better understood why his clan viewed him the way they did.
He actively tried to avoid thinking about his affliction, as his mother called it, for the devils never bothered him... but his grandfather, who'd been kicked off the council ages ago after getting into a row with the poison oracle, insisted that in his day Sullen would have been a great shaman, to be so marked by the gods.
"Marked by devils, you mean." Sullen's mother shuddered, making the sign of the Chain as they finished their bowls of rice and cassava porridge. "My poor boy. I don't blame you, Sullen, you know I don't."
At ten, Sullen was bigger than any other pup in the village, and by sixteen he was the tallest, broadest Horned Wolf in the clan. He could do the work of five (and frequently did), and when Old Salt's donkey pitched over dead halfway through the planting, Sullen hitched himself up and finished the field. He tried never to let his strength go to his head, and went out of his way to help those less physically blessed than himself. For all his might, he was a gentle, caring boy.
And with the exception of his mother and grandfather, every single person in his entire clan hated him and wished he would die. He was marked by the devils.
"I _mean_ marked by the gods!" Sullen's grandfather crowed at his daughter, tossing his empty bowl onto the dirt floor of the hut. Sullen retrieved it so his mom wouldn't have to. "We call ourselves Horned Wolves, but here's a real beast, one of the chosen of old, and they all despise him! A boy with the blood of shamans treated like an oath-breaker, it's enough to—"
"I told you the last time, we will not speak of this again," said Sullen's mom, in her most dangerously even tone. "Our ways are the only ways, and the council has been merciful with him. With both of you."
" _Our_ ways?" said Grandfather with a sneer. "Our ways are _dead_ , child, ever since those toothless greypelts decided we should forsake our ancestors and start bowing before a Samothan devil. I don't even know these people anymore. Where do a pack of limp-horned Chainites get off—"
"Old man, I won't warn you again to pay me more respect," said Sullen's mother, rising from the floor with all the foreboding solemnity of a gathering storm. "Had I not shamed myself by letting you back into my hut, I would have taken another husband by now. And if I were to cast you out, who else in the clan would take you? Either of you?"
"It's all right, Fa," said Sullen, coming between the two to clear the rest of the dinner mat. "It's all just a test, is all. The Fallen Mother tests us all."
"The Fallen Mother is a lie," Grandfather hissed much later that night, when even the coals in the hearth were trying to get a little shut-eye. "A _liiiiiiie_ , cooked up by Imperials to take our teeth. What kind of goddess doesn't show herself to her people, eh? When the Old Watchers wanted to test us, they put a damn monster in our path to see how well we fought! None of this walking 'round with your hands at your sides, playing the anvil to those backbiting little hyenas!"
"I ain't been hit in ages," Sullen said, forgetting that his mother wanted him to pretend to be asleep when her dad went on his heretical rants. "Not since I lost my temper with Yaw Thrim all them summers back."
Yaw Thrim was now known as One-arm Yaw, on account of Sullen's slippery temper. Sullen had been fourteen at the time, Yaw twenty-three. Sullen didn't even remember what had happened after Yaw pinned him down in the permafrost and started pummeling his face; everything after that was as hazy as the devils that danced just beyond his vision. Yaw remembered, though, and his family said he still woke up screaming some nights, clutching at the twisted burl of scar tissue with his only remaining hand.
"They almost done you for that," said Grandfather. "Even with you just defending yourself, they would've done you for sure if you'd had one more hair on your balls, or that bullyboy had one less hair in his beard. Next time you stick up for yourself they'll kill you, boy, they'll kill you twice to make sure it takes."
"It'll be all right, Fa," said Sullen, rolling over to face the dark wall.
"It won't be all right until you act like a ruddy Horned Wolf and leave these pagans in your dust," said Grandfather. "When I was your age we didn't trade with no Immaculates, we raided 'em! Now we don't even build boats no more, and moved too far from the sea to hear the songs of the Deep Folk. Horned Wolves, digging fields and building churches like Red Imperials. I wish they'd had the decency to burn me alive so I didn't have to see such things come to pass. Craven knew what was coming. I've cursed him every dawn and dusk for leaving us the way he did, but now I wish he'd come back and taken me with him. He could've lashed me to his back and carried me out of here—Horned Wolves my arse, we're just plain old sheep these days."
"Do you think Uncle's still alive?" asked Sullen, forgetting he was trying to sleep and rolling back over to face his crotchety grandfather on the prickly cot they all shared.
"Might could be, might could be," said Grandfather, as though considering the possibility for the first time. Sullen's mother snorted in her sleep, and even lower than before, Grandfather said, "I don't see a man die I don't assume he's dead. The last time we seen him he was alive enough, I expect you remember that."
Sullen definitely remembered more than he cared to from the day Uncle Craven had forsaken them... the day Sullen's father had died, the day Sullen fought his first battle against a rival clan. The day he took his first kill. He remembered how rich the air tasted before the fighting started; it was the first time he had come close enough to the Bitter Sea to smell salt and sand mingling with the scent of fresh snow. He remembered how he had pretended he was fighting alongside his ancestors in one of the old songs, how he had believed Old Black would shield them from their enemies. He remembered the glint of sunlight on the blade that ran through his father's heart, and the way the blood seemed to turn the sword to black ice when it was pulled free of his breast. He remembered how weightless his arm had felt when he threw his sun-knife, and how heavy it became when he saw his weapon enter a man's hip and bring him crashing to the ground, to be stomped and stabbed in the chaos. He remembered how the Jackal People had laughed as they fought, laughing harder as they lost, laughing until the last of them was brought low on the blood-thawed battlefield. He remembered how sad and scared he had been, remembered it like it was yesterday.
He also remembered what had come after, would remember it until his dying day. The dead eyes of his father, staring past his sobbing son and into the whiteness beyond. The gleaming eyes of the snow lions creeping in to eat the dead before the victorious Horned Wolves had even quit the scene, eyes that were the same as Sullen's. Grandfather lying howling in the gore-spattered tundra, hacked through the tailbone by a pepper-smeared sword. And the backs of their people as the Horned Wolves headed home, his mother, Uncle Craven, and the rest of the clan following custom by leaving his wounded grandfather to the scavengers, and Sullen, too, when he wouldn't leave the old man's side.
Sullen had been eight thaws old. He killed his first snow lion that night, and started dragging his grandfather back to the village. It had taken six days, Sullen collecting snow in the mornings for their waterskins and frost-termites for their breakfast. By the time they'd made it back to the disbelieving scowls of their clan, Uncle Craven was long gone. Again.
"But you said—" Sullen paused as his mother rolled over beside him, so excited he could barely keep his voice to a whisper. "You said they'd ambush Uncle before he got a week out, kill him good to make sure he couldn't shame our people ever again."
"Wishful thinking of an angry father. If those runts the council sent after him had actually caught the boy they'd have come home singing about it, instead of playing it too fierce to talk about. No, my boy can't be any deader than the cold cod we got around here," said Grandfather longingly. "I got half a mind to see if I can't track 'im down before I find my doom, or it finds me. Fess to him he was wise to leave, a fool to ever come back, and wiser still the second time he lit out. Tell him... tell him his dad don't understand why he did what he done, but he's finally ready to listen."
The wind whistled through the thatch of their hut, and in the darkness Sullen squinted to see the wraithlike devils capering over his bed. No wolf worthy of his horns would leave his pack, no matter how worthless a gang they were... a real horned wolf would whip them into shape or die trying rather than turning tail. How many times had Grandfather said that?
So this must not be the same as turning tail. Grandfather just wanted to find Uncle Craven, and then they would come back. The same as Uncle Craven, really, who'd gone missing as an unnamed boy, only to return a thaw or three before Sullen was born and live as a proper Horned Wolf up until that dark day of the battle. Even after Uncle Craven broke their laws by leaving the first time, when he'd come back the clan had welcomed him. That Uncle Craven had just run away again a few years later and the clan now cursed his name more than any devil didn't matter so much, because once Sullen and Grandfather returned they'd never leave again. This would be a quest for Sullen to earn his honor, not too different from the Songs of Rakehell or the Saga of Old Black. He knew their tales by heart, kenned the heroes of old in a way he had never understood the Horned Wolves he had come of age alongside. He had always longed to have an adventure of his own, and they were thin on the ground here in the Frozen Savannahs.
The thought of meeting his uncle—of demanding to know why he'd abandoned him and Grandfather on the battlefield just to abandon the clan altogether—filled Sullen with a strange and powerful hunger. Not a small hunger, neither; no, this felt like he'd just smelled a thick slice of barley bread topped with a scoop of lye cod after the midwinter fast. He could let Grandfather talk to Uncle Craven, and then he could talk to him, and then all three of them could come home together, and Sullen would bring along such treasures as he'd found along the way as to make all the clan love him... or maybe just respect him a little. It wasn't as though he and Grandfather would be terribly missed—they would probably be home again before anyone noticed they were gone. Theirs would be a song worth singing, even if he only ever sang it to himself when he was sure he was alone.
Looking back and forth between his snoring mother and his eager grandfather, Sullen made up his mind. Would his mother be heartbroken when she awoke and found both her father and son gone, or would she secretly be relieved? Sullen didn't know, and as always, the not knowing made everything so much worse.
# [CHAPTER
5](toc.xhtml#toc-chapter005)
What an absurd, appalling day.
_Take some initiative_ , his father was always saying, like the chorus in the tragedy that was Sir Hjortt's life, _for the love of your ancestors, get off your doughy ass and take some initiative_. And the one time he took that advice, the one fucking time, where did it get him? Right fucking here, apparently. Thanks, Dad.
Sir Hjortt straddled a painful fence, split between hatred at the probably deceased Brother Iqbal for neglecting to detect the old woman's witchcraft and good old-fashioned self-pity. The mayoress clearly had the aid of devils, for she'd dodged the knight's sword with the speed of a water weasel and then broken his arm with the strength of an ox. An angry one. The steel cop covering his elbow had actually popped loose from her barehanded assault, dangling as worthlessly as the arm it had failed to protect.
The knight had been in his fair share of scrapes—well, one or two, anyway—but the agony of his arm being snapped backward had beggared belief. By the time his mind had recovered from its shock the old witch had dragged him back inside her kitchen. His sole attempt at further resistance had resulted in her frogging him in the eye with a curled finger and then twisting his broken arm until he retched from the pain of it all. After that, he did as he was told and let her tie him to a chair with the coil of thick cord she had scared up. The most that could be said for his situation was that he barely registered his headache anymore.
Now she was stomping around upstairs and Sir Hjortt's thoughts were beginning to crawl back toward rationality—she had undone both Iqbal and himself, doubtless with some fell sorcery, and now he was her prisoner. Even if Sister Portolés came straight back after giving the order to purge the town, it was a long walk up the hill. He might be alone with the old woman for a while, and had best ensure she knew what a healthy ransom he would command before she did anything regrettable. Well, anything _more_ regrettable.
Footfalls on the stairs in the other room, and then she bustled back into the kitchen and deposited a pile of clothing onto the table. She paused, then picked up a linen shirt and draped it over her husband's head, covering it and the scones. Next she pulled her dirndl over her head, and then her blouse. Although she didn't seem to possess an extra breast on which her familiars might suckle or any other witchly deformities, her inexplicable stripping sat poorly with her captive.
Her head snapped in his direction, and Sir Hjortt realized with horror that he must have inadvertently made his displeasure known with a groan or something. He tried to play it off, lolling his head and staring down at his broken arm as he moaned. She walked over and backhanded him across the cheek, which was entirely uncalled for and flew in the face of all acceptable conduct regarding noble prisoners of war. He knew because he'd memorized those passages of the Crimson Codices, lest he ever find it necessary to surrender rather than die an easily avoided death on some random battlefield.
"You should have let me speak," she said, putting her face right in his, her breath stinking like that awful tea. "Instead of sending your Chainwitch down to murder my people, you should have let me have my say. You'd be counting coins right now. A lot of them. I'd follow you and kill you, of course, for what you did to Leib, but I'd have given you a few weeks to put this place behind you, lest anyone suspect the motive and return to Kypck. You might have enjoyed those extra days of easy living."
"This 'Leib' is your husband." Sir Hjortt frowned, his face stinging from her blow. "Kypck's your town."
"Leib was my husband, before you killed him. Kypck was my town, before you killed it, too. If you're not on a battlefield, you should learn the names of those you slaughter, if only to taunt any vengeful pursuers."
"From his first breath to his last, the wise general never leaves the battlefield," said Sir Hjortt sagely. "Only thus is peace won."
"Ugh," said the witch, wrinkling her nose. "They're still hammering Lord Bleak's _Ironfist_ into the Crimson command? No wonder you're such a shameless bastard, swallowing that fascist dog shit."
"You've read it?" said Sir Hjortt, surprised.
" 'Poor strategies should be studied as well as wise ones, for generals shall adopt the former more oft than the latter.' You know who said that?" The naked old sorceress was still leaning over him, and as one of the waves of pain rolled back out to sea he realized she was actually waiting for a response. He shook his head. "Ji-un Park," she said.
"They no more taught us the tactics of Immaculates than they did the stratagems of squirrels," said Sir Hjortt. "But I think it's high time we talked ransom, my lady, as—"
"My lady, is it?" She snorted. "You'd have been better off studying the squirrels than Lord Bleak—they have the sense to stay away from beehives, even if they are full of honey."
"I... uh." Sir Hjortt felt the heat spread from his broken arm up to his cheeks at the lewd way the matron breathed the words in his face, and he looked away from her nakedness. By all the devils and deacons of the Burnished Chain, what was she going to do, cast a spell?
Instead of ensorcelling him, the woman turned away and went back to the clothes piled on the table. After fishing out a tan pair of trousers, she squeezed into them with a grunt and then fixed a leather... thing across her bosom. Over that went a shirt or tunic or something—the knight had stopped paying attention in order to try and wriggle his ankles free, get some options going... but when she'd tied his legs to the chair she'd been thorough, and he couldn't do more than impotently squirm in his seat.
She left the room, banged around the rest of the house, and then came back into the kitchen with a stout, one-handed war hammer and an unstrung bow. Setting these on the clothes pile, she disappeared again. Sir Hjortt stared at the hammer nervously. She returned with an already bulging backpack and set to wrestling the remaining clothes into it, save for the shirt covering her husband's head.
"My lady," he said, but she ignored him, and so he tried again. It was like reasoning with his father, only worse. He hadn't thought such a thing was possible, prior to this moment. "Madame Mayoress, if I might—"
"You might shut your mouth before I decide to cut out your tongue—you could choke to death on your own blood. For all I know your Sister Portolés is halfway up the hill, and I don't intend to be here when she finds the remains of your other pet witch."
"You're the only witch here," said Sir Hjortt, although now that she mentioned it he wondered if Portolés had somehow sensed it when Iqbal died, if she was even now racing up the trail to—shit on fire, the hag was messing with his broken arm again!
"You can't know how much I hate being called that," she said, running her hand down his agonized arm, then holding up a sinew bowstring for his inspection. "But you'll find out soon enough how it feels for fools to think you're something other than what you are, for them to attribute your accomplishments to witchcraft. They'll call you a sorcerer, do you know that?"
"What are you... don't!" Sir Hjortt felt his numb thumb in her bony fingers, then the bowstring dug sharply into the base of the digit. A tear formed in the eye that wasn't swollen shut as his thumb immediately began to sing louder than its broken arm.
"They'll be wrong, of course, but it won't change things—Colonel Hjortt of Azgaroth: demonologist. Or maybe diabolist, it amounts to the same thing. Colonel Hjortt, summoner of devils best left in hell. Not bad for a young prat of a noble, eh?"
"This isn't my fault," Sir Hjortt blathered over his shoulder. "I'm a decent man, I didn't want to go into the army, I wouldn't, I'm not a bad sort, I just... just..."
"Did as you were told?" She paused in her work, her voice low. "Carried out the orders you were given?"
"Yes, exactly!" said Sir Hjortt, eager to tell her whatever she wanted to hear, anything to make her stop. "Orders! Not my idea! Never!"
"You certainly seemed reluctant to carry them out," she said, her voice hardening as she looped the bowstring around the base of his other thumb, the one on his good arm, and pulled it tight. As she deftly tied it off in a knot, an immediate, awful throbbing filled both thumbs, as though they had been stung by something highly poisonous. She stood, went to the cooling kettle, and picked up a kitchen knife she had been warming beside it on the woodstove.
"Please," Sir Hjortt gasped, his skull pounding in tandem with his arm and, worst of all, his thumbs. He tried to stay calm, but she'd tied them so tight the sensation would have been unbearable even if he hadn't guessed what she intended. "Please, there's no cause for—"
"No cause?" said the witch, coming back to him. Fallen Mother save him, the black blade of the knife in her hand was actually _smoking_. "We both know the punishment for theft in your homeland, don't we, Colonel? You've stolen my husband from me, you've stolen my friends, my _family_ , so this should hardly come as a surprise. The tourniquets will keep you from bleeding too much."
"Please, I didn't have a choice, I—" But then the witch crouched behind his chair, and though he thrashed in his seat, she made short work of it. The pressure in the thumb of his broken arm was released first, and then, more palpably, he felt his other thumb sawed through in several brisk strokes. The bone gave her trouble, though, and he shrieked as she snapped it off. When he was again sensible of his surroundings, his tormentor was back in front of him, wiping the bloody knife clean on the vair collar of his cloak.
"You said you didn't have a choice," said the witch, sliding her unstrung bow into a scabbard on the side of her backpack and then shouldering it. "I believe you, boy—you're just a good little doggie doing what he's told, aren't you? An innocent lad, cursed with bad luck?"
"You evil, evil woman," Sir Hjortt whined, the fire where his thumbs had been now spreading through his hands. "I'm a colonel of the fucking Queen of Samoth! They'll find you, my father, Sister Portolés, the queen, the pope, they'll find you and—"
"And _what_ , boy? And what?" She took the hammer off the table and advanced on him. "You don't know a devildamned thing about _anything_ , do you? What could they do to me, eh? What could they take that you haven't already stolen?"
"You're dead!" Sir Hjortt knew he was being pathetic, that he was courting further punishment, but he couldn't stop himself. "You've fucking crippled me! How am I supposed to get on without my _hands_ , you monster! It would be a mercy if you'd kill me instead!"
"Mercy. Now there's a devil I won't have any truck with, not from here until my dying day," she said, but she reached around and slipped the handle of her war hammer through a loop on the side of her backpack instead of using the weapon on Sir Hjortt. Then she went to the table, flipping the shirt off her husband's head. After a moment's pause, she picked the skull up by the hair and returned it to its satchel, which then went over a shoulder. It hung awkwardly against the backpack, and as she looked back at Sir Hjortt with those flashing blue eyes he knew what he should have from the very first—he was totally, utterly fucked.
"What can you do?" he said, his voice cracking. "What can you possibly do? Where can you go? They'll find you, they will, to make an example—"
"An example," said the witch, nodding. "That's what I'll do, make some examples. Now, let's take a look and see how the example you set for me is going."
She walked behind him, grabbing the back of his seat in both hands and dragging him out onto the deck. The legs of the chair screeched as he went. How could Iqbal have missed such obvious deviltry, a grey-haired gran capable of hauling around a fully armored knight? What was the point of keeping witchborn bodyguards if they couldn't even recognize their own wicked kind? It was hard to think anything so coherent, though, the pounding grief in his hands consuming everything, all the blood that should be flowing through them instead backing up into his brain, drowning his mind in a deluge of pain. It took some grunting and cursing, but she finally maneuvered the chair so that he could look out over the valley. There was a lot of smoke coming up, but he couldn't make out much else. The mocking aspens made him reel, and if he hadn't been tied in place he would have collapsed. Damn the Fallen Mother for her deafness.
"Don't worry, Colonel Hjortt," she said, still standing beside him. "If your weirdborn nun is half as clever as I expect, you'll be saved long before the fire spreads out here. And if not, well, hopefully the ropes will burn away first and you'll get off with a light charring. I know masks are quite fashionable in Azgaroth, especially Cockspar. They used to be, anyway."
He tried to speak, to beg, maybe, or threaten, but his tongue felt as heavy as brass.
"Before, you generously offered me the freedom to weep, should I need to," the madwoman breathed in Sir Hjortt's ear. "I think I'll wait, though. I'm not going to cry for all those honest, blameless people down there, much as I love some of them, much as I like most of the rest. I'm not even going to cry for my husband."
She tousled his hair, her lips now brushing his earlobe. "The only one I'm going to weep for, good knight, is you, and my tears will only fall after we've been reunited. That's right, boy, once every other individual responsible for this travesty has been dealt with, after every _single_ one of them has been paid a visit, _then_ I'll find you, wherever you go, wherever you hide, and I will deal with you at my leisure. Then, oh brave Hjortt of Azgaroth, Fifteenth Colonel of the Crimson Empire, _then_ , when you've finally escaped my vengeance, either through madness or death, _then_ I will weep, but only because I can no longer torment you."
"Holy shit," Sir Hjortt managed before the first sob wracked his gallant chest. From the pain, yes. And the shock of being made a cripple, certainly. Yet the true source of his misery, the thing that made him half hope that the fire she set in the house just before fleeing into the mountains would consume the deck he sat upon before Sister Portolés could rescue him, was one simple fact: he believed every word she said.
# [CHAPTER
6](toc.xhtml#toc-chapter006)
Maroto sat atop the rim of the canyon, leaned his mace against a rock, and strapped his sandals back on. The sandstone felt warm against his bare legs with the bloody sun just peeking over the cracked plateau; in a few hours the rock he leaned against would be scalding to the touch. Even complemented by daybreak's bouquet of rose, hyacinth, and lilac, the Panteran Wastes looked even worse up here than they did in the labyrinth of ravines and gullies that cut through the desert. Down in the shadow roads there were cacti and twisted cedar, the infrequent spring surrounded by cattails and stunted willow, but nothing grew on these exposed plains and ridges save umber tufts of grass, ivory lichens, and blasted black rock formations. Maroto knew he could have found a worse place to lead his party, but doing so would have taken more work than he was willing to put in without extra pay.
Beneath him it was still too dark to see much. They had a cooking fire going, so he supposed the caravan had finished circling the wagons as best they could in the tight canyon—the gaudy convoy reminded him of an emperor centipede winding across the smoldering desert by night and then coiling up in some hole when dawn threatened. A cooking fire, in the Wastes! Maroto couldn't decide which was a greater marker of his party's absurd affluence: that they insisted on eating half a dozen hot meals a night, or that in between they snacked on sorbets and other frozen treats. Witch-powered or not, keeping the ice-wagon cool must cost a pretty princedom. Almost as much as the aquaricart, probably.
The money was good, though, so here he was. No, the money was great, princely, or else he never would have taken the gig. Repeat the mantra. As if money could ever be anything but devilish...
He really ought to start climbing back down before it got too hot, now that he had confirmed that the horizon was free of encroaching swarmclouds and the sky was clear of thunderheads, but he couldn't bear to return right away. He could (and indeed, had) slept through battles and coronations, orgies and sieges, but something about the shrill tittering of his charges kept him up long into the morning, every morning. Besides, scrambling out of the gorge as every other hold crumbled beneath his weight had given him a parched throat to go along with his raw fingers and toes, and climbing down was always far worse than coming up.
Most folk, his party included, watered down their cougar milk, but then most people, his party especially, were utterly, irredeemably weak. Knocking back his boozeskin, the draught burned like it ought to, few things restoring a man's perspective better than a pull on the licorice-sweet lava those Pertnessian alchemists cooked up. He fondly recalled a bar fight in Old Slair when a goon had swung on him with a lit torch and he'd used his flagon to breathe fire in the man's face. That he'd set his own dreadlocks alight in the process only lent the tale flavor—by all the forgotten gods of his heathen ancestors, what had he been thinking, twisting his hair into those ropes? Why not just fix a handle on your helm for people to grab hold of and sling you about...
The clattering of rocks bouncing down the ravine, and a grunt just beneath his heels. Somebody was coming up the cliff after him, and they were almost to the top. Of all the empty-skulled plays these lordlings had made, this had to be one of the worst. He'd allowed Sir Kuksi to accompany him up on their first morning out, and the ponce had slipped a mere twenty feet up the sandy slope, skinning his palms and twisting an ankle before landing in a heap of torn satin and silk at the bottom, to the jeers of his comrades. After that Maroto had made it abundantly clear: leave the scouting to the scout. Up until this juncture they had listened, but the brats were getting surlier by the night as crossing the Wastes revealed itself to be every bit as awful an ordeal as one ought to expect, given the name of the place. They claimed to want adventure, Lady Opeth going so far as to demand a giant scorpion to battle, yet they squealed like children when they found examples of the regular variety in their shoes after a hard night's day of drinking, drugging, and gambling 'round the campfire. It took all of his willpower not to grab one of those boot scorpions in his bare hand and let it sting him into blessed oblivion.
A soft and bloody palm slapped up, manicured fingers digging into the sandstone edge of the cliff, and Maroto darted forward. He grabbed the idiot's wrist before any further weight could be put onto the dangerous handhold, before he could put any thought into whether or not it might be better just to let this moron fall to their death and serve as an example to the rest. The noble cried out as Maroto hurled them up and over the lip of the cliff, the petite lordling dangling from one of his thick hands. It was Tapai Purna, because of course it was Purna.
Even after a week in the Wastes, Maroto had no idea if this particular fop identified as man, woman, or neither. The majority of the party came from the Serpent's Circle, and there in the old-and-then-new-and-then-old-again capital of the Crimson Empire they still used the obvious titles like _Duke_ and _Duchess_ , _Zir_ and _Sir_ , so getting a rough idea of how to address someone wasn't too hard. The Ugrakari honorific _Tapai_ , on the other hand, could apply to anyone, and Maroto couldn't remember enough of his campaigns on that side of the Star to recall if the name _Purna_ skewed in any particular direction. Among most of the coxcombs certain unavoidable physiological differences helped make things easy, but Purna Antimgran, Thirty-ninth Tapai of Ugrakar, was one of the exceptions. Despite looking about thirty years old, the noble didn't reveal enough in the chest or shoulders, arse or hips to give Maroto a solid clue. Tapai Purna may have hailed from a different homeland, but had adopted the Serpentine style of the rest of the nobles with gusto: an already androgynous, if handsome face was buried under lead foundation and cerulean lipstick, and the powdered wig only further befuddled matters. Purna's choice of fashion was as confounding as that of the others: the most popular attire, despite the climate, consisted of puffy lace collars, enormous ribbon bows, and layers and layers of embroidered shirts and vests tucked into frilly cream bloomers. These bloomers would have looked bad enough beneath one's clothes, but they were even worse when worn as an outer layer, Purna's admittedly shapely legs swathed in parti-colored hose and tipped with delicate, black-buckled shoes.
All of which were now scuffed or torn, stained and dripping, as Maroto set Purna down on the jagged ridgeline. Harlequin tears spattered the stone as sweat excavated gullies in the fop's makeup. Purna's garish facepaint reminded Maroto of a diva he'd performed with a time or two, way back in the bad old days, except Carla Rossi's foulmouthed drag routine was a good deal more entertaining than anything he'd yet seen out of the nobles.
"Made good time," Maroto thought out loud, almost impressed by the lordling. Almost. "You in some kind of hurry?"
"I—" Purna gasped, head shaking, and readjusted the damp wig that had migrated to the side. "Damn."
"Yeah," said Maroto, then left the panting noble to peer back down the cliff. "Any more of you coming up?"
"No," said Purna. "Water."
"That how you ask for something?" said Maroto, passing Purna his cougar milk. He grinned when the fop coughed on the liquor, then chided himself as Purna spit out a mouthful—he shouldn't waste a drop of good drink on his charges. "Ah, gave you the wrong skin—here you are, Tapai, my mistake."
"Thank you, barbarian," Purna said, after recovering enough to properly speak. "I should have brought my own. Your first rule."
"How's that?"
"You told us the first rule of the Wastes was never to leave the camp without water."
"Half right," said Maroto, remembering now. "I said the first rule was to never leave the camp, period, but if you did, never to go without water. Sound advice. I know what I'm talking about."
"Of course you do," said Purna. The noble unbuttoned a removable velvet panel and used it to mop away grime and mascara sludge from around eyes as amber as a comb of dreamhoney. These popinjays always had something up their sleeves, if only another handkerchief. "You're even better than we were expecting."
Maroto sighed. Here it came, then. From their first night out the dirty lordlings had been trying to seduce him, which had initially flattered him. That was, until Maroto politely declined an invitation to share Duke Rackcleff's pleasure wagon, whereupon the jilted ninny had huffily informed him the proposition was solely due to a high-stakes wager the party had decided upon: who would be the first to bag the barbarian? Of all Maroto's wards, Purna was far from the worst on the eyes, but even if there hadn't been the pride angle, he still would have thought twice about rolling in the sand with the fop; in his experience, the upper crust were twice as likely to give you a pox as a prostitute, and half as inclined to finish you off if they came first.
"So I'm impressive, am I?" he said, eyeing the raggedy Ugrakari. "You're so impressed you came up here to what, rub my shoulders, maybe give me a token of your affection?"
"I beg your pardon?" This noble was a cool liar, no doubt—Purna almost seemed genuinely confused.
"I know about the bet, and I fear none of you stands to profit from my prick. Maroto is no whore, nor a rich lord's plaything," he said, studiously keeping his mind from the dark old nights when he had been so far down the hive that he couldn't even remember what he'd done to get his next sting.
"Oh, _gross_!" cried Purna. "I am _not_ involved in that, I don't care how much lucre they put in the kitty. So disgusting!"
"Yes, well..." said Maroto, thinking that maybe Purna wasn't just referring to the ethics of such a wager, and flinching a little inside. "Then why follow me here? Such a climb is no place for a young, uh, person. Of distinction."
"Oh!" said Purna, eagerness replacing revulsion. "Diggelby let me use his hawkglass, and way over, ah, south of us, on this ridge, there was this great big lizard mooning itself on a rock. I thought we could hunt it!"
"Big lizard?" Maroto's sweaty skin went cold. "This ridge?"
"From where you were climbing up it looked to be just over that, what do you call it... _escarpment_? Those rocks there, I mean, over those a little bit—ah!" Purna shrieked upon noticing that he or she had pointed directly at a godguana, the horse-sized lizard watching them from atop a rock shelf some twenty yards away. It could be on top of them in three bounds of its enormous, banded legs. "There he is!"
"I see her," whispered Maroto, meeting the black gaze of the carnivorous calamity rather than glancing to where his mace rested against the stone. He knew where the weapon was, could snatch it without looking, but would give his two pinky fingers if he could avoid having to use it. Female godguanas grew bigger, could disembowel you with their hooked claws, poison you with their noxious bite, but were less territorial than the males, so maybe she was just investigating them, and when she saw that they were no—
"Get it!" howled Purna, charging past him at the godguana. Maroto didn't waste his breath on a curse as he sidestepped toward his mace. Even as his hand found it missing his eyes located it. Purna. The noble held it high, bum-rushing a creature that half a dozen experienced hunters would have balked at taking on, and ululating all the way. "Wooooo!"
It would have been better to flee down the cliff, trusting the creature to gorge herself on Purna while he made good his getaway, but that mace meant a lot to Maroto. Purna closed the distance over the rough ground, dainty shoes gliding over the rocks with admirable alacrity. The godguana hissed and rose up on her hind legs, and even at this distance the stench of her maw made Maroto's eyes water as he seized up a melon-sized chunk of sandstone.
The monster dropped down from the rock shelf, directly on top of the charging fop. Maroto hurled his rock. Purna was crushed to the ground by one of the godguana's claws, and then Maroto's missile nailed the creature's left eye with such force that the sandstone exploded in a cloud of orange dust. The godguana's head listed sharply from the blow, but only for a moment, her long, black-scaled snout straightening back out as she surveyed Maroto, one eye beady as ever, the other a raw, bleeding wound. She tensed her claws, Purna moaning as the lizard's foot ground through cloth and skin alike. Maroto hoped the idiot noble lived long enough for him to kill this monster so that he could then have the satisfaction of hurling Purna off of the cliff.
The rock had certainly gotten the creature's attention; she launched herself straight at him. Smaller godguanas had an almost silly gait, their wide-armed dash anything but graceful. There was nothing silly about a full-grown female charging him, each stride covering half a dozen feet. Maroto whipped the dagger out of his belt as the godguana bore down on him. He braced himself, and when she lunged forward he ducked to the side of her mouth and went for her spiny neck. Grabbing her in an awkward headlock with his off hand, he was carried off the ground as she jerked away.
He clung on as she attempted to buck him loose, claws narrowly missing his tucked-up legs, his head pressed against that of the direlizard. As she thrashed, the edge of his flattop caught in her gnashing jaws, and he felt the tug on his scalp as she chewed his hair, the stink of the rotten mouth bordering on the sublime. All the while Maroto plunged his dagger through the tough scales between her shoulders, over and over, nicking himself on her ridge of spines in the process, blood flowing freely down the arm he held the creature with as it ground against her sharp hide.
It was a tried-and-true approach, and would have worked, too, if the luck gods hadn't taken a shit on him in the form of a boulder onto which the godguana slammed him. He lost his strength for but a moment, and then he was off the lizard, laid out atop the rock like a human sacrifice as the bloodied, raging monster reared back up... and here she came again, crashing down like a hammer on an obstinate walnut. He tried to roll away, knowing even as he did that he was too slow, that it had taken him too long to get his wind back, and now, yes, ugh, the full weight of the lizard crashed upon him, pinning him halfway off the boulder with her chest. Woof. So much for Maroto, his guts were about to be squeezed out either end, and—
Then she was off of him, hissing louder than ever, her tail whipping the boulder a hairbreadth from his chin. The edge of the sandstone splintered off from the impact and he fell off the rock after it, landing in a crouch and bracing for the claws or bite that were surely coming. He had dropped the dagger at some point and was seeing double for the first time in years—this was it. He was irredeemably screwed.
Yet the twinned lizards shimmering in the dawn had turned their backs on him, and as his vision came back into focus he saw that one of her hind legs had been busted wide open at the haunch, the useless appendage oozing red through a mess of knotted muscle and torn scales. Purna limped just out of reach of the wounded godguana, warding off her snapping mouth with Maroto's mace rather than chancing another solid swing at it. Purna looked about as rough as the lizard, the noble's left side stained red from missing wig to torn bloomers, the priceless attire shredded to the skin and deeper still by the lizard's claws, and hold on, yes, there was a petite but decidedly feminine breast under the blood and tatters.
Even as Maroto registered this he stooped to get another missile, which stunned the godguana when it exploded against the crest on the back of her head. Purna didn't close the deal like she should have, instead using the opportunity to put more distance between herself and the lizard, so Maroto went for another rock. As he grabbed a good one the godguana gave up the fight, skittering away over the narrow ridge, trailing gore, but before she gained the shelter of a high rock formation his third stone popped her in the back, just above the tail, and, tripped up, the monster slid over the far edge of the cliff.
"Woof," said Maroto, slouching back to lean against the boulder that had almost been his gravestone. What a disaster. "You okay, Tapai?"
Purna waved the mace, then slumped her shoulders and dragged her feet over to him. She was missing a shoe, her stockings sullied and full of runs. Maroto still wanted to toss her down the ravine, but it would have been bad form, given how she'd just saved his life, so he settled for laying some hard truths on her.
"That was the dumbest damn thing one of you golden goblets has pulled yet," he growled. "And that includes bringing a fucking fish tank to the desert."
Maroto had, in fact, been rather impressed when he first saw Princess Von Yung's aquaricart, but after he learned that none of the vibrantly colored marine life was actually edible, his opinion on the matter had soured considerably.
"That was..." Purna shook her head, clearly on the edge of tears. Seeing how deep the gouges in her chest went, and the bruise rising on her scraped cheek, Maroto began to soften. Until she said, "That was the best. So fucking awesome. I saved _your ass_ , barbarian! Woo!"
"You saved _my_ arse?" Maroto could not believe his fucking ears. "Girl, the next time you put your head in a kiln to watch the devils dance, I'll let you look as long as you want instead of pulling you out. You nearly got us both dead!"
"Were you scared?" asked Purna. "It's okay if you were. I was scared, too. A little."
"Scared?" Maroto felt his cheeks flush, and then a fury that only escaped its bonds in his blood on the rarest occasions. But before the lordling could push him over the edge, Purna sat down on a rock, dropped the mace, and buried her head in her hands. Maroto watched her shudder with emotion for long enough to confirm that she wasn't laughing at him, and after having a gander over the far cliffside to make sure the beast was truly dead, he fetched the cougar milk to pour on their wounds. Neither had suffered a bite, but even so, godguana claws were nasty enough to carry nine kinds of plague.
When he came back Purna was sitting up straight, the mace propped against her knee, and Maroto did his best not to be too obvious in his ogling as he washed her wounds in booze. With her makeup sloughed off by the righteous trinity of blood, sweat, and tears, her stupid wig gone, and her cropped black hair spiky with lizard ichors, she looked a sight better. Not that he felt anything but scorn for the puffed-up little dandy, but few folk didn't look good with blood on their tits and a weapon at the ready.
_There_ was a thought to please the devils. Maroto amended his musings: it wasn't that he liked the idea of an injured woman, gods no, just that warriors always looked better bloody than clean, and warriors always looked better than anyone else. Nothing wrong with thinking the truth.
"I think you've got it pretty well sorted," said Purna, standing up, and Maroto realized he'd perhaps been overly diligent in his application of the absinthe-soaked rag. "Come on, let's get you washed and then we can go after it."
"After it?" He winced as he applied the cloth to his wrist. He'd almost scraped it to the veins, riding that lizard's rough neck. "I checked; thing's busted open on a ledge fifty feet down. Even if she wasn't, though, you don't follow a wounded animal unless you have to. You think that monster put up a fight, see what one would do if you cornered her."
"Sure, sure," said Purna, fiddling with her shredded vest until she could tie a strip of it into her collar, giving her a beggar's modesty. "I just want its head. To, you know, mount? That's the whole reason we're out here, isn't it, for this sort of thing? What's the point in battling monsters if you don't get a trophy?"
"Come on," said Maroto, getting up. "We're going back before another one shows up."
"I'm not leaving without my trophy," said Purna. "If you don't climb down and get it, I will."
"Fine," said Maroto. "Good luck. I'd say I'll meet you back at camp later, except I probably won't because you'll slip and break an ankle and lie on some spit of rock crying until something comes along to eat you."
"What's your price, barbarian?" said Purna, sounding as simultaneously bored and annoyed as a noble buying their bratty kid out of trouble. "To get me the head, how much would it cost me?"
"More than you're worth," said Maroto, but he couldn't help but feel the itch in his least honorable organ: his purse. It hadn't looked to be too hard a climb down to the direlizard... "Ten thousand rupees."
"Let's make it twelve," said Purna with a smile, which was how Maroto found himself cleaning off the mace he had almost lost, along with his life, and descending to where the godguana had fallen. She had begun to cook in the morning heat, and the stench made him gag as he broke through her ridge of spines and the bones beneath, mashing her shoulders into reptilian paste. Would've been a sight easier with an ax instead of the dubious duo of mace and dagger, but then it would've been a damn sight easier to just tell Purna where to stick her twelve thousand rupees. He was half-baked himself by the time he rejoined Purna on the summit, whereupon he discovered she had drunk all his water while he was doing her dirty work. Yet not even the realization that to get them both down safely he'd have to carry her on his back compared to the frustration he felt when they were at long last back on the under-roads, returning to the caravan, and she said, "So twelve thousand rupees will take some doing, but while we were climbing I hit on the perfect solution."
"While _we_ were climbing?" Maroto tried to keep a level tone; until he had the money in hand it wouldn't do to spook her. "You promised me something you couldn't pay, Tapai Purna? I thought you nobles were reliable about paying your debts."
"If we were there would be far fewer of us," said Purna. "My shoulder really hurts, are you sure it's all right?"
"I'll stitch you up at the camp. But only after I've been paid."
"Ah, yes. But see, I don't have the money yet."
"When will you? I'd be quick about it, personally. You want those sewn up right away."
"That depends on you," said Purna. "We could have it as soon as tomorrow."
"Depends on me," said Maroto, a cannonball sort of weight settling in his guts.
"As I said, I wanted no part in their vile little wager. No part. Bleh." Purna stuck out her tongue. "But I can go back to my chums and enter a share, saying that after our adventure today I've warmed to the beast, and decided to take a chance on seducing it myself."
"Seducing _it_? The _beast_?"
"Yes, that's what they call you. Not me, though. I always just call you the barbarian."
Some improvement. "So you lay a wager, then later today or tomorrow we go off and have a screw and—"
"No, no, no!" said Purna. "What sort of a person do you take me for? I lay the wager, then we sneak off and _pretend_ to fuck, preferably tucked away in one of these canyons where the echoes can reach the rest, just so there's no room for doubt. Then I get paid, and in turn you get paid."
"Absolutely not," said Maroto. "Under no circumstances. I have pride, girl, a word unfamiliar to you so-called civilized folk, but one dear to me as the true name of any devil."
"Have it your way," said Purna. "I think the pot's closer to twenty thousand, so I'd go so far as to give you fifteen and keep a modest five for the injury to my reputation, but if you'd rather be silverless and proud, then—"
"All twenty," said Maroto, dropping Purna's reptilian trophy in the sand. The wagons were just ahead. "All twenty, and you have to tell them that you convinced me you weren't actually part of the wager before I agreed to fuck you. I won't have it said I'm a whore or a rich lord's plaything."
"Seventeen, and agreed on your condition," said Purna, squatting down and hoisting the lizard head herself. Her arms were shaking but she managed it. "Final offer."
"Eighteen."
"Seventeen-five, and you're no whore nor rich girl's plaything."
"Agreed," said Maroto, though he was no longer so sure about that last bit. They returned to the campfire, the coterie of coxcombs squawking and hooting at their bedraggled appearance and Purna's prize. Revolting a scene as it surely was, Kōshaku Köz's valet revealed herself to have both a barber's bag and the skill to use it. Purna was treated first, naturally, while Maroto fended off the demands of the rest to be taken on a dragon hunt at dusk. Later, he overheard Purna's version of events over brandy and cigars while his significantly worse injuries were tended to. He told himself that declining the valet's offer of a centipede prior to setting in was a victory, albeit a small one, but every stab of the needle and tug of the thread reminded him of his weakness, his failings; here was a man who couldn't even trust himself to take a painkiller before undergoing surgery, lest he backslide into his old ways. And after the day he'd had, all he had to look forward to was a make-believe tryst on the morrow.
There was a time when Maroto wouldn't have entered the Panteran Wastes for the far more lucrative and enjoyable proposition of raiding just such a party of wealthy fools, a time when he would have laughed in the face of anyone who suggested he might end up playing Great Barbarian Hunter for a bunch of second-rate fops. There was a time when Maroto would have gestured at his priceless armor, his witch-touched weapons, his lands and titles and holdings, to say naught of the bloody devil that served his will—here was a man with everything silver could buy, and many things it could not.
When he squinted into the past, he could almost make out that man through the mists of bug- and drink-filtered memories and increasingly poor decisions. The simpering choir of the nobles carried on into the early hours of the night, and sleep was as elusive as dignity as he lay on his too-soft cot in his too-nice covered wagon, dreading the future every bit as much as he loathed the past. He told himself that once they were out of the Wastes he would never again debase himself so... but he'd broken that promise many, many times before and he would, sad to say, break it again.
# [CHAPTER
7](toc.xhtml#toc-chapter007)
It was long after midnight when Choplicker caught up to Zosia in the high country. Hearing him crash through the low ring of deadfall she had piled around her camp, she drew away into the junipers, into the darkness, into the focused wrath that was the only thing that let her rioting mind relax into silence... and when the miserable scavenger appeared across the fire, she pulled her bowstring back even farther, and loosed her arrow straight at his muzzle. The missile veered off course and disappeared into the night, just like she knew it would, but she nocked another anyway, storming out of the shadows at him.
"Why?" Zosia's voice broke as she drew her bow again, just across the small fire from the beast now. "Why the fuck didn't you take it? I know you could've, I know it would've been child's play for you to honor the terms I offered, so _why_?"
Choplicker whined at her, keeping his wagging tail low to the ground the way he always did when he knew he was in trouble. This, this right here was how he'd lulled her into thinking they were all right with one another, this grotesque charade was how he'd convinced her that she had nothing to fear from him. That they were friends. And then he'd as good as murdered Leib.
Zosia almost fired her second arrow but then she noticed that Choplicker had not returned alone. The arms of a child were wrapped around his furry neck, its bloody back limp atop his own. Even freshly fed, it must have taken some effort for the old beggar to drag a corpse all the way up the mountain—and just to rub her nose in it.
Zosia relaxed her bow and tossed it onto her bedroll. Then she stalked around the fire, meaning to take Choplicker apart with her bare hands, when the child slid down his haunches, letting out a moan as he collapsed onto the cold, moss-cushioned earth. Cursing, she hurried to the boy and rolled him onto his side, the firelight turning his bloody tunic to molten gold. He moaned again as she tore the cloth and prodded the wound, a rude, deep puncture that had narrowly missed the base of his spine.
"Mayoress." The boy's voice was raspier than the junipers in the wind that stalked these heights. "It hurts."
Zosia sighed, letting out as much of her pain and rage as she could. It would only distract her now, and after the events of the day it wasn't as if she was in danger of exhausting her stores in this lifetime. She bit the inside of her cheek, focusing herself as best she could. The wound was deep, no doubt from a spear, and his long, jostling ride up the mountains couldn't have done him any boon. It would have been better if the boy had never woken up, if Choplicker had just dragged him into the underbrush and torn out his throat rather than delivering him to her. Which was the point, she supposed, and, hearing his slobbering, she scowled at the scavenger. He was licking the boy's face, plastering the lad's hair up, and if the wounded child hadn't obviously welcomed the diversion from his pain she would have murdered the beast then and there. Or tried to, anyway.
"You'll be all right," she said, straightening up. She had recognized the boy, for all the good it would do her to know his name. "I've got something in my bag to heal you, Pao Cowherd, just don't go making any trouble while I get it. Lie very still."
"Yes, ma'am," Pao whispered, trying to pet Choplicker. "Sorry, ma'am."
"Should be," said Zosia, her voice almost catching. She'd grown soft, all right—the stone was still in her somewhere, but she'd buried it so deep under years of easy happiness that she couldn't seem to find it. Tending a badly wounded child was not the time for grief or doubt, and once she would have been able to smother these things, if she felt them at all... once, but ages past. Now the deep coldness inside her teemed with a hundred different splashing, thrashing thoughts and memories and emotions, and try as she might she couldn't find the placidity that once came as natural as breathing.
Fishing in her pack, she took out a wool shirt and brought it back to the boy, cutting into it with her deer knife as she hunkered back down. He was pallid as a corpse already, and trying not to cry. "Tying off a nanny goat's tail is a dark deed, boy—you recall what I said I'd do if I caught you up by my place again?"
"Said you'd... beat the devils out of me." Even half dead, the boy grinned at her. There was blood shining between his teeth in the firelight. "Ain't my fault, ma'am. Your dog... he brung me up here."
"Well, I suppose it's all right then," said Zosia, rolling the boy farther over to examine the wound before plugging it. There hardly seemed a point at all, but he was still talking, so who knew, maybe there was some hope... "This will hurt, but it's got to be done. Then I'll stop the wound and you'll be right as rain before you know it."
"I feel sick, I—" But whatever the boy might have said next was lost as his voice turned into a gasping, gulping sob. Zosia had peeled back the soft crust that had formed over the wound and slid her index finger in, making sure there wasn't a broken arrow or spear point lodged inside. Something hard and sharp met her fingertip, but she couldn't tell if it was a piece of weapon or bone—too long since she'd rooted around in a body. Nothing she could do about it, anyway, wedged that firmly in there, alone on a dark mountainside. The boy was sucking the cold air in catfish gulps, his body basted with sweat, and she slipped her finger out.
If he lived through the night, come morning she'd clean and cauterize the wound, but for now she would spare him that ordeal. Rolling a scrap of shirt into a plug, she quickly packed it in the wound. He found enough air to let out a wail at that, then fell totally silent. She tied the remaining woolen strips tight, the boy shivering as she hoisted his hip to get the bandage all the way around his waist. Cinching it, she watched his wracked face, wondering if this was it, if she had gone and killed the boy.
No. His face was still locked in a rictus, but his shallow breathing was evening out, his almost imperceptible whines growing in strength even as the rest of him weakened. She stood back up, the speed with which she had gained the high country after dealing with Hjortt and setting the house aflame catching up with her in a series of twinges and aches. Devils below and devils above, but her left knee was angry with her. She wanted to rinse the tacky blood off her hands, but, knowing they'd like as not be bloodied again before the night was over, decided not to waste the water just yet. She held her hands over the diminished fire, the drying blood dark on her fingers. They were still shaking. They would be shaking a lot in the nights to come, with winter on the wind that gutted her blaze.
"I'm thirsty," Pao called with more strength than she would have expected. He had curled into a ball despite the pain it must have caused to bring his knees to his chest, and she brought him both a waterskin and her flask of enzian. He coughed more on the sip of water than he did on the slug of bitter booze. "Those soldiers... they killed everyone."
"That's what I figured," said Zosia, taking a pull on the enzian herself. She gave up on trying to keep the inevitable at bay and let herself remember harvesting the plants with Leib. While she excavated the roots from the flinty alpine soil, her shirking husband strung her small, pungent crowns from the yellow flowers, setting them with the rare purple bloom. A jewel for her diadem. The smell of earth and root, the feel of cold hands slipped under the back of her blouse to provoke a squeal. She took another aromatic dram, thought of the pot-still bubbling away in its hut behind the village's communal longhouse, and wondered if the murderous Imperial soldiers were even now toasting with pillaged bottles of the same spirit. If she started back down now she could be there just before dawn, when even the sentries were caught in limbo between being drunk and being hungover...
The boy—Pao, she told herself, his name is Pao Cowherd, though she'd called the rascal other things in the past—started to cry again. She forced another drink down his throat, then sealed flask and waterskin and went back for her war hammer. Twirling in her hand, the fist-sized face and icicle-shaped pick became a steel cyclone that caught the boy's attention, and Choplicker's, too.
"Will I... am I dying?" the boy asked.
Yes.
"No." Zosia released the spinning hammer and caught it in her other hand, the familiar sting of the handle against her palm making her grimace. "I'm a witch—many times as you've called me that, I'd think you'd believe it! And enzian's a medicine, isn't it, so even if I weren't possessed of dark powers you'd be on the mend already. You'll live, boy, you'll live, and then you'll go after those soldiers who did this to you."
"I'm scared," said Pao, shuddering.
"Only because you're green," said Zosia, reckoning she'd been even younger than he was when she'd first taken up arms. "I was green once, too, but you'll firm up. Don't think we'll go after them tomorrow! Need to train you in the sword, the hammer, the bow, everything you ever pestered me and my Leib about teaching you. Need to turn you into a warrior!"
She was sure this would have cheered him, but he just stared off into the blackness between the junipers, his back to the fire. The bandage had already soaked through. Glancing at Choplicker, she could tell it was taking every drop of what little self-control the beast possessed not to lap at the sodden wool.
"You're special, Pao Cowherd," Zosia told him. "You're not like anyone else out there in the whole world. You're destined for this, boy, destined to be the one to change things, to make the Star a better place. And you do that with a sword. A magic one. That's your destiny."
That got his attention. The boy turned his head toward her, winced, the desperate hope on his shadow-cluttered face sickening. "A magic sword? My destiny?"
"That's right," said Zosia, feeling Choplicker's eager eyes boring into her but refusing to look at the beast. "Why do you think you survived, eh? Why do you think Chop brought you to me? You're a very special child, Pao, and your father trusted me to look after you, to wait until you were old enough and then teach you sword craft. To help train you up so you can rid the world of devils, restore peace, that kind of shit."
"My dad," whispered Pao. "But you always said he was a drunk asshole and that's why Mama ran him out of town."
"Of course I said that," said Zosia, seeing the resemblance to his good-for-nothing father writ in the boy's thick brows and broad nose. He would've grown up to look just like the man. Still might, she thought, but scarcely believed it. "I was trying to teach you some humility with that yarn, wasn't I? For all the good it did. Couldn't well tell you he was really a great knight and that someday I'd take you on a quest to retrieve his special sword, could I? You gave me little enough peace as it was, can't imagine how awful you'd have been if we'd told you the truth."
"I couldn't..." Pao's eyes were half-lidded, the boy drifting into some dark depth that only time would reveal to be slumber or death. "Mama..."
The wind stirred up a plume of embers, the coals pulsing, and she tucked the hammer in its loop on her backpack, put more wood on. Pao shivered on the bare, rocky ground, eyes clenched as tight as his jaw. She only had the one bedroll, and if she gave it to him it would likely be soaked in blood by morning. Choplicker rose from where he'd lain beside the fire and went to her side, his ever-thirsty tongue going to the hand that hung limp at her side. She numbly let him clean the blood off her, staring at the boy, and when he was done she offered him her other hand.
"And here I thought you hung around because you liked me," she said sadly, meeting his canine eyes and trying to convince herself this was all his fault, instead of hers. "No fool like an old fool, I suppose. Lie beside him, unless you're itching to see just how much of your wickedness I'll abide in one day. Not much more, devil, not much at all, I promise you that."
The thing that pretended to be a dog went to Pao. Even in the flickering light of the campfire she could see that all the white had left his coat, the black had left his teeth, that he was as young as when she'd first laid eyes on the fiend. Didn't take much to keep him going, didn't take much at all, but he would never be sated, not as long as the sun and the moon danced their way around the world. Maybe not even after they stopped.
Zosia left the camp, left the junipers, stumbled up the night scape of shrubs and stones above the tree line, until her fire was a distant devil's eye beneath her, and above her burned a thousand more, silver instead of gold but just as remote, just as cold. She rubbed her hands, turned, and looked down the ridge, down the mountain, down the starlit valley, out toward the highway, out toward the world she had left behind... the world that had followed her trail even to this distant hiding place.
So Choplicker hadn't taken her offer after all. In all her years, she had never heard of a bound devil turning down its freedom, but seeing was believing. She didn't claim to be the expert on the monsters that some of her old confederates were, but still, it didn't get more basic than that: you bind a devil, it has to protect you, and if you offer to set it loose, it will grant any wish. Any fucking wish. The songs were full of cunning mortals who received whole empires in exchange for setting a devil loose, and all she had wanted was to leave an empire behind.
"Just keep us safe." She repeated her wish to the darkness, the words echoing out from her broken heart twenty years after she had given them voice. "I just want to grow old with Leib, for both of us to live safe, boring lives until age claims us. Your freedom for our safety."
It was all Choplicker's fault.
As if wanting a thing was enough to make it real—didn't this whole fucking tragedy prove that wishing for something wasn't enough? No, the truth of it was that this wasn't Choplicker's fault. It was hers. After all she had seen and done when she'd led the Cobalt Company, she'd still gone and trusted her future to a devil? Trusted her husband's life to a monster the likes of which not even the craziest sorcerer on the Star wanted to treat with? Zosia had captured the Carnelian Crown of Samoth, controlled the whole Crimson fucking Empire, schemed and plotted against the most devious minds on the Star to achieve her ends, and yet she'd made the most amateurish mistake imaginable—she'd stopped watching her back.
Even when those Imperials had shown up at her door that very morning, she hadn't believed it, had held out hope that Choplicker would magically solve her problems. If she had attacked Hjortt and his two weirdborn guards before the order was given to kill everyone in Kypck, maybe the whole village would still be alive. Instead, she was so convinced that a devil had granted her wish that she'd just sat on her fat old ass and let the worst thing imaginable transpire under her nose. Choplicker deserved some blame, oh yes, he fucking did... but she deserved even more.
Except—and it was an elephantine exception—neither she nor her devil had beheaded Leib. In twenty years of living here, neither of them had harmed a single citizen of Kypck. Both Zosia and Choplicker would pay for their crimes eventually, but there were others to share the blame, and until then guilt would only distract her from some very important business. Devildamn every one of those responsible for this... but of course the devils never minded, so it was dependent on her to do the damning.
She should have killed Colonel Hjortt instead of leaving him for later, she knew this, and she should have lain in wait at the house until that Sister Portolés had returned and then killed the weirdborn, too... It was sloppy, very sloppy, leaving things like this. They hadn't seemed to know her real name, though, and she had burned the house with all its evidence, so if she bided her time before going after the soldiers who had massacred the villagers there was reason enough to hope that this incident might not draw the full scrutiny of those who might identify her.
They would know her name before it was over, that they certainly would, but the longer it took them to put the pieces together, the less prepared they would be to meet her retaliation...
Except this couldn't just be an unhappy accident, could it? Every hamlet on the Star did the same as Kypck had done, trading supplies to whomever came knocking. Yet of all the remote towns in the Empire, hers was the one they selected to make an example of? They hadn't even sent her a worthy enemy, just some half-grown nobody of a noble, an errand boy charged with delivering her an unmistakable message... and Zosia had a fairly keen notion of who had sent it.
She hated that it almost felt good, to realize Queen Indsorith must be behind this. Choplicker wasn't the only monster Zosia had made a deal with, and the more she thought about it, the more obvious it was that the Crimson Queen had orchestrated this entire attack. Now that it had transpired, Zosia saw how inevitable it all was—she'd been an even bigger fool to trust her successor to the Crimson Throne than she had been to trust her devil.
Quick as the flash of illumination and flush of excitement came, it was gone again, leaving Zosia cold and melancholic. Going after the sovereign of the Crimson Empire had been hard work when she was a whole lot younger, when she had her Five Villians and the rest of the Cobalt Company behind her, but now? Now she had nothing. Less than.
It should have been the boy. How many had she met who claimed to share his lot, how many songs had she heard that began this way? The sole survivor of a tribe, driven by a need for revenge, all their strength ahead of them, young enough to learn, to prepare, to adapt. Young enough to succeed. It should be this boy, who didn't deserve anything worse than a mild ass-beating for his frequent trespasses.
It should be the boy. If she had been a witch, like that idiot Colonel Hjortt had thought, if she could have given her life for his...
And predictable as a water clock, there was Choplicker, padding between the small bushy willows that sprouted here, when all other trees fell back. A smile tilted at her mouth. All she had to do was say it, _My life for his_ , and then it would be done, wouldn't it? An innocent child in exchange for her black heart would entice a deal out of any devil within hearing range, especially one who despised her as much as Choplicker must, to have refused her before. The jackal-dog's eyes glittered like the stars as he approached. _My life for his_.
Maybe such an oath would work this time around, and maybe it would be but more noise on a wind-lashed mountainside, but Zosia wasn't taking any chances. She couldn't afford to, not until she had her revenge. She swallowed the sentimentalizing and cuffed Choplicker on the back of the head as she returned to camp. He snapped at her but knew better than to land a bite, just as she'd known better than to strike him as hard as she'd wanted to. They would be working together for a little while longer yet.
Sleep never arrived as she lay on the rough ground, letting her body rest even if her mind declined the offer.
In the morning the boy was dead, her only bedroll frosted with his frozen sweat and blood. She carried him to the top of the ridge and laid him out for the animals. After erecting small cairns at his head and feet, she removed the severed head of her husband from its satchel and set it next to Pao Cowherd, so that their cold brows touched. Zosia offered no prayers, only curses, and then she turned away, into the clouds that enveloped the upper reaches of the Kutumbans.
It was time to begin her last, bloody work. The thing she hated most about herself was how warm the prospect made her. Choplicker would feed well before it was over. All the devils would.
# [CHAPTER
8](toc.xhtml#toc-chapter008)
Two days after he left home with little more than his weapons, his clothes, and his grandfather on his back, Sullen was attacked. It would have been one thing if those doing the attacking had been from a rival tribe, maybe those deranged, pink-skinned Troll Lions from the Grey Savannah, or their old enemies the Jackal People, but the sad truth was that Sullen was ambushed by members of his own clan. Shameful.
The attack came at Flywalk, the rope bridge that spanned the Agharthan Gorge. His people had hidden on the far side of the jagged trench that separated the Horned Wolf Clan's territory from that of the Falcon People, and as soon as Sullen stepped off the bridge they came at him. Due to the time-honored popularity of ambushes at this spot, the thick, mossy pines had been cleared for a good hundred yards on both sides of the crossing, and so Sullen had just enough time to process what was happening as five named Wolves and two pups rushed across the stumpfield at him.
"It's me!" Sullen announced, holding up his spear and sun-knife in a friendly gesture, hoping against hope that this was a misunderstanding. It wasn't, as evidenced by the sun-knife Oryxdoom hurled at him as the lead hunter closed the last dozen yards. Sullen sidestepped the multiflanged missile, and without putting any thought into it, really, whipped his spear around to meet Oryxdoom's charge. It sounded rather a lot like spitting a practice gourd when the weapon connected with Oryxdoom's armpit, the man's ax flying from his upraised arm as he was skewered. The other six Horned Wolves drew up short, forming a half-ring around Sullen and the ravine behind him, the hunting party in low stances, spears, axes, and throwing knives ready.
From his sling on Sullen's back, Grandfather shouted, "You've wanted the boy gone all these years, now you put up a fight when he tries to leave?"
Sullen knew Grandfather was only tying to help but blushed nevertheless. He could fight his own battles.
"I'm sorry," he said, well practiced in offering undeserved apologies to keep the peace. "I'm not leaving the clan. I just have to take Grandfather on a quest, then I'll be back. And I didn't want to hurt him. I didn't want to hurt you, Oryxdoom."
From where he lay on the black earth at Sullen's feet, Oryxdoom did not say whether or not he accepted the apology. This was probably because Oryxdoom was deader than donkey shit, the brother of One-arm Yaw sprawled on his side in the loam, blood pooling toward Sullen's flaking leather boots. Sullen tugged his spear free and took a slight step back from the mess he'd made, and would have taken another if he hadn't remembered the dropoff behind him. The bridge was just there to his left, if he broke past Swiftspear, but the two pups had taken up positions behind their older sister, and Sullen really, really didn't want to chop down the unnamed kids. And even if he somehow made it back across, what then? He'd be right back in the one place he knew his uncle wasn't—his homeland, where nobody wanted him. When none of his clanfolk broke the silence nor rushed him, he tried again to explain:
"I'm not turning tail like Uncle Craven did. I'll come back," he said, but now that he thought about it, that was exactly what his uncle had done the first time around that made the council so mad: left the clan without permission, and then came back without invitation. Looking at the mean faces of his people, he supposed they'd be fine with his following Uncle Craven's footsteps as far as leaving the Noreast Arm went; they just wanted to make sure he didn't return.
What were they waiting for, then? Wise-eye would be the alpha, with Oryxdoom dead, but she just shifted her weight from boot to boot, her spear from hand to hand. Sullen told himself they hesitated because they didn't really want to fight him. That Oryxdoom had put them up to this. That each wasn't simply reluctant to be the first one to charge, or to lose their sun-knife by throwing it at him while he stood on the edge of the gorge. He could still talk them out of this, give a speech like the one from the ballads that Old Black had given the night-rovers, when she'd convinced those monsters not to eat her during the Worst Winter...
He could do this. Clearing his throat, Sullen said, "You thought I was just running away, shaming the clan, but it's not like that! I swear on my name it's not! I'm going to find out why Uncle Craven disgraced us the way he did! I'll get a worthy answer from his lips, or bring him back to face the judgment of the council! I vow it on the names of all my ancestors!"
Wise-eye relaxed her shoulders a bit, and from the corner of his eye he saw Swiftspear look to her for guidance. Witmouth was nodding thoughtfully, no doubt recognizing the cadence of Sullen's oath from the tales he himself had sung to the boy, back before Sullen had alienated himself from his people. They were hearing him out!
"I swear on my parents I never meant to break the codes the way I did," he went on, "and I don't want to hurt nobody else. So why don't we just—"
"Kill them all!" Grandfather yowled, and Sullen stumbled to the side as the old man strapped to his back hurled one of his sun-knives at Wise-eye. She tried to dodge it, but Grandfather knew a thing or two about his business and two of the weapon's curved points caught her square in the gut. She collapsed to the ground, the other woman and two men charged, the pups hurled knives in his direction, and Sullen obeyed the wordless impulse in his panicked skull—he charged straight ahead, slashing Witmouth out of the way with his spear and fleeing toward the tree line.
Someone cut his side with something.
Grandfather was boxing his ears, commanding him to turn and fight.
A sun-knife skimmed the side of his scalp, ripping through his hair and stinging like an icebee.
Sullen ignored everything but the rough, root-slippery ground beneath his feet as he crossed the stumpfield and gained the cover of the forest, sun-knives shying off the trees around him, another thunking into the earth just between his pumping legs. Whipping through the pine boughs, he immediately crossed the trail through the Raptor Wood, ignored it, plunged back into thick timber, underbrush clawing his calves and thighs, branches scratching his face.
His clanfolk howled behind him, close, and then the downward slant of the ground sharpened considerably. Sullen cut sideways along the incline to keep his balance, but even still he began to slide down the hill, only keeping himself upright by grabbing at branches with his free hand. The descent steepened, and he half fell down the wooded mountainside, his stride lengthening with each breath as though he wore the enchanted snowshoes from the Ballad of Cleverhands. A fallen tree reared out of the blurry forest, but he bounded over it, landing thirty feet down the slope with such force he felt it rattle his bones all the way to the marrow. He kept going until he hit a hollow in the hills and cut to his right, running up the narrow valley for all he was worth.
More howling came from back the way he'd come, farther off now, but he knew that only the ones in the rear would be announcing themselves until the lead Wolves caught him. This was not at all how he had pictured his morning. Grandfather hissed at him as a tree limb snapped at his neck, and the lad grunted an apology, barely able to hear himself over the sound of his own panting. He almost stepped on a startled armadillo, tore through sticky spiderwebs, abruptly changed direction, and plowed up the far hillside. The Raptor Wood was new terrain to Sullen, denser of tree than the lightly wooded steppes on the other side of the Agharthan Gorge, and beset with toe-breaking stones far fiercer than those of the Savannahs where his village lay. But then the song-singers said that all woods are home to a Horned Wolf.
"Enough," Grandfather said after they had scaled and descended half a dozen more hillocks with no sign of immediate pursuit. "Rest a moment, damn your face, rest and let me think."
"All right," said Sullen, promptly dropping into a crouch just over the crown of the newest rise and gulping the air. With a surge of nausea he realized the cramp in his side that he had been ignoring was actually a gouge that went clean through his hempen shirt and into the meat of his ribs. Half of the garment was dripping red. Prodding the wound, he wondered how he came by it. Swiftspear proving her name, probably, back when he first fled.
"You'll need to bind it before we go on," said Grandfather, leaning over Sullen's shoulder for a look at the mess. "Quick as you can, boy, they'll be on you like termites on a juicy log, and this is no place for a showdown. Never would have happened if you'd just stood your ground."
"Why would they..." Sullen tried to get his thoughts in order as Grandfather dug through the pack that strapped him to his grandson. "Why wouldn't they... Why did you... Why?"
" _Why?_ " Grandfather whined, his imitation of Sullen cutting deeper than the wound in his side. " _Whhhhhhy?_ Because they're not Wolves, they're dogs, that's why, dogs of their foreign masters."
That hardly seemed to explain anything. "Oryxdoom always had it in for me, but Wise-eye seemed kind enough, and Witmouth taught me every song I know. Why'd they all come so fast after us? Do they think we're cowards? Disgracing the clan?"
"Thank your uncle for that when we find him. When he came back they invented some special excuses for him, on account of all the treasure he gave the elders, but that only brought more embarrassment on the council when he quit the second time. You don't let a rabid dog flee, not when you have a chance to put it down, and since we all share the same blood, well, they assumed the worst. Fool a wolf once and all that shit." Grandfather unspooled a blanket from the pack, bit into the cloth, and tore. Passing the sizable strip to Sullen, he stowed the rest. "Oh, quit your pouting, I never said you were mad—they're the crazy ones, not us. They've suckled at the Crimson teat all right, and liked the milk. A pup like you _should_ be appalled at the depths of depravity a soul will sink to, once it's been exposed to paganism, but I'm sorry to say it don't surprise me none. The only thing that caught me off guard was their waiting until we were across the bridge before springing the trap."
"I'm ready," said Sullen, tightening the bandage and tucking it in on itself. He'd packed some moss into it but already the blanket was darkening over the wound. "Hold on, I'm going to pick up the pace."
"Oh no you're not," said Grandfather, tugging on Sullen's puffy saddlehorn of hair. "Enough of this acting the oryx, laddie, it's time to be the Horned Wolf I know you are. They'll follow your trail easy, fast as you've been moving, so slow it down till we find a prime place to pounce."
"Pounce?" Sullen looked around nervously, but nothing moved on the hillside. Grandfather was making him twitchy with this talk. "Nah, Fa, I can outrun them, and they'll have to turn around at some—"
Grandfather flicked Sullen's ear, his old-man breath overpowering the smell of blood and sap and torn moss. "I told you, boy, it's not right to let a mad dog loose, not when you have the means to stop it, keep it from spreading its poison."
"Mad dog," repeated Sullen. How many times had they called him that? Still, the prospect of killing his clanfolk filled him with gloom. In all the songs he'd heard and hummed, not one had a hero doing for his own people like this. Maybe so long as he hated that he had to he could still be a decent Horned Wolf...
"You'll find me a good roost to wait in, then we'll set a trap of our own. You think a king wolf like you can handle a few rabid jackals, laddie?"
Sullen thought about all the times he had barely held in his tears when his people tormented him. Thought about all the songs he'd made up for himself, ballads where he taught them a bloody lesson. Thought about what it would mean, to lay a trap for the Horned Wolf hunting party instead of only fighting back when they cornered him. He set his jaw, and braced himself for the hardest act he had ever contemplated, something he never thought he would actually do. It would hurt, but he didn't see any alternative.
"I... I'm sorry, Fa, but there's no way I can take 'em. I want to, right, but a branch hit my head back there a-ways, and I'm having a real hard time even running straight. Forget about fighting; if I tried to I'd just fall over and get us both killed." Sullen couldn't believe he had actually lied to his grandfather, couldn't believe he was actually swaying in place a little to sell the song, acting all woozy. Couldn't believe he actually thought Grandfather would believe his stupid ruse, that he actually thought he had a choice in the matter. Grandfather was being dead silent, the way he got when he was real, real angry, but then the old man's hand gave Sullen's bushy dome of hair a gentle rap.
"All right, Sullen," said the old man softly. "If you say you can't, I believe you."
That hurt the worst, so bad Sullen almost fessed to the fib then and there, but then he remembered how scared those pups had looked after he killed Oryxdoom. He didn't want to ambush those kids. He'd always had a soft spot for the unnamed pups of the clan, maybe because while the adults had hated him as long as he could remember, he had actually had a few friends when they were all younger, before they'd come of age. He'd even been naïve enough to think Stoutest might be his wife one day, good as they got along as teenagers, but after she earned her name she stopped spending time with him, same as the rest. Small wonder that when he thought about hurting kids, about them even seeing the kind of hurt he had endured, his hands got clammy and shaky.
"Better get moving if we're really just going to run out of here instead of doing the right thing," said Grandfather. "They catch us they'll kill us, and then I'll be able to tell you I told you so."
"They won't catch us," said Sullen, and smiled, because he had half a mind that Grandfather had known he was lying and still let him get away with it. The old man loved him that much, and next time Sullen had the chance to impress Grandfather, he'd do better. But for now he'd run like Count Raven when he was being chased out of the Seventh Void, back before the Frozen Savannahs got iced over and Sullen's ancestors had to run fast as leopards to keep their feet from being scorched on the blazing earth. A plain old Horned Wolf could never catch Sullen, if he ran that fast.
None even came close.
The next day was considerably quieter, and a week later they emerged from the Raptor Wood and stood on a hillside overlooking the withered plains that marked the border of the Crimson Empire, where Sullen's uncle had disappeared twice over. He hummed a verse of Rakehell to himself, swearing he would follow Uncle Craven's tracks only so far as they led him out into the Star and then back home, and once he returned he would never go away again. If Uncle Craven hadn't run off the second time, Sullen never would've had to leave the once.
# [CHAPTER
9](toc.xhtml#toc-chapter009)
Winter in the north is liable to make a grumpy panther of anyone, even those fortunate enough to have a roof and a hearth to stave off the snow and wind. For those seeking shelter in the lees of rocks and the boles of ancient pines as the sleet blew straight across into their face, spoiling any hope of a campfire, it was a fair bit worse. A cave Zosia had provisioned two decades prior for just such an unhappy need had evidently been discovered and cleaned out by some lucky traveler through that desolate high country in the interim, and so while she passed the worst of the season sheltered from the constant gale, it was a lean and icy refuge. She wiled away the snowed-in weeks mourning her husband and village, plotting her vengeance, talking to herself and Choplicker, and sharpening a body gone dull with age and comfort. When the worst of winter passed, allowing her to resume her trek, her muscles popped beneath her taut skin from more than the mild starvation she'd endured.
In light of all this, Zosia's foul mood was well earned when she at last reached the border of the Immaculate Isles.
The sea was still miles away, but the persistence of the Immaculates had won them a rather tidy amount of coastline in ages past. As the recent years of internal Imperial squabbling had drawn the most able forces to the heart of the Crimson Empire, the holdings of the Immaculates had casually expanded inland. It was easy to see how far they had gotten; halfway down the foothills Zosia spied a giant fucking wall. The dark serpent of stone snaked across the whole of her vision, and it didn't take a tactician or scholar to hazard that it stretched from one end of the Norwest peninsula to the other. Nicely done.
Zosia's assumption that the wall came just short of Linkensterne proved to be off by less than a mile, as the (presumably former) Imperial city turned out to be on the far side of the fortification. _Very_ nicely done. This part of the wall must have been built first, as there was none of the construction she had glimpsed farther to the east. A series of thick iron portcullises barred the tunnel through the wall, the gate absurdly narrow in contrast to the wide, ancient road. A solid defense, sure, but also a nice bite of the thumb to the Imperial traders who had once given the Immaculates such a hard time of it. As Zosia left the gorse and put her boots on the first real road she would stick to since leaving Kypck, she surmised that the encampment of caravans on this side of the gate must be a fixture of modern Imperial trade with the Immaculate.
"Mind your manners, or I'll sell your ass to the first merchant to make me an offer," Zosia told Choplicker. "Imperials have a taste for dog meat, and I doubt the Immaculate gourmands would turn their noses up at trying a new delicacy, either."
Reasoning she would have time aplenty to explore the caravan camp if they didn't let her through the gate on her first try, she made straight for the guardhouse. There wasn't one, she found, but the rampart dipped low over the gate, and as soon as she passed the last scowling merchant ensconced on his riding board at the side of the road, a guard poked her head over the edge. She couldn't have been twenty-five years old but had the simultaneously weary and haughty expression of a put-upon empress.
"Interviews are at dawn," the guard called down in Crimson. "Come back then."
" _Hello, honored friend_ ," said Zosia in the Norwest vernacular. She'd been brushing up on her Immaculate over the long months in the mountains. Since she hadn't had anyone to practice with, only Choplicker knew how much she'd actually retained, and he wasn't saying. A pleasant greeting was easy enough to remember, though, and it might be all she needed to get her toe in the gate.
" _Hello, honored friend_ ," the guard replied reflexively, then scowled and reverted to Crimson. "There's the queue behind you, and some of these rats have been waiting for weeks. You'll have to bribe one of them, and heavily, if you even expect an audience tomorrow."
"What if I just bribe you now?" Zosia smiled up at the gatekeeper. "And heavily."
"Would that it were that easy," said the guard ruefully. "We'd both be happier, eh? Take your bribes to your own people."
"These cheats and scoundrels aren't my people," said Zosia, well aware that in order to be easily heard on the wall she had to shout loudly enough for the merchants at the front of the line to hear her as well. "I come on the personal request of one of your court, and he will be displeased if I am late."
"Ooooh, a noble? Well, that changes everything!" The guard leaned farther over the wall, her scale-armored forearms crossed on the rampart before her. "Sister, I'm a noble, and so's my captain, and so's his commander, and so's a thousand handmaids and houseboys on a hundred different isles. I don't suppose this noble of yours was important enough to give you a stamped invitation we could see?"
"Alas, he placed his order with me before this wall of yours went up," said Zosia. "I'm an artisan who has spent two decades aging her briar for Lord Kang-ho of Hwabun, not some button-seller seeking entry to Linkensterne."
"Kang-ho, the _Lord_ of Hwabun?" said the guard, but her tone seemed to have shifted from sassy to mildly interested. "Briar, eh? His husband gives him enough allowance for that sort of luxury?"
"Lord Kang-ho paid in advance," said Zosia, pleased for a change by the gossipmongering that was endemic to the Immaculate Isles. Get two royals together and the rumor mill will turn for hours; fill a nation with nobles and it'll run till the Sunken Isle rises from the deep. "So you understand why he will be eager to see me admitted at once."
"I suppose I might," said the guard, nodding thoughtfully. "The Flower Pot's in need of some pleasant news. Tell you what, toss up that ten-mun piece I dropped and I'll run it past my captain."
Zosia rooted through her purse and fished out the smallest coin she had. "Your eyes aren't great for a wall-minder—it's a Crimson krone."
"So it is," said the guard, catching it in a gloved hand. "My captain will want to have the name of a carver so illustrious as to wait on the King of Hwabun's husband."
"Moor Clell," said Zosia, an alias she hadn't used since the Brackett entanglement some thirty years past. What a fucking fiasco that had been. There had been many times she had missed her shock of blue hair, but now that she had cause to travel incognito she gave thanks that the alchemy of age had turned what was once as cobalt as her eyes to an innocuous silver.
"Get comfortable, Mistress Clell," said the guard, disappearing from sight.
So Kang-ho was alive. He'd always been the lucky one, and she'd hoped that of all the Five Villains he, at least, was still around and kicking, which was why she'd come to the Immaculate Isles first. Nice to know it wasn't going to be a totally wasted visit, though as the sun inched low over the wall she supposed the journey wasn't over yet. Bureaucracy, be it Imperial or Raniputri, Usban or Immaculate, put her in a foul mood. This was why she had left in the first place. Even the tribes of Flintland were supposedly succumbing to the allure of pomp and pretense, though they had the decency to spice up their hoop-jumping with the odd dash of ultraviolent ritual combat. She imagined Leib sitting beside her, wearing away at her ill temper with his effortless wit, but the ghost of his memory only darkened her mood.
"She's not coming back." The merchant at the front of the encampment had descended from his gaudily painted covered wagon and approached Zosia, who sat in the wiregrass on the side of the road with Choplicker curled at her side. The trader's embroidered sarong marked him as Usban, or a dark-skinned convert to the Ten True Gods of Trve. He had none of the paunch that merchants were notorious for, and his middle-aged face would almost have been good-looking, if not for the perpetual sneer. "I tossed that rogue, or one of them anyway, a copper dinar, and she said the same thing: wait here. It has been a week, and I am still waiting, having reached the front of the line a coin shorter and wiser, but, I fear, no quicker."
"What a song." Zosia yawned. "You have a gift for storytelling, friend."
"And yet you seem to have missed the moral," said the merchant. "While you have been lolling in the dust, waiting for the crow you fed to return with a jade ring, another train has arrived at the rear of the queue. By trying to hasten your entry, you have only delayed it further."
"The ballads just keep on coming," said Zosia. "I thank you for your concern, but if it's all the same to you I'll wait a little longer."
"In point of fact, it is not the same to me," said the merchant, crossing his beefy arms. "Nor will it be all the same to the dozen travelers behind, none of whom will be amused if you are still sitting here, at the front of the queue, come dawn. I have five stout swords in my company who will be more than happy to assist you to the rear, should you persist in this flagrant disregard for good manners."
"Or?" asked Zosia, unimpressed. "You would have brought your muscle if that was your first option, so what's the pitch?"
"My first option, as always, is those same good manners I mentioned, which seem so alien to your ear. But my second is a simple proposition, for you see, when I arrived here I had but three swords in my company. The other two I discovered some wheels behind me in the queue."
"Uh-huh," said Zosia, glancing at the dark wall. The sun had slipped behind it, but no torches were lit on the rampart. "How much does a sellsword make on your wagon, and what's to stop me from cutting loose as soon as we get through the gate?"
"Why, nothing is to stop you from going your own way once we enter the Immaculate Isles," said the merchant, his sneer teetering on the pleasant now that they were opening up negotiations. "Though I hear it is difficult to get far without an escort these days. As for payment, I regret that I will have to ask slightly more than the two men I already hired, seeing as your period of service will be so much shorter than theirs."
"Uh-huh," said Zosia, getting to her feet. Try as she had to get herself back into shape during her trek through the mountains, she still felt as haggard and run-down as a fat monk's pony after pilgrimaging to the Secret City of the Snow Leopard. "How much?"
"Hey-o!" The guard's voice came down through the gloaming. "Looks like you're coming in, Moor Clell. Step up to the front so the guards can get a good look at you."
"What's this!" cried the merchant as two guards with red paper lanterns began making their way through the small barred doors built into each portcullis. "I paid you a week ago!"
"Oh, it's you," said the guard. "Don't worry, it took some time but I've got it all worked out so you can come through first thing in the morning."
"May your kindness be rewarded in the next life, and hopefully this one as well," called up the merchant, then turned his forced smile on Zosia as the last door was opened before them. "I don't suppose you and your hound require a sword for your perilous journey through Immaculate customs? I could offer you a very competitive rate."
Once, Zosia would have laughed in his face, maybe even given him a light slap on the cheek. Once, she had been a really unpleasant, self-important kid. Now, heeding her beloved Leib's wisdom that it was much better to run into a friendly face in an unexpected location than it was to find yourself with enemies you didn't remember making, she extended her hand.
"I would if I could, friend, but we both know that won't work this time around." She nodded at the entryway cut out of the last portcullis, which wasn't wide enough for both guards to pass through abreast. "Unless you can fit your wagon through that door? I'm Moor Clell, by the by, pipemaker."
"My carriage has many marvelous properties, but that is not one of them," said the merchant as he took her by the forearm and shook. "Ardeth Karnov thanks you for the sentiment, though. Perhaps we shall meet again, Moor Clell, pipemaker, in Linkensterne, Little Heaven, or stranger markets still. I have amongst my treasures the finest latakisses, so perhaps we could sample one another's wares."
"I should like that," said Zosia, her mouth watering at the thought of the rich, smoky tubāq of the Usba. She had burned through the last of her latakiss blend on the trail and was down to flue-cured vergins and dusty deertongue; she would have lingered to discuss a purchase on the spot had the guards not barked at her to get a move on. "Safe travels, Ardeth Karnov."
"And you as well," said the merchant, turning back to his wagon.
_Not much hope of that_ , thought Zosia as she allowed the guards to escort her into the Immaculate Isles, Choplicker wagging his tail as they went.
# [CHAPTER
10](toc.xhtml#toc-chapter010)
Maroto went along with Purna's scheme, because of course he did.
They opted to wait a few days before enacting the plot, so as not to make it obvious. During those long nights of caravanning through the Wastes, vainly trying to scare up some sort of game for the nobles to hunt that wouldn't actually kill them, Maroto let his imagination drift through scenarios in which Purna actually wanted to screw him. Which would, as a matter of principle, actually make him a whore, but he had known many, many whores over the years, and found them to be a generally good sort. Better to be a whore than a rich girl's plaything, anyway, and she'd hardly have been the first or the worst trick he'd turned in his time.
The long nights and sleeplessly hot days seemed longer with only these thoughts buzzing around in his head like trapped icebees, especially during the desert's twilight hours when the fops were hooting and giggling under their pavilions in the shale dust. Maroto did his best to ignore the glassgazers, taking every opportunity to partake of their food and drink without actually engaging them in conversation. Setting himself up as the stoic, quiet type had been something of a coup, but as the nights had turned into weeks their patience with his taciturnity had grown thin. If he couldn't provide them with adventure, he had damn well better feed them stories of it, but he wasn't big on that, either. Such songs as he'd lived through weren't for the likes of them.
One such evening he was standing in the shade of a collapsible gazebo, picking at a freshly set table of gleaming lamprey caviar and deviled moa eggs, sipping a bloody marīam out of a gilt teacup, when Pasha Diggelby and Count Hassan sidled up on either side of him.
"What ho, Hassan, it seems our fearless leader has discovered quite the monstrous nest," Diggelby smirked, his curled goatee drooping in the heat, the bow-bedecked, alabaster-coated lapdog he held in his arm even more ridiculous looking than its master. "Pray, what sort of fell beast deposited these eggs, hmmm? And by stealing its brood, do you mean to entice the creature down upon us, so that we might at last have some of this sport you've been promising?"
"Mrumph," said Maroto. He wasn't actually saying anything, just making noise and letting half-chewed caviar run from his mouth as he spoke in the hope of repulsing these clowns into leaving him alone. "Mra mruphh mra."
It didn't work. Bracing himself on his camel-pizzle swagger stick, Hassan reached up on the tips of his suede boots and dabbed Maroto's chin with a monogrammed napkin. "It would seem our expert hunter has left his manners back on the canyon-top where he treated Purna to a private hunt. Tell us truthfully, oh veteran of a hundred wars, did she sing true when she told of your falling beneath the dragon's claws, of how she saved you from its clutches?"
"Wasn't a dragon," said Maroto, remembering too late that he didn't intend to actually talk to them. "Godguana, is all."
"A _godguana_!" said Diggelby. "Oh, that sounds even better. So when do _we_ get to bring one down?"
The thought of putting these two in front of a territorial direlizard, with Hassan in his toga and gilded laurel wreath and Diggelby in his baggy pantaloons and carrying a bite-sized dog, brought a long-absent smile to Maroto's lips. Fuck these fucking nobles—if they wanted it so badly, he was only too happy to oblige. "Right now, lads. As soon as you retrieve your weapons and waterskins, we'll scale the far cliff there—the ripper vines will make it easy climbing, so long as you've got good gloves. Don't tell the others, though; we'll spook our quarry if there's more than a few of us along."
Hassan and Diggelby both looked skeptically at the side of the ravine in question. It was two hundred feet of vertical rock to what Maroto suspected to be a false summit. For all their talk, these two idiots didn't have much to say now, did they?
"What's all this about a climb?" said Tapai Purna, rounding the corner of the pavilion and allowing Hassan's stiff-backed Raniputri butler to pour her a frothy flute of bloody marīam. Draining his teacup, Maroto wondered where in the First Dark she had found a proper receptacle for her drink—every time he asked for glassware, be it a coupe or a flute, snifter or stein, the hovering servants brought him a teacup. Probably another of the fops' stupid pranks at his expense. "Certainly you two gibs don't mean to go off for a hunt before our guide has espied the horizon? What a fine mess that would be, if you got all the way up to the top, only to be caught by a glass storm, or even better, a swarm!"
"Yes, naturally, we had no plans for an immediate departure," said Hassan, hastily backing away from the table, Diggelby at his side. "We haven't even had breakfast yet."
"You scout the firmament, barbarian, and when you're back down, we can go up," said Diggelby. "Ta."
"Thanks for that," said Maroto. "Now I get to climb twice, assuming they don't weak out."
"You're very welcome," said Purna, sliding the empty teacup off his thick pinky with her slim, kid-gloved fingers. "Don't worry, we'll give them plenty of time to soak up some courage. First, though, let's see about getting you paid, shall we?"
Scrambling up a narrow defile with the mischievous lordling and then leaving her to make a faux lovenest while he summited the increasingly sheer slope was no fun at all. Clear skies improved his mood mildly, and coming back down to find she had packed several bottles of sparkling Eyvindian wine, a partially smushed wedge of pungent, green-veined cheese, and a crock of olives perked it up even more. "Precocious" was certainly not a word Maroto ever would have used to describe himself, but there was something undeniably amusing about sitting on the shelf of sandstone overlooking the camp and punctuating his snacking with lusty roars. Purna's moans and wails would have made a greener fellow blush, but Maroto had long since outgrown such things as being discomfited by a fake orgasm. Between mouthfuls, he gave her pointers—like most youngsters, she was overselling it.
A decent way to kill a morning, then. It brought back happy memories of his too-brief acting career, where he'd first learned how Imperials thought barbarians were supposed to behave. Those had been the days, traveling from one Arm of the Star to the next with Kiki and Carla and Two-eyed Jacques and all the rest, back before he'd ever heard of the Cobalt Company, let alone got mixed up with them... Back before he'd been fool enough to think he could better the world. Before he'd been fool enough to fall in love.
As was always the case, warm memories cooled quickly in Maroto's breast, and he gave a climactic bellow to refocus himself on his current endeavor, which was a lot more enjoyable than stewing in his usual barrel's worth of regrets. Not as enjoyable as actually screwing, mind, but that went without saying. Then again, Purna was slathered in her fashionable corpsepaint, midnight blue designs orbiting out around eyes and mouth, and between that and the imponderable puzzle of her stiff-ribbed petticoats he doubted he would have been able to do the deed, even if she'd been of a mood. It would be like trying to fuck an amorous ghoul after you'd rolled it up in a rug.
Guzzling the dregs from the last bottle, Maroto stood, woozier from the heat than the booze, and extended his hand to Purna. "That ought to be more than sufficient, I'd say. Let's get down before the rocks are too hot to climb."
"One last detail," said Purna, taking his hand and pulling herself to her feet. She sprang upon him with the speed of a devil, wrapping her legs around his waist and her arms around his neck, furiously kissing his throat. He nearly struck her off him in surprise, but then warmed to the ardent attack. He gingerly lowered them both back down to the steep, sandy ground—who knew if a randy ghoul in a rug might be better than your hand, until you try? On his hands and knees over the girl, her lips moved from his neck to his mouth, and Maroto gave a genuine groan at the taste of this pretty wee drag-faced noble.
Then she was away, nibbling his ear, and his fingers clumsily kneaded the layers of whalebone girding her chest, running his hand from her inaccessible bosom to her insulated groin and back up again.
"Rip it," she breathed, the salty musk of wine and olives not exactly sultry, but close enough. Yet as soon as he dug his fingers into the fabric and came away with a handful of lace, ribbons, and drawstrings, she gave a little squeal and dropped her legs and arms from around his body. He almost apologized, but then she wriggled down beneath him, hands and then head pressing up against the thickening throb in his short breeches...
And then she scooted the rest of the way out from under his legs, leaving him straddling a girl-shaped dust angel. Her voice, breathy but not heavy, put the shrivel on him like he'd been touched by a lich. "Perfect! Nobody will doubt our story now."
Clambering up, he had to fess that they both looked... tousled. He peevishly tried to wipe her makeup tracks off his crotch, but only succeeded in rubbing them in. Great. Purna beamed at him as she put her gloves back on. Maroto scowled, knowing exactly what this little tease needed, and being of half a mind to give it to her, here and now, and damn the consequences.
And why shouldn't he? She had it coming, that was beyond question, and better he just take care of the business now, while they were safely away from the rest. A strong talking-to would do her a world of good, yes it fucking would.
Of course, Maroto knew that lecturing the brat was the last way he'd ever get into her bloomers, but the old devil of his pride forced his mouth.
"Being a flirt is one thing, Tapai Purna," he said, wagging his finger at her, "but nobody likes being made the fool. It's an ugly business, leading somebody on. If you don't fancy a fellow or lady or whatever, that's fine as good wine, but making play like you do only to have a laugh at their expense is about the lowest prize you can claim. And if you truly take comfort in such sport, _well_. I'd expect such behavior from your friends, but thought better of you."
"Oh, tosh. You never would have, if I'd asked, but it was necessary," said Purna, shifting her wig so that it sat off kilter before picking up her wide-brimmed sunhat. "We'll be lucky if Duchess Din doesn't demand to inspect me for your spendings before paying out."
"Buh!" said Maroto, these nobles even loonier than he'd reckoned. Then again, they'd come too far to risk the bet now... "I mean, if you think she might..."
"If she does I'll just say you shot off in my mouth," said Purna, turning her corseted back on him and eyeing the descent. "After giving me lots and lots of scrumptious orgasms, of course. I know you've got your reputation to think of."
Maroto tried to cheer himself up by imagining what might make an orgasm scrumptious, but soon gave up. Too bloody hot for such thoughts, let alone such deeds. So he told himself, anyway. Shaking his bubbly-tickled head, he clambered back down to camp.
The plan worked. They bought the deception. What a fool Maroto was.
Before, he'd been loaded in the one currency these miserable parasites lacked: honor. And now he'd traded it all away for what amounted to a pittance of their collective material fortunes. Well, maybe he hadn't actually been that respectable to start with, but they'd certainly thought highly of him, and in any case he'd been worthier than they, refusing to play their little games.
Well, except for the little game of leading them on a dangerous adventure from which some of them might never return. _That_ little game he'd signed on for without hesitation, and for not a great deal more than he'd just earned from Purna.
Be that as it may, things felt different now, and not for the better. Before, he'd pretended not to give a devil's damn that the coxcombs all whispered and pointed and giggled whenever he was around, but now the jeering note in their attention cut into his ear far more keenly. He wasn't only a rich girl's plaything, he was a lordling's object of ridicule, a second son's punch line, a zir's zinger. He wasn't just a beast, but a trained one, same as any circus bear taught to beg for his breakfast. When the crowds taunted those miserable creatures, did they dream of escaping to some deep, dark den in the Black Cascades, away from the bright lights and cruel attentions, or did they dream of having their claws back, their filed-down teeth sharp again, the chain 'round their necks broken? Did a beast fantasize of revenge on its captors, the same as a barbarian might, or a weirdborn certainly would? Those last were quick enough to turn on their tormentors, Maroto knew.
"Ho, the fancy stallion approacheth!"
It was past midnight several days after the event Maroto had come to think of as the Shaming, and he'd ridden his dromedary to the front of the caravan in hope that Captain Gilleland and his men would prove better company than the arsehole richies. Apparently not. The barb had come from the captain himself, and the dozen other chevaleresses, sellswords, and bodyguards laughed at their ringleader's jest. Unlike the anonymous lesser nobles who had jogged zero memories in Maroto, he had recognized some of their hired muscle, by reputation if nothing else, and from the grudging respect they'd given him he knew that his own ballad-worthy history was known to them as well.
Now they laughed at him, too.
"Find any wondrous caves we could plunder, stallion?"
With the nobles, it was unlikely he would ever climb back into their good graces. They had paid him for adventure, whatever the fuck _that_ meant, and he had failed to deliver any of the expected fortune, glory, or excitement—only lethal heat and ugly terrain. Bad enough, but by throwing his lot in with Tapai Purna, first in a private godguana hunt and then a sexual conspiracy, he'd alienated himself further from the bulk of them by playing favorites, and with an Ugrakari to boot.
"Silent as any stud, eh?"
There was still time to patch things up with these roughnecks, though—take their burns on the chin, make a joke at his own expense. Play it off. No shame in fucking a fair young noble, unless the world had changed beyond recognition. If anything, it would humanize him to these toughs, bring the legend down to their level, make him one of them. How long had it been since he'd ridden with hard folk who thought him equal, rather than better than they, or, sure, as was more often the case of late, their lesser? Maroto sat straighter on his dromedary, giving the heavily armed outriders his stoniest stare.
"Now I know why they hired him—after the way he fucked the Crimson Empire, they figured him to be the best lay on the Star!"
But, and it was a pretty important but, _fuck these fucking fucks right in their fucking faces_. He had stared down devils, laid low mighty kingdoms, and they dared speak to him thus? He wheeled his camel away from them, knowing if he opened his mouth he would say something that would result in them stopping their steeds and demanding he fight them then and there, for honor's sake. A younger Maroto would have fallen right into the trap, but he wasn't some hornless pup anymore—he would wait until they were safely bedded down for the day, murder the lookouts, and then slit their throats, one by one, starting with the guards and working his way down through the nobles, until he was alone in the Wastes.
Except of course he wouldn't. The thought gave him enough succor to tactically retreat from the hostile situation without his mouth landing him in an unmarked grave, but once he was safely in the shadows between pleasure wagons he let the cowardly notion float up into the broiling night air. What he would actually do was wait until they arrived in Niles, take fops and fop guards alike to an inn, and then promptly instigate an epic bar fight. This would provide him with the opportunity to smash in Captain Gilleland's teeth, and the gold-flecked grills of a few nobles while he was at it, but the city militia wouldn't let it actually progress to a dozen bodyguards chopping him down in cold blood. Probably. In any event, Niles was only a few nights' ride away, and once there he would beat some manners into the lot of these highborns and their dogs.
Except of course he didn't. Before they had even unhitched the wagons and unbuttoned their ruffs at the caravansary in Niles, Maroto strode away into the City on the Edge of Hell, shoving Purna aside when she ran after and tried to talk him into returning to the party.
"You were contracted to take us here _and back_ ," said Purna, shrugging off the blow far easier than Maroto expected. "You won't receive any wages for taking us across the Wastes but not providing passage home. They'll make you pay them, in all likelihood, for breaking your contract, and for the food and drink you consumed, to say naught of the inconvenience of—"
"Here." Maroto yanked the purse she had given him and threw it at her feet. He regretted it before it even hit the packed black sand of the street. "I'd rather be a poor man than a rich dog."
"You really shouldn't take everything so seriously," said Purna, making no move to retrieve the purse. More than one veiled passerby was slowing to watch the altercation. "If you like I'll see if I can discourage them from riding you so hard. It would certainly help matters if you could find someone or something for them to fight; I know I've felt worlds better about the whole affair since you and I took down that drag—"
"Lizard!" barked Maroto. "It was just a big fucking lizard, nothing more, and if I had my way I'd feed the lot of you to the godguanas!"
"So there's nothing I can do to convince you to come back?" Her glittery lips pouted. The lecture he'd given her had clearly been a waste of breath. "Tell me your price, and I'll see what I can't muster. I... I really respect you, Maroto. A lot."
"You talk about _respect_ in the same breath you ask what my _price_ is? There is no damn price! I'm _done_ with the Wastes—I'll never set foot there again, _ever_. And as for _you_ , I'd sooner float through the Sea of Devils on a raft made of meat than sail a pleasure pontoon across Lake Jucifuge with you dandies and your hired goons. You're all alike, and I'm done with you. Forever."
"I thought you were a lot smarter than this," said Purna sadly, plucking up the purse. "And what's in here won't even begin to cover what the lawyers will demand for this gross breach of bond. They'll come for their silver."
"Yes, well, first they'll have to find me," said Maroto, wishing he'd come up with something smarter even as she turned her back on him. Which was rudeness on top of rudeness, since he'd been the one storming off, yet there she went, depriving him of even a proper exit. The small crowd of Usban travelers who had gathered now wandered off, too, leaving Maroto to stand in the middle of the busy street, wishing he hadn't just given up the bulk of his money in an unappreciated gesture.
What meager funds he had left he promptly set to drinking away in the first dive he came to, a wide adobe complex a few blocks from the caravansary. Before long he'd consumed enough to convince himself that this, as with everything else that had led to this moment in his life, wasn't such a bad turnout. He could head farther down into Usba proper, hit the Honeyed Coast at Trve, and pick up work on a ship heading... well, anywhere but here. The Southern Arm was too devil-loved hot for a Flintlander out of the Frozen Savannahs.
The barkeep was evidently Geminidean, and as he served a pair of chain-draped pilgrims recently arrived from the Crimson Empire they filled him in on sundry rumors of import from back home. Maroto initially paid the tonsured women no mind, but then one of their voices sliced through his sun-stewed skull:
"... more than a few rebels, though—they're professionals, is the thought, given how effective they are, maybe a mercenary band hired by the Raniputri or Immaculates to stir up trouble."
Nothing exciting, that, but then the other pilgrim interjected:
"Hear this, though—they're led by a blue-haired general with the faceplate of a devil dog, and at least one of her captains wore the helm of a Villain, if not more. Need I tell you what color banner they flew?"
For the first time in a very long time, Maroto felt dizzy from more than the drink, and he clung to the basalt bartop.
"That story's older than my firstborn," said the barkeep, nodding at the wench serving mugs of kumis at the other end of the tavern. "I haven't heard it in ages, though; glad to hear it's making a comeback. It'd be a shame if people stopped telling it."
"That's what I told her," said the first pilgrim.
"I heard it from my sister, who heard it from her superior," argued the second. "These are holy women, not song-singers looking to attract a crowd. The company ambushed a garrison outside Agalloch not a month past."
"If not a tall tale, then clever impostors seeking to hijack a legend rather than build a reputation," said the barkeep. "Unless you believe in ghosts, sister?"
"No one knows for sure what became of the Villains after their queen was executed," said the first pilgrim. "So perhaps the captain is genuine, and their leader a fake. That way you're both right."
"I never said I believed it was really her," said the second pilgrim defensively. "Simply that mercenaries waving the Cobalt flag were seen outside Agalloch. Unlike others I could name, I prefer to repeat facts, not speculate on rumors, even when the details of such facts are admittedly scant."
There may have been more to the conversation, but Maroto did not know, for he staggered out of the tavern. From the caravansary, he quickly picked up the trail of the fops. Following their tinny cries through the baking streets, and occasionally stumbling into the walls of the tight-packed houses that scalded like the sides of a tandoor, he eventually caught up to them at an establishment of decidedly grander stature than the one at which he had drunk.
Purna had not gotten around to informing the others of Maroto's desertion, and so all seemed as he had left it. Within an hour he was contentedly asleep on the cool tile floor beneath one of the inn's plush benches, and two dusks later they were rolling back out into the desert, Maroto having successfully convinced the testy nobles that he had a hot tip on some "real adventure" to be found on the Desperate Road: the most direct, and therefore most dangerous, route back across the Panteran Wastes.
# [CHAPTER
11](toc.xhtml#toc-chapter011)
As Zosia repacked her gear in the customs house on the far side of the wall, the guard who had brokered her admittance sauntered into the brightly lit chamber. Compared to the polished, spotlessly maintained armor of the Immaculates, Zosia's old adventuring kit looked downright shoddy. Choplicker did his tottering, just-an-old-dog-shaking-his-butt approach to the young soldier, who scratched him behind the ears and cooed to the foul monster.
"Thanks again," said Zosia as she pulled the drawstring tight and turned around to maneuver the massive pack from the table onto her aching shoulders. It was full dark now that customs had finally gotten done with her, and she still had to find an inn or flophouse in Linkensterne. "Anywhere cheap and clean you'd recommend in the city?"
"Sure," said the guard, patting Choplicker and straightening up. The fiend whined as she took her hand away. "Let's get moving. You can tell me if you're talking food and drink, men or women or what-have-you, or just a bunk."
"You're my minder?" In the old days many of the isles required an escort for visitors, but on the coast foreigners had been free to come and go as they pleased.
"Bang Lin," said the guard with the faintest suggestion of a bow, her back barely curving. "It's my neck if you're a spy or assassin. Told the captain you seemed friendly, so I get to play chaperone until you prove me right. Or wrong."
"That's one I owe you, then." Depending on how things shook out with Kang-ho it could go either way, but for all their sakes Zosia hoped she proved Bang Lin correct. Anyway, there were worse traveling companions than handsome youths... but as soon as her thoughts started down the path to private chambers instead of a common room, she remembered the weight of her husband's severed head in her hand, the butcher's-stall smell of his hair. The mountain crossing had been cold and lonely enough that she had actually considered letting Choplicker curl up against her when she slept, but it was still too fresh to entertain thoughts of companionship. She'd lost lovers before, plenty of them, but this was something else entirely—the ache had only grown worse with time, and though the thought that she was further fattening up Choplicker turned her stomach, there was nothing she could do to soften the hurt. Not until she had the means to go after the ones responsible for what had happened.
"So long as you don't cause any trouble, we can call it even," said Bang. "What's your dog's name? He's cute."
Choplicker barked his assent at this, nuzzling his head back under Bang's dangling palm. The soldier was delighted. Zosia grimaced.
"I call him a lot of things, but cute ain't one of them. Dumb mutt comes no matter what you say."
"So long as you don't call him late for supper, right?"
"Right," said Zosia, remembering Choplicker as he had been on campaign twenty-odd years before, feasting on the suffering of the dead and dying until his gut dragged on the ground. It might have been comical, like something you'd see on a Samothan woodcut of a half-forgotten fable, but to witness such wanton gluttony, to watch the creature's flesh warp to accommodate its appetite... there was nothing funny about it. "A bath, food, drink, smoke, and a bed. That order."
"We can do that," said Bang, ushering Zosia out the door. "But Linkensterne's liable to be different than you remembered, and not for the better."
"I remember it being a real shithole," said Zosia as she stepped out into the chill night.
"Then maybe it hasn't changed much," said Bang, saluting the customs officer lounging on a bench by the door as they headed up the road.
This had been farm country, but all of the old outlying ranches had been demolished, the buildings scrapped to construct barracks. A string of pink paper lanterns hung from poles leading back to the gate, and ahead of them the lights were strung from the dwarf pines and plum trees that bordered the road cutting through the overgrown fields. The city glowed at the end of the lantern string, the biggest beacon of them all.
The Immaculate influence on Linkensterne had always been stronger than just a few bun-carts and noodlehouses to offset the typical sausage-and-beerhall eateries of the Crimson Empire, and a higher proportion of Immaculate whores than you'd find in the nonspecialty brothels of Nottap or Eyvind. The city proudly displayed its bordertown lineage on its skyline, with half-timbered pagodas and stupa-based, steeple-crowned churches towering above the narrow streets, the sharply angled roofs of Imperial-styled rowhouses bumping end-tiles with the swooping curves of Immaculate construction. Far from feeling as though two cultures had been awkwardly pressed together as you saw in some cities on the Star—places in which the people and the architecture stuck to their own quarters—in Linkensterne it felt as though the city had been jointly raised in harmonious collaboration. The reason for this was simple: it had. A fire had leveled the spot some hundred years before, and a broad mix of Imperial and Immaculate interests had rebuilt it. The city stood as a testament to the potential for two peoples to come together and erect a shared future.
The city was also a total dump, with the exception of the Merchant's Quarter, which was judiciously walled off from the rest of Linkensterne and could only be entered by appointment. The rest of town was run-down and rampant with crime both petty and violent, in contrast to the more sophisticated corruption that took place among the governing merchants. The only thing worse than a royal city was a free one, where the ruling elite rarely forked over the funds for sanitation or a decent municipal militia.
When they tromped into town Zosia could see at a glance how much things had changed. They were entering the Black Earth district, which was on the opposite end of Linkensterne from the Merchant's Quarter, yet the streets were fairly clear of shit and refuse, and a pair of uniformed militia thugs stood on the corner of most intersections. Lit lanterns on lampposts were the rule instead of the exception, and four blocks in Zosia had yet to see anyone lying dead drunk—or just plain dead—on the too-clean street.
"You were right," she said, "things _have_ changed."
"I heard it was a lot of fun before we incorporated it," said Bang wistfully. "Now it's just a broke-down version of an Immaculate city."
"Did a lot of merchants pull up stakes? They can't have been happy about being conquered."
"Oh, they hate the handover like you wouldn't believe, but it's not like they've got a lot of options—you know any other free cities on the Norwest Arm? Me, neither. So most of those crooks stayed put and have tried to make the best of it. Hard as a barnacle's breast, doing shady trades with Immaculate oversight, but a tough tit is better than none at all, eh?"
"That's why the caravans are lined up for days outside the wall." Zosia hadn't been back a day and was already soured on Star politics.
"Days or weeks, depends on who they're here to trade with," said Bang. "Those merchants who were more... receptive to the handover, they get invitations so their guests breeze through customs with a municipal pass instead of waiting in the queue. The merchants who aren't so amenable about Immaculate overseers, well, their goods take a little longer to clear the wall."
"And bad luck for any poor saps waiting on the merchants to provide medicine or supplies, right?" It filled Zosia's mouth with vinegar, all this familiar squabbling, with the commoners caught in the middle.
"Bad luck for some, but good luck for others," said Bang. "Merchants who were on the outs with the old Linkensterne elite have found their prospects much improved by finding new slippers to kiss."
"Bully for them. Now, a bath, food, drink, smoke, bed," said Zosia, yawning at a militiaperson who was sizing her up. "Let's get on with it."
Zosia had fond memories of Immaculate bathhouses in Linkensterne from long before the takeover, but she didn't remember any being as clean as the one Bang led her to. Jade tiles gleamed in the candlelight, the wide, terraced pools steaming like soup bowls. There were a dozen other bathers spread out in the tubs or lounging on the warm tiles, and as Zosia lowered herself into the hot water she felt true contentment for the first time since she had been forced upon this road she walked. Bang settled in beside her, and, seeing her out of her uniform, Zosia's interest in the girl increased substantially. She smiled to herself at the younger woman's flirtatious glances and offer to wash her back... but as soon as the smile arrived it wilted. Zosia dunked her face in the water and stayed down as long as she could, as if she could hide there forever from her past, and from her base nature. As if warm water and a rough sponge could scrub away what was wrong with her.
In a refreshingly dingy tavern off the main drag, Zosia and Bang were served up a steaming supper fragrant with long-missed spices. They ate at a yellowed floor table, filling their dishes from the large chipped bowl set between them. Mixing up the rice, fried quail eggs, peppery bean paste, and sautéed ferns and radish, Zosia passed the seared venison, curds, and sauerkraut to Bang—it had been decades since she had enjoyed real Immaculate cuisine, and didn't care to sully the experience with these concessions to Crimson tastes. Besides, she had eaten little else but deer jerky on her journey. She ate and she ate and she ate, offering no scraps to Choplicker even when he whined until the quail yolks turned red, the melting faces of people Zosia had killed leaking out into the rice. She raised bowl to lips and shoveled in the lot, imagining all the new victims Choplicker would haunt her with, once her work really got under way.
Zosia liked to drink and she liked to smoke, and she liked them best when she could enjoy them together. Once Bang had gotten the measure of her ward's preferences, they ambled through Linkensterne. They passed the tall, teetering kaldi houses (hash and bud of the saam only, please) and the fluttering silk panels of the sting warrens (insects, arachnids, and the odd kidnapping), arriving in their own full-bellied time at a longhouse that reeked of bitter beer, bitter sweat, and, sweetest of all to Zosia's nose, bitter tubāq. Even this early in the season the rice paper shutters were slid open, the chill outside mitigated by the large firepit in the center of the room and the dozens of smaller furnaces the patrons puffed upon. Cheap clay tavern pipes were bought for pfennigs from the proprietor, a reedy old gent from distant Vasarat whose longstanding devotion to his brown mistress was writ across callused lips, stained teeth, and the yellow finger he dug into his nostril as though it were an obstinate bowl clinging to its dottle.
Having the end but not the means, Zosia sidled up to the bar, shrugging off her pack as she bumped past a woolly-bearded barbarian nursing a porcelain-headed jaegerpfeiff. Up and down his arms and neck sinuous indigo tattoos wrestled with jagged white scars, his lionskin cloak stank of wet dirt and old blood, and his pipe gave off the cloying aroma of lavender. Once upon a time she would have challenged the giant to a duel for smoking his pungent aromatic weed within sniffing distance of her; once, but long ago. Pushing her wide-brimmed hat back onto her neck, she settled onto a stool and plunked her smallest purse on the lacquered bar.
"Hi, honor friend," said the proprietor, his Immaculate even worse than hers.
"Right back atcha," said Zosia in Crimson as she undid the flaps of her enormous backpack. Withdrawing a pouch smaller yet more precious than the coinpurse set before her, she removed a pipe carved in the cutty style, its gently bent antler stem as long as her hand and its smooth briar bowl canted slightly forward, like a tipsy sailor leaning against a mast. Two tiny spurs descended from the base of the bowl, allowing it to sit steady on the bartop. "I'll be filling this with your finest vergin flake, my horn with your darkest stout, a dwarf of your smoothest ryefire, and a private room. That order."
It was the dwarf glasses of ryefire that got her. Bang matched her tipple for tipple and horn for horn at first, the pretty soldier doing her regiment proud. As she eyed Zosia's pipe the conversation flowed into the safe waters of stormy seas and naval entanglements, of which Zosia had seen more than many in her youth. Bang obviously had the brine in her veins, and as night gave way to early morning Zosia found herself genuinely enjoying the eager young fool's company—the girl seemed intent on seeing herself washed into an early grave, and it seemed a pity to send her off to sea without a bit more sand under her nails.
"Should've said something sooner, would've been easy to arrange a bedmate," said Bang as she ducked away from Zosia at the older woman's door. "Still could see, send someone up?"
"Nah, haven't paid for it in so long I wouldn't know the etiquette," said Zosia, trying to mask her embarrassment with braggadocio. Just as she'd known that last dwarf of ryefire was a mistake before it even hit her belly, she realized now that she had totally misread the situation, that she had mistaken basic kindness and mild flirtation for something more. "Just being friendly, was all."
"I _am_ flattered," said Bang. "Really. Good night, friend."
"Sure," said Zosia. "Night."
Closing the door, she looked to Choplicker. He had nosed the paper screen over and had his front paws up on the windowsill, looking out into the dark city. Much as she disliked sharing her room with him, the alternative was to let him loose on the streets of Linkensterne.
Or she could set him free once and for all, in exchange for vengeance upon all those responsible. That would take the burden from her aged shoulders and ensure that none escaped their due. She wouldn't have to take another step into the Immaculate Isles, wouldn't have to bet her already slim chance of success on a hundred thousand variables—it had taken her over a season just to get this far; how long would it take her to achieve her ends? Why not just let the monster do what monsters did best?
"Not on your life," Zosia muttered, sprawling out on the mat. Hoartrap had claimed that devils could only speak to the sleeping and the dead, but Zosia knew better than to put faith in the word of a witch. She often wondered if the fiends couldn't also project a thought into your mind, the notion planted so surreptitiously as to make you think you'd conjured it up yourself. That would certainly explain how often she thought about turning Choplicker loose, even after he'd declined her previous offer for freedom.
And why she would have tried to screw the first available person she came across, with Leib not yet half a year dead. She remembered the wink and slap on the bottom he'd given her before riding out for the crossroads that last time and barely made it to the chamberpot in time. When she was sure that her guts were done, she wiped her mouth and looked to where Choplicker had curled up beneath the window, pretending to sleep.
Would that devils were responsible for our weakness _,_ Zosia thought as she crawled back onto her mat. Would that there was somebody, anybody, _anything_ else to blame for her lot. In the morning she would find many likely candidates, with Queen Indsorith of Samoth at the top of the list, but for now, squinting in the glare of sleeplessness, she could only twist deeper into herself, into her responsibility for the death of Leib and his village.
"My village," she whispered in the dark, " _my_ village," but she never quite believed it.
# [CHAPTER
12](toc.xhtml#toc-chapter012)
It was late spring when Sister Portolés's transgression at the village of Kypck truly caught up with her.
In the meantime, she had been lashed by Father Eddison as soon as she had led the cavalry back down the valley to rejoin the main force of the Fifteenth Regiment, the charred corpse of Sir Hjortt she had recovered from the ruins of the mayoress's house lashed to the back of his horse. She had fully expected this. She had been lashed again by the regiment's acting colonel once her clerical superior was done with her, which, again, she had both anticipated and welcomed. Finally, she had lashed herself in penance on every new moon since, but she had prayed to avoid any substantial probing into the particulars of that nobleman's ignoble death in a remote mountain town. Alas, it seemed a well-connected young colonel could not burn to death on a war nun's watch without a full inquiry taking place.
The summons came the week after she finally returned to her cell in the quadrant of Diadem's central Chainhouse known as the Dens. The Fallen Mother saw through the selfishness of Sister Portolés's prayers, and so the summons, and as the anathema read the letter in the dimness of her cell she nodded to herself. She deserved this, just as Sir Hjortt had deserved to die in the fire. Just as Portolés had judged him, now, too, would she be judged. Everything happened. Not for a reason, mind, for the Fallen Mother was beyond the need for justifications, but everything happened.
Sister Portolés set the summons down on her penitence bench and prepared herself to enter the Crimson Throne Room of Diadem. Her ablutions took the better part of the day, all of the hair on her body, and the odd patch of skin when her razor found resistance. Better to lose a little flesh than leave behind a trace of what she had been before this day. To be before Her Grace was to be reborn, and what babe comes to its mother already dressed in fur? A babe worthy of the pyre, not the teat.
Too late, she thought to call on Brother Wan, thinking he might be persuaded to sin with her one last time, the way they used to, but this was the thought of Portolés, anathema and sinner, and the penitent nun who crouched naked in the cell slapped herself across the face. Hard. And again. And now she wanted to see Brother Wan more than ever, so she stuck out her tongue and pinched it between her fingers, digging into the ridge of scar tissue that marked where the church had made her almost human when she was but a fledgling monster. She could no longer recall the tastes of the wind, of the night, but she could well remember the tang of blood and hemp as the papal barbers had sewn her forked tongue together.
A knock at her door. This was it, then. Rising, she dropped the black robe included with the summons over her stocky frame and went to meet her fate. Except instead of an escort to her judgment, it was a far more welcome visitor.
"Oh, Portolés." Brother Wan gazed up at her in the doorway. The pocked knot of flesh where his nose and upper lip should be, where his beak had been, trembled with emotion. "I would have come as soon as I heard about the summons, but thought... you might wish to come to me. Shall I go? I shall go."
"Temptation," growled Portolés, wondering if the Fallen Mother or the Deceiver had put this penultimate obstacle in her path. Not really caring either way. Kissing her brother-in-chains right there in the hall of the Dens, kissing him until her file-dulled teeth knocked against the wooden ones the church had given him, and then pulling him into her cell. They tripped over her penitence bench, came down with limbs tangled, and for what must be the final time rooted their hands beneath one another's vestments, groaning prayers together between kisses as they worked one another to forbidden rapture.
Employing only their hands did not betray the letter of the law, true, but as Brother Wan had always told her when they were done and he was regretting his weakness, their actions certainly ran against the spirit of it. He was correct that a lesser sin is still a sin, which only prompted Portolés to argue that that was all the more reason for them to consummate the greater evil their bodies craved. Everything happens, she would breathe in the humid darkness, but he always stopped her before she could damn them both.
When they were growing up together in the Dens, he had always set an example for Portolés to aspire to, and his ability to know her heart even better than she knew it herself had no doubt saved her from many a graver sin. Since becoming an attaché to Cardinal Diamond several years prior, he had soared to such lofty reaches in his piety that he had rebuked her every suggestion that they resume their discreet meetings. That he had come to her this last time filled Portolés with the buzzing ecstasy that she only ever seemed to attain through committing a new sin; what did it say about her that frigging Wan was so much more exciting, now that he was so much holier?
"What _happened_ out there?" Wan whispered as they lay together when they were both finished, Portolés licking her fingers clean. "The clerks are saying all sorts of horrible things, and Cardinal Diamond—"
"Pray for me, brother," said Sister Portolés, kissing her fellow anathema on the cheek and smoothing her robe. She had to go, now, or she would tell him everything, and she cared about him too much to burden him with more of her sins. "That's what we always used to do, after."
Giving Brother Wan a final sad smile, she went to meet her queen and, holier still, her pontiff.
Sister Portolés had only been inside Diadem's Jewel once, when she had been called by Abbotess Cradofil for enlistment in the Imperial military, and on that occasion she had been surrounded by a thousand other novices in the parade grounds on the bottom level. Now she walked alone—as all mortals truly are in the eyes of the Almighty Matron—up winding stairs carved into the ossified corpse of the volcano that housed Diadem, moving from the city below to the castle above. Daunting a journey as it would have been were she only meeting her pontiff, the knowledge that the Crimson Queen would also be present filled Portolés with terror.
It was not the ferocious reputation of Queen Indsorith alone that terrified Portolés, but the anxiety that stemmed from not knowing exactly how solid the ground was beneath her feet, now that another political seismic shift had settled. For most of her life Portolés had been taught that Queen Indsorith was second only to Pope Shanatu in the eyes of the Fallen Mother, and after praying to the Black Pope every novice turned her prayers to the Crimson Queen and her royal castle in the old capital of the Serpent's Circle.
But then the Burnished Chain had declared Queen Indsorith a traitor to the Fallen Mother, and in the ensuing civil war Portolés had fought the forces of a woman she had once worshipped... only to have Pope Shanatu declare a truce, restore the queen to grace at the Council of Diadem, and then promptly retire from his post, with his niece succeeding him as Black Pope. As if matters weren't turbulent enough, after the reconciliation Queen Indsorith had moved her court back to Diadem, ruling from the Crimson Throne Room for the first time in nearly twenty years, the old queen and the new pope governing their respective spheres from the same chamber. In a few short months Portolés had gone from killing Imperials at the Battle of Brockie to serving as personal bodyguard to one of their colonels... a position she had proven woefully inadequate for.
No wonder a lowly anathema struggled with her faith even before what the summons had called the Encounter at Kypck—like all of her monstrous ilk, Portolés was born to sin, and only the intervention of the Burnished Chain brought goodness into her brutish heart. She couldn't understand how anyone, even the Crimson Queen, could be excommunicated from the church one year, only to be declared the spiritual equal of the Black Pope after the war went poorly for the Burnished Chain. Brother Wan sternly admonished her not to ask questions beyond her comprehension, but Sister Portolés couldn't help herself; she wanted the world to make sense again, the way it had when she was young. Sadly, she was losing the war she fought with her own devilish nature, and now that she had effectively murdered Colonel Hjortt there could be no saving her: the two holiest women in the world would see her for what she was, and as Portolés went to fulfill the summons she knew she would never return to the Dens, the only home she had ever known.
After being admitted through a dozen gates of narrowing width and increased guard, she was given a black candle as thick as her wrist, and with the aid of a blind officiant melted its base onto her shaven head until she was able to affix it in place. Only when it was firmly welded to her scalded skull was she permitted to proceed up the unlit avenues of Castle Diadem, her pace painfully slow lest the flame flicker out. Gargoyles leered at her from every arch and buttress, gobs of wax mingling with her tears to leave a trail for her to follow back out should she be permitted to leave after the audience. The way was known to her by the will of the Fallen Mother, channeled through the pure heart of the Black Pope, who waited with the Crimson Queen... or so the summons had alleged, but Portolés found herself guided solely by the smears of phosphorescent slime on the flagstones that directed her ever upward. Perhaps they knew her sin was so great she could no longer feel the touch of the divine, and had thus provided her another means of finding her way.
An hour passed, maybe two, stair after stair, ramp upon ramp.
Everything happens, but still Sister Portolés struggled. The echo of Brother Wan's fingers now seemed shrill between her legs, and she would have cursed her weakness had her breath not been required to keep her chant at a respectable volume. It was not for the unclean to judge any but themselves—how many times had Abbotess Cradofil made her repeat that? And yet Sister Portolés had judged Sir Hjortt, and now she would be judged. The Fallen Mother loved her, and a war-worn sister should walk with her head high, even an anathema, yet the wax dripping down her nose and cheeks made her shame public. Any hope she had felt in her cell was gone here in the house the Almighty Matron had fashioned for her hierophants.
Once Sister Portolés gained the throne room's antechamber, the lighting improved even if her mood remained dark. Candelabras illuminated a posh old man dressed in the chartreuse regalia of Azgaroth. He waited on a bench, Abbotess Cradofil beside him, and both stood as Sister Portolés shuffled down the last shadow-draped corridor. Neither appeared happy to see her.
"Sister Portolés," said Abbotess Cradofil, her lips as slick and bulging as a pair of tadpoles. "I present you to Baron Domingo Hjortt of Cockspar, Retired Fifteenth Colonel of the Crimson Empire."
"Sir." Sister Portolés bowed as best she could without risking her candle. A rivulet of wax arced across her eye, but she did not cry out. This old rooster looked just as puffed up as his broiled chick. "I pray for Sir Hjortt's soul, and trust the remains and effects I returned to the Fifteenth safely found their way home to Cockspar."
"Let's get on with this," Baron Hjortt addressed Abbotess Cradofil. "I have no desire to speak to this creature."
"Perhaps, but Sister Portolés has something to tell you of your son," said Abbotess Cradofil, those dead eyes of her cutting across Sister Portolés. "Don't you?"
"I lament the death of Sir Hjortt," said Sister Portolés, but before she could stop herself the words came rushing out of their own accord. "I believe you would have had him die a hero, not a coward. Allmother forgive him."
Well, it was the truth, though the nobleman's horrified expression confirmed that he had not come to the Imperial capital for such insight into Sir Efrain Hjortt's final moments. Abbotess Cradofil's slimy mouth pursed tight, and Sister Portolés silently apologized for the wildness in her bedeviled tongue. Perhaps it would have been better if they had just removed it altogether, as Abbotess Cradofil had always said.
"I'll watch you burn ere the moon next rises," Baron Hjortt snarled, and Sister Portolés supposed he was right. She remembered the look that had appeared on his son's face when she had not braved the burning terrace to save him, the hatred and fear and confusion... The familial resemblance was unmistakable. She wondered if she would die better. She couldn't possibly die worse.
"After all I've done for you, this is the tithe you offer," Abbotess Cradofil murmured as she ushered Sister Portolés to the great white oak doors. No guards stood sentry here, the queen decreeing that any assassin was entitled to the same chance at her throne that she had once enjoyed. In twenty years of her rule, forty-seven contenders had breached this final portal, and forty-six skulls lined the archway, grinning down at the nobleman, the abbotess, and the anathema. The one missing skull supposedly belonged to a man unworthy of a death by the queen's blade, a wastrel cast out to seek a more fitting tomb among the scavenging devils of the Star. "Fallen Mother heed me, Portolés, if you speak so freely before our pontiff, I will snap your neck myself."
"I praise your mercy, Superior, but I shall not accept it," Sister Portolés heard herself reply, and marveled that sinning had apparently become something she did on reflex. Had the deviltry she had fought her whole life to smother come loose once she let Sir Hjortt die? Was the wickedness of the Deceiver stirring this mutiny in her breast? As much as she wanted to believe such excuses, in her soul Portolés knew that her love for sin was nothing new, that hard as she had fought against her base nature, transgression gave her more succor than obedience ever had.
The Crimson Throne Room was built into the rim of the petrified volcano, a roofless half-moon of polished obsidian ending in a two-thousand-foot drop down to the gables and cupolas of the city beneath the castle. It was told in songs that the stars blazed hotter here than anywhere else in the world, even when the moon was full, as it was this night, and other than Sister Portolés's candle no earthly light disturbed the chamber. She suspected that even had she a pair of pure eyes the room would seem bright as the flush of dawn.
The Queen of Samoth, Keeper of the Crimson Empire, sprawled across a huge throne of carven red fire glass that erupted from the obsidian floor, the flowing lines and steep curls of the seat making Her Majesty appear to float atop a plume of blood. The Black Pope, Shepherdess of the Lost, sat stiffly beside her queen in a shorter, plainer throne, this one crafted of onyx and inlaid with thick silver chains. Both women were opulently enrobed, but the queen was barefoot. The doors swung shut and Sister Portolés's candle guttered out. Three pairs of knees slipped to the hard floor, three heads bowed.
"Your Majesty and Your Grace," began Abbotess Cradofil, "I present unto you this worthy pilgrim, Sir Domingo Hjortt, Baron of Cockspar, Retired Fifteenth Colonel of the Crimson Empire, and the sister whom you seek, an anathema we have rehabilitated and given the name Portolés, for Saint—"
"Rehabilitated, you say?" came a surprisingly high voice, and Sister Portolés peeked up, one-eyed from the wax she dared not wipe away, to see if her queen or her pontiff spoke. It was Pope Y'Homa III, Voice of the Allmother, now sitting straight up, the tip of her conical hat nearly, but not quite, as high as the jagged carnelian crown of the seated queen. "This devil-spawned witch had but one purpose in the life we built her, and you dare allege she is reformed, after what befell her charge? Small wonder my cardinals counsel me to raze the Dens and be done with this ill-guided quest of yours."
"Your Grace, a single transgressor—"
"I did not call you here to debate theology." The Black Pope's pale sneer pushed through Sister Portolés's robes, into a secret tenderness she had never believed existed in her breast. That she was a sinner she readily admitted, and she prayed for punishment, but to hear that her actions might reflect upon all her wretched brethren was a poison to her nerves, a brand to blister her very soul. "You have claimed, to myself and my uncle before me, that an anathema may serve but a single purpose: to put itself between danger and the righteous. To serve as shield, however sullied. To protect the clean. Yet here we have a monster that dares return to its post not with the living pureborn it swore to serve, but his blackened bones! And as if such a travesty were not crime enough, it wears the robes I have given it, mocking this very office. And you would lecture me on the difference between one and legion?"
"Your Grace, I never meant to imply—" Abbotess Cradofil began.
"I know well the difference between a single devil and an army of them, Cradofil—the latter currently enjoy every comfort of Diadem while all across the Star faithful pureborn go hungry and cold, and the former has aroused such disgust in our queen that it has been brought here, to befoul the most sacrosanct space in all of the Empire as we ponder its punishment."
The words scourged Sister Portolés far deeper than the physical lashes she had brought upon herself, and she silently wept. Doubt was her devil, forever goading her, and she had fed the beast as eagerly as a disobedient child slipping scraps to a forbidden puppy. She had doubted Sir Hjortt, and that doubt had made her feel befouled when she had delivered the order to exterminate that village, and fouler still when she had personally executed the five members of the cavalry who refused the will of their colonel. And after the slaughter, it was her doubt that had kept her on the edge of the flames at the mayoress's house, it feeling just and good to watch Hjortt burning alive, after what he had ordered Portolés and the Fifteenth Cavalry to do...
Ever since Kypck she had been deceiving herself, pretending that killing the villagers was the true crime and Hjortt the true criminal, Portolés an avenging angel of the Fallen Mother, but now she recognized just how deluded she had been. Her innate corruption always perverted the truth, sin tasting sweetest upon her tongue and goodness smacking of ash and lye, which was why she had let him die, and why she had told no one of what really happened that day. Instead, during every confession after the event she had cast his death not as the result of her inaction but as the inscrutable will of the Fallen Mother. She had almost convinced herself that it wasn't a lie, not really, but of course it was, and of course the only sin that had been committed that day was her refusal to help the pureborn colonel who needed her aid. She remembered how he had thrashed in the chair he was bound to as the deck of the mayoress's house burned around him, hurling insults and promises and prayers at Sister Portolés while she watched him roast. From the corner of her eye she saw Baron Hjortt shake with silent laughter or barely contained emotion at the pope's condemnation of Portolés, and she would have whispered an apology to the grieving father had she not feared a cry would escape instead.
"That's all a bit much, isn't it?"
Sister Portolés's heart stopped, a half-birthed sob aborted in her throat. The queen had spoken. She sounded tired, her bare feet still dangling off the edge of the throne she lounged across.
"Sister Portolés, I wonder if we might hear from your lips what transpired in Kypck, and how Baron Hjortt's son met his doom there." Queen Indsorith shimmered, bathed in celestial radiance... or so she looked through the lens of Sister Portolés's tears. "My Askers have interviewed dozens of the deceased colonel's cavalry, so I have established a certain chain of events, but would have you enlighten us with your account. Mother Cradofil recounted the basics from your last confession for us, but I am interested in a more detailed telling."
Sister Portolés swallowed, willed her venomous tongue to work as her queen commanded. Finally, it managed, "If it pleases Your Grace?"
"Whether or not it pleases Y'Homa means less than nothing here, in my throne room, in my capital, in my province, in my empire," said Queen Indsorith, reclining farther into the ebon seawolf furs that bolstered her throne. "Whatever your station before you entered into the service of the Crimson Empire's armies, you are bound to heed my will. Unless you disagree?"
Sister Portolés was unsure if this last was directed at her or the pontiff, but when no response came from Pope Y'Homa, she steadied herself and began her confession, sparing no detail of her own failings. This time she would tell it true. And so she did, from her hubris to her disrespectful tongue, from her reluctance at carrying out her colonel's orders to her guilt and self-loathing at staving in the heads of the soldiers who wouldn't assist in the slaughter, and finally her doubts over the righteousness of killing the villagers in the first place. Yet just when she reached the climax, as she was about to confess how she had returned from the cleansed hamlet to find the mayoress's hut likewise aflame, the trapped Sir Hjortt wailing for help, and her own heart hard to his pleas, the queen cut her off.
"—And so when you returned to the mayoral house it was already on fire, and Sir Efrain Hjortt along with it. This is as I had heard from the men in Sir Hjortt's command, and those whom you previously confessed to. Please explain, Your Grace, how exactly does Sister Portolés's faithful enactment of the orders given her by Sir Hjortt qualify as sedition or"—the queen gasped dramatically—"deviltry?"
None spoke in the Crimson Throne Room, and then Baron Hjortt cleared his throat. When no response was elicited he tried again, and this time the queen snapped, "What do you have to say for your idiot son, Baron? Before I gave you permission to pass your command down to your boy, you always struck me as a worthy colonel, one well versed in the Crimson Codices. I believe you taught him to uphold my laws of war, did you not?"
Baron Hjortt was obviously at a loss for words, and the queen went on, finally leaning forward in her throne as she berated the retired colonel.
"Everyone in my armies from drudge to colonel knows better than to sack a single farm without my express orders, let alone an entire town, so what, pray tell, could inspire the dearly departed Sir Hjortt to commit such an atrocity? Did you accidentally tutor him in the ways of ancient barbarians instead of the civilized Empire? When you gave him your command, did you forget to mention the commandments of his queen, laws which were old when he was young?"
"Your Majesty!" Baron Hjortt finally spluttered, and then, clearly stalling, said it again: "Your Majesty!"
"Perhaps this creature blasted him with some geas or hex," supplied Pope Y'Homa, keeping her dark gaze on Sister Portolés. "That would certainly explain how a _crone_ , as the anathema so eloquently put it, could murder both an experienced war monk and a knight of Azgaroth. It would be a pretty trick indeed to have Colonel Hjortt commit such evil and then dispose of him and her brother-in-chains when the crime was done."
"No!" cried Sister Portolés, surprising even herself with the outburst. "Never! I... I am not pure, I have _never_ been pure, it is true... But I strive to be as good as the Allmother allows me to be! I am no witch, nor a conspirator—I am nothing if not loyal to you! To both of you, my pope! My queen!"
"Loyal to both of us?" the queen asked, exchanging a queer smile with the pope, and Sister Portolés blushed at her own folly. "Tell me, Your Grace, do you think this wretch tells honest, or do you still believe that the rust of corruption has eaten so deeply into the Chain that even the holy soldiers you place in my service are compromised?"
The wind picked up, roaring over the high wall of the volcano and stirring the queen's long auburn hair around her haughty face. Again, none spoke for a heavy moment, the two women staring at each other, and then the pontiff threw up her hands. It was an oddly petulant gesture, and for the first time Sister Portolés appreciated that the Voice of the Fallen Mother was decades younger than the queen, the pontiff sixteen years old if she was a day.
"I leave her future in your most capable hands, Your Majesty," said the Black Pope as she rose from her throne. "For now I must away and counsel with the abbotess and my cardinals, but as always you and I are of one mind on the judgment."
"As always," said the queen, slumping back in her high seat. "Take the old man with you before I decide to attribute his son's exceptionally poor judgment to bad parenting. Rest assured, Baron, if Sister Portolés had returned in time to rescue your offspring I would currently be flogging him in Diadem's square—already his actions have polluted our relations with a dozen outlying provinces. I will not see the Empire fall back into the savage cruelty of old. I never would have let you retire had I suspected your son would prove such a pitiful imitation of his father."
"Your Majesty," Baron Hjortt managed a final time, and then he quickly backed away toward the portico as the pontiff approached.
Abbotess Cradofil knelt until Pope Y'Homa III stopped before her and extended her jet-ringed hand for the superior to kiss. To Sister Portolés's bafflement and delight, the pope then offered her hand to the kneeling anathema. Sister Portolés kissed the ring with more love and tenderness than she had ever kissed Brother Wan, and then the Black Pope strode out of the room, Baron Hjortt stumbling backward before her, Abbotess Cradofil scurrying after.
The doors creaked shut behind them, leaving Sister Portolés alone with her queen in the Crimson Throne Room, only the dim stars, the looming moon, and the chill wind party to what came next.
# [CHAPTER
13](toc.xhtml#toc-chapter013)
From Linkensterne, it was a long and rocky coach ride to the coast. When they eventually hit the end of the Norwest peninsula there came the worst leg of the journey, Zosia, Choplicker, and Bang crushed together in the back of a rickshaw and carried along the miles and miles of nauseatingly high boardwalks that linked the closest of the Immaculate Isles to the mainland. When they ran out of wooden roads they rented a boat, and after a long voyage Bang finally delivered Zosia to Hwabun, the last isle before the Haunted Sea, and the family seat of her old crony Kang-ho.
Both smaller and taller than its neighbors, Hwabun did indeed resemble the flower pot it was named for, grey stone cliffs laced with pink mineral deposits rising hundreds of feet above the waves before leveling off into a plateau of variegated vegetation. Bang steered their small catamaran directly at the walls of the island, and only when they were rapidly closing in on the rocks did Zosia make out the sea cave that housed Hwabun's modest harbor. Their way lit by an enormous blubber chandelier that hung from the ceiling of the subterranean cove, Bang maneuvered the vessel around to the docks, where a dozen craft of various sizes and makes were already moored.
A white-gowned old woman helped them tie off, and after a quick Immaculate exchange with Bang, the harbor keeper directed them down the dock and up a wide staircase built into the wall of the cove. They passed through a carven tunnel and emerged into a gazebo, where they were greeted by another servant along with a pair of armed guards, all of the staff dressed in the same bright white livery as the harbor keeper. Zosia couldn't remember if white was the traditional Immaculate color of mourning, of death, or of public shame, but none of the options boded well. They were led out of the gazebo and onto a black gravel path that led through the gardens to the main house.
Kang-ho had done well for himself—he had told her at length of the sorry state his ancestral home had been in when he left, as well as the improvements he planned to make if he ever returned. The structure before her, like most of the newer Immaculate estates she had glimpsed on her voyage, fused traditional island architecture with foreign designs. Unlike many of those attempted, the castle before her actually worked as a conglomeration of Gothic Crimson, Classical Immaculate, and Modern Raniputri... though the Usban onion domes on the outbuildings might have been a bit much. At least the wind chimes were old-school Ugrakari, singing sweet songs of better days to come in the soft sea air.
A pair of servants slid open the massive bamboo screens of the main hall, and a heavyset man dressed in a starched white overcoat scurried down the wide walnut steps to intercept Zosia, Bang, and Choplicker. Another staccato exchange in Immaculate, during which Zosia heard Bang mention her alias of Moor Clell no fewer than three times. The man must have been Hwabun's majordomo, to take such a snotty tone with guests. The majordomo gestured emphatically at Zosia, who, glancing down at her raggedy attire, allowed that it would have been a good idea to buy some more appropriate clothes during her passage through the country rather than spending all of her leisure time reacquainting herself with peated rice liquor, rare tubāq blends, and spicy pickled cabbage. The majordomo spun away, his cape slapping Bang's chin, and hurried back inside.
"That could have gone better," said Bang. "But I think he'll take your request to King Jun-hwan's husband anyway. You're just lucky I know the family names this far out; nowadays most Immaculates seem to think the Isles end at Othean."
"He was always just Kang-ho to me," said Zosia, though to be honest she had probably known his full name, once. Was this how old age made itself known—the sudden, embarrassing realization that you have forgotten little niggling things, like the names of your closest friends?
"Let's just hope he remembers your name, then," said Bang, kicking idly at the gravel. "Here's a thought, though—if he doesn't, and they kick us out, what do you say about a little detour before I take you back to Linkensterne? It's a beautiful trip down and around to the Cuttlefish Cays where my family's from, and there's no sense in rushing back to the wall when we've got a cat just—"
"That didn't take long," said Zosia, noting the majordomo's almost genuine smile as he came back out.
"Hwabun welcomes the lady Moor Clell," said the majordomo with a bow, his Crimson better than Zosia's. "My Elegant Master King Jun-hwan Bong cordially invites you and your warden Bang Lin to take kaldi with his family upon the Mistward Balcony. I will have a servant house your hound in the kennels until your departure."
"Trust me, squire, you don't want him anywhere near your dogs _or_ your servants." Zosia patted the majordomo's shoulder as she walked past him up the steps, Choplicker at her heels. "Don't worry, though, his paws are clean, and I won't let him out of my sight."
Cosmopolitan as the exterior of the castle was, the inside was strictly Immaculate, with the foyer nothing more than the intersection of three sparsely decorated hallways. Before the majordomo had even caught up with them, the sound of slippered feet swiftly gliding over polished hardwood floors came to Zosia from the central passage. She tried in vain to keep the smile from her face as Kang-ho slid to a stop in front of her, eyes bulging.
The Second Husband of Hwabun looked a sight better than she'd expected. His cheeks sagged a little and his hair might have been thinning, but otherwise it was Kang-ho as he'd been twenty years past. For all his whinging about how bad he looked in Immaculate fashions, he cut a dapper figure in his square horsehair hat and silk robe, the black roses embroidered on the garment's shoulders and the owlbat on the chest clearly copied from his tattoos. The only thing missing was Fellwing, but knowing Kang-ho, the devil was hiding under his hat.
"It's really you," Kang-ho breathed, looking from Zosia to Choplicker and back again. "You're alive!"
His eyes filled with tears, and Zosia felt an unexpected tightness in her throat. The presence of Bang on one side of her and the majordomo on the other quickly helped her to suppress the awkward emotion, and she said hurriedly, "Yes, well... After my warehouse caught fire I knew rumors of my demise had spread, but I didn't expect they should have reached all the way here, to the home of one of my old customers. Fear not, good sir, the pipe you commissioned all those years ago is safe, as am I."
"Of course," said Kang-ho, blinking his eyes clear as his face brightened into a winning smile. "Moor Clell, as I live and breathe. Let us away to a private spot where we can discuss the matter at our leisure."
"His Elegance has extended an invitation to our guests for kaldi, and anticipates us directly," said the majordomo, in Crimson rather than Immaculate. "And as your annual allowance was exhausted shortly after the New Year, sir, I suspect he will want to be a party to any and all discussions you and this merchant have on the matter of new acquisitions."
If Kang-ho was irritated to have his servant call him out so blatantly in front of a guest, he didn't show it. "Ah, but this commission was paid for in advance, many years before our marriage, and so it will be of less than no interest to my husband—isn't that right, Mistress Clell?"
"Quite," said Zosia.
"Now, Hyori has been reading all sorts of military tales of late, so perhaps Mistress Clell's warden here can entertain the family at kaldi," said Kang-ho, bowing to Bang. "My youngest daughter would be delighted if you could occupy her, dame. I can assure you that your charge will be quite secure in my company."
"It would be my privilege," said Bang, bowing in return. "I am humbled to be a guest in your home. Word of Hwabun's beauty is just that; words, however poetically chosen, can never hope to match the glory of the thing itself."
The majordomo rolled his eyes but nevertheless escorted Bang away into the house, while Kang-ho took Zosia back outside and across the gardens to where a green hill rose up almost as high as the lower towers of the manse. At the summit a bench looked out over the island and the greener waves beyond, and not even the perpetual pillar of thunderclouds to the north that marked the grave of the Sunken Kingdom could cast a shadow on the serenity of the setting. So long as that drowned isle didn't choose today to fulfill the mad prophecies of the Burnished Chain and reemerge from the Haunted Sea, it was shaping up to be a lovely afternoon.
As they settled onto the seat a flock of servants came scurrying after, carrying trays of food and drink and a little table. As the staff erected the table and set it with an Usban sand bowl for the kaldi, Kang-ho and Zosia made small talk about her crossing from Linkensterne, each of them trying not to break out in another stupid grin. When the servants finally retreated back to the base of the hill, Kang-ho raised a mug at Zosia and said, "Wasn't Moor Clell what you used when we were in Brackett, just before everything went to the devils?"
"That's the one. You've got a better memory than me, brother; I couldn't even recall your family name. Hwabun stuck in the grey stuff since you looked so panicked the time you let it slip."
"The oversight in my name might be because I never told any of you what it was," said Kang-ho. "If I ever needed to betray the gang, I didn't want to make it too easy for you to find me."
"Oh, I would have found you," said Zosia, admiring the scenery. "You may live at the ends of the earth, but that's not far enough to hide from me."
"It's not you I was worried about! I'd double-cross the others, if I really had to, but I'd never be crazy enough to turn on you. Do I look like I want to die?"
"No more than usual," said Zosia, leaning down and rooting through the backpack she had fought the servants off of carrying for her. "You have a coalstick? Mine died in the mountains, and I don't think I'll be able to get a match going in this damnably refreshing sea breeze."
"It's all in the jade box there, along with my go-to mixture these days. I call it 'Thunder of Immaculate Hooves.' "
"That's a terrible name for anything, especially a tubāq blend," said Zosia.
"Bah, what's in a title!" said Kang-ho. "The point is it smokes well. It's an Oriorentine sort of mixture, and the leaf in it's as old as we are—Azmir leaf, orange and lemon vergins, and prerevolution Usban lat. Stuff's hard to come by, ever since Linkensterne got snatched by my beloved nanny state. While you're in there, why don't you pass me my—ah, thank you, Zosia."
It was the first time she had heard her true name spoken by anyone but her husband in twenty years, and even then Leib only whispered it in the dark of their bedroom as they made love. Well, there, and in their kitchen, and on their deck, and in that meadow of wildflowers above the house, and all the other places they had made time for one another... Zosia's hands shook as she removed from the velvet-lined case the long-stemmed pipe she had carved Kang-ho a quarter century past and handed it over. "You were always the cleverest, brother, so tell me—why do you think I'm here?"
"The smartest of the Five Villains? That's damning with faint praise, sister, and besides, Hoartrap was wiser than any of us."
"I didn't say wise, I said clever," countered Zosia. "To know that old serpent is to know the difference, too, so enough dodging—tell me your theory while I pack my briar, and then I'll tell you how close you are."
"Very well," said Kang-ho, launching straight into it as he watched her fill her pipe from the terra-cotta jar of campfire-scented tubāq. "You faked your own death because your life was in such danger that you didn't know any other way of thwarting your enemy. Telling anyone, even your closest friends, was too risky to yourself, and to us, so you fooled us all. Devil magic must have been involved, for there were a thousand witnesses who saw you fall, and I was one of them. After twenty years in hiding, living under an assumed name, that threat to your person has passed, and so you return... Am I warm?"
"You got the obvious one," said Zosia. "Bungled the rest."
"Give me a bone, woman. I'm not some wildborn to peer into that ugly skull of yours! I didn't even think I was right about faking your death—why would you take such a path when you still have that hound of yours? Why not trade his freedom for a less drastic measure than abdicating your people, forsaking your friends?"
"He had his chance to be loosed," said Zosia, glaring at where Choplicker rolled in the grass a short distance down the hill, trying to provoke the servants into playing with him. "Now he'll never be free, no matter how great my need. I'd rather die. And they were never my people—they were glad to be rid of me."
"Wellllll..." Kang-ho scratched his head, grinning at her. "People don't always know what's best for them."
Zosia snorted. "I was a lot of things, but I wasn't what was best for anyone. But believe me, Kang-ho, I never forsook my friends—had it been safe to contact you, I would have."
"So I was warmer than you let on," he said. "Let's have the full account, then."
"I..." Zosia wanted to tell him everything: why she had abdicated the Crimson Throne, how she had orchestrated the deception that had fooled the entire Star, what had become of her afterward... But watching Kang-ho's face as he packed his smooth templewarden, she found she couldn't. Not yet, anyway. "In time you'll hear the whole of it, brother, but not yet. Knowing the details now would do you no good; if anything, it could bring you harm."
"A guarded reply to an open welcome." Kang-ho's familiar pout warmed her heart. By the six devils she'd bound, she had missed her friend. "When will I hear this story, I wonder? Will it be after I give you whatever you've asked for?"
"I haven't asked for anything," she said, and waited until he had his pipe lit before adding, "But since you mention it..."
Kang-ho passed her the small leather-wrapped rod he'd heated on a candle, and she put the glowing end of the coalstick to her bowl. Puffing away on the pipe, tamping it down with the brass butt of the tool, and then lighting it again, she watched Kang-ho from the corner of her eye. His smile had returned.
"That's more like it," he said after they had both smoked in silence for a spell. "Rich tubāq on a warm spring day, old friends reuniting, the sea beneath and the heavens above. All is right in the world."
"No, it's not." And because there really wasn't any point in drawing it out, she said, "I need your help, brother. Will I have it?"
"Of course." Kang-ho sounded offended that she would even ask. "I swore an oath, didn't I?"
"And I released you from that oath," said Zosia.
"Doesn't mean I had to accept it," he said, his kindness picking at a wound on her heart that would never heal. She kept her eyes from flitting toward Choplicker but knew he must be watching her. "Then again, the oath I swore was to a woman called Cobalt Zosia, blue of hair, fiery of spirit, and cold as the Frozen Savannahs to her enemies. She was the greatest warrior I have ever fought beside or against, the first in a hundred years to take the Carnelian Crown of Samoth by her own hand, and the first in legend to take the rest of the Crimson Empire in the bargain. I saw that woman plummet to her death, Moor Clell, and unless I hear some explanation of why a humble pipemaker such as yourself would choose to impersonate my dead friend and captain, well..."
"Say I eloped, then," said Zosia, the pipe overheating in her hand as she puffed it far too vigorously. Eloped was close enough.
"And just who was the lucky lover?"
"Leib." Zosia whispered his name for fear that saying it any louder would crush her spirit anew. "Leib Kalmah."
"Leib," said Kang-ho, and he sipped his pipe until it came to him. "Not the blond stripling who worked that upscale brothel? The one in Rawg we'd always hit coming back west from the Forsaken Empire?"
"Yeah, that's him," said Zosia, the most exquisite smoke she'd tasted in twenty years turning acrid on her tongue. "Mountain boy who ran off to find adventure in the Empire, and found me instead. The best lover I ever had, bought or otherwise. Best friend I ever chanced on."
"You expect me to believe you gave up everything, your own hard-won empire, for a whore you could have installed in your castle?"
"It was the only chance for peace," said Zosia, remembering how earnestly she had believed that. "I was a fool, Kang-ho, I see that now. I've made more mistakes than there are isles in the Immaculate Sea, but none worse than thinking I could just walk away, after all the things I'd done."
"All the things _we'd_ done, you mean," said Kang-ho, patting her shoulder. "You're too smart for regrets, Zosia. We both know that the one truth on all the Star is that you possess only what you take and what you are given. Some are blessed enough to rely on gifts, but for the rest of us, well, that's why the devils gave us steel."
"The Ugrakari say the devils never meant for us to have it, that we robbed the secret of swordmaking from them," said Zosia. "They tell a tale of how a mortal crept down into the First Dark and stole a devil's ploughshare, and when the fiend tried to take it back she showed him another use for the tool."
"The Ugrakari eat their own dead," said Kang-ho. "How much stock do you put in the myths of cannibals? And I ask this having married one, mind you."
"About as much as I put in the justifications of a retired warlord who would have inherited this lovely island even if he hadn't turned to villainy."
"I would have inherited nothing if I hadn't married the man my parents selected," said Kang-ho. "Why do you think I left home in the first place? As far as barbaric customs go, forging my own destiny appealed to me quite a bit more than an arranged marriage."
"And yet here you are."
"Here I am."
"What happened after I left?" asked Zosia. "After everyone thought they saw me die at the hands of that girl, what happened?"
"We Five all owed you our titles, but really they were just a means of prolonging the dream, and with your death we woke up... some faster than others. For Samoth and the rest of the Empire, it was bad, bad as it ever was. Your death brought a lot of factions together at first—as you surmised, conquerors aren't usually held in high esteem. But any unification was short-lived. Despite what you announced before the duel, and despite Indsorith's popularity with the people after she cast you down, there were many in the Empire who thought they had a stronger claim to the Crown than some upstart girl they'd never heard of.
"Whether from loyalty to your wishes or their own interests, Hoartrap and Singh helped Indsorith solidify her rule, but Fennec sided with Pope Shanatu. After a few years of civil war both Fennec and Singh lost enough capital or gained enough sense to cut out for greener pastures. Hoartrap stuck around longer, but last I heard he'd quit Samoth, too, maybe the whole Empire. Maroto sought revenge but was too drunk or crazy to do it properly, and instead of leading a rebellion with the troops you gave him the lunkhead tried to single-handedly take on the Dread Guard of Diadem. Made it through 'em, too, and got all the way to the throne room, but then Indsorith showed him just how she'd wrested the Crown from you."
"Maroto's dead?" The news was hardly surprising, but what did catch her off guard was the sting in her chest.
"Maybe by now," said Kang-ho. "He survived the duel, though I'm not sure how exactly he slipped away after the new queen spanked him. Last time I saw him he was in a bad way. Strung out, gone to bugs if I had to guess the poison."
Well, that was better than dead, maybe, and just as plausible. Maroto would have been all right, if he ever could have gotten his shit together. "And you?"
"I left the day I saw your body land in the street," said Kang-ho, drawing a line across his throat with the stem of his pipe. "Kang-ho out, along with more loot than my family has ever known. I should have been smarter about it, taken the Empire for everything it was worth, but nobody knew what would happen next, so I got shy while the getting was good. Came home to find my mother dead and my father in poor health, and the next thing I knew I was seduced by the same stud my parents had betrothed me to as a child. Or maybe I seduced him, but the end result is the same—a new ruler with a new name at Hwabun, one nobody would associate with a certain legendary Villain who terrorized the Star for all those years."
"How's that work, exactly?" asked Zosia. "If your husband's Ugrakari and you came back rich before you even married him, why is he King of Hwabun? I thought this isle had been in your family for generations. I'm not judging here, but I thought I heard your steward back there refer to your _allowance_?"
"It's a long and boring story," said Kang-ho grumpily. "The short version is I came back rich, but Jun-hwan was _rich_. Rich enough to fix this place up, fix the family up, and still let me keep my Crimson nest egg for other investments... investments that have rotted on the vine thanks to my homeland's blatantly illegal conquest of Linkensterne, but that's an ulcer for another day. Anyway, I was happy to have him take over as King of Hwabun—even when the kingdom's small enough you can shoot an arrow from one end of it to the other, being regent is more trouble than it's worth."
"Tell me about it. Huh. Kang-ho, living happily ever after as a househusband." She looked down at the expansive garden and grounds, the picturesque sea to the south, dappled with high green islands that jutted up in single peaks like the jade teeth of some seabeast. Even the eternal storm that raged to the north over the Haunted Sea looked pretty from this distance. "Somehow it doesn't seem your style."
"What's the point of doing all the things we did if you don't get to sit back and enjoy yourself someday?" said Kang-ho. "Living comfortably and quietly, indulging my every whim, and raising a family's not such a bum deal. Beats the shit out of getting stabbed out in some pointless bar brawl or falling to my death scaling a tower to rip off some wizard's treasure."
"And the thrill of combat? The exhilaration of adventure?"
"Bad for the humors—I have an excess of bile as it is."
"We always had a lot in common, didn't we?" said Zosia, imagining Leib sitting between them on the bench, picturing the reunion that never was but should have been. Safer to stay hidden, they had thought, yet here Kang-ho sat, secreted in plain sight, enjoying his retirement. Until her arrival, anyway—the longer she smoked with him, the more she attuned herself to his old ways, and it was obvious some underlying anxiety played at the edge of his mood. Well, there might be, she supposed, for what good could come of her reappearance in his life? She almost felt bad for him, but then he could always say no if he wanted to. "If helping me meant giving up this life you've won for yourself, would you?"
"Maybe," said Kang-ho. "I owe you a debt, of that there is no question. What sort of help would you have me give?"
"War with Samoth," she said. "I'll need an army and the element of surprise, and the Immaculate Isles can give me both. If anyone can give me the Isles, it's you."
"Oh, is that all?" Kang-ho canted his head to the side, running through the angles. "Why?"
"Leib is dead." Zosia wished her voice would break along with her heart as she told him everything that had happened when the Imperial soldiers came to Kypck, but all she felt was eagerness to hear his response. Far below, the waves crashed against the Flower Pot.
"I see," said Kang-ho at last. "But if you're right and this is all Queen Indsorith's doing, why wage war? Why not assassinate the queen and spare us all another dark age?"
"So the Burnished Chain can swoop in and fill the vacuum I leave? _Does_ that sound like a good plan?" Zosia was pleased to see the grimace the prospect raised on her friend's face.
"Ouch. No, no, it does not. But you can't fight a faith, Zosia."
"Watch me."
"Damn, girl." Kang-ho shook his head. "So all you want is to take out the Crimson Queen _and_ the Black Pope."
"Tell me they don't have it coming and maybe I'll reconsider."
"It's not a question of who is owed what. This is the first peace in memory, and if you start banging up Samoth and rattling the Chain, then the rest of the Empire is going to take an interest. And then the rest of the _Star_ will take an interest. And then we're right back to where we started, before we even went to war against King Kaldruut, before we earned a single ally, before we won a single battle... Except we're all thirty years older."
"Thirty years wiser."
"Thirty years fatter and slower. You killed Kaldruut almost a _quarter century_ ago, think about that! Hells, don't tell me you weren't feeling old _twenty_ years ago, when you pulled your disappearing trick. I know I was, and I don't feel much younger now. We fought for peace, Zosia, and peace is finally here, so maybe—"
"You fought for silver, Kang-ho, silver and steel and glory and power, same as me," said Zosia, angrier than she should have been at his fair and reasonable points. "It was only later we brought peace and prosperity and a better tomorrow into it, when we started feeling the years and saw we might have a chance to do a little good after a lifetime of bad."
"Better late than never?"
"Devildamned right. And any peace they know is peace I gave them, and they betrayed me. Samoth calls itself the capital of the Crimson Empire, well, it's time I reminded them how the Empire came by that color. They brought this on themselves."
" _They_ didn't do anything," said Kang-ho, that damnable conciliatory tone needling at her. "If the queen betrayed you and gave the orders to have your people killed, then she's to blame, obviously, and those soldiers who carried out the deed have blood on their hands, no denying that... But why plunge the whole Empire into chaos? The whole damn _Star_?"
"Because it's not enough to pay blood for blood." As Zosia spoke the smell rising from her neglected pipe carried the whiff of iron. "Because whoever comes after us must know what it means to be righteous—not just the next province who tries to control the Empire, either, but, as you say, the whole damn Star. All the world will learn what comes of a broken oath. I made a mistake all those years ago when I left the way I did, and I've returned to set things right. I've paid for my crimes, and I'll continue to pay for them—I'm ready for that. I deserve it. But I'm not going to hell alone, and I'll damn everyone I lay eyes on before I let the Star carry on with its business as though nothing happened. Peace was bought for a price, Kang-ho, and since Samoth has decided to renege, I'm afraid they'll have to find another means to that end."
"You would see every Arm of the Star burn alongside the Empire just to have your vengeance?" Kang-ho frowned into his dead pipe. "Well, you've set my mind to rest in one regard."
"What's that?"
"You're definitely the real Zosia."
That she was, much as she'd pretended she wasn't for the last twenty years. She felt those years now, that she surely did, and all that speechifying on an empty stomach and a fat bowl of tubāq was making her feel a little floaty. Fortunately there was only one question left to ask.
"So you'll help me?"
"And in exchange I get my daughter back, is that it?" Kang-ho didn't sound irate, only sad. "That's a cold play, even for you."
"Your daughter?" The words were fuzzy and thick on Zosia's tongue, in her mind, and she tried to stand. Fell to her knees, knocked the kaldi table over. A subtle poison, she hadn't felt anything but the pleasant prickle of strong tubāq, and then she was in the grass. Kang-ho's betrayal was less surprising than that of Choplicker—the devil had not only warned her of danger but actively protected her a thousand times over, yet now he let her fall without so much as a bark. The devil padded back up the hill to flash his bright white teeth in her face just as she lost her grip on the waking world and drifted into his realm.
# [CHAPTER
14](toc.xhtml#toc-chapter014)
The Desperate Road ran far deeper and straighter through the Panteran Wastes than any other crossing, and consequently it was infested with perils. The only time bandits weren't lying in wait was when something even worse had fallen upon them, taking their place in the caves overlooking the road's entrances at the southern and northern edges of the desert. While the narrower, shadier canyons of the Desperate Road put off most godguanas, the far worse dunecrocs preferred the cooler sandslides and shale piles that routinely blocked the path, and wastewasps wove their barn-sized nests wherever the slightest rumor of a spring bubbled out of the rocks.
Even if one wasn't robbed, eaten, impregnated with larvae, or befallen by some worse fate still, it was weeks of long nights from either end of the Wastes to the road's only way station, the Shrine of the Hungry Sands. The lepers who ran it insisted that travelers perform a number of absurd, dangerous, and heretical rituals—on top of paying the stiff toll—before passing through their gate. Maroto had traveled the Desperate Road but once before, nearly thirty years prior, and clearly recalled promising himself that he would never again enter the Wastes if he could help it... and even if he could not, under no circumstances would he take this particular route.
He was fairly decent about keeping his promises to others, above average, even, so why was he so inconsistent with himself?
But hey, the nobles were happy with him again. It had been touch and go when he'd first proposed the Desperate Road at the tavern in Niles, the fops having grown less easily wooed by their guide's counsel. But then Captain Gilleland and several other bodyguards had advised against that course in the strongest terms, insisting it was far too dangerous for their wards, and that was that. As they rolled out of the caravansary, the party had saluted itself with a twenty-one-cork salute.
Their first night they lost an entire wagon of supplies when a funnel python dragged the camel team into its conical pit, and during their first day four of the bodyguards standing watch were carried off, presumably by the cannibal cult that hunted the southern end of the Wastes. Of course, it might have been something worse that got them. It could always be something worse, out here. Yet Maroto's mood had never been better, not in the company of his fops, nor in the Wastes in general.
For one thing, if they were going to be ambushed by bandits, it probably would have happened already. No robber would be so mad as to eke out a living on the Desperate Road proper, rarely as it was taken in these enlightened days when one could sail down to Usba at a fraction of the cost and risk. No, any sane brigand would have made an arrangement with someone at the caravansary to be informed whenever a prime target departed, so they could dry-gulch their quarry before they entered the inhospitable desert. Rumors had been raised suggesting the local cannibal cult had once been a humble outlaw gang who tarried too long in the Wastes, but Maroto cared little for speculation.
In addition to enjoying the typical satisfaction one experiences at not being robbed, Maroto felt his spirits rise in equal measure to the declining humor of the fops, as though they sat across from one another on a dunking board. Well, the nobles were entitled to a decent pout—the clammy, sulfur-stinking canyon walls that hedged ever tighter around them would take the wind out of anyone's sails. That, and the company's temperament had never fully recovered from the shock of seeing Lady Opeth yanked wailing into the funnel python's pit when she had heroically sought to save the last crate of pâté from the sinking supply wagon. Based on the hollow stares the remaining nobles directed at the swirling sands where she'd vanished, Maroto supposed the sight of her wig being pulled down into the earth would haunt them for the rest of their days. He certainly hoped so.
_Let's have an adventure in the Panteran Wastes!_
Yes, yes, let's! Beyond the more immediate relief of having a good day's sleep, since the party seemed disinclined to roll dice and hoot and giggle in the perpetually dim, stagnant, and inexplicably swampy heat of the Desperate Road, there was also the bartalk that had drawn Maroto here. _A blue-haired captain with a devil dog helm_. Accompanied by one of the Five Villains, if not more, and flying the old flag. Each time he allowed the pilgrim's voice to repeat in his head he felt shivers from his toes to his elbows. Deep down, in spite of everything, Maroto had always dared to hope... and stranger still, some worrying sensation at the back of his brain, like a nearly forgotten dream—or an almost-remembered one—told him that he had always known this, that he had been waiting all along.
That she had not sought out Maroto before starting up the old business did not trouble him a great deal. It troubled him a _little_ , because he was only human, for saints' sake, but not a _great_ deal. She had surely tried to find him, but he could be a hard man to run down. Surely. Maybe she even thought he was dead—he had believed her to have fallen, so why not the reverse? It would be just like Kang-ho's sorry arse to talk her into thinking Maroto was dead as some sort of a sick joke. Well, they'd sort that out soon enough, when he—
"I'm talking to you, beast!" said Count Hassan, bouncing a grape off of Maroto's nose. The nobles and Maroto all sat around a merrily blazing fire while the servants brought them supper and the remaining guards took their posts on the edge of camp. Dawn lingered longer down here on the Desperate Road, and so they'd stopped for the day much later than usual that fifth night out from Niles; everyone had an excuse to feel worn out and grumpy. That said, throwing food at Maroto was a mistake no peasant nor princeling would make more than once. "I said—"
"If you ever do that again I'm going to give you the adventure of a lifetime, your lordship," said Maroto, so quietly that perhaps the junior patrician didn't hear, or perhaps Hassan had taken the threat as some sort of challenge. Whatever the reason, another grape plinked off of Maroto's cheek. A third fell from Count Hassan's fingers as Maroto lifted him out of his divan chair by his thin neck, having leaped over the fire in a blur of furious motion. It felt damn good to hoist a man by his throat again, and Maroto spoke loud enough for all assembled to hear, and hear well: "I've never met such a pack of middling, chickenshit gasbags in all my days, and I've spent a season or two at Diadem's Court. You runts can do whatever you like in your wagons, or when I'm not about—fuck each other, cheat each other, insult each other, even kill each other. But from here on out, there's a new king in camp, and the king demands respect."
Silence. Blessed, righteous silence. Well, except for Hassan's gurgling. He clung to Maroto's wrist, trying to take some of the pull off his neck, but the more he struggled, the more Maroto's fingers tightened. Old habits and all. He would let the noble go in a moment, but first he wanted to make sure his point had well and really, truly stuck. Looking around the fire, he supposed he was closing in on it.
Pasha Diggelby had not risen from his rattan throne but had dropped his wineglass in horror, paying no mind as the cerulean liquid soaked through his hose. Princess Von Yung had frozen in her seat, a fork-speared morsel of melon hovering at the bow of her lips. Kōshaku Köz had jumped to his feet but was clearly unsure what to do now that he was the only one up, frantically puffing on his cigar as though he could hide behind the wall of smoke. Duchess Din fanned her husband Denize, who seemed to have fainted. Zir Mana, who had talked endlessly about the expertise of this blade tutor or that martial trainer, held a pudding spoon in a defensive manner, spangled earrings clattering as the ninny shook in fear. Even Tapai Purna appeared humbled by Maroto's display, the girl numbly clinging to a silver plate even as she dropped to a crouch, ready to flee. Beyond the nobles, the bulk of their servants waited and watched, although Maroto was calming down enough to suppose that more than one had hurried off for the guards, and so decided that he had best wrap this up quick lest things take a turn.
"You wanted adventure, you cut-rate royals? The king shall provide!" Maroto at last released Hassan, who had gone as green as the fashionable patina on his laurel crown. The second son collapsed gasping on his divan as Maroto cast a wagging finger over the party. "King Maroto will deliver all the entertainment you wish, ladies, lords, and lapdogs, all you need do is ask. And unless one of you craven, conniving curs works up the moxie to usurp the king, my word is law. Let's call this adventure of yours 'A Mouthful of Thine Own Evil,' and see how you posturing, primping, posing little losers enjoy the taste."
A single beam of morning sunlight finally penetrated the narrow canyon, and while it shone directly in Maroto's eyes he stood still in the hope that it might reflect upon his sweaty brow like a crown of light. He couldn't decide which was odder, the fact that no guards had yet appeared to tackle him, or that no nobles had yet screamed. Squinting through the glare he saw that the expressions on most of their makeup-plastered faces were not quite what he had expected.
They no longer seemed afraid of him. They looked... disgusted. Or, in the case of Zir Mana and Princess Von Yung, enraged. Good. Fuck these twerps. Maroto snatched an open bottle of bubbly out of the ice bucket built into the arm of Hassan's divan and turned his back on them—if the devils saw fit to temporarily spare him a beating or worse at the hands of their guards, he was damn well going to enjoy the rush of having schooled these punks for as long as possible.
Count Hassan landed on Maroto's back with a shriek, his arms closing around the bigger man's bull neck while his legs wrapped around Maroto's ribs. It reminded Maroto of how Purna had pounced on him during their faux-affair, only even less effective—now that he was aboard his target, Hassan didn't seem to know what to do next. Maroto ignored his shrill stowaway and knocked back the bottle, guzzling the fizzy grape juice even as Hassan tried to squeeze his throat. There hadn't been as much bubbly left as he had hoped, so he stretched his arm back and casually rapped the empty bottle against Hassan's noggin. Something cracked, and as the noble fell away Maroto held up the bottle to make sure he had just broken the glass and not the boy's skull. Devils knew, Maroto hadn't meant to murder him, and truth be told he respected that the lordling—
Maroto's left knee buckled as a pointy patent leather shoe connected with the soft tissue there, but it wouldn't have been enough to bring him down had Purna not immediately followed the kick with a silver platter to the back of his other leg. He fell forward and landed on his knees in the rough sand, eyes widening at the improbable sight. Guards he'd expected, yes, even a bandit ambush would have made sense, but this?
"Get the king!"
The nobles bum-rushed him, and Maroto scrambled up just as the wave of taffeta and velvet broke over him. Kōshaku Köz's cigar burned his cheek, and Duchess Din's platinum-veined fan snapped into his nose. He knocked them back, his open palm sending them rolling. Pasha Diggelby hurled a card table, which crashed into his shoulder. Princess Von Yung came at him with a bread knife. Zir Mana dove at one leg. He intercepted the knight with a kick and the princess with a punch to the jaw, but then Purna slammed a chair into the small of his back.
Maroto stumbled, fallen fops rising even as others tumbled back, and the cry came again:
"Get the king!"
There were a lot of them, was the problem. And all right, sure, some of them were better at this than he'd expected. Duchess Din went low and nearly headbutted him in the crotch, but he danced over her. He swung and missed Diggelby's ruffled throat by inches, and, cocking his elbow back for another go, smashed it into Kōshaku Köz's painted mouth. Teeth loosened, blood flowed, and Maroto threw a second elbow, this one connecting with Köz's temple and sending him tumbling into his comrades. Someone pulled a Hassan, landing on Maroto's back in a flurry of brocaded silk. He fell backward on top of his assailant, letting his rider break the fall as they crashed into a table. Tureens tipped and plates shattered, with Princess Von Yung left moaning on the board as Maroto slipped back into the fray.
The punches Maroto took ranged from the pitiful to the unexpectedly painful, and in short order his shirt was shredded and bloody from the rings adorning the fists that pummeled him. There'd be some broken fingers, no doubt. He deflated Purna with a sucker punch, but as he pulled back Duchess Din seized his wrist, and Zir Mana caught his other arm. They held him in place just long enough for a deranged Pasha Diggelby to splash his face with liquor. It blinded him, burning his eyes, and the fops who clung to either arm were lifted into the air as he howled in indignation—these runts had just doused him in Pertnessian absinthe, and if so much as a spark landed on him he'd go up like one of their flambéed songbirds.
Before, he had been too amused to take the fight seriously. Now, as one coxcomb flew loose from his thrashing while the other held tight, shanking him with a fork, he realized that things were perhaps not as cut-and-dry as he'd expected. For weeks these bastards had insisted they wanted to hunt something, to catch it and kill it, and all along he had scoffed at their ambitions. He wasn't scoffing now, fighting blind and dirty, ripping wigs and tearing out piercings, as the fops yowled and hissed, mad as wet cats. What if one of them hit him with a lantern, or if he stumbled into the fire? A few years ago he would have laid these scoundrels out with one blow apiece, but his blows weren't falling as heavy as they should have, too much old muscle given over to fat, and despite his attacks the fops harried him as mercilessly as hounds barding a bear.
Blinking one eye clear of the stinging liquid as he beat Purna and Mana away from him, Maroto saw that Diggelby's use of the liquor had been well thought out, the dirty so-and-so returning from the firepit with a brand blazing. They meant to roast him alive! And after all he'd done for them, too.
Duchess Din crept up on him from the side, meaning to take advantage of his preoccupation with Purna, Mana, and Diggelby, but Maroto spied the sneaky lass and made his move. Before Din knew she'd been spotted, he had her by the bejeweled belt, and, hoisting her over his head, he hurled the squealing woman into Diggelby. Both nobles went down hard, and Maroto gave a triumphant whoop to see the brand go flying from Diggelby's hand...
Directly into the tent wall of the cooking pavilion, which quickly caught fire. Maroto hurried over to extinguish it, brutally slapping Purna and Mana aside when they tried to flank him, but he paused when he licked his lips and tasted licorice. Going anywhere near the growing inferno would be suicidal. He looked back to the fops, meaning to give the obvious order that they postpone their fight long enough to contain the conflagration before it spread to the wagons, and the magnitude of what he'd just done truly sank in. There was foolish, and then there was this...
The center of the camp was a ruined battlefield, broken furniture jutting out of the sand like crooked palisades, shattered glass, crockery, and spilled food ground into the earth like shrapnel. And everywhere he looked, bodies, bodies, bodies. Silky ones draped over tables. Satiny ones lying on the ground. Velvety ones staring at him from the dirt, blood oozing from their slack mouths. Oh _shit_.
He felt hands grab him, the long-delayed guards finally arriving to do unto him what he had done to their employers... but no, they were servants, forcibly moving the war-dazed Maroto out of the way so they could try to put out the burning pavilion. When he turned back to the carnage, letting the servants swat at the blazing tent as best they could, he saw that most of the nobles were stirring now. More servants were coming out from their hiding places, giving him a wide berth as they hurried to tend to their fallen masters. A limp hand rose from behind a crushed divan, and he saw Count Hassan wave a bloody handkerchief that might have been white, once, before everything got out of control.
"Villainy!" Captain Gilleland appeared from between the wagons closest to Maroto, four of his heaviest heavies and Princess Von Yung's valet in the wings. The muscle had their weapons in hand, and the valet pointed, rather unnecessarily, at Maroto. His eyes fell to where he had left his mace—beside his discarded dinner plate, on the far side of the fire. Now that the guard dogs had finally returned, the nobles set to groaning and moaning and crying, the post-battle calm gone along with the cooking pavilion. He stepped farther back from the blaze, but even this innocent movement was enough for a guard he hadn't noticed on the far side of the circled wagons to fire his crossbow. The bolt whipped beneath the hand Maroto was raising in peaceful protest of his innocence, passing so close that the fletching grazed his palm.
"Hey now!" Maroto said. "Let's not get carried away. This isn't what it looks like."
"Captain Gilleland," Hassan managed, a pair of servants lifting him enough to lean against his ruined chair. "Captain, get him..."
"They started it," said Maroto, as if the truth ever did a doomed man any good.
"I heard." Captain Gilleland waved Maroto silent with his broadsword. The blade glowed in the light of the collapsing tent. "Hardly the end you saw for yourself, eh, hero? Should have kept that pride of yours locked away, for all the good it's done you now. Do you think the singers will remember it was we who cut you down, or do you think it'll make a better song if they leave us out, let these richies here take the credit? Captain Maroto Devilskinner, Villain of the Noreast Arm, put in his grave by unarmed dandies!"
"Not in my grave yet," said Maroto quietly. A guard was creeping up behind him, and in three quick steps he could wheel around the sneak and have some human protection from the crossbows. "You want to be in a song, Gilleland, all you got to do is ask."
"Captain, get that man..." Hassan paused to spit out a tooth. "Buh!"
"Uh-huh." Captain Gilleland was not an ugly fellow, but one would never make the mistake of thinking him handsome. He usually looked like he was gloating, and at a time like this, when he actually was, the effect on his countenance was as off-putting as adding another ladle of oil to an already over-greased curry. "We'll just see what they sing about this night, you soft old fossil. I've been waiting a long time to—"
" _Captain Gilleland_." Count Hassan's voice had steadied a bit now that he'd taken a swig from the flute one servant held and a pull on the smoking bone the other lackey had raised to his lips. "Captain, get this man _a drink_!"
Maroto had set his foot to pivot backward and seize the creeper behind him, but was so flabbergasted by Hassan's hoarse cry that he nearly stumbled into Purna as he twisted around. It was she and not a guard who had snuck up on him, a long, curved dagger in one hand, a bottle in the other. Before Maroto could decide whether or not to put her in a headlock to use as a meatshield, the battered little lordling extended the bottle toward him, neck first, then sabered off the cork with her blade. Cold bubbly exploded in his face, going up his nose but also washing off the cougar milk.
"Huzzah!" cried Purna. "A drink for the king!"
It was difficult to say whether Maroto or Captain Gilleland was more dumbfounded when the rest of the haggard fops took up the cry, and as Maroto wiped sticky wine from his face he saw that everyone save for Duchess Din and Kōshaku Köz was cheering him from where they sat in the sand or stood propped up by their servants. And who knew, had Din and Köz been conscious, they might have joined in, too. Maroto grinned at Purna, then grinned even wider at Captain Gilleland.
"Long live the king, eh, Cap'n?" he said, licking the finest sparkling brut he'd ever tasted off his lips.
"Or not," said Captain Gilleland, and Maroto didn't like the man's wink as he turned away, not one bit.
# [CHAPTER
15](toc.xhtml#toc-chapter015)
Zosia returned to pain, as she so often did these days. Not the familiar aching in her knees and joints, but a chisel in her brow, right between the eyes. As she had aged, hangovers had grown from annoyances into ordeals, but this was an entirely different sort of bullshit, one she had not experienced in many a thankful year: the comedown from a poisoning. The dim echoes of monstrous visions reverberated through her skull, but already the hallucinations or nightmares or whatever the fuck they were started fading, fading fast, and she had made no effort to hold on to them. Kicked away from them as hard as she could.
Opening her eyes, she found herself splayed out in a tastefully appointed bedroom. Choplicker lay beside her, but the beast had the sense to stay on the floor instead of sharing the sleeping mat. Candlelight silhouetted two figures who sat on cushions by the foot of her bed, their shadows looming halfway up the painted screen behind them. Kang-ho, and a handsome older man in sumptuous Ugrakari silks, his scarlet wig pinned up in half a dozen small buns.
"You're the King of Hwabun?" Zosia asked, trying very hard not to notice just how awful her mouth tasted. "Jun-hwan?"
The lord of one of the Star's tiniest sovereign states nodded. "Mistress Clell, I am pleased to make your acquaintance, and apologize for any misunderstanding that arose this afternoon. I hope you are recovered from your fainting spell?"
"Uh-huh." Zosia closed her eyes, willing the pain to recede. She'd actually been able to pull that sort of thing off, once upon a time, but now the grief in her skull just laughed at her presumption. "Thanks for your concern."
"Now, I have other guests to attend to, and so I will speak plainly with you and expect you to do the same with me. Do we have an understanding?"
"Absolutely," said Zosia, sitting up in the sheets and taking a better stock of the room. None of her possessions were present, save the devil who lounged beside her. Kang-ho looked nervous, as well he might—the cheek of the man, selling her out to his husband.
"We've already spoken very plainly, you and I, while you were under the influence of the harpy toxin. Do you remember what we spoke of?" Whatever face Zosia made must have pleased Jun-hwan, for he smiled all the wider. "Mistress Clell, I assure you that anything you divulged shall be kept strictly between us. Not even my husband was party to our discussion."
"No?" What in the devil's ken was this creep playing at?
"I was deeply saddened to hear of the death of your husband, Mistress Clell. I am sure that if anything happened to Kang-ho I would likewise seek justice, even if such a course was not strictly judicious."
Zosia sighed, lying back on the warm mat. So much for the element of surprise. Staring at the black-paneled ceiling, she said, "You claimed we'd speak plainly, so let's get on with it. What happens next?"
"That is entirely up to you," said Jun-hwan. "Again, I am not entirely unsympathetic to your plight. In fact, I empathize with you much more than you may suspect. You see, our daughter Ji-hyeon—"
Kang-ho interjected something fast and fresh in Immaculate but went silent at a glare from his husband. Kang-ho's frown deepened, but he did not interrupt again as Jun-hwan went on.
"Our daughter, Princess Ji-hyeon, has been missing for several months. We have reason to believe she was kidnapped by agents of Samoth. Given the history that you and my husband share where the Crimson Empire is concerned, it is most interesting to me that both your family and his have been so recently targeted by their interests, albeit in different fashions."
"Huh," said Zosia, almost forgetting her headache for a moment there. Almost. "Kidnapped princess, eh? That's obviously a sight worse than the murder of a few hundred peons, but I guess I can see how you'd draw a comparison. I'm flattered, really."
"I have no interest in pitting my grief against yours, madam, I simply point out the facts."
"And the fact is, we don't actually know it was Imperial agents who took her," said Kang-ho, fidgeting. "For all we know—"
"For all we know it was simply one of my dear husband's dear friends seeking to turn a dear profit from a ransom," said Jun-hwan. "The last time one of his _war buddies_ came to call we wound up losing our daughter Ji-hyeon, so you can understand my interest in you when I was informed that yet another unexpected guest claimed to be an old acquaintance of Kang-ho."
"How's this, now?" said Zosia, eyeing Kang-ho just as hard as his husband was. "Who?"
"He introduced himself to us as Brother Mikal," said Jun-hwan. "Supposedly a missionary of the Burnished Chain, and for reasons quite beyond my understanding my husband insisted we take him on as a tutor for the girls. As I have entrusted their education to Kang-ho, I thought no more of the matter until it was too late. That my helpmeet failed to mention he knew this Brother Mikal from his time as one of the Five Villains, albeit by another name, was a most disappointing revelation."
"Hoartrap?" said Zosia, raising her eyes at Kang-ho. "You let him around your children?"
"No, Fennec," said Kang-ho quickly, his husband watching this exchange with obvious interest. "True devils and false gods know I would never let a sorcerer set foot on this isle, let alone in my home!"
"Fennec?" It hurt to smile but there was no helping it. "You installed _Fennec_ in your house? That's even worse than Hoartrap! I hope you people don't put a high value on the virtue of your princesses."
"That is not our primary concern here," said Jun-hwan, looking none too happy with his husband. "But I have since learned all there is to hear of this rogue's character, and I can assure you I am unimpressed with my husband's judgment on the matter."
"I doubt you've heard all there is to know about him," Zosia said helpfully as Kang-ho squirmed. "Did you tell him about the time he seduced that Usban abbotess with the—"
"He blackmailed me into giving him the job," said Kang-ho. "Swore he just needed a place to lay low for a year or two until some storm he'd conjured blew over. I turned him down initially, but then it got ugly. I relented when he gave me his word that he would play the part of Spirit Guard and nothing more, and we used to be able to put stock in one another's oaths, didn't we? Besides, he left me no choice in the end—I couldn't afford to send him away."
" _That_ is a matter of some conjecture," said Jun-hwan sharply. "What is not is that he disappeared a short time ago, along with Ji-hyeon and one of her other guardians."
"Who's the other missing guard?" asked Zosia.
"Choi," said Jun-hwan, "my daughter's Martial Guard. She had been with our house for many years before this Brother Mikal came along. Which would imply a longstanding conspiracy to abduct my daughter, or else Choi's body has yet to wash ashore. For her sake I hope it is the latter."
"So when I rolled up you assumed I was in cahoots? Maybe delivering a ransom letter?" The man didn't give his husband's friends much credit if he thought they'd send a collaborator to negotiate instead of brokering the terms from a safe distance. "It's bad for business to keep a family waiting this long without sending something—you sure she hasn't kidnapped herself? Princesses do that, I hear."
"There was a witness," said Kang-ho, though his husband was again watching him with unmistakable skepticism. "Her Virtue Guard, Keun-ju, saw Fennec and Choi carrying her off, and when he tried to stop them they threw him into the cove. He nearly drowned."
"Good thing he didn't, or you'd have nobody to tell you what happened," said Zosia.
"I expect he will give you the full account on your voyage," said Jun-hwan, standing. Peering down his nose at Zosia, he cut an imposing figure. "I want you to find my daughter, Mistress Clell, and bring her home. Then I will give you what assistance I may in your quest to bring justice against Samoth."
"A princess for an army?" Zosia's headache throbbed, spoiling any emotion this proposal might stir in her. All she wanted was to bury her face in a cool pillow for the next day or three. "And how do you know I'm not really in on it with Fennec, that this isn't how we're leveraging a martial ransom out of you? Maybe we've got her squirreled away in some Linkensterne stinghouse, and I'll be back in a week with the princess to get my payoff?"
"As I said, we spoke, you and I, when you were swimming with the harpies, and at those depths few can tell a convincing truth, let alone a convincing lie," said Jun-hwan. He nodded at Choplicker. "And if I had any doubts, your companion disavowed me of them. You always keep your word, apparently."
"That a fact?" Zosia tried to shrug off the ice water that ran down her back. The Immaculate were eerily comfortable with spirits, weirdborn, and all other sorts of horrors, but it was common knowledge that only practitioners of the black arts could truly speak with devils. Drugging and interrogating Zosia against her will was one thing, getting chummy with her fiend was quite another. "Choplicker put in a good word for me, did he?"
" _Choplicker?_ " Jun-hwan looked aghast. "You should treat such a being with more reverence, Mistress Clell."
"Yeah, I bet he said as much," said Zosia, limply kicking the sheets in Choplicker's direction. "Fucker still knew better than to get on the bed with me, though, didn't he?"
Choplicker growled low in his throat, which finally inspired Zosia to sit up straight, but only so she could swat him on the nose. That was exactly what she needed, the old monster putting on airs just because some kooky Immaculate communed with his evil ass. Jun-hwan hissed through his teeth but did not comment on Zosia's treatment of her devil, and Choplicker whined reproachfully at her. She raised her palm but didn't pop him again. Staying upright took all the energy she had.
Jun-hwan reached down and petted Choplicker, his eyes on Zosia's. "It is said that in the Black Lands, the Great Dark King craved light for his subjects and so sent two fire dogs through the Gate of the Sunken Kingdom, into our world. One tried to bring back the sun, and the other, the moon. Yet the sun burned the first dog's tongue, and so she dropped it, and the moon froze the second dog's teeth, and so he dropped it. Yet knowing the Great Dark King's disposition toward failure, the two fire dogs try over and over to carry off our celestial lights, and they will continue to do so as long as the sun and the moon rise over the Star."
"Eclipses, right?" Zosia remembered the song Kang-ho had sung her nearly three decades previous, when they had taken advantage of the distracting religious hysteria the event brought on in Yennek to sneak in and rob Castle Illicitus blind. "You saying what, he's a moon-eating fire dog? If you saw the hassle his own hindparts give him when he's munching down back there you wouldn't give him so much credit!"
"I do not suggest the old myths be taken literally, but I do know they come from an age when mortals were not so alone upon the Star as we fancy ourselves now. All cultures have legends of black dogs, and while these songs are different, the universal truth is that such beings are due deference," said Jun-hwan, offering the beast another respectful nod.
"Mister, you need to lay off your fish oil," said Zosia, though the man's legend dredged up all kinds of weird memories of her harpy dream, memories that sank back down in oily blackness before she could focus on them: enormous, squirming monsters that were but fleas upon greater nightmares still, leviathans churning in the lightless center of all things...
" _Anyway_ ," said Kang-ho, "our honored guest was just leaving, weren't you?"
"Keun-ju will travel with you," said Jun-hwan, and when his husband gave him a wicked glare, the king shrugged. "He has been desperate to go after Ji-hyeon ever since the abduction, and what use have we for a third Virtue Guard when we have but two children left?"
"Zosia doesn't need one of our servants spying on her!"
"Mistress Clell," corrected Jun-hwan. "Though it is also true that Keun-ju can act as an interpreter for her, should the need arise, and confirm any and all reports sent to us."
"I've already got a translator," said Zosia. "The soldier brat, Bang, she can come with me. I don't need nor want anyone else tagging along."
"Keun-ju goes with you," said Jun-hwan. "If you also require the services of Lieutenant Bang Lin, I am happy to write to her commander at Linkensterne and explain my need to furlough her for a personal matter. Kang-ho, I trust you can see to sending a decommission fee to the mainland headquarters?"
An Immaculate spat was the same as any other kind—tedious—and Zosia awkwardly got to her feet in a bid to distract herself from their exchange. As she wobbled, Choplicker rose beside her, looking up at her with his hungry black eyes. She put a hand on his furry head, but only to steady herself. Princess hunting. Ugh. Nobody said bankrolling a private war would be easy, though.
Zosia felt marginally better that evening, but as soon as she returned to her mat she sank through it, splashing futilely in her bedding before going under. All through the night she floated higher and higher in moon-greased clouds, drifting up the haunch of a monstrosity bigger than any city, any mountain, any idea or ideal, the moon behind its many heads glowing like a silver crown... But other than the lucid dreams, it seemed a milder detox than most of her previous poisonings. It was mad to think she and Kang-ho had once smoked harpyfish oil on purpose, one wild night in Thao.
They set out the next morning, by which time Zosia was feeling invigorated, if only to get shy of the island. His Elegance Jun-hwan stayed behind to tend to his unseen guests, but Kang-ho accompanied them to Othean, known to foreigners as Little Heaven, the capital of the Immaculate Isles. After various wheelings and dealings they were admitted into the northern harbor of the massive island. White-uniformed soldiers watched them from the moment they left their small ship until they reached the walls of the Autumn Palace, and from the ramparts more hard eyes monitored their progress as they followed a gravel road out into the dead fields that surrounded the Temple of Pentacles. It was beginning to feel like old times, drawing this kind of hostile attention from the locals just by taking in a little sightseeing.
"We were here when the spirit attacked us," said Keun-ju, the missing girl's Virtue Guard. Young, veiled, and bright, the lad presumably hailed from a lower-class isle, or maybe even the mainland.
"And here I'd always thought you Immaculate were cozy with devils," said Zosia. "Who'd have thought one of them would try to gobble up a princess?"
"Respecting something is not the same as assuming it is safe," said Kang-ho. "Quite the contrary. You don't live on the sea without learning that lesson."
"If a houseboy, a couple more servants, and a teenage princess put it down, it can't have been too dread a beasty, eh?" said Bang from where she brought up the rear, Choplicker at her flank.
Neither Keun-ju nor Kang-ho seemed willing to respond to the soldier, but Zosia smiled. "So that was the first time she snuck off, was it? To go devil-hunting near a Gate, of all places—I wonder who put that idea into her head."
"Keun-ju?" asked Kang-ho, and when the Virtue Guard cast his eyes into the barren field, Kang-ho puffed out his cheeks in exasperation. "I'm hardly going to have you whipped now that she's gone, so let's have it—I can think of one or two other occasions on which Ji-hyeon was not where she was expected, so what of it?"
"He was sly about it, but I always thought Brother Mikal protested Princess Ji-hyeon's fancies a little too strongly," Keun-ju said bitterly. "He counseled against certain actions, yes, but always in the most alluring fashion possible. That night was no exception, and he was instrumental in helping us surreptitiously depart the palace. Since we all seemed in peril, and especially considering we overcame that harvest devil together, I did not suspect him of treachery until after it was too late. Now I wonder if he used Chainite witchcraft to summon the monster himself, to draw the princess closer to his confidence."
"And the other one, her Martial Guard, did she ever rub you wrong?" asked Bang, expressing more of an interest in the plot than she'd previously displayed since Zosia had filled her in.
"Choi was always beyond reproach," Keun-ju sniffed. "Right up until she threw me in the sea when I tried to stop them from abducting my princess."
"We're getting ahead of ourselves," said Zosia. "Back it up to when you four came out here, during the festival—what went down _exactly_? You snuck away, ran afoul of some devil that slipped through the Gate, beat it down, and came back to the party covered in gourd guts—that's it?"
"The expression on Jun-hwan's face when Ji-hyeon burst back into the ballroom, pumpkin string in her hair..." Kang-ho smiled sadly. "It was the last festival she attended. That was last autumn, and then a few months later she disappeared, just before the Winter Moon Ball. Fennec and Choi shoved the boat back to sea after they landed here under cover of dark, but it was spotted by a guard. They found tracks leading from the shore all the way up here, to the temple. Even with the help of Ji-hyeon's betrothed we haven't been able to unearth anything more—the trail goes cold at the Gate."
"I bet it does," said Zosia, slowing her pace even more. The paths through the fields extended like spokes from the five-sided temple they were approaching, a pearlescent stone shrine that seemed to mute the air around it, to dim even the sunlight. She had gazed into the Gates on three different parts of the Star, but had never before approached the Immaculate one. As always, she began to feel the tug in her very blood, felt the hairs on her arms all stretching toward it... "Betrothed?"
"I didn't mention she is engaged to Empress Ryuki's second son?" said Kang-ho. "Keun-ju, Bang, you two wait here while Mistress Clell and I continue our discussion a bit closer to the temple."
"Whatever you say, sir," said Bang, planting her spear and leaning against it while Keun-ju wiped under his veil with a puffy sleeve.
"Prince Byeong-gu, Ji-hyeon's husband-to-be, is beside himself," said Kang-ho when they had moved off a distance. "Our house is not the only one wearing white these past few months. It's why we haven't sent anyone else to search for her; Ji-hyeon's intended has already ordered a dozen soldiers through the Gate after them, and has personally sailed south to hunt for her in the Empire."
"He sent people _through_ the Gate?" Zosia shuddered. Spooky goddamn Immaculates. "Let me guess, they never came back."
"This was shortly after Fennec and Choi carried Ji-hyeon through it, so if the soldiers all emerged somewhere else on the Star it might take them this long to send word home, either by land or sea." Kang-ho was clearly trying a little too hard to sell himself on the possibility.
"Or they're all floating at the bottom of the ocean with the rest of the Sunken Kingdom," said Zosia. "Oooh, or maybe they're off with the people of Emeritus, wherever those poor fuckers ended up, or some worse hell yet. You ever hear of anyone actually using one of these things successfully?"
"I know Fennec wouldn't jump into one if he thought there was the slightest risk to his person, not when he could just make a break for it in a boat." Kang-ho almost sounded sure of it. "They came here with purpose, not as a last resort. Which means Fennec knows how to use them."
"Or thinks he does, anyway," said Zosia, eyeing the temple. Devils below, but it was a cold sight, to contemplate the darkness beyond those mighty doors. There were Royal Guards positioned at each of the structure's five corners, which Kang-ho had told her was a new addition following Ji-hyeon's abduction. Before, any dotty Immaculate with the fancy could stroll right up and let themselves inside... and never be seen again on this world. But what if Fennec really had found the method to using the Gates to travel across the Star, stepping into this one and emerging from another a thousand miles away, just like the legends told? "I wonder if Fleshnester had something to do with it."
"I thought about that," said Kang-ho. "In all the time Fennec was with us I never saw his devil, so I assumed he'd let her go long before he came to me for sanctuary. Of course, a fly can hide anywhere, so maybe he still had her... But why waste such a precious thing as a devil's boon on using the Gate when you could flee by boat, save your devil for an emergency?"
"That's it," said Zosia, sure of it—not a bad play, Fennec, not bad at all. "Why free a devil for a one-way trip across the Star when you could make it teach you the art of doing it yourself? I'll bet he loosed it in exchange for the secret of using the Gates."
"You think they have such power to give?" Kang-ho looked dubiously at Choplicker, who had trotted ahead and taken a seat in the dust, staring at the temple.
"Never know until you ask, eh?" A wince at that, wondering what she'd done wrong when she'd tried to free her own devil, and for such a smaller wish... "Couldn't help but notice Fellwing hasn't made an appearance; don't tell me you let yours go for a never-ending pipe bowl, or a night with some radiant beauty? I've heard they can insert a notion so deeply into a person's skull they never suspect the idea wasn't their own—is that how you caught such a fine husband, by making _him_ think he wanted _you_?"
"I loosed her years ago, as soon as you loosed me, and for nothing at all," said Kang-ho, but either he'd grown worse at lying over the years or Zosia's long absence from the subtle whiff of bullshit had better attuned her to its bouquet. "It is wrong to bind them, and wrong to wish upon a devil's freedom. If you seek to traffic with such powers, you should do so with mutual exchange, not torture and bondage."
"That right?" said Zosia, wondering if Kang-ho wasn't on to something. Maybe she had gone about it all wrong, maybe it was all her fault Choplicker hadn't accepted her offer. Maybe, but probably not—he was just a monster, same as any devil. "You always were a bit squeamish about them, even that owlbat of yours."
"She was never mine," said Kang-ho, still watching Choplicker. "We just walked the same road for a while."
"Yeah, well, poetic as that is, me and Choplicker have a slightly different arrangement. He doesn't do what I say, and I don't do what he wants," said Zosia, watching her devil carefully. He didn't turn away from the temple when she said his name, but that only made her more certain he was eavesdropping. "Say for the moment I don't assume you set this up with Fennec as some sort of scam you're running on your husband and the Immaculate royal family—"
Kang-ho seized her coat and got in her face, eyes bulging, cheeks red, arm cocked back as he hissed, "Suggest it again, Zosia, and I'll toss you through that fucking Gate! I swear on the devils we freed, I'll do it!"
"Cool it, old man," said Zosia, slapping him lightly on the forehead as she jerked her sleeve free of his fist. "I said I _wasn't_ assuming, didn't I? And since I'm not, what do you think Fennec's angle is? A payout from your kid's fiancé is obvious, with her marrying into royalty. If this Prince Byeong guy—"
"Byeong- _gu_."
"Yeah, him—if he received ransom demands, you think he'd tell you? Or would he try to handle it on his own? Maybe by going after the kidnappers instead of paying them off?"
"Why would he do such a thing?" asked Kang-ho, a little calmer, but not much.
"Shit, I don't know—honor, maybe?" Zosia shrugged.
"I don't think the prince is familiar with the word," said Kang-ho. "If the royal family had received demands for Ji-hyeon's safe return, they would have contacted us at once, if only to politely suggest we pay part of the ransom."
"Well, maybe the plan was to kidnap your kid and ransom her back, but something went wrong, so they never got in touch," said Zosia, realizing the dark implications of her words only after they'd left her mouth. Nothing new there.
"Something like they jumped into a fucking Gate and are gone forever," said Kang-ho heavily. "The possibility has not eluded anyone."
"Well, say it's not as bad as all that. Other than the obvious ransom, why would Fennec abduct your daughter?"
"I honestly don't know, Zosia, and that's what frightens me." Kang-ho shoved his hands in his sleeves and looked heavenward. If he was peeking for portents, the encroaching rainclouds couldn't have been a great omen. "Ji-hyeon is... she's a special girl. Her sisters are equally loved, truly, but for better or worse I see myself most reflected in my middle child. Perhaps Fennec is working for one of my trading rivals, an Immaculate house that would not see the Bongs connected with the royal family. Or perhaps this is long-simmering revenge from Samoth for all my old sins, same as the attack on your village. Or perhaps Fennec seeks to cause me trouble for his own end. You know him better than I; what do you think he might want from all of this?"
"I aim to find out," said Zosia, looking back to the temple doors. To be able to strut right through there, into what realm only the devils knew, and come out from any one of the other five Gates, in the Raniputri Dominions or Flintland or even in Diadem itself, a knife's throw from the castle where Zosia's revenge patiently awaited her attention... Could there be a greater gift from the devils than the use of their Gates? If Fennec's devil had unlocked the way for him to travel with several companions, then surely turning Choplicker loose would grant her the means to bring an entire war party through—what defense could be mustered if an army appeared in the heart of Samoth's capital? She wouldn't need to raise much of a force at all, if instead of campaigns and sieges she could sack the Crimson Empire with a single attack, the work of one bloody night...
Choplicker gave a happy bark and scrambled to his paws, finally turning away from the temple. He trotted back to her, wagging his tail, excitedly nuzzling at her hand with his heavy, slobbery muzzle. She snapped the drool off her digits, wiped them on her coat sleeve. "Now why would I do a thing like that, when I can just find Fennec and make him do it for me?"
"What?" asked Kang-ho, but neither Zosia nor Choplicker responded, both turning their backs on the Temple of Pentacles and returning to the harbor. Wherever she had gotten to, it was obvious this princess wasn't going to find herself.
# [CHAPTER
16](toc.xhtml#toc-chapter016)
After the Battle of the Extended Pinky, as the fops took to calling it, Maroto unexpectedly found himself all but adopted by the noblesse. It wasn't that he had beat some much-needed sense into them, for they seemed silly as ever, if not more so. It wasn't that he had stood up to them, because _really_ , who needs a presumptuous servant? It wasn't even that he had saved the day when, midway through their passage on the Desperate Road, the party had run afoul of the leper-monks who kept the Shrine of the Hungry Sands, because all Maroto had done there was holler at them to run for it, which they'd already been doing anyway. No, it seemed to be entirely the effect of his having provided them with dearly desired entertainment, and at last a story with which to impress their friends back home: they had stood against Captain Maroto, the Fifth Villain himself, fought him in brutal combat, and lived to tell the tale.
Fine and good for those who had escaped the brunt of his blows by fleeing to a wagon or faking a concussion, but Maroto had expected Count Hassan, if no one else, to hold a grudge on account of his broken nose. Then there was Duchess Din's torn earlobe, the result of Maroto ripping out the thick turquoise plug that had graced it. Yet if anything, the fops he had been the hardest on were the friendliest, something he could not for the life of him fathom until Tapai Purna clued him in while they rode together on the satin-padded bench of her pleasure wagon. Maroto drove, his massive sandals crowding the footboard beside her dainty shoes.
"Scars, barbarian, scars." She sounded jealous as she prodded her mostly faded black eye, winced. "You've given them treasures they could never purchase, not with all their wealth or station."
"See, you're wrong there," burped Maroto, passing her the fen-brandy decanter they shared, their wagon leading the caravan through what ought to be their last sweltering night on the Desperate Road. "For the right kind of dosh, I'll give you scars a lot more impressive."
"It wouldn't be the same, though," said Purna dolefully. "Anyone can pay a barbarian to rough them up, but you're not just any thug, and you weren't doing it for coin. You were really giving it everything you had, fighting us for all you were worth. That's what makes their wounds special."
Maroto nearly coughed on his bognac, but thought better of correcting her. He shuddered to think of how different the aftermath would have played out had he put just a wee bit more effort into it. He was glad he hadn't. Far as fops went, this lot weren't as bad as some, not by half. He'd actually started to feel bad about encouraging them to take this road, especially considering what had happened to Pasha Diggelby and his guards in the Shrine of the Hungry Sands. That the pasha himself had escaped that situation physically unscathed Maroto was counting as a big win, despite the fate of the lad's would-be protectors. There was no helping it, though; if the rumor was true and Zosia lived, there wasn't a day to lose by taking the long way 'round...
"You did all right," he said, feeling more charitable than he had in... years, really. "The rest never would've got a toehold, you hadn't bumped me at the get-go, opened it up for them. And with that godguana before, too, and then again when we got into it with those lepers at the temple over the importance of novices actually wanting to convert. Didn't take any of you pansies for being worth a kitten's claw in a tiger fight, but you've proved me wrong. I'll fess to that."
Purna vibrated from more than the rough road rocking the springs under their bench. He hadn't meant to do more than pay her what she was owed, but doubted he could have puffed her up more if he'd been trying. Soon as it came, though, she played it off, setting her empty snifter into a gold wire holder built into the riding bench and taking a snort straight from the decanter the way he did. Then she started talking weak again. _Kids_.
"You're better than I expected, too. It was my idea, you know, to hire you for the expedition. Everyone else said you were washed up, even if you'd been hard way back when, long, long ago. And for the first week we were out here I started to wonder if they were right, if you were gone to seed. If you'd ever done half the things they sing about."
Ouch. Fair, but ouch.
"I was wrong, I, um, _fess_ to that. I do fess it." Purna let him take the decanter back. It got quiet on the box seat, but Maroto was tipsy enough to take the silence as a challenge: he'd been dodging the truth long enough, and what was he doing now, leading these idiots back through the Wastes by the hardest road, risking the leprous shrine-keepers and worse, if not to face the past?
"Truth is, I probably haven't done a quarter of what they sing about. The things I did don't make for good songs." Now _that_ was playing the viola a little hard, wasn't it, Maroto? This girl was obviously looking for a role model, and given the company she kept she could do a sight fouler than him, so why piss on her fire? "But some of it was doubtless true... But in all the tales, what'd you hear that made you think hiring me to take you on some grand adventure was a wise investment?"
"You're the Fifth Villain!" said Purna. "What tales haven't I heard? You rode with the Stricken Queen when she was but a bandit chieftain, and from the slag of cutthroats and sellswords you forged an army. You conquered mortals, you conquered monsters, you took on the whole bloody Crimson Empire and seized it for your own. You hunted down devils and bent them to your will, you shook the very pillars of heaven, and—"
"And blehhhhhhh," said Maroto, sticking out his tongue and blowing. "Just what I thought, a pack of crap. For one thing, you'll call Queen Zosia by her name or not at all. For another, she wasn't a bandit, she was always a—how'd she put it, _revolutionary_ —and the Cobalt Company weren't no cutthroats. Not all of us, anyway. For a fourth—or third, rather—for a third, we never hunted down no devils. Or I didn't, anyway, though she sung songs of doing such business all by her lonesome. Fine enough tales at their root, I'll allow, but Zosia's singing always sounded like a constipated hound howling for release. Now, the devils, we bent them to our will, as you say, but we didn't go looking for them—they came to us."
It was quiet again on the riding bench, as Maroto fumbled in the breast pocket of his tunic for the pipe he had lost years ago. Old habits to make a man blush. He missed that briar more than he missed his devil. What would this kid think of him if she knew all the awful truths?
"Go on!" said Purna.
"Light me a cigar and I will."
"You're _such_ a moocher. Moochroto."
"Smart girl like you could do better. But I'll split your lip if you do."
"Promise?" Purna fished out two of the black-skinned Madros monsters she always kept close at hand. As she squirmed around and unhooded the bouncing lantern that hung on a hook above them to light the cigars, she said, "Of all the details, I thought for sure the devils were embellishments."
"And why's that?" said Maroto, removing the syrupy cigar from his lips after one puff and scowling at its familiar yet unexpected sweetness. The girl's glossy lip paint, he deduced, all papaya and pineapple and other fruits that would never grow within a thousand miles of this place. Now that he knew the cause, he popped it back in his mouth at once. "Don't you believe in devils?"
"Of course I do," said Purna, trying to blow a ring like he'd taught her to, but this close to the end of the Wastes a blessed bit of breeze finally wafted through the canyons, smearing her smoky hoop as soon as it left her lips. "But they're nothing more than animals. Rare ones, sure, but just another part of the world—monsters and devils are what people call creatures they don't have another name for. Only peasants, barbarians, and religious crazies think they're something more."
"You just jammed most of the Star and all of the Empire into three little pots," said Maroto, inhaling a hit on the cigar and immediately wishing he hadn't. It burned like a toke of dried centipede, but without any of the menthol numbness as he let it out. "Myself included."
"There's this wonderful new trend going around called 'education,' Maroto, I think you might find it interesting," said Purna, and took advantage of a lull in the gentle wind to blow a grey ring up into the canopy overhanging their seat. "The rest of the Star is catching on to what the Ugrakari and Immaculate have always known—devils aren't much different from any other animal. Calling them devils and ascribing them an infernal origin is just how scared people explain the unexplainable. Same as gods."
"Opinionated _and_ a heretic," said Maroto, trying and failing to blow a smoke ring of his own. "Knew there was something I liked about you. Let's get something very clear, Purna, devils are real. I know, because I've seen 'em, and they're not just another variety of critter. As for the Immaculates and how they look at devils, what you're talking about is a translation issue—they call 'em _spirits_ and say they're harmless, because they're pretty much both of those things, most of the time. Immaterial, I mean, and mostly invisible."
"Uh-huh. So _how_ exactly are they dangerous fiends from hell again?"
Purna's skepticism had initially annoyed Maroto, but now that he'd gotten used to the brat he kind of liked it, truth be told. It felt strangely rewarding, to be imparting wisdom to an eager youngster. An old regret welled up in his throat; how different would his life have been if he'd gone against the clan and saved his nephew? If he'd stayed with the boy on the battlefield until his dad croaked, and then slung the youngster on his back and booked it out of there? Maybe he would've gotten clean a decade and change earlier; hells, without that added guilt pushing him into the stinghouses, maybe he never would've gotten so strung out in the first place. Maybe he'd have given that unnamed kid a name, and they'd have had all kinds of times together... But dead was dead, and he ignored the familiar throbbing at the scar tissue girding his heart. He was an old hand at suppressing such things. The key was never to let yourself look back, unless something was actively chasing you. Even then it was usually better not to know how close it was on your arse.
"Yo, Maroto?" Purna waved her hand in his face. "You in the spirit world or whatever?"
"Mmmm. What was I saying?"
"You were arguing about devils and Immaculate translations, I guess, but doing a shit job of it."
"There's this wonderful thing called education, Purna, you should try it." Clearing his throat in what he presumed was an academic manner, he went on, "So yeah, the Immaculates call devils _spirits_ , on account of their not being real the way you or me are, but we're all talking about the same monsters. And the thing about devils is that they _want_ to get their touch on, but they can't... until they possess something real, preferably something alive. The really strong devils can do this on their own, under special circumstances. Not being a fucking diabolist I couldn't say what those circumstances are. Anyways, when they do possess something, whether it's an animal or a plant or even a pile of rocks, they can cause all kinds of trouble for us mortals... but taking possession of something can also trap them in our world, make it so they can't flee back to whichever hell they came from. That's how binding devils works—if you summon one up from the First Dark you can offer it a living animal to inhabit, and when it takes the bait the poor fucker's bound to you. It can't go home until you let it go."
Maroto had assumed this would spook her into silence, but no dice. "So you're saying devils aren't animals themselves, but are something... intangible, imperceptible, that somehow enters a normal creature, assumes control of its body, and in this body the devil's free to do as it pleases. That about it?"
"What I just said, isn't it? Halfway, anyway. The flesh they wear gives 'em freedom to move about our world, sure, but it's also their prison: they're trapped inside whatever animal was available when they were first summoned."
Purna withdrew the cigar from her pursed lips and tapped it thoughtfully. "Are you familiar with Raniputri medicine? Plague theory?"
"Yeah, sure." Over the years and entanglements, Maroto had been stitched up, smeared with fragrant creams, and even cupped with hot glass bulbs all across the Dominions, but that was beside the point. "Were you even listening?"
"Diseases can be like that, like your description of a devil. Something invisible that gets inside you, fucks you up from the inside. Affects all your organs, your brain included, but not by accident—by design. It's intriguing, thinking about pestilence as a living creature, instead of the wrath of the Fallen Mother or the Barrowkings or whatnot. It makes sense, especially if you think about how illnesses spread through communities, and travel from one region to another along trade routes."
"You're close!" said Maroto, remembering all too well Hoartrap's plague devil, Lungfiller. Not that he'd seen it, of course, except for when they'd first bound the fiends and their true shapes were hinted at, before they entered the mortal vessels the Cobalt Company had prepared for them... "A devil can wriggle its way into something smaller than a butterfly's eyelash. You know Hoartrap the Touch, the Third Villain from the songs? He had one he kept in a bottle, so small you couldn't see it, but when he let it out, it brought death, and worse, to anyone who breathed it in. Nastiest of the nasty, that one."
"See?" said Purna. "You just proved my point. Devils are just what you call some animal you don't understand, like a disease. They don't come from any hells beneath the earth, they don't have mystical powers, they can't tell the future, or grant wishes."
"You're wrong," said Maroto, the charm of illuminating the unenlightened beginning to wear off. He'd seen devils with his own eyes, kept one within reach for over two decades, and this pup thought to talk down to him? "Devils are real, and they're more powerful than a child like you could even imagine."
"And you know because you bound one, right? That's how the song goes, you hunted it down and—"
"I told you, we didn't go looking for them. I'm stupid, not crazy. They came to us. Stalked us from battlefield to battlefield. Feeding."
"Like lions following a pack of hyenas, moving in on their kill once the dogs do the work?"
"Nothing like that," said Maroto, the booze bubbling in his stomach at the memory. "It wasn't flesh they ate. It was something else. Pain, anger, sorrow... I've heard a lot of theories, but I don't like to dwell. They didn't just feed on the dead and the dying, Purna, they fed on _us_. When we'd won, and settled in to celebrate another victory, they slunk through the shadows and drank their fill from our black hearts. If our warlock hadn't suspected them, we never would have known they were there. But Hoartrap knew, hells, maybe he summoned them in the first place. But they were invisible, hidden, until we bound them."
"How?"
"Doesn't matter," said Maroto, the cigar turning tarry in his mouth. He would never, ever speak of what had happened the night of the ritual, but even down all these years, what he'd seen—what he'd done—haunted him worse than any devil. How had they ever let Hoartrap talk them into it? Or had it been Zosia who'd first proposed it, another dire gambit by the blue-haired general so ruthless that even her own troops had taken to calling her Cold Cobalt? With everything that had come after, the lead-up to the ritual had largely fallen from memory.
"So you bound the devils," said Purna. "Sure, I've read plenty about that sort of thing."
"Have you?" What if this girl was some amateur demonologist? Eyeing her hot pink collar and chartreuse vest with heart-shaped brass sequins, Maroto decided it didn't seem likely. Not impossible, but not likely.
"Yeah yeah yeah. But isn't the whole point of binding them so you can force them to do what you want? Lead you to long-forgotten buried treasure, or write down the formula for turning coal into diamonds... or grant your wishes?"
"They only grant a wish if you let them go," said Maroto quietly. "Otherwise, they tend to be pretty sore on the person who bound them. But since I guess it goes real bad for a devil whose master dies without freeing it first, they do try to keep you safe from harm however they can, even if they hate you. How they manage it, I couldn't tell you, but it definitely ain't natural—I've seen blades coming straight at my neck suddenly fly wide of the mark, and poisoned mugs of ale start to bubble over when I went to take a sip."
"And your devil, the one that you bound—what is it?" Purna sounded right respectful now. "A pox, like that Hoartrap you rode with? The songs don't match up on that count at all."
"Crumbsnatcher," said Maroto with a smile, almost able to feel his devil squirm across his shoulder and nuzzle at the overgrown hair where his fade had been, back when he'd given half a damn about maintaining a respectable haircut. The devil had loved using its paws to trace where Zosia had shaved a stylish M into the stubble on the side of Maroto's head. "A grey rat. Smaller than you'd think."
"Can I see him?"
"I let him go," said Maroto, remembering all too vividly the horror when he came back to his senses and realized he'd loosed the fiend. The creeping black cliffs of the canyon they rolled through could have been the walls of any number of stinghouses, Maroto too stoned to move from the cot even as the world slid away from him. "Ages ago."
"So you released your devil."
"What I said," said Maroto, flicking his cigar away even though there was plenty of life in it. Bad as the taste of his memories could be, it was the bitterness of all but forgotten fuckups that had seeped into the end, poisoning its flavor—instead of a girl's gloss or strong tubāq, it smacked of stale hornet toxins oozing out of his swollen lips the morning after a bender.
"Now do you see why I'm skeptical about devils having any real supernatural powers?" said Purna.
"No," said Maroto grumpily. "You didn't even ask what I wished for."
"Unless it was to end up so broke and desperate you'd take a trashy gig leading people you despise through country you hate, I can't imagine your little devil granted it. You don't seem like the sort to squander a once-in-a-lifetime wish on something like the perfect sandwich, so there's the proof—if you'd gotten your heart's desire, you wouldn't be such a sad case, would you?"
"I... wait." After years of uncertainty, of fearful doubt, it finally came to Maroto, what he must have wished for back in that last stinghouse where he'd almost died repeatedly, where he'd lost weeks at a time and probably shaved years off his life. When he'd finally sobered up enough to realize his devil was gone, that he had wished it away, the possibilities had seemed endless, and mostly terrible, given the propensity for wishes to somehow turn out bad for their recipients. Realizing he'd freed a devil and couldn't even remember why had been the absolute rock bottom of a middle age riddled with potholes, and had freaked him out so badly he'd never touched insects again.
Now, though, half a year off of the bugs, it occurred to him that in a drug-blind haze he must have simply requested to be free of his dependence on the stuff. Old Black knew he'd wished to be clean enough times, when he was doing some depraved act in order to score another caterpillar or coming down from an icebee bender... and the last time he'd wished it, Crumbsnatcher must've heard his prayer. He should've guessed it wasn't just his iron-steady willpower that had enabled him to walk out of that last stinghouse and, after a few rough weeks of withdrawals, start his life anew.
For all the good it had done him. It hadn't returned any of the wealth he'd lost or traded, it didn't bring back dead lovers or dead dignity. He'd wished himself a new life, and, surprise surprise, it was just as shitty as the last one, only now he was far more conscious for it. Better still, it was liable to stretch on for year after miserable year, instead of abruptly terminating in a painless overdose. That was a devil's wish, all right—nothing crueler than giving people what they ask for. Why not score some firewings when he got the caravan to Katheli, see if good old Crumbsnatcher had given him the ability to handle the stuff without getting hooked all over again? That was something to look forward to...
"You all right, big chief?" asked Purna, and Maroto shook his head, realizing he'd been drifting. "Didn't mean to pry," she said.
"Yes you did, but it's no matter," said Maroto. The kid was probably getting off on talking to a legend, albeit one fallen on hard times, but the truth was it felt good to have an ear to bend about it all. "Crumbsnatcher granted my wish, Purna, though it's taken me a long time to realize it. Young as you are, you shouldn't doubt something just because you can't fully wrap your brain about it. Yet. Devils are real. Everything you've heard about them is true. And then some."
_And if Cobalt's really alive, if we find her and the rest, you'll see for yourself_ , Maroto almost said but didn't. Telling Purna about his destination, his true motive for returning to the caravan, would surely get the girl's blood up, but he balked at repeating the rumor lest he make it false by speaking it aloud. A secret of the gods, or devils, entrusted to him, and him alone. Well, him and the pilgrim he'd heard it from, and the sister or whomever _she'd_ heard it from, and on down the line, but still: you don't count pelts from untrapped cats.
Purna was giving him some sass, and he was about to put the question to her of just what the merry hob she thought the Gates were if not wells dropping straight down into hell, when something caught his notice up the road. _This_ was why he insisted they take the lead vehicle and wouldn't have it any other way. They were almost out of the Wastes, the gunmetal strip of predawn sky overhead widening with the canyon, and by its faint light he saw that Captain Gilleland and his two outriders had come upon a large cart or wagon parked in the center of the road. The three guards were still on their steeds, talking down to a small cluster of silhouettes. Of all the miserable dick-kicks destiny could deliver...
Grabbing the reins and stopping their camels short, Maroto winced as one of the beasts vocally expressed its displeasure. The animals pulling the vehicles behind theirs gave similar protests as they, too, stopped, the caravan bottlenecked in the canyon. "Ambush. Kill that lantern and get everybody ready to fight. Bring the rear guard in, let them know. Fast."
"What are—"
"Now, girl. Miserable guana-fucking bandits couldn't hit us when we were going into the Wastes, no, we have to run into a crew on our way out. Wake those bums up, at this point the Giggle Collation outnumbers the guards we have left. We're already in their killzone, so anyone who wants to live is going to have to fight, and dirty. These vultures are a ways worse than a lizard or some lepers."
Purna didn't second-guess him, credit where due. They slid off the riding bench in opposite directions, Maroto pausing to root his chainmail vest out from behind the seat. Not his favorite kit by any means, but he could shrug it on fairly quickly, and once he had the armor fitted he drummed his fingers on the two handles jutting up from the recess. He decided on the ax, since he was quicker with it, and no mangy desert bandit deserved the taste of his mace anyway. Would that he still had one of his sun-knives to chuck around, but ages back he'd pawned the last couple he hadn't lost. He'd have to invest in some new ones, if he came out of this, but for now, well, it was never good to put off doing a job for want of better tools. A favorite of Zosia's mantras, trotted out whenever one of her Villains was whinging about the long odds she'd set before them.
When they finally caught up to the Cobalts, what would Zosia make of Maroto's new sidekick? For that matter, what would Purna make of Zosia, after all the songs she'd heard? Zosia was bound to be less of a disappointment than Maroto had proven!
His past and his present were barreling toward a collision, and when they connected the whole Star would tremble before the second coming of the Cobalt Company. He gave silent thanks to Crumbsnatcher for freeing him of his bug habit in time to hear about Zosia's return and pick up her scent; how tragic would it have been if she'd come back but he never knew it, too busy mourning her loss in some stinghouse?
Assuming it really was Zosia leading these mercenaries, of course, that the pilgrim's rumor was something more than gossip. But no, there'd be time aplenty for doubt in the days to come, and for now he must have faith. It _had_ to be her. If anyone could cheat death this bad it would be his old general; not even a devil could bring back the dead, but leave it to Zosia to find a way back from hell.
If he wanted to see her again, though, if he wanted to introduce her to his new buddy Purna and see the rest of the old gang and, later, when they'd snuck off somewhere, hold her in his arms and breathe in her bad boozy breath and know for certain it was truly her, first he had to get past whatever death-hungry fools had blocked his path.
It felt all right, walking fast up the canyon with the ax casually slung over one shoulder. Felt like old times. In the blushing dawn he saw that Captain Gilleland and his men had dismounted, the morons, and it occurred to him that for all his fantasies of reuniting with Zosia, every single person he had led into this canyon might be dead inside of five minutes. Himself included.
And then, darker still: even if they weren't butchered, even if everyone walked out of the Wastes without a scratch beyond those he'd given them, there was Tapai Purna, the second daughter of an Ugrakari noble house he'd never heard of. Even if that girl lived out the night, when she died it would be because of him—long before he'd even met her, he'd derailed her life from its easy course, filled her with ambitions of the glory you found not at a card table but on a battleground. It wasn't just that she knew his songs that told him this, it was that she'd doubted their veracity and still sought him out—she didn't want to hear stories, she wanted to live them, and find for herself where the truth lay. That girl didn't want to play a part in some drawing-room drama, either, she wanted to star in the theater of war, and whenever death came cleaving for her, it would be all Maroto's fault.
Good for her, and good for him. A barbaric thought, something to make his ancestors proud as they sat around Old Black's Meadhall. Good for her, and good for him. Besides, whenever blame needed to fall somewhere, it always seemed to end up landing square at his feet.
Maroto walked right into the bandits' ambush, a caravan of fools behind him, and somewhere far ahead, Cold Cobalt. The Stricken Queen. Zosia. Zee.
# [CHAPTER
17](toc.xhtml#toc-chapter017)
Sullen and Grandfather were sitting around their campfire sharing a bulging beedi of crumbly old saam rolled in a dried tubāq leaf when the witch emerged from the darkness. Neither of the keen-eared Wolves detected his approach, the gargantuan geriatric materializing out of the smoke like the Deceiver in a tale of the new faith, or a prophetic ghost in a tale of the old. One of those born-again heathens Sullen had given the slip back in the Falcon People's forest would have doubtless leaped up and begun bellowing invocations to the Fallen Mother to cast out the interloper, but Sullen and Grandfather were not heathens, and so knew that nothing happened without reason. It was better to hear out a traveler, however dubious, before deciding on a course. That, and they were both blasted out of their minds, and until Grandfather spoke Sullen wasn't sure the big man was actually there.
"The night is cold, our fire is warm, and friends are made as easy as foes," said Grandfather, and, just as in a fable, their guest responded to the ancient greeting in the true tongue:
"The night is cold, your fire is warm, and I would have friends before me than foes behind." The big man was white as a bone bleached by the sun, white as moonlight on polished ivory, white as treachery, but still Sullen felt strangely undisturbed by his grinning, withered visage. He'd killed a living man he had known all his life, so what harm could a foreign corpse do him, even one that walked and spoke? That was, until the ancient guest continued, "You pups are far from your pack, and these lands are haunted by that which even the Horned Wolf might fear."
Sullen wanted to shout this stranger down, to impress his grandfather, to impress himself, and most of all to impress upon this fucker that they feared neither witch nor devil... but nothing clever came to his tongue, and his grandfather had impressed upon him that when you have nothing to say, it is best to say nothing. Grandfather, though, always kept his cleverness close to his tongue.
"All I see by the light of my fire is a weary pilgrim, one with even more harvests than I under his back. One who would do well not to raise the ire of his hosts, lest they bash in his sly mouth so that they might again enjoy the more honest crackling of the fire." Grandfather looked pretty smug about this pronouncement, as well he should. It was solid, and Sullen felt a shiver in his marrow at discovering himself in the midst of a song in the making.
"Horned wolves," said the stranger, shrugging off a wicker-framed pack of such impressive size that the rucksack reached to his chest even when he set it on the grass at his feet. Considering how tall he was, that was some pack. "Do they still stalk the Savannahs, pray tell, or have they been hunted to ruin, all so that you might have a cloak less warm than that of the same-horned ram?"
"I wear no skins save that of the sheep," said Grandfather. It was true; Sullen remembered how he had been made to watch as Grandfather burned the hides of all the horned wolves he had killed on the day the council voted to accept the Fallen Mother and reject the Old Watchers. "You can sit down and act the role of guest at a fire you took no hand in kindling, or you can keep talking that weakness and see what happens."
The beedi had burned down to Sullen's thick fingers, scalding him, and he quickly popped the end of it in his mouth, puffing it back to hotness, the skunkiness of the bud mixing with the acrid yet earthy tubāq wrapper. Passing the smoke to his grandfather, he saw that his hand was shaking. The old giant had not sat, but he wasn't talking any more shit, either, instead watching them with that unwholesome smile on his shriveled apple of a face. Grandfather still didn't seem particularly concerned, though, so Sullen tried not to be, either. If great deeds needed doing, they'd announce themselves.
"Is it both of you, or just the boy?" said the old man. "Maroto's blood?"
Sullen's head swayed from the weight of trying to hold up this nonsense for a proper inspection. What in the name of the first fires was a Maroto? He glanced to Grandfather, who reclined against a rock with his legs folded beneath him in such a way as to give the illusion that he was just sitting down, could stand on his own anytime he wanted. Grandfather coughed on the hit he'd just taken, ground out the beedi in the dirt, and sat up straighter, his eyes narrowed.
"You've got a nose on you, to smell us out," he said.
"My nose is keen, yes, but not as sharp as that boy's eyes," said the stranger. "As I approached I saw them flashing in the firelight, and they gave me quite the fright—why, I thought a snow lion had wandered all the way down to the Empire! Now that I see you both up close I know I have nothing to fear, do I?"
"Sullen, if you have to kill this creature be sure to cut off the head," Grandfather growled. "Burn the lot of it. When the snakes and spiders try to flee the blaze, push them back in."
That dumped some water on a fellow's hearth, to be sure, and as soon as the words sunk in, Sullen found his feet already planted beneath him, his body in a tight crouch, ready to leap across the campfire at the stranger. In one of the Deeds of Boldstrut, an assassin sent by the Shaman King of Hellmouth had bewitched her around just such a campfire, and Sullen had no intention of allowing such a fate to befall him and Grandfather.
"Peace, peace, oh Horned Wolves," said the colossal man, raising a tattooed palm. "Maroto and I are friends, old friends, and I do not seek to quarrel with his family. There is a mistake, nothing more—I sought my ally, but found you instead. These things are known to happen. I assure you my nose is as plain as yours, if not plainer, and while I have been called worse things than 'creature,' I am simply a man, the same as either of you."
"You a witch, then?" demanded Grandfather. "Or do you expect us to trust that out of all the fires burning across the Star this night you just happened on ours and saw the familial resemblance?"
"There was a time in my memory, and surely yours, when those who walked both worlds were not always so cursed," said the stranger, sounding a touch nostalgic. "Now the Horned Wolves lie down with the Crimson lambs, turning their backs on the world their ancestors built for one promised after death. Such have things changed that I recently heard a traveler refer to burning a wildborn as a 'barbarian exorcism.' To think I should live to see such decline... Maroto always nodded to me, and I'd hoped his blood might, too. More's the pity."
Sullen would have lunged at the man, Grandfather having already warned this witch about talking more noise, but an epiphany breezed through his skull-smog at that very moment: this "Maroto" must be what Uncle Craven took to calling himself after he left the village. Grandfather had told Sullen there were so many Cravens in the Empire that their relation might earn himself a new name to stand out from the crowd, and they would just have to ask around for a rangy, russet-skinned wanderer with the tattoo of the Horned Wolf on his biceps. There had to be fewer of those in the Empire than there were Cravens. Still, again, what in all the songs sung by bard and beast was a Maroto, and how had Uncle Craven come into such a weird name?
Grandfather spoke again, reminding Sullen that he'd meant to attack the witch before it bestowed curses upon them. From what Grandfather was saying, though, it was all right that he had lost the moment in a saam trance. "Blunt my teeth, but it's true the respect your kind ought to command is in short supply these days. Like you say, things change, but when has change ever been good? It's just another word for rot and ruin... But there was never a time when I'd welcome some pasty Outlander to my fire without having him offer a name for himself, and never a time I'd balk at burning a shaman if he sought me harm."
"Hoartrap the Touch," said the stranger, with a bow that brought his embossed leather robes closer to the firelight so that Sullen could see that they glittered with embedded jewels and charms, an alien constellation of symbols and sigils. "And whose fire do I share this night, may I ask? Kin of Maroto's, yes, but father or uncle, son or cousin? What shall I call you?"
"You can call us both 'sir,' " said Grandfather. "I look green enough to give my name to one of your kind, whether we call you shaman or witch, mudwife or warlock?"
Hoartrap's smile began to appear strained, and Sullen's neck nodded of its own accord at Grandfather's wisdom. If anything happened to the old man, Sullen didn't imagine he'd last one day in this fallen Star, where nothing was as it should be. From the first step he'd taken outside of their ancestral lands, everything had gone to chaos; clanfolk trying to kill him, and now a witch trying to undo them with words... if that was even what was happening. He really wasn't sure what in the hells was going on here, other than his mouth was parched and he was squatting in front of a too-hot fire, not sure if he was blundering into an epic saga or an overlong joke.
"If you're not even willing to share your names with me, however are we going to get along on the road we must share?" _That_ didn't sound like it boded well. "I told you I sought Maroto, and that he was a friend, and both of these are truths. You two likewise track him, and so it would seem best that we seek him out together... yet now I wonder if such a course is wise."
"Well, you might," said Grandfather warily. "Don't know if the boy and I really need to be sharing a trail with any shaman what calls himself 'the Touch.' I'll tell you straight, that's far too peculiar a handle for my liking—not one for getting touched myself, as a rule."
"So you do seek him," said Hoartrap, nodding. "You must have been between myself and Maroto, and what with your blood, our shared target, and your closer proximity, it must have thought this a suitable substitute. It's young and stupid. I'll just have to ask another."
Again, Sullen wondered if he had dozed on his feet, or if the beedi had been stronger than he'd thought—the words this witch spoke made less sense than the lowing of cattle. Before he could glance at Grandfather for clarification, though, a piece of the night tore itself loose from just behind his ear, drifting past him and over the fire to land on the witch's outstretched hand.
It was a large, hook-winged owlbat, its ebon fur and dark feathers shimmering like freshly shed blood in starlight, and Sullen fell flat on his arse, rocked to his bones by wonder so pure and profound it seemed to sober him up and make him reeling drunk all at the same time. Never before had he seen a true devil, not this close anyway, and though it mostly looked like a mundane creature, Sullen knew he was right, for beside him he heard Grandfather give an oath at the sight of the being. Sullen was not the sort of boy who divided the world into poles of beauty and ugliness, ideal and flawed, but in that instant he realized he had never before encountered something so sublimely perfect.
More than that: the songs and sagas weren't just made-up stories, the way Grandfather sometimes implied. There was more to life than dirt and blood, love and grief. Devils were real, so what else might be possible? Anything and everything, was the obvious answer.
And more than that, still: if Sullen was looking at a true devil, which seemed certain, that meant he had achieved something no Horned Wolf had in a generation. Here, without even seeking it out, he had passed that final test of the council. He gazed upon a devil made flesh, saw the creature in the shadow and _knew_ it was more than just an animal, and that _meant something_. Watching the devil crawl over the old witch's knuckles, Sullen felt a knot in his throat, wishing his mother could be here to see that her son was more than just a misfit, that he deserved to be a member of the clan. Sullen wasn't a kid anymore... and yet just beholding the devil filled him with childlike wonder and delight. His first devil...
Then, before he could even sort out his feelings on the matter, Hoartrap the Touch clutched the devil in a wide fist and shoved its head into his mouth, biting down with a sickening crunch. The devil convulsed in his hand, trapped wings straining against their bonds, dark blood jetting out to hiss on the fire and spit up rainbow-colored smoke, and the witch's jaw dropped wide like a pit viper's to accommodate the rest of its meal in one go. Even Grandfather was dumbstruck by the appalling sight, and so there was no sound in the night save the brittle chewing of a living creature, and then a series of thick gulps. When next Hoartrap smiled at them, his teeth were as black as his dripping chin.
"They always have their uses, even when they don't do as you tell them," said the witch, smacking his lips.
"The first devil I've seen in twenty thaws, and you..." Grandfather's voice had the dangerously low tone Sullen had only heard a few times, and he worried the old man might crawl on his belly across the coals to get at this monster.
"If you find your kinsman, you'll see plenty more," said Hoartrap with a leer. "Do not fret, though, even if you don't live long enough to meet the man your Maroto has become, I can still show you what you seek. They grow dimmer to the likes of you, old wolf, but I'm sure your cat-eyed whelp can attest they are as plentiful as ever, lurking around us, feeding off your every movement, fattening on your faintest sensation. If all you wish is an audience, I would be happy to light the candles for you to see beyond the shroud of—"
"Kill him!" Grandfather barked, his voice cracking, and the desperation there chilled Sullen more than anything else he had beheld that night. "Kill him now!"
Sullen tried, but he was too slow. Perhaps it was the saam they had chiefed, perhaps it was some inner weakness, or perhaps it was just the will of the Old Watchers, but by the time Sullen had scrambled to his feet and gone for Hoartrap, it was too late. Like Boldstrut before him, he had tarried too long in the company of a witch, and his song was sung before he could contribute a verse.
The witch wiped the devil's ichors from his face and intoned an incomprehensible, earache-inducing phrase as he snapped his bloodied fingers, and the tip of every blade of prairie grass for fifty meters burst into flame. A wildfire would not have frozen Sullen in his tracks, even one incited by such witchery—fires are made to be tramped out. No, it was what the Horned Wolf saw illuminated in the sudden brilliance that pinned him in place so suddenly he toppled over, all the strength he had drawn to propel himself at Hoartrap banished mid-lunge. There he lay for the rest of the night, only chance sparing him from landing in the fire, too scared to even close his eyes.
They wheeled above and around and even through him, some with forms close to that of animals, others strange beyond the imagination of saga singers, and in the depths of his paralyzing dread Sullen vaguely recognized that the devils that had always haunted his dreams and played at the edge of his vision were but hatchlings to the great and terrible entities that exist beyond this world, ever waiting, ever watching. Ever feeding.
Everything Grandfather had told him about such things was wrong, he saw that now, or if not wrong, then incomplete. Naïve.
Grandfather and Hoartrap were far gone, even the grassy earth pressed against his cheek faded, and the longer he watched the more he saw, the devils dipping down through the sky and up out of the ground to bury their beaks, jaws, and proboscises in his sacrificial flesh. Yet he felt nothing at all from their bites, nothing but devastating horror that this was how his song ended, the Saga of Sullen nothing more than a cautionary tale against straying from the pack lest you spend eternity gnawed by monsters...
Until the first rays of dawn snuffed out the burning tips of the grass, and then they were gone, leaving him cramped and sore and half mad. At first he didn't believe it, couldn't believe it—the devils had fled, and he was still alive. Or close enough; his ragged body dripped translucent gore from a hundred numb wounds that opened and closed as he watched, winking at him... so he stopped looking at them. They weren't real, or at least not real in a way that would slow him down.
"New plan," Grandfather croaked when they had both recovered enough to look up and blink at one another, crumbs of blood crusted in the corners of their eyes. "We'll still find your uncle, but first we hunt down that witch and give him one of them _barbarian exorcisms_."
Yet when the late spring sun slouched high enough for them to follow the witch's barefooted tracks, the traces only went a short distance out into the singed prairie before terminating in a wide circle of stinking grey tar. The grass and earth were covered in the foul residue, and just looking at the stuff made Sullen's neck sweat and eyes pulse.
Grandfather swore to impress the ancestors, and not just the usual bunch of heroes and hunters but even the especially pernicious ones. Sullen, to his shame, was relieved that the trail could not be followed. It was hardly a valiant sentiment worthy of the songs, but he wished he were back home in the Savannahs, where he knew at a glance who meant him harm, and where the devils kept their distance.
# [CHAPTER
18](toc.xhtml#toc-chapter018)
The ax felt lighter on Maroto's shoulder than it had in a long time as the cluster of well-armed individuals at the stopped wagon turned to face him. A pale, scrub-bearded youth led the five new arrivals, all of whom wore sand-colored cloaks on their backs and blades on their belts. From the nervous glance this scrub shot Captain Gilleland, Maroto kenned the score in nothing flat. Rather than getting nervous at the betrayal, it put him at ease—with Gilleland having set this up, they'd be cocky, maybe even cocky enough to have all their number down here where he could reach them, instead of camped in the rocks above with bows and harquebuses. At a minimum, it meant he could finally stave in Captain Gilleland's skull before these bandits sent him screaming into whatever hell the devils had reserved just for him.
"Ho, barbarian!" said Captain Gilleland. Unlike the bandits, who were green enough to think they weren't rumbled yet, the mercenary and his two toughs drew their swords. Gilleland jovially gestured with his cavalry saber. "Just the man I was hoping to see. I must say, that chain can't be comfortable in this heat!"
It wasn't, the armor a fair bit snugger than Maroto had remembered, especially in the belly, but he said, "Don't worry on my account, I won't be wearing it long. Got some sort of problem here?"
"Nothing you can't handle, I'm sure. These pilgrims think they may have broken an axle; might you be good enough to crawl under and have a look?"
"Oh, sure," said Maroto, counting the steps between him and Gilleland, minding the loose flap of the wagon's cover where an archer or three surely watched him. Every step he took reduced his chances of being shot before he could do some good. "Always happy to help a pilgrim get where he's going. Let me see if I've got the measure of this—those guards you said got carried off by cannibals the first night, you just necked 'em and rolled 'em into a ravine?"
Gilleland's smile widened, and when Beard Bandit put a hand on the hilt of his sword the other four punks did the same. That was fine. Maroto was an easy two bounds away from Gilleland, and had come in at such an angle that the captain and his two goons were now between Maroto and the wagon, spoiling the shot of anyone inside. Not the shot of anyone hiding in the cliffs around him, granted, but you can't expect everything in life to be easy.
"Tell you what, barbarian," said Gilleland. "You stop right there and we talk through this."
Maroto obliged. He was close enough. "And in the Shrine of the Hungry Sands, you maybe put the idea to those lepers that Diggelby and his knights were interested in having a religious experience?"
"Just Zir Sisoruen and Chevaleresse Halford, actually," said Gilleland. "The Diggelby boy wandered in at an inopportune time, so you can imagine my relief that he wasn't harmed. You're smarter than your reputation, Maroto. I wonder just how smart."
"Dad, what—" Beard Bandit began, but Captain Gilleland's sharp frown cut out the boy's tongue. Oh, this was getting good, all right—the lighter the sky grew, the softer these bandits were looking. They were red with sunburn, not dark with tan. Probably hadn't been in the Wastes a week. For the first time since Maroto had made his sneering acquaintance, Captain Gilleland looked a little on edge.
"Smart enough to figure we lost everyone on the road who'd be loyal to their charges instead of going along with your plan," said Maroto.
"And here you stand, neck unslit despite your mouth," said Gilleland. "Advantages to sleeping in a noble's carriage with servants all about, instead of taking your turn on watch like the disgraced scout they thought they were hiring."
"I wondered how that red recluse got into the wagon. Lucky I always check my bedroll. Creeping things never stand a chance against the Villain Maroto—no matter how much venom they carry, a sandal settles them flat." Truth be told, it had taken a bit of willpower not to see if he could get high off the spider first.
"Game doth recognize game, Maroto," said Gilleland. "That's the only reason we're talking."
Maroto snorted. It would be bad enough if Outlanders just adopted Flintland slang, but they usually mangled the meaning. On the Frozen Savannahs, hunters meant a very different kind of game when they busted out that burn on a punk—even a scared hare knew the difference between a mouse and the maned wolf that stalked them both, was the idea.
"How would you have gotten them to take this route, if I hadn't put it out there?" Maroto recalled the captain's protests when he'd found the party at their inn and proposed the Desperate Road—he was cool as snowmead fresh out the ice-wagon, no doubt about it. "Your brat might have been waiting out here for nothing."
"Getting nobles to do what you want is simply a matter of telling them that they can't," said Gilleland smugly. "Now, dawn's upon us, so let's be done with this. I know you, Maroto, and to put it plainly you're not invited to this final fete. As a token of deference for your many heroic deeds during the Cobalt War, we'll give you a head start of a hundred heartbeats. In that time you can proceed through the caravan, taking what you can carry, and then travel a respectful distance back down the road. An hour after we depart, you can follow, leaving the Wastes however you like. Simple terms, yet generous."
"Simple is definitely the word," agreed Maroto. "What if I take the opportunity to rally the troops?"
"The rear guard, who are in league with us, or the fops? Either way, it doesn't end well for you."
"And how does it end for them?" Maroto's eyes kept flicking around the canyon walls as they came into clearer sight. So far, no glint of sunlight on arrowhead or gun barrel. "Ransom?"
" _Ransom?_ Those chumps?" Captain Gilleland shook his head. "Sadly, much more trouble than it's worth. They have enough on their persons to make this a handsome enough windfall without our getting greedy and complicating things."
"Point," said Maroto, weighing his options. He wasn't being offered such a bum deal here, and it would pay out nicely for all parties. Well, other than the fops. Captain Gilleland wasn't so simple after all. One minute alone in the caravan and Maroto could seize enough loot to ride all the way to Agalloch in his very own pleasure wagon. He hadn't really thought much beyond traveling with the nobles back through the Wastes, anyway—what was he going to do, lead these hooting idiots all the way over the Star to Zosia and the Cobalt Company?
He only had two plays here: swing on five greenies and three hardscrabble toughs, with more sure to follow and a decided lack of dependable support from the only ones to benefit from such a suicidal move, or take Captain Gilleland's offer. He'd have a bit more blood on his hands, but what of it? They were stained enough he'd never notice another coat. Wasn't this exactly what he'd known might happen, taking the Giggle Contingent on the Desperate Road? Wasn't this what they'd expressly _asked_ for, a gritty adventure in the real world?
_Fight for your lives, fops, because Maroto won't!_
The old Maroto would have already taken the deal, Old Black knew. He might've been the one to set up the betrayal himself. He might be stupid, but he was no fool.
"Tapai Purna comes with me," he decided.
"Not a chance," said Gilleland. "Your word means nothing, but hers might. What if she contacts the families of those unfortunate friends of hers who are about to be lost in a swarmstorm? Come on, Maroto, we both know this doesn't work if she walks."
"Yeah, I see that." There was nothing to stop him from accepting the offer, snagging Purna on his way back through the camp anyway, and then riding away with her. Tough luck for the rest of the fops, and tough luck for Gilleland if he felt like pursuing Maroto and Purna. That was the only move, when you got down to it—anything else was madness, and where had madness ever gotten him, other than right where he stood?
"Good. Now, that minute of yours starts now. It's been a real pleasure, hope we can do this again sometime." Gilleland waved Maroto off with his swordpoint, and his son's taut knuckles relaxed on his pommel. Beard Bandit thought Dear Old Dad had sorted everything. Well, sorted it soon would be.
"New terms," said Maroto, committing to his decision. "I'm afraid I can't give you a full minute to answer, though, just about ten beats of your chicken heart. You throw down your weapons and walk away, or I'll chop you all in half with my ax—if your own skin isn't worth the saving, Gilleland, think of your son."
Beard Bandit took a step back, bumping into one of his cronies, but Captain Gilleland was unimpressed. "Even in his prime, I doubt the Mighty Maroto could kill eight steady hands before one of them—"
" _Chop in half_ ," said Maroto, trying unsuccessfully to arrest the grin crawling up his face, the ax nearly floating off his shoulder. "Didn't say I'd kill you, said I'd chop you all in half. With my ax."
"Had we the time, I might _actually_ like to see you try such a—" Captain Gilleland began, but the hard man never got to finish acting his part, because Maroto took him at his word.
Maroto had heard of Gilleland long before they'd met at the outset of this ill-fated job. The wiry ginger had made a name for himself at the Siege of Old Slair—if memory served, he was the one who'd taught the survivors of the first month how to trap the rats and vultures that went after the castle's dead, so the besieged would have something other than their fellows to eat. Maybe if they'd just sucked it up and eaten their fallen comrades they could've mustered the strength to carry the day when the gate finally fell, instead of getting their half-starved arses handed to them by the Usbans. Whatever the case, the treacherous veteran was about to discover that trapping a bear takes a lot more preparation than goes into catching rats.
Captain Gilleland had enough sense not to try to parry the double-headed ax. Instead, he dodged to the side, jutting his saber out to impale the charging barbarian. It might've worked, too, if his son hadn't been underfoot. Beard Bandit spoiled his father's play, leaving Captain Gilleland nowhere near so far from harm as he'd have liked as he bounced off his boy. And then Maroto proved himself an honest man.
Captain Gilleland's swordpoint missed Maroto's side by a good six inches, and Maroto's ax snapped through the smaller man's collarbone at an angle. The weapon hewed through meat and bone, grinding to a stop in Gilleland's ribs just beneath the captain's opposite armpit. To the amateur observer it might've seemed that Maroto had failed to deliver, but then he wrenched his wrists, twisting the ax's haft in his hands and leveraging Captain Gilleland's head, arm, and shoulder completely off his ruined body. Only the undamaged flank of Gilleland's leather dress uniform kept him from falling in two easy pieces, the upper half of the bisected man flopping sideways on the hinge of armor.
There was no moment of stunned wonder as everyone considered this feat, much as Maroto would have appreciated a brief reprieve to admire his handiwork. No, the fight was well and truly on, Gilleland's two goons already on top of him. The hard man and harder-looking woman had him pinned between them, and even a star of the Immaculate ballet would have been hard pressed to dance around their flashing blades.
You wouldn't guess it to look at him, but Maroto was one devil of a dancer, and as his two new partners assailed him, his hands jerked the ax free of Gilleland's teetering wreckage and his feet spun him away. Before the captain's carcass had even hit the ground, Maroto was tagged on the cheek by the man's sword and felt the whisper of the woman's blade open breeches and thigh alike. He'd also maneuvered himself directly into the pack of stumbling, fumbling wannabe bandits, and as the two heavies pressed their advantage Maroto put the greenies between himself and the real danger. He waltzed through the cluster of youths before their steel had cleared leather, the two mercenaries barking at the kids to "Get him, get him!"
Easier said than done, a single blade managing to swat his back only to bounce off the chainmail vest. Fast as he'd launched his retreat, Maroto braced himself and heaved forward again, the side-armed arc of his ax a grey blur. It nicked the side of a stubbly, sunburned bandit on its way to its true target. As the full measure of the weapon sheared into the hip of Gilleland's hard man, the first kid struck by the weapon collapsed against his fellows, guts falling out of the modest rend in his shirt. Maroto kept his ax _sharp_.
Eight against had turned to five, and Maroto was really only counting one of those. Yet he no longer had surprise on his side, and a volley of gunfire from the halted caravan implied that the four other traitorous guards were executing the fops with due haste and might ride to the front at any moment. Gilleland's sole remaining mercenary had the sense to follow Maroto's example and insulate herself behind the four upright bandits, none of whom seemed eager to be the first to charge the barbarian now that he had darted back out of striking distance. There came the breathy pause Maroto had wanted back when he'd hewed Gilleland in twain, a moment to appreciate what he'd done—lazy as he'd been these last few years, he hadn't lost his touch!
From the corner of his eye, he saw several riders break toward them from the caravan. Better sort this lot fast, before—
Thwack. He reeled to the side, wondering how in the hells one of these runts had blindsided him, the pain in the side of his head rapidly rising from bad to White-Hot-Fucking-Agony. The arrow was still vibrating from its impact with his skull, sending dizzying waves of awfulness into the numb flesh of his ringing ear. Greenies and hard woman alike rushed him then.
Beard Bandit led with a saber clearly modeled after his father's, and Maroto went to the place he always did in a tough fight, the place from which there was no coming back, not until the last foe had fallen. His vision cleared, his heart slowed, his mind focused, even the church bell clanging in his ear fading away to a distant chime. He had made a promise to these scrubs, and he might not be able to keep an oath to himself, but he always kept those he made to his enemies.
Captain Gilleland's son came apart in a cloud of blood. Maroto's ax kept going, into a greenie behind Beard Bandit, lodging in the poor wench's rib cage. The hard woman almost nailed him but he yanked the ax free of the dying bandit girl in time to parry her slash. The noise of the world fell away into silence, save the riot his partners made for him—a grunt, a gasp, a boot heel grinding in the dust. Even deaf in one ear, Maroto heard them all so clearly he could have closed his eyes and cut them down by sound alone.
Probably. He had no intention of testing that theory at present.
Maroto danced with the bandits, with his ax, with the blades darting at him from all directions.
Chop. There went a hand, split down the middle, all the way up the wrist.
Step. There went a cutlass, skidding off his mailed chest.
Chop. There went a whole arm.
Step. There went a sunburned punk, blundering between Maroto and the hard woman.
Chop. There went the top half of a head.
Step. There went a rich spume, Maroto bringing a red rain to this parched earth.
Chop. There went Maroto, spinning away on the ground before the mercenary could hit him again with her sword. The slash across his knuckles shouldn't have been enough to make him drop the ax, but there it was, lying on the ground amid the splayed legs of felled fools. He rolled farther away from it. He'd put enough space between himself and his attacker to leap back up, but as he finished the roll the arrow in his ear dragged across the rough earth. The sensation utterly poleaxed him. It felt like wizard's lightning, his body shutting down completely, his mind as rattled as his flesh. He lay shuddering in the sand just long enough for the hard woman to tower over him, a long sword diving down to spit him...
First lightning out of nowhere, and now a thunderclap came just before its storm cloud, the whole order of the world running backward. The hard woman collapsed atop Maroto even as the fume of peppery gunsmoke enveloped them both. They sprawled like lovers, the contents of the mercenary's fissured skull running down into Maroto's stunned face. The cloud quickly rose, but Maroto was unable to extricate himself from the dead woman's weight. Either the arrow in his head had struck deeper than he'd thought or that first cut he'd taken to the leg was bleeding him out. Either way...
"Ho, Your Majesty, should I give you and your new friend some privacy?" Purna's voice came from far, far away, but then she leaned over him, a flintlock pistol in one hand and a kakuri in the other. Smoke rose from the muzzle of the richly filigreed gun and blood ran down the bow-shaped curve of the long knife, beading off its tip. She had clearly taken the time to apply several black and orange stripes of makeup beneath her eyes before rallying the rest of the fops to the greater cause. She wiped the blood from her blade on her victim's back, then sheathed her weapons in the black leather holsters on her studded white belt. "You two make a cute couple."
"Hey," said Maroto, his own voice seeming to drift down from somewhere high above him. "Get me up."
"Sure, I— _ugh_ , is that _in_ you?" Purna snatched back the hand she'd proffered him and pointed to her own ear. "Are you dying? Is it in your _brain_?"
"Get me up and I'll tell you," said Maroto, his voice even farther away now. He needed to get this done quick, before he blacked out. "Slow about it, now."
Purna obliged, rolling the dead mercenary off him with her foot and helping him up. As soon as she tried he slapped her away, collapsing back into the sand and trying not to puke. Standing hadn't been such a good idea after all. Woof.
Her voice sounded even more remote as she prattled on. "The rear guard were in on it, you know? They thought they were slick, telling us to hurry out of the wagons without even dressing. A fine thing I'd already roused everyone and told them to ready their weapons before I went looking for the guards, or who knows what would have happened! They didn't like us coming out with guns primed, and said as much, which was when I took a look with Diggelby's hawkglass, just in time to see you swing on Gilleland. I gave the order, and we shot them down."
Purna took another deep breath before concluding her account. Maroto reckoned she could probably hold her breath for minutes underwater.
"So we took their camels and rode up to help you, and Diggelby, Din, and Hassan went after the two who got away—they were hiding in that decoy wagon with crossbows, but we flushed them out. Hardly any casualties... other than you."
"Wonderful," groaned Maroto. Even lying flat in the dirt he felt like he was balancing on the prow of a dinghy in a hurricane, relying on chance to keep him from falling overboard. "You make an all right sidekick, kid."
"Sidekick?" Purna raised her penciled-on double brows at him. "Have you ever even _listened_ to a song, Maroto? I'm the brash young hero, and you're the tired old master I have to persuade to teach me."
"Sounds awful," he said, suddenly wondering if he was going to die. Looking down the length of his numb body, he saw that his entire left leg was soaked red. "That mean you'll do what I tell you?"
"Until you die, sure," said Purna, her faint voice causing the invisible sea beneath Maroto's back to roil even fiercer. "You'll probably have to sacrifice yourself to save me before the end."
"Don't count on it," he said, the hot air tasting of blood and harsher metals.
"Well, we'll see if you last the day—you may have already gotten the jump on that part of the song."
_There_ was a devil-blessed thought. The possibility did little to improve his outlook. "You want to be my protégée?"
"More than anything." Purna clasped one of his massive hands in both of hers. "When the time comes, I swear I'll avenge you, Maroto."
"Great," he said. "In the meantime, be a good girl and help me chop up these bodies."
"Excuse me?" Purna dropped his hand. It landed on his chest with the weight of a maul.
"In half. Every one." A nap seemed like a capital idea all of a sudden. Why didn't he take more naps? Devils knew he deserved them.
"Are you sure you don't need Köz's valet to tend you?" said Purna skeptically, and before Maroto could point out that he'd never said anything about not needing a sawbones, the darkness that forever lurks behind the eyes of mortals rushed up to give him a hug. _I missed you, too_ , he thought as he blacked out in the sand, an arrow in his ear and a bloody-toothed grin straining his mouth. He still had it.
# [CHAPTER
19](toc.xhtml#toc-chapter019)
The queues to the public booths were a constant of Diadem. Hundreds upon hundreds of citizens lined up each morning, the succession of sinners stretching out the wall of doors of the Lower Chainhouse and down the wending stairs to the streets far below. After a feast or festival, the lines numbered in the tens of thousands, the citizenry waiting all day and all night to have five minutes alone in the confession box.
The members of the clergy and the noblesse had their own booths in the Middle Chainhouse, and the wait there was rarely more than an hour. When Sister Portolés reached the front of the line and a confessional opened up, she did not wait the customary cooling time before entering. The old priest leaving the box before her had barely removed his thin, guttering candle from beneath the bench when Sister Portolés inserted her wider tallow into the alcove and entered the cramped booth. Settling onto the narrow bench, she found the iron bands of the seat still warm from the previous candle.
"Mother forgive me, for I am unclean."
Portolés never enunciated so well as when she was in the confessional. In all the corners of the Star, in all the chambers of the church, there was nowhere she felt more at home... save at her penitence bench immediately after a confession. Anticipating her sentence, she had exchanged the undergarments that usually protected her from the rough wool robes for a hair shirt and collar, tightly cinched garters of jagged glass rosaries around her legs. Each of the four thousand steps from her cell to the confessional hall had been a private hell of rasping friction, the hair of her vest turning to steel wool with the first drop of sweat, and despite the armor of calluses her chafed nipples and scarred thighs were bleeding by the time she arrived at the queue.
"How long has it been since last you cleansed yourself?" The grate separating penitent from confessor bubbled out in an iron reproduction of a face. Portolés had heard the grate was designed so that the innocent should see the benevolent visage of the Fallen Mother, Savior of Humanity, but that the guilty would instead behold the inhuman face of her brother-husband, Creator of the World, Deceiver of Angels and Mortals alike. Portolés only ever saw the one, but then she had never come to the box free of sin.
"Nearly four and twenty hours," she said, marveling at just how much the world had changed in such a short span.
"How much sin could one of the Fallen Mother's chosen accumulate in so few hours?" asked the confessor, and Portolés squirmed on the rapidly heating seat. Before Kypck, this had been the pinnacle of her desire, to come here and confess her wickedness so that she might be free of her deviltry, if only in the moments when the bench singed stripes into her robes and the flesh beneath, and after, when the scourge's chains licked her back and breasts, when the crown of barbs kissed her brow. Now her eagerness for atonement warred against the orders Queen Indsorith had given her, and despite the queen's confidence in her charge, she struggled with how to proceed.
"I defiled my temple," she began, reasoning that if she started at the beginning of the previous day she might better chart a safe path to the end. "Again."
A heavy sigh from the grate, which led Portolés to believe it was Mother Kylesa on the other side. "How many times have you committed this deed, sister, and how many times have you atoned for it?"
"I... I am not sure. Many times, Fallen Mother forgive me."
"She forgives those who regret their actions, and who struggle to improve their behavior." Even filtered through the molded grate, the confessor's voice carried a caustic tone. "It is a grave enough business when a lowly peasant chooses to sin and sin again, thinking so long as she confesses after she can do as she wishes. For a sister to behave so repulsively is another matter entirely."
"It's true," said Portolés, shifting from side to side on the bench despite herself. The scalding lines radiating from the seat made sitting still impossible, much as she deserved the pain. "I keep sinning despite your efforts and mine. I can overcome temptation, I can, and I do, more often than not... but sometimes I am weak, and I think it is not such an evil thing I do, so long as after I come here with an honest heart."
"What you are doing is the greatest sin of all." The Deceiver's face seemed to breathe in the heat of the box, sweat stinging Portolés's eyes. The light from the candle under her seat cast writhing shadows on the walls, as if she were already engulfed in flames. "You do not sin of ignorance, or even passion. You do not fall victim to temptation. You make a choice, sister, a choice to commit foul acts abhorrent to your Savior. You do this in spite of the example you are supposed to set for your peers and the laity, in spite of our many conversations on the matter. Yes, perhaps 'spite' is indeed the only applicable term, for why else would you continue to do this to those who love you?"
"Spite?" Of her many weaknesses, Portolés had never believed that to be one of them. She knew she had rebellious impulses, but truly believed in the goodness of the Fallen Mother with all her heart. "Mother, I swear I do not commit these acts out of ill will."
"No? And whom do you hurt with your actions? It is not only yourself, is it? You seduce your fellow anathemas, and then you come here, sin after sin, forcing we sisters who are far above such wickedness to sit audience to your crimes. I wonder, is it the sin itself or the act of rubbing my nose in it after that gives you more pleasure?"
"I'm sorry," whispered Portolés, bracing her arms on the warming walls of the narrow box and pressing herself down on the bench. The much-needed pain brought clarity, as it always did. The confessor was absolutely correct, yet try as she did to feel remorse, all Portolés felt was an eagerness for further penance. "I do try, Mother, I do, but you're right. I am base, ruined, wicked. It's what I am."
"Excuses," hissed the Deceiver, his mesh face leaning inward to Portolés, as though he meant to whisper in her ear, or steal a kiss. "It's easy, isn't it, to blame your nature? To lay all the fault on whatever ancestor of yours lay with a devil? To abuse yourself and others to sate your criminal appetites, and then shrug your shoulders and say it's a defect of birth? To blame the Fallen Mother for your own weakness?"
"Yes!" whimpered Portolés, her upper half warring with her lower to keep her buttocks pressed to the bench. She could smell the steam rising from the sweaty wool of her habit, taste the curl of smoke on her scarred tongue, and pushed herself down harder, knowing none of this yet was the worst. That would come when she had to rise from the seat. "Yes, yes, yes!"
"Of course." The Deceiver's breath stank of her musky sweat when she lay beside Brother Wan, defiling herself. "You are not so different from the pureborn, Sister Portolés, much as you deny it in your heart, much as they deny it with their tongues. Everyone wants an excuse for their bad decisions, for their selfish desires. Everyone wants to pretend they can't help themselves. Everyone wants to put the blame on the Deceiver for creating them with evil already festering in their souls instead of thanking the Mother for giving them both the awareness to know their own sins and the strength to fight them."
Too ecstatic to speak, Portolés nodded and wept. It was all true. She caught her left hand reaching down to pull up her habit and shoved the fist into her mouth, biting the knuckle until she tasted her own salty blood. Still she throbbed, and clenched her thighs together to grind the rosaries in deeper, pulling the scalded flesh free of the bench as she did. This brought on a dizzying rush far more perfect than anything she could effect with her fingers—the touch of the divine upon her wretched frame.
Before, when Portolés was at her most vulnerable, her confessor had insisted the witchborn's thirst for sin came from the Deceiver. That she sinned for base pleasure, to blaspheme. Her confessor was wrong. Here, when the candle of Portolés's faith burned away all distractions, she knew the true motive for her own compulsive sinning: she was seeking her Savior. For a good and pious anathema like Brother Wan, faith must come effortlessly, but Portolés never felt the presence of the Fallen Mother during prayers or mass or carrying out her holy duties. She had to hunt for her god, and in a lifetime of obedience to the Burnished Chain, the only times she found her were when she dared to transgress the holy laws, when she risked her very soul to capture the attention of its keeper. It was the touch of the Fallen Mother that gave Portolés the courage to sin, and it was her touch that released Portolés from the agonies of confession. If Portolés's sins were acts of rebellion, as the superiors insisted, they were rebellions against the Chain, not its maker; for all Portolés's doubts in herself and her monstrous ilk and even her church, with all its contradictions and cruelties, the one thing she never doubted was her elusive Savior.
Fast as it came upon her, Portolés slumped back on the bench, empty again, confused and scared as she always was after surviving another confession. She shivered, and realized the seat beneath her had cooled, and the booth had gone dim. Her candle must have burned lower than it ever had before. Wiping sweat from her face, she nervously met the mute gaze of the Deceiver—had she cried out?
"You shall wear the Mother's Crown, which her jealous husbrother forced upon her brow before casting her out of heaven," the confessor recited in her clear voice, what had appeared to be the Deceiver again but an artfully wrought grate. "And you shall lash thyself with the Scourge of Angels, as she was lashed by those anathemas loyal to he who made the world with his word, instead of she who questioned it with hers. Two score and six lashes, and the Crown until you are next called from the Dens by a superior. Perhaps you may provide an example yet."
Forty-six lashes. Portolés could not even offer the customary thanks, her scarred tongue glued behind her file-corrected teeth. _Forty-six_. She had never heard such a sentence. The most she had ever received at one time was a score, and that instance had nearly killed her. Brother Wan had tended her throughout her long recuperation. No pureborn could undergo such an ordeal and live, and Portolés doubted one of her kind could, either.
"Now, before you undergo your penance, we do need to discuss another matter. Lenience may be retroactively applied to your sentence, and indeed, those given for future infractions. All you must do is offer up the truth of what transpired last night, omitting nothing of what was said or done."
What was this, now? No wonder Mother Kylesa hadn't even asked if Portolés had more to confess before handing down the sentence—it was always going to be a fatal penance. The queen had warned Portolés that her superiors would likely pump her for information following their private meeting of the night before, but Portolés had believed they would simply ask her. This sort of low trick she had never expected, and it hardened her heart. Had Mother Kylesa plainly put the question to her before, as she was undergoing her righteous agonies, she might have ignored the orders of her queen and freely told all there was to tell. She would have betrayed the first person who had ever placed absolute trust in her, even knowing as she must that if she repeated the queen's secret to a confessor the sovereign could lose her very throne.
But now, being threatened instead of asked, Portolés found herself all too eager to accept Queen Indsorith's standing offer of absolution. The Crimson Queen of Samoth had powers of spiritual dispensation equal to the Black Pope—it was one of the Chain's major concessions to the Empire during the Council of Diadem, the parley that had ended the civil war. Portolés had never before found herself in such a precarious position, forced to make a decision that would not only affect the rest of her life but doubtless the fate of her eternal soul. This was a test of the Fallen Mother, a test every bit as dire as any found in the Chain Canticles, and until this moment Portolés herself had not known which path she would take... To refuse a confessor of the Burnished Chain was so grievous a sin that Portolés had never even fantasized of it, but now she found that like all her transgressions, it came as naturally as breathing.
"Why, Mother, to what incident might you be referring?" she said. "I cannot believe you would press me to reveal anything our queen might have spoken to me in private. Surely to betray the confidence of our sovereign is tantamount to treason."
"A crime against the state, even one punishable by death, is nothing when weighed against a crime against the church. Presuming your mortal frame can bear the weight of your mandated penance, sister, I shudder on your behalf to think of what further tolls you must incur if you blatantly go against the will of your Savior."
"Of course," said Portolés. "I understand your meaning, Mother."
"It relieves me to hear this," said the confessor. "I am ready to hear you testify as to what was discussed."
"Then you'll be waiting some time," said Portolés, ashamed of the pleasure it gave her to speak the words. It almost felt better than lifting her scalded bottom off the bench as she pressed her forehead to that of the Deceiver, a little skin coming off her buttocks like damp flesh adhered to frozen metal as she hissed into the grate, "I have a decree from our sovereign absolving me of all existing sins, and any new ones I might accrue in the service of carrying out her orders. If you wish to know what the queen and I spoke of, I suggest you ask her yourself, or wait until I am finished and return here of my own volition."
The confessor was silent, but just as Portolés put her trembling hand on the handle of the booth the woman spoke. "We count pride as a virtue, for 'twas pride that gave our beloved Allmother the strength to turn from her husbrother when he cruelly forsook her. It was pride that gave her the courage to turn her prison into paradise, to take what he crafted as a hell and transform it into heaven. It was pride that gave us this world, and the promise of salvation after. Yet like all virtues, pride can be dangerous, little sister, if it is allowed to swell beyond all dignity—you did not come here to confess, you came here to gloat, and you ought to be frightened by such compulsions. What sweeter fruit for the Deceiver than one of his children laughing in the face of those who seek to save her? What greater prize than a headstrong fool whose vulnerability is the very strength granted her by the Fallen Mother?"
"I shall pray for both of us, Mother," said Portolés, turning the knob. "For now, though, I have another appointment, and after that I fear I'll be beyond Diadem's reach."
"Oh child," said the confessor, whom Portolés was no longer sure was Mother Kylesa. "No matter how far you run on hooves, paws, or feet, you shall _never_ be beyond our province. Safe roads guide you to her breast."
"Safe havens keep you at your rest," said Portolés, completing the Prayer of Exodus and hurrying out of the confessional before her accursed tongue could betray her further. The queen had expressly mentioned the importance of keeping secret her imminent departure, and what had Portolés done the first chance she got? Pathetic.
The confessor's words haunted her as she returned to her cell and changed into an unburned habit, the old one going into the Dens' sackcloth collection, where it would become a patchwork robe for a novice or orphan. It had seemed laughable at first, the idea that such a wretch as she should be prideful, yet the more she meditated upon it, the more sense the accusation made. Of course in the toxic tabernacle of her malformed body a natural virtue would be corrupted, strength becoming poison. If she truly believed her queen had the power to absolve her, why go to the confessional in the first place? And if she doubted the authority of her queen, how dare she spurn the orders of her confessor? Did she really think she could get away with turning to whichever power patted her head at the moment? Did she actually believe the Allmother would forgive her for using what ought to be atonement as a source of vile pleasure? Portolés shuddered as she rubbed twice-blessed salve into her burns, kneaded the ointment in harder to remind herself of the purpose of penance. The truth was, she never felt so close to the divine as when she was forcibly reminded of her mortality. Of her own baseness.
"Knock knock," said Brother Wan, opening her lockless door to find her kneeling on the penitent bench, habit hiked up around her waist. "Can I assist you with that, sister?"
"Would that the Fallen Mother granted us the time, brother," said Portolés, wiping the excess salve on her hip and letting the habit fall as she rose to her feet.
"How many? Five for me." Brother Wan shuddered, having a more typical view toward penance. "I thought we could supervise each other, and fetch help if one of us atoned too fervently. When I found you last time I thought you were... I thought you had been called home."
Blunted teeth dug into Portolés's lips as she imagined herself kneeling on the bench, habit unlaced and pulled down around her waist, the scourge held in both hands to keep from dropping it in fear. Brother Wan standing over her, watching. The thought made the burns on her arse throb, and other places beside. Forty-six lashes would certainly deliver her home, and spare her from navigating the impenetrable waters where she found herself floundering. She would die performing penance, and she would take the queen's secrets with her to the hereafter—neither Crown nor Chain could fault her for divided loyalties if she made such a sacrifice. Why not put an end to all this endless stalling before damnation? Or perhaps with such an offering she might find her way to salvation yet...
Verily, if the queen had not asked for Sister Portolés's help, she would have beaten herself to death right there. Yet Queen Indsorith, Heart of the Star, Jewel of Diadem, had requested that Portolés take on this mission, and carry it out by any means necessary. She had not ordered Portolés to action, not demanded her obedience—she had asked, and that made all the difference. The forty-six lashes would be waiting whenever Portolés returned. If she returned.
"It's like you're already gone," said Brother Wan, wiping his sleeve over his mouth to catch the saliva dripping from the permanent snarl of his exposed gums. Portolés's heart ached at the thought of leaving Brother Wan again, when he had only just begun visiting her again, but then it rehardened. If he really could see into her soul, with all the secrets it carried, he might put his own life in danger if he stumbled over—
"Get out," she said. She would risk herself, her salvation, but she could not risk her innocent brother, and so she pointed to the door. "Now, Wan. You won't see me again until it's done."
"I'm not spying, Portolés, I'm just worried," protested Wan, reaching one of his gaunt hands out to her. The edges of his fingers were ridged from where the webbing had been cut. "You never let anyone help. Let me try—"
Portolés seized the collar of Wan's robe and pulled him in, her devilish tongue slithering past the defenses of his wooden teeth, and she filled her thoughts with memories of their trysts. He returned the kiss, and then she broke away, gently shoved him out the door. "I've stained you enough, brother. Safe roads guide you to her breast."
"Safe havens keep you at your rest," said Brother Wan, bowing to her and then scurrying away down the hall. Portolés could still call out, tell him to come back—after all, the queen had given her writ to conscript anyone she could trust to her mission. Brother Wan had never left Diadem, and since he was apparently indispensable to the upper echelons of Chain bureaucracy, it seemed unlikely he ever would if she didn't take him with her now. _By any means necessary_...
Together on the road, away from the ever-watchful eyes of the Dens, would it not be a worthy test for the both of them? And with the queen absolving all sins they might accrue, succumbing to temptation would never be safer. To fully know his flesh after all these years of teasing, fleeting contact, and for him to know hers... Yet the queen had said only those Portolés trusted absolutely should be taken into her company, and can any truly trust a lover who looks into your mind?
In the end, Portolés told herself she left Brother Wan behind to save his soul from her malign influence. The monk looked back down the rough obsidian corridor and offered a sad wave before rounding the bend. Again, she was alone. Never had she been more so.
# [CHAPTER
20](toc.xhtml#toc-chapter020)
In her day Zosia had sailed every sea of the Star, and had always loved the Golden Cauldron best. Departing from Hwabun aboard Kang-ho's ship the _Crane's Bill_ and sailing down along the Isles was a new experience for her, though; the sloops and galleys she had crewed had always set out west of Linkensterne at Darnielle Bay and immediately headed south to the Raniputri Dominions in order to avoid the Immaculate customs ships, who were essentially state-sanctioned pirates. Well, once or twice she had worked ships that crossed over from the Bitter Gulf and snuck through the narrow expanse of open water between Hwabun and the so-called Haunted Sea, where storms forever crashed above the Sunken Kingdom, but they had always raced far to the west before veering south into the Cauldron proper. That passage was not so scenic as this one, and a devil's load more tense. Call her superstitious, but something about the wall of lightning-torn fog that marked the watery grave of an entire civilization unsettled Zosia a bit; not even the Lost Waters or the Sea of Devils gave her the same goose bumps.
As they skirted the Isles and left both Hwabun and the Haunted Sea far behind, she finally let herself relax and enjoy being back at work on a boat—it was a long voyage down to Zygnema, where she would begin her search for the missing Princess Ji-hyeon. That fabled Dominion housed the Souwest Gate, and so it seemed the most sensible starting point; the next closest Gates were the one in Diadem, which she had no intention of visiting until she had an army at her back, and the one in the Noreast Arm, which Maroto had always said was overrun by crazed cultists, so it didn't seem likely Fennec would take the girl there. If Zygnema was a dead end they had Jun-hwan and Kang-ho's permission to sail the boat across to the Southern Gate in Usba, and if they hadn't gone through there, well, that left Emeritus... but Zosia could not believe Fennec would risk using that Gate, not after what had happened the last time they had been there.
It was actually liberating to be stuck on a boat, passing her days in honest labor and feeling her strength return with each climb up the crow's nest. It might've been different if they'd been dodging the Bal Amon reefs, but not a whole lot could go wrong on the Golden Cauldron. Except a sea monster. Those could be anywhere, though they usually preferred colder waters. Or a mutiny, for that matter, but it didn't do to dwell on worst-case scenarios—there'd be plenty of time to worry if such bad luck actually came to pass.
Which it did.
The pair of beasts that menaced the _Crane's Bill_ came the night of the new moon, so there was no telling what they looked like. Wide, sticky snailtrails crisscrossed the deck where the monsters had evidently boarded and prowled the ship before someone had sounded the alarm. They dropped back into the sea as Zosia and the rest burst abovedecks to repel them, their scales flashing blacker than the waves in the starlight as they glided away across the surface of the waves. Nobody cared to speculate if the wild laughter that accompanied their departure originated from the creatures or the three members of the night watch they had carried off with them.
Well, these things happened at sea, so Zosia didn't become properly annoyed until a storm blew them off course a week later, and then half the bloody crew mutinied. It happened in the dead of night, as these things usually did, while Zosia, Bang, and Keun-ju were on night watch. The chaos erupted belowdecks and boiled over in moments, interrupting Bang's caterwauled sea shanty and forcing the trio to fight for their lives by the light of a half-moon. Even if Zosia had been sober it would've been a desperate fight, but she and Bang had been sharing her last bottle of canefire when the fighting broke out, and she nearly dropped her hammer a time or two before the killing was over. Choplicker must have been dozing in her hammock throughout, for a pair of mutineers barded Zosia into the prow and came desperately close to splitting her open, before Bang speared one through the back while Zobia clobbered the other overboard. It was hard to tell who looked more surprised, the sailor Bang had ambushed or Zosia herself, as she looked down the deck and saw Keun-ju holding his own against three.
The Virtue Guard had some serious moves, and even more serious steel to complement them—what Zosia had assumed was a humble tiger sword in his unadorned sheath revealed itself to be a three-tiger instead, the complex characters embossed in its dark blade glowing in the moonlight. Exchanging an impressed glance, Zosia and Bang raced—or rather, staggered—to his aid, and together they turned the tide of the mutiny. Alas, it was too late for Captain En-rang, who had been murdered in his bed before the fighting even started, and both of his mates, who had gone overboard in the melee.
Well, these things happened at sea. Enough crew remained to still see them safely to Zygnema, and Bang was promptly elected interim captain, so she had something to grin about all the way down the Cauldron. It made Zosia feel damn good, seeing the bossy kid earn herself the regard of an experienced crew so fast—reminded Zosia a bit of herself when she'd been that age. Given all the smoke the girl had blown back in Linkensterne and the Isles, Zosia had figured she'd been overselling herself, but coin where earned, Bang knew her way around a boat. And as far as skippers went, she was certainly a lot more pleasant than the recently departed Captain En-rang, tripling the canefire rations and sometimes leading the small crew on sing-alongs when the day's work was done. Celebrations were had when they sighted the northern Raniputri coast, again when they successfully rounded the Horn of the Rhino, and then a final late night was enjoyed when they neared Zygnema, on the southern side of the Souwest Arm.
Having bonded through all of this, Zosia, Bang, and even Keun-ju were all a touch closer than strangers as they approached the city-state where Fennec might have escaped with Princess Ji-hyeon and her traitorous Martial Guard, Choi. Four of the stoutest sailors rowed a dinghy to the Zygnema piers, the _Crane's Bill_ waiting out in the bay. Choplicker lay under a rowbench, Zosia, Bang, and Keun-ju sat piled into the prow.
Zosia felt unexpectedly glum to be leaving the ship; she'd be back aboard it soon enough, if she couldn't find any clues here, but that she half hoped the Raniputri Dominions would be a dead end so she could spend more days and nights taking the vessel over to the next Gate at Usba probably said quite a bit about her mind-set. She should be champing at the bit to get back to tracking down her old Villains and plotting her vengeance after so long at sea, but instead she was sorry that her nights of drinking and flirting with Bang might be coming to an end—times like this, she had to admit she was a pretty rotten person. That she knew Leib would have wanted her to seek such happiness and diversion only made her feel sick.
Taking a deep breath of salty harbor air, she tried to get her head right. She had to find the princess, and here in Zygnema the key might be right under her nose... She blinked as the morning light caught the pommel of Keun-ju's sword. This close up, the hiltwork looked even nicer. If Zosia remembered her Immaculate Zodiac, three-tiger swords could only be forged on three days out of every thirteen-year cycle, on the third day of the third month of Tiger, Samjok-o, and Pulgasiri years. Regardless of the finer points of Immaculate weaponsmithing, this glorified servant wore princely steel, and wielded it with far more skill than most of the idle rich who could afford such a thing. Either Kang-ho and his husband took remarkable care of their servants, or somebody else did. Interesting.
"Lookie here," said one of the rowers, nodding over the side of the boat.
"You weren't kidding," Zosia said as their shallow vessel glided over an enormously thick chain stretched just beneath the gentle waves. "That would butcher any boat much bigger than this. I thought peace reigned throughout the Star."
"Throughout the Empire, maybe," said Bang, scratching under the kerchief she wore around her head. "But definitely not throughout the Souwest Arm. Zygnema's been at open war with two of her neighboring Dominions for the last year, so if you want in to trade you have to be willing to wait."
"Took two days, last time we were down," supplied one of the tarshirts at the oars. "Customs met us at the docks, we had to bribe 'em there. Then we had to follow 'em to their office, bribe some other ones. Then we had to bribe 'em to get the dinghy out o' the harbor impound, where they'd moved it while we were in the customs house. Then we had to take the officials out to inspect the holds and all, and, you guessed it, more bribes. Then we had to take 'em back to shore, another set o' bribes, and after all that? Still got to sit a day and a half before they lowered the chain for us to come in. All to snag a few little fishies. As if we didn't have enough trouble since Linkensterne got Immaculated!"
"Fish, huh?" Zosia glanced back at the _Crane's Bill_. That name must look good in a marina manifest next to the demarcation "fishing boat," but anyone who saw her knew she was built for two things: to be fast in a fight, and to be fast in a flight, if the fight didn't go well.
"Square mackerel," said Bang, tapping the side of her nose.
"So it's a sin to eat fish in the Raniputri Dominions, but not to sell them to foreigners?" said Keun-ju with the snotty superiority of one who had never left his homeland. "Hypocrites."
The two nearest rowers chuckled, which the Virtue Guard clearly mistook for validation. Zosia decided to set him straight rather than letting him be a punch line.
"Square mackerel is a rare breed of fish, Keun-ju, the kind you only see in the water when a customs boat is gaining on a ship that doesn't wish to be caught. Must be a dangerous catch these days, with Linkensterne regulated by Immaculate oversight."
"How's that?" Keun-ju looked at Zosia like _she_ was the thick one, and the rowers laughed again.
"Whatever Kang-ho's importing from here in Zygnema—and knowing him it could be anything—it's not the sort of thing he's keen to have assessed by an officer of the law, either here or at home," said Zosia, and when Keun-ju still didn't get it Bang snorted and slapped him on the back.
"Mistress Clell's being overly polite," she said. "Smuggling, man, smuggling."
"Absurd!" said Keun-ju with that unmistakable air of misplaced certainty in his world. "King Jun-hwan would never allow his husband to engage in such behavior."
"Don't be so naïve," said Bang, throwing an arm conspiratorially around his shoulders. "We're all bloody-handed buccaneers now, aren't we? I saw the way you cut down those scurvy seadogs, and a lonely raider always has need for a fit lad or three—what do you say about joining Bad Bang's crew?"
More laughter from Zosia and the rowers as Keun-ju tried to squirm away from Bang in the cramped prow. If she could con her way into being discharged from the Immaculate army, the girl could definitely be a real captain someday, and a good one at that. She was warm to most everyone, but that warmth belied a need to break the gaze of any who dared to try and stare her down... exactly the sort of thing that could turn a young and talented hard-ass into a young and talented corpse. Well, if Zosia had survived her turbulent twenties, maybe Bang could, too.
"Ah, here we are," said Bang as they bobbed up to the end of the mile-long dock, one of dozens reaching out into the harbor of Zygnema like the arms of a devilfish stretching for deeper water. "Quick quick quick, those are customs agents coming up the quay, and I want our friends here rowing back to the _Crane's Bill_ before the longfingers arrive to shake us down. I already worked out a signal with the bosun for when we're ready to be picked up."
Zosia was up first, and tied the dinghy's rope around a bollard to keep them in place. Keun-ju nimbly followed, and Bang passed them their bags. Choplicker deigned to let one of the sailors hoist him over the side and deposit him on the deck. The monster licked the man's hand and barked good-naturedly at his new friend. Zosia wondered what atrocities this friendly sailor had committed in his past to earn the approval of Choplicker... or maybe the man had just been sneaking him scraps of saltfish. It could go either way with the devil.
The customs agents were hurrying down the dock but still had some planks to cover. As Bang passed the last pack to Keun-ju, however, the soldier's eyes widened in their direction. "Devils have a laugh, is that who I think it is?"
"Who?" Zosia cupped her hand over her eyes to block out the Raniputri sun as she squinted at the agents. From here the figures could be anyone, and Zosia didn't think their pink saris were anything other than regulation issue... Oars splashed behind her, and she dropped her hand.
What a devildamn amateur move. It took some willpower, but she kept herself from spinning around in a tizzy and making a bigger fool of herself. Keun-ju was still peering at the customs agents, but Zosia turned back to the dinghy, which was, of course, already twice as far from the dock as she could have possibly jumped, even in her prime. The end of the cut rope hung limply from the bollard where she had tied them. Bang saluted from the prow of the dinghy, and at her word the rowers locked their oars, letting the tide slowly carry them out.
"You're smarter than this, Bang," Zosia called. "Stick with me, help me find the missing brat, and you'll be rewarded with a bigger boat than that wreck, and a full crew to boot. You have my word."
"The word of a woman who won't tell me her true name isn't worth much, I'm afraid," Bang replied cheerily. "Pretty silly, considering I figured you out before we even left Linkensterne. Everyone knows about Crafty Kang-ho's exploits, and his old commander! You're nothing like I imagined, I'll confess."
"So you know I can get you anything you want," said Zosia.
"You already have," said Bang, gesturing to the _Crane's Bill_. "I'm a humble woman. Not all of us want to be queens."
"Lieutenant Bang, you swore oaths to serve—" Keun-ju began, but Bang shouted over him.
"Did I forget to tell you guys the whole reason I ended up on wall duty was I got kicked out of the Immaculate navy? They accused me of breaking oaths, sowing dissent, and some worse crimes, but couldn't prove any of it. Probably should have mentioned that before you trusted me with your boat."
"The seas aren't wide enough to hide you once word of this betrayal comes to Hwabun," Zosia called, knowing it was fruitless but needing to shake the branch anyway. "How angry do you think Jun-hwan and Kang-ho will be when they find out you stole their ship and convinced their crew to mutiny?"
"About as mad as you'll be when you find out I stole your pipe," said Bang, taking Zosia's cutty out of her pocket and popping it in the corner of her mouth.
Zosia almost dove in the water then and there, but checked herself. "You really shouldn't have done that, Bang. Stealing the boat's one thing, I can respect that. You're young and stupid, so I'll cut you some slack. But you take that briar and I'll hunt you to the ends of the Star. You know who I am, that means you know what I've done, what I can do!"
"Tell you what, Cobalt Queen," said Bang, taking the pipe out of her mouth and pointing it at Zosia. "You catch me, I'll give you a kiss wherever you want, and your pipe back besides!"
"When I catch you, Bang, I'm going to mess you all up!" Zosia shouted to be heard, the dinghy drifting farther away. "Pirates always look better with an eye patch, so I'll give you a matching set! Hooks and peglegs, too!"
"And here I thought you wanted to give me a different sort of pegging!"
"I'll be seeing you, Bang, count on that! Gonna keelhaul your ass!"
"Then till we meet again upon the waves, fair Zosia!" called Bang, doffing an imaginary hat at Zosia as the rowers unlocked their oars. The sandaled feet of the customs agents were shaking the boardwalk as they approached.
"Or beneath them," Zosia growled, turning away from the dinghy to face the authorities. First these functionaries would be dealt with, then Princess Ji-hyeon would be tracked down, then Kang-ho would help her war against the Empire... and then Zosia would get her pipe back. First things first, though.
"Zosia?" The Virtue Guard sounded startled, and then impressed. "Cold Zosia, the Stricken Queen?"
"I am Moor Clell, a pipe-carver, come to trade my wares!" Zosia loudly announced in Immaculate to the arriving customs agents. Each Dominion had a dozen different local languages, few of which were shared with their neighbors, so most Raniputri were multilingual, and Immaculate was nigh universally used along the coasts of the Star. With a warning glare at the Virtue Guard, she said, "Moor Clell is my name, and my apprentice here is Keun-ju. Right, Keun-ju?"
"Right," said Keun-ju enthusiastically. "Definitely her apprentice."
"Then you are both under arrest," said the lead officer, stepping back and drawing a gauntlet-sword in each hand. The five other pink officers followed suit, and Keun-ju's three-tiger blade cut the air beside Zosia. Things had certainly changed, that she was the only one keeping her cool in a bad situation like this. Well, her and Choplicker—he rolled over on his back to invite a belly rub from the hostile new arrivals. "Moor Clell, tell your apprentice to sheath his weapon at once. You're both in enough trouble already."
"What's the charge?" asked Zosia, knowing they could probably take these officers, but also knowing they were on the wrong end of the territory to start chopping up government agents. It was one thing to kill a customs officer when you could just run across the border, but quite another when you had open sea behind you and an entire Dominion to cross. "And yeah, put that away, Keun-ju. You're not helping."
After giving her a doubtful look, Keun-ju did as he was told, and the customs agents visibly relaxed. They didn't sheath their weapons, though, and the leader said. "You are suspected of smuggling, conspiracy, and lying with animals."
" _Lying with animals?_ " said Zosia, kicking Choplicker when he gave an amused snort. "Is this a joke?"
"Do we look like jesters?" asked the jowly leader. "Abuse your dog again and we shall show you what wages a defiler of beasts is paid in Zygnema."
Choplicker barked his support of this plan as Zosia and Keun-ju allowed the customs agents to lead them down the long dock, and Zosia whispered, "Just you wait, fleabag, just you wait."
# [CHAPTER
21](toc.xhtml#toc-chapter021)
An anonymous black-robed priest delivered Baron Domingo Hjortt to the Middle Chainhouse confessionals, and together they waited in the shadow of a gargoyle-wreathed column for the anathema who had murdered his son to leave her booth. Here he was, sixty-five years old, veteran of a half century's worth of dangerous battles and the far deadlier arena of Imperial politics, and he felt as queasy and anxious as the day his mother had delivered him to Azgaroth's military academy in Lemi. He had been a mere boy, but one on the cusp of manhood, and with an impressive military lineage to uphold. Years later, that scene had repeated itself... to a point. _He_ had hidden his fears, as he knew his mother expected, but Efrain had but poorly concealed his nerves as they'd waited outside the dean's office, the stripling shifting his weight from foot to foot as though it would somehow enable him to better carry the burden of destiny that bore down upon his narrow shoulders.
At the time, he'd been annoyed with his son's weakness, but now Domingo found himself imitating that scared little boy who haunted his heart, rocking from heel to heel in hopeless reflex. Catching himself in the act, he had to wonder if he'd always had the habit, if young Efrain had mimicked his father from the very beginning, and he'd just never been able to see it before now...
Black oak creaked as the confessional's door opened, and the bulky anathema oozed out of the narrow box. She seemed weak in the knees as she donned her mask and hurried out of the cavernous chamber. Domingo pictured himself sprinting after her and hacking her right leg out from under her with his cavalry saber. He knew the exact sound it would make, when his steel cut through flesh and shankbone, and smiled as he heard it in his mind. He imagined her screams for mercy echoing through the Middle Chainhouse, imagined her confessing it all, the truth coming out of her in bright spurts to match the crimson of her executioner's dress uniform...
"Baron?" Domingo blinked at the priest beside him, then cast a final glance at the anathema as she vanished out of the hall. He wondered if she had come clean for her crime—if there would be no need for this plot to go any further. For the first time in his life, here, in her house, he almost offered a prayer to the Fallen Mother, but caught himself. Everything happens, regardless of the hopes of mortals—on this, if nothing else, the Burnished Chain and the godless baron agreed absolutely.
The hooded priest handed Domingo a skinny candle and directed him to the booth. As he opened the slot beneath the bench he saw the anathema's far thicker tallow had burned low but still illuminated the compartment. He tossed his own in beside it and, without the slightest sense of regret or worry over blasphemy, blew them both out before closing the slot. Domingo's pain was far sharper than a hot ass, and he had felt it every devil-praised minute of every day since word of his only child's death had come to Cockspar. He felt no need to add to his misery out of lip service to the figment of some mad prophet's imagination, no matter how fashionable the delusion may have grown in recent years.
Before stepping into the confessional, he unbuckled his belt and slid off his saber so that he could actually sit in some remote proximity to comfort in the narrow box. Planting the scabbard between his feet and sitting down, he found the bench still plenty warm from its previous tenant; the confessional reminded him of the saunas of Flintland, with the added flourish of gruesome bas-reliefs etched into the wooden walls. A mesh face peered out at him from the iron grate, somewhere between masculine and feminine, angel and devil, and beyond it a shadow moved. After an awkward silence, Domingo sighed loudly enough for the woman on the other side to hear, but when she still didn't speak, he begrudgingly went through the motions.
"Mother, forgive me, for I am unclean."
"How long has it been since last you cleansed yourself?" asked the confessor, her insistence that they carry on this farce a patch of sandpaper grinding over his already bruised pride.
"Never," he said brusquely, only having known the appropriate opening from the plays his sister-in-law, Lupitera, was always dragging him to at the Iglesia Mendoza, Cockspar's only decent theater. Confessional scenes were an easy way to get information to the audience, according to Lupitera. "I didn't come here to play altar boy, Your Grace, so—"
The Black Pope hissed at him through the grate, and Domingo checked himself. Whatever his feelings on her pagan customs, she was the only one who had reached out to him, the only one who had offered him something other than a red candle to burn at Efrain's tomb. What kind of a military man was he, driving his only allies away with stubbornness?
"Mother, forgive me, for I am unclean," Domingo murmured, starting fresh. "I come here a stranger to your ways, a sinner seeking succor from the balm of the Burnished Chain. Forgive a pilgrim his weakness."
"Overselling it is even more insulting, Baron," said Pope Y'Homa III, but she sounded impish rather than irate. "I sympathize with your weakness, and have from the first. That is why I reached out to you—a good man of little faith is far worthier than a woman of the cloth who betrays her vows."
"On that we are agreed," said Domingo, though not without a twinge of guilt at what he'd done in the name of goodness that very morning, what he was conspiring to do this very moment. It was not only the clergy who could play fast and loose with their vows. "It may interest you to learn that I am once more an active colonel of the Crimson Empire and agent of the queen."
"Did she make much noise about it?" Domingo didn't like how eager for gossip about their queen the pope was, but it certainly hammered home her humanity—Y'Homa didn't speak with the confidence of a vessel of the divine; she sounded like a teenager thirsting for canard. Which was all she was, really, but try telling that to the so-called civilized world who worshipped her as a god herself.
"Questions were put to me, alternates suggested," he said. "But the wise general never leaves the battlefield, and I am a nimble fencer with tongue and saber alike. Besides, what choice did she have but to accept my pledge? The Fifteenth is worth more to the Empire than every regiment from the Serpent's Circle to Diadem, and she wants Azgaroth's soldiers active, not twiddling their thumbs while the appointment process drags out for a new colonel."
It went without saying here as it had in the throne room that Chain-worship had broken out like a bad rash in Azgaroth, and if Queen Indsorith declined Hjortt's offer she might end up with some born-again noble leading the Fifteenth instead of an open heretic. And yet here he was, conspiring with the Black Pope—it was almost funny.
"Had my uncle enticed you into breaking your oaths sooner, the civil war would have ended faster, and to far happier result."
"I've broken no oaths," said Domingo testily. "This morn I swore to protect the Crimson Empire, the same oath I swore fifty years ago, the same oath my son... the same oath my son gave when he took over command of the Fifteenth last summer. The same oath my mother swore before me. In the hundred years we've been a part of the Crimson Empire, no colonel of Azgaroth has betrayed their duty to the Crown."
"Not to the Crown, just to the fool who wears it, eh?" Y'Homa's snide timbre grated almost as much as the truth behind her insult. "As I recall, you bucked the reign of the Stricken Queen more than any pony in the Crimson stable."
"I doubt you recall any such thing, considering you but were a twinkle in some cardinal's eye when Indsorith cast the pretender down. The vows I swore were to King Kaldruut, long before that Cobalt witch ever took up arms against him. And I rebuked her rabble at every pass until she snuck into Diadem and murdered her way into the Crown. But I'm not here to discuss her history; it's her future that interests me. Did you pry anything more out of Portolés? I saw her leaving the booth."
"Not as much as I had hoped, but her silence is just as damning as an outright confession," said Y'Homa. "She is definitely a double agent of Indsorith's, I'm sure of that now. And the anathema let slip that she's being sent out of the city... which can only mean that the queen has ordered her to finish the assignment your son left uncompleted in the mountains—to track down and assassinate Zosia before the rest of the Star discovers that the Stricken Queen is still alive. Indsorith must want her killed quietly in her tent, rather than risk martyring Zosia a second time on some battlefield with countless witnesses."
The hated name sent unwelcome images flashing through Domingo's mind. Bloody memories of bloody times: the rout at Yennek where the Fifteenth had stampeded over a mob of peasants, hooves and spears stained red as the riders' standards; the forest outside Eyvind, where every tree was strung with hanged soldiers captured by the Cobalts; the madness at Nattop that could only be explained by deviltry; and the worse business at Windhand that he had only heard rumors of, but the rumors were bad enough. And now Cold Cobalt had risen from her grave to murder Domingo's only child...
Perhaps it was payback for the difficult time Domingo had given Zosia's peasant army during the Cobalt War, or perhaps it was just a coincidence that Efrain had been the one Indsorith had sent to Kypck. It scarcely mattered. What did, what mattered more than Efrain's murder or Queen Indsorith's shielding that Chainwitch Portolés from justice, what mattered even more than the games the Crimson Queen and the Black Pope were playing with one another, was the simple fact that if Zosia had truly returned, all the Crimson Empire was in danger.
"Have your spies delivered any more news?" Domingo asked.
"My _informants_ tell me they are close to a breakthrough," said the Black Pope. "Queen Indsorith is playing this hand so close to her chest she might lose a card down her cleavage, but she is running out of time. Everyone already knows this rebel army terrorizing the south calls itself the Cobalt Company, and word is spreading that Zosia herself leads them."
"I return to Azgaroth tonight," said Domingo. "I'll have the Fifteenth ready to move before the summer's out, and then we'll run the Cobalt Company to ground and execute every single one of them. The Second Cobalt War will end before it starts."
"I thought you wanted to wait for more evidence before proceeding!"
"Consider me convinced that these rebels need to be stopped," said Domingo, not pleased to have his words parroted back at him by this girl. "I had assumed the queen's reluctance to bring the full might of the Empire down on this new Cobalt Company was a calculated move, that she was conserving our strength to take Linkensterne back from those thieving Immaculates. That explanation makes less and less sense as the Cobalts grow bolder and bolder in their attacks, and still no royal order is given for the northern regiments to free Linkensterne before the Immaculates complete their wall."
"Don't even get me started on the Immaculates," said Y'Homa. "I've received intelligence that some important princess of theirs has supposedly been kidnapped by one of my missionaries. Every isle in the Norwest Arm is frothing mad about it. I have yet to work out if Zosia took the girl to leverage the Immaculates into aiding her rebellion, or if Indsorith is behind it for her own ends."
The third possibility was that Y'Homa had stolen the noble and would use her to bring the Immaculates to her cause when the Burnished Chain made another grab for the Carnelian Crown, but that went without saying. Domingo hardly expected the Black Pope to bring him in on every scheme; no, he was already far more deeply embroiled in her plots than he was comfortable with. The Fifteenth Colonel of the Crimson Empire, conspiring with the Burnished Chain—what would Domingo's mother have said about such a scandal? Nothing appropriate for church, certainly.
"Immaculates business aside, I am glad we are in agreement on your course," said Y'Homa.
"What kind of a father would I be if I didn't consider your information?" said Domingo, flinching as he relived the pain it had brought him to hear that Efrain had been killed by none other than Cobalt Zosia, and that the Crimson Queen whom both father and son had faithfully served had known it all along. That sham interrogation of Sister Portolés in the Crimson Throne Room had only confirmed the truth—nobody else knew who had given Efrain the order to attack Zosia's village, because the order must have come directly from Queen Indsorith herself, and she would risk the entire Empire to preserve the secret that Zosia had never actually died.
"What kind of a _colonel_ would you be?" said Y'Homa, clearly thinking he was every bit as pliable as he pretended to be when forced to attend court. "With the aid of the weapon I offer you, the Fifteenth alone could slaughter the Cobalts before their ranks swell any further. And with the Ninth and Third Regiments already harrying the rebels, I doubt you'll have any trouble at all. What could be better for the continued peace of the Empire than an army of thugs eradicated without mercy, rather than awaiting the machinations of the queen to allow for their fall?"
Remembering all the engagements he had taken part in over the years, Domingo could think of quite a few things better than open combat against well-armed, well-trained rebels led by the cagiest opponent he had ever faced, but he kept them to himself. Whatever her motivation, the Black Pope was right that the Cobalt Company had already quaffed barrels' worth of Imperial blood, and their thirst was unlikely to slacken as they grew in ranks and reputation. Better to kill them all, as fast as possible, for the good of the Empire. For the satisfaction it would bring him, to go deaf from their screams as his Fifteenth took them apart by inches. If all was as it seemed, and the Stricken Queen truly led this new Cobalt Company, there was the chance, however slim, to meet her on the field before the battle. And if that happened, if he had the chance to avenge his son and his old king and all the dreams of the Crimson Empire that Zosia had cast down into shit twenty-odd years ago, well, then his oath never to strike an enemy before the horns of combat have sounded might just be forgotten for a moment or two.
"And what of the weapon you promised me, Your Grace?" said Domingo. "Now that I have fulfilled your terms, it is time you fulfill mine."
"With pleasure," said the Black Pope. "When you leave the confessional pay a visit to the offices of Cardinal Diamond. He is expecting you, and will deliver something more deadly than any army. Now, before you and I never had this conversation, is there anything else I can answer for you?"
How many times had he told himself that he'd been the same way at Efrain's age, a little soft and a little spoiled and more than a little reluctant to ride to war? How many nights had Domingo lain awake telling himself that his son was worthy of his title and station? That he hadn't somehow sired the sort of colonel the grunts would sing mocking songs about, a noble who bought his medals instead of earning them? How different would their lives have been if he'd given Efrain the kitten he'd wanted for his tenth birthday instead of a sword and a library of martial philosophy? But these were not the sorts of questions a deranged poppet with pretensions of divinity could answer, so he simply said, "It's hard to believe the peasants were right all this time, isn't it? They've been chanting it ever since she first fell from Diadem's throne room: _Zosia lives_."
"Not for much longer, Colonel Hjortt," said Pope Y'Homa III, Shepherdess of the Lost. "Not for much longer at all."
# [CHAPTER
22](toc.xhtml#toc-chapter022)
Nobody likes to have a knife held to his face, which was why Maroto did what he did to the scout he had captured. The squirrelly little man—more of a boy, really—lay on his back hyperventilating while Maroto squatted beside him in the mossy bole of a maple, his blade nicking his captive's septum and his thumb resting on the bridge of the fellow's nose. They both knew Maroto could pare off the man's twitching, running bit of cartilage as easily as taking a wedge from an oddly shaped cheese, yet still the scout refused to give up the goods. It was almost as if the blighter knew about Maroto's oath, could tell at a glance he'd sooner cut up his own face than torture a sworn servant of Samoth.
Rare was the day where Maroto didn't regret vowing to Queen Indsorith that he'd never again raise weapons against her or her people save in self-defense; he hadn't had much choice in the matter, given the circumstances, but still, it was damned inconvenient that a poor decision made twenty years ago continued to hamstring him. He still had no idea how much use he'd be to his old general once he finally caught up to her, what with that meddlesome oath, but he'd burn that bridge when he got to it—first he had to reach Zosia. Since they had followed the trail of the Cobalt Company here to Myura, it was a safe bet she was barricaded inside the nearby castle that the Imperials were laying siege to. Now if only he could get this fucking scout to open up without opening him up.
"Come on, man," he said, hoping the knife would lend weight to his bluff. "If I have to take it off you'll scream, and if you scream I'll have to cut your throat. Who wants that?"
"I dunno what you're talking 'bout, I swear!" repeated the scout, too loudly, and Maroto sighed. He hated the very idea of taking off bits of people—if you were going to cut, not cutting to the kill was a dark business. As if he knew any other kind.
"I told you I'd give you two chances. That was your first, now your second is going to be whether or not you scream. Being noseless is better than being dead, so I'd hold it in were I you."
The scout whimpered, his bulging eyes big as goose eggs, but still didn't confess. Maroto was stumped—unless he actually cut this kid they weren't getting anything out of him, but Maroto wasn't keen to find out what happened if he broke an oath he'd sworn on the name of his devil.
"Maroto, why—" Purna began from her perch in the tree above them, but he cut her off with a hiss.
"Kiss the devils on their mouths, girl, now you've done it," he said, secretly relieved she'd set him up with the opportunity for one last play. "How many times have I told you not to use my name? I could have let this runt off with a nosing, but now... sorry, lad."
"Maroto." The scout whispered his name as reverently as that of a saint. "You... you're Maroto the Conqueror?"
"Yeah yeah," allowed Maroto. "And you're Noseless the Horribly Dying Scout if you don't—"
"The Cobalt Witch," said the scout quickly. "That's who you're lookin' for, ain't it? Your old queen."
"Your old queen, too," Maroto reminded the boy, trying to rein in his excitement at the scout's use of an epithet he hadn't heard in decades. "Although maybe you weren't born when she... while she... She's not a witch, is the point you've got to come to. Cobalt Zosia is fine, or, what was it she liked..."
"Cold Cobalt," Purna called down. "Oooh, and 'the Banshee with a Blade' is the name of one of Vuntwor of Nin's better ballads about her—that's what I'd go by, I was her. Has a wicked ring to it."
"I always just liked the sound of 'Queen Zosia,' " Maroto mused. "But really, any such title that doesn't denigrate her character will do, and help keep your nose attached for the moment."
"It's true," said the scout, wonder seeming to have chased off some of the blind terror he'd evidenced ever since Maroto had snatched him from behind the tree and pinned him down. "It's really her, isn't it?"
"Devils lick your bones, that's what I'm asking _you_ ," said Maroto. "The mercenary company your regiment's cornered at Myura Castle, who leads them?"
"A woman, I told you, thass all I know for sure," said the scout. "The brass must not have toll us all for fear it'd affect morale. It's _got_ to be her."
"What makes you think that?" Maroto took some of the pressure off his blade.
"I ain't seen her, let 'lone close enough to tell the color of her hair, but the flag she's run up the castle poles is blue, dark blue, with a broken red crown in the center and five silver pentacles circlin' it." The scout gulped. "One for each Villain, right?"
"That's new heraldry, but sure sounds like her style," said Maroto, trying not to grin and failing spectacularly. Five pentacles on her flag! She was expecting him! "That's information to save your nose, if not your life, scout!"
"Scout?" the scout said. "I'm not a scout."
"I told you I didn't think he was," said Purna. "And the only thing I can see from up here are more trees. Can I come down?"
"No," said Maroto, and guffawed almost convincingly. "Not a scout—and just what do you think a scout would say when captured, eh? Why's else would he be skulking around this border wood when there's a siege on in the town below, and with the Crimson sigils on his armor all blacked up? Not a scout!"
"No, Captain Maroto, sir, I'm not," insisted the scout. "Thass what I was tryin' to say when you put the knife to me—I'm not now nor 'ave I ever been a scout. I tried to cover the red on me tabard to blend into the woods, it's true, but if I was a real scout I wouldn't have just walked into your ambushin' me, yeah?"
"Maybe yes and maybe no," said Maroto, considering the boy beneath him. Not a scout? "I've caught plenty of scouts in my day."
"And what would I be scoutin' out here in the forest, miles from Myura, with the sun 'bout to set?"
"Easy," said Maroto, wondering whom he was trying to convince here. "Patrolling the hinterlands to make sure reinforcements aren't sneaking up from behind to break the siege, or deliver supplies."
"Yeah, that makes sense," the scout agreed. "I didn't think 'bout that. But if I _was_ a scout don't you think I'd know that an' be ready with a better excuse?"
"You're talking into my deaf ear," said Maroto—the only good to have come out of taking that damn arrow to the head was getting to use that tired expression as much as he wanted.
"What kind of scout—"
"Shhh," said Maroto, pressing the blade firmer. Even with only one good ear he thought he'd heard—
"Someone's coming up the hill behind us," Purna stage-whispered from the maple boughs. "Shall I open fire?"
Hearing the crunch of leaves under several pairs of boots, followed by a tinkling silver bell and a high-pitched giggle, Maroto seriously considered it. Half their running crew had returned to the capital if not their familial houses before Maroto's wounded ear had even stopped oozing lymph, and most of the other nobles had fallen off along the surreptitious trail from the edge of the Panteran Wastes to Agalloch, from Agalloch to Geminides, from Geminides back around to Katheli, and finally from Katheli to here outside the castle of Myura, where the elusive Cobalt Company had been cornered by the local Imperial regiment. Those few fops who remained were the most dedicated to adventure, if not to following orders, a sad point that was made for the umpteenth time as Count Hassan, Duchess Din, and Pasha Diggelby emerged from the underbrush.
Count Hassan was dressed in his dramatically sheer fencing gown and carried an ivory-handled machete in one hand and an enormous drinking horn in the other, the sloshing vessel supposedly carved from a megapotamus tooth. Duchess Din's thigh-high magenta boots were fashionably gartered onto her gleaming scalemail singlet, the prow of her wig skewered with a golden quarrel that shone in contrast to the dull oak of the one nocked in her enormous crossbow. Pasha Diggelby wore the leather vest and skirt he had modeled after Maroto's own garb, a crystal waterpipe in one bony hand and a leash in the other. At the end of the leash was the fluffy white lapdog he insisted was a devil that his father had bought him from a Kravyadian diabolist but that was probably just an Ugrakari spaniel. The bell Maroto had heard announcing their arrival hung not around the pup's ruby-studded collar, but its master's.
"What ho," cried Diggelby. "Maroto's caught us some supper."
"Looks too lean," said the duchess. "I can abide a gamey cut, but never a stringy one."
"Oh, fellows," said Hassan. "I do not know if I can stomach the sight of Maroto sating his appetites, tranquil sylvan backdrop or not. It's all too beastly."
"Didn't we tell you to wait with the wagons?" said Purna, descending from her roost.
" _We?_ We! Purna, love, that's absolutely adorable," said Diggelby. "Tell us, when are the nuptials, and shall we sit with the bride's side, or the groom's?"
"I really ought to be merciful and cut your throat now," Maroto told the scout.
"Who's your new playmate?" Hassan asked as Purna dropped the last few feet to the ground. "He looks about as old as your last opponent. Good thing we arrived in time to save you another hiding."
"My name's Lukash," said the scout, beginning to squirm out from under Maroto but freezing when the barbarian's blade tapped his face.
"His name's Noseless the Horribly Dying Scout," said Maroto, imagining the looks on these fops' faces when he made that first awful cut. If only he could go back and undo his vows; they needed a reminder this wasn't all some lark, this was war, or close enough, and this poor scout could provide just the—
"I'm not a scout," said Lukash, rather peevishly. There was some cheek there you usually didn't get from desperate fuckers.
"What are you, then?" demanded Purna, squatting down beside Maroto and putting one bark-stained thumb directly against the boy's left eye before he could blink. "Tell me now or they'll call you One-eyed Lukash the Noseless Idiot from here on out."
"I'm... a deserter," said Lukash, closing his other eye in shame. "I'm Khymsari, it's against my faith to wage war. I been lookin' for the chance to sneak off ever since the Myuran regiment drafted me."
"Uh-huh," said Purna. "Sure you are. Take off his lying lips, Maroto."
"Oh, let him up already," said Diggelby, leaning over to light his waterpipe on the match Hassan had struck for him. "This is all perfectly barbaric."
"Khymsari, huh?" Maroto reached up and pulled the boy's iron skullcap off as the fop's pipe gurgled in the background. Sure enough, there was the crown of shorn squares in his otherwise thick black hair. If Maroto hadn't stuck to his sacred oath he might have disfigured a pacifist. Wouldn't have been the first time. "Devils' mercy... Let him up, kid, he's telling the truth."
"Bravo," said Duchess Din, juggling the crossbow around in her arms to accept the smoldering waterpipe from Hassan as Diggelby coughed up a lungful of skunky smoke.
"You'll let me go, then?" asked Lukash, not daring to move from his imprint in the rotting leaves.
"Once you tell us everything there is to know about your regiment, the Siege of Myura Castle, and how one might sneak past the former into the latter... well, maybe," said Maroto. "Come on, let's get back to camp. I've got a hankering for balut, and don't expect we'll find any eggs out here."
The merry posse—for they seemed always merry, these few remaining richies, even with the last of their servants having deserted a few days past—picked their way back through the autumn woods, the brilliant topaz, amethyst, and garnet leaves that remained on the maples, oaks, and wild damsons turning the whole wood into an arboreal treasure chest. The nip in the evening air felt like a belated gift from long-absent gods to his ever-sweaty brow, and Maroto hummed an old marching song to himself as they walked. Purna followed, questioning the prisoner and thus giving Maroto a respite from her yammering, and just ahead Diggelby, Din, and Hassan argued over the wording of an anthem Maroto had never heard. Nothing could dampen his mood, not now. Sure, they'd taken a tour of the whole bloody Crimson Empire after leaving the Panteran Wastes, only to end up back here, less than a hundred leagues from where they'd first quit the desert, but that was the way of the world, wasn't it, to forever be winding up just where you'd started? There was a time when Maroto would have resented his cyclical trajectory, but at present he found it hard to complain. The reason for his excellent humor was simple: over the last few months, as they'd picked up more and more scraps of rumor along the trail of the blue-haired mercenary captain, Maroto had finally let himself believe the bartalk he'd overheard that spring night in Niles. Zosia was alive, and if the last twenty years had been him wandering out in a wide circle, wide as the whole Star and then some, now he was coming right back to the beginning. Back to her.
How? Well, she must have been imprisoned instead of killed, as everyone had claimed, and now she had escaped and rallied her old army to take back her rightful due. Impossible as it seemed, his queen, his captain, his one true love yet drew breath. And she was here, just over these hills, holed up in a castle while the forces of her former captors surrounded her.
Maroto couldn't wait to break her out.
# [CHAPTER
23](toc.xhtml#toc-chapter023)
Come clean, Keun-ju," said Zosia for the hundredth time since they had left the Immaculate Isles, and the fourth or fifth since they'd been seized at the harbor. "You can trust me."
"Nothing to tell," said Keun-ju, turning his veiled face to the whitewashed wall of the sandy cell the customs agents had locked them in. She was wearing him down, she could tell, and he would crack eventually. "Why must you badger me so?"
"Call me a romantic, but I want to know why before they kill us," said Zosia, hitting on the idea and running with it. The Virtue Guard knew less about Raniputri culture than Zosia did about guarding one's virtue. "The crime for bestiality in these parts is execution. They don't do trials here, either, so odds are when the guards come back for us it's death by elephant—they train the beasts to take their time with it, too, so we'll be in agony for a while. I'd like to go to the devils knowing why."
"They're not going to kill us, and certainly not with _elephants_ ," said Keun-ju, but he didn't sound convinced. "And why do they think you would... ugh."
"It's a setup, obviously," said Zosia, thinking out loud. "Bang could've sent word somehow, I guess, via homing albatross or some other means. Definitely a good way to make sure we don't come after her."
"So why not, you know... give them your real name instead of the alias?" Keun-ju whispered the last, heathen gods of his people bless and keep him. "Why tell them to look for Moor Clell instead of Cobalt Zosia?"
"That's a good point," said Zosia. "I'd hazard the guilty party thought customs wouldn't believe such a claim, considering I'm supposed to be twenty years dead."
"Or if the locals did believe it, they probably would make a big deal out of it, yes?" said Keun-ju. "A very, very big deal, if they have any wits at all. So why don't you tell them who you are? If nothing else, they might delay the execution long enough to attract some more fanfare to the occasion."
"You think they'd believe me?" Zosia shook her head. "We're doomed, kid, so you might as well spill the royal beans, die unburdened of secrets. We both know Ji-hyeon kidnapped herself; the only thing I can't figure out is why you didn't go with her, since you obviously love her."
"I do?" Keun-ju swallowed. "I don't. I mean, yes, or rather, no... She is my mistress, of course, so I do... um."
"Wow," said Zosia, recognizing that feeling all too well. "You've got it bad. She gave you the sword, right? A tri-tiger like that must have set her back a lot more than a week's allowance."
"It's not a three-tiger, it's a four," said Keun-ju, not even trying to mask his pride. "It's been in her family for three generations, and the swordmaker was an Ugrakari who could trace her lineage back to the Sunken Kingdom. She left no heirs to her art, so there's probably no sword like it left in the world. And now it's in the hands of a filthy Raniputri, thanks to you."
"The Raniputri put a higher commodity on bathing than Immaculates, so I wouldn't go down that road were I you. And the only reason you're still alive is thanks to me—if you'd killed those agents, you never would have gotten off the dock. Those lighthouses we passed coming in? The best archers in the Dominion keep watch from up there, just waiting for an excuse to shoot some foreign idiot."
"Better to have died with her sword in my hand than with it locked in some drawer," said Keun-ju.
"Well, that would make for a better ballad, I'll admit," said Zosia. "Personally, I can't believe they took Choplicker. The insinuation is beyond disgusting."
"What makes you think Ji-hyeon ran away instead of being taken?" asked Keun-ju, and Zosia caught her smile before it gave her away. Maybe he just wanted to talk about anything other than the crime she was accused of, but from the needy tone in his voice she guessed he might've bought the story she'd spun him about an imminent pachyderm execution. Granted, maybe they _were_ about to be killed, but not for the reasons he supposed, and probably not with an elephant as the murder weapon—the beasts were rare outside of a couple of Dominions way to the east.
"Princes and princesses are always kidnapping themselves," said Zosia. "She takes after her dad, it sounds like, and that would be his style for sure. Add to that the lack of ransom note, and I'm guessing Fennec sweet-talked her into making a break for it. Fennec would be Brother Mikal to you. They're probably off somewhere fucking like rabbits while we await a grisly death."
Keun-ju crossed his arms. "No."
"No? Keun-ju, my lad, believe me when I say you don't know the first thing about it. A feisty young princess, stuck in an arranged marriage, and then along comes a silver-tongued fox with promises of a bright new future far away in Usba, or the Empire, or somewhere more exotic still? At this point he's probably impregnated her and made off with whatever treasure they nicked from Hwabun. I'd bet she's too embarrassed to come home and admit she's carrying the bastard of her tutor."
"No," said Keun-ju, more forcibly. "You don't know anything."
"I know the human heart, kid, which isn't something you learn by being a horny rich girl's sewing instructor," said Zosia, which was downright nasty but she was on the cusp of provoking him into righteous honesty, she could feel it. "I'm sure you thought you were best friends, sharing all your secrets, but the truth is a noble never shares everything with a servant, _especially_ a Virtue Guard. You guys are notoriously gossipy, and—"
"We love each other," said Keun-ju, tears running down from under his veil but his voice steady as good steel. "A coldhearted crone like you could never understand that, but we do."
"Ah, the love of a lordling for her slave, and the attendant for his mistress," said Zosia, despising herself a bit in the moment—that was funny, she never used to think twice about playing people, but for some reason she was profoundly unhappy with herself over this exchange. She was already committed to it, though, so dealt the killing blow. "She's probably already forgotten you, and here you are about to be executed, all for—"
"We're lovers," said Keun-ju quietly, wiping his face and looking at the ground. Fast as Zosia had teased it out, the Virtue Guard had reeled his rage back inside. "I'll die for her, whether it's today or another, but I'll never doubt her. She hasn't forgotten me. She will never forget me."
"Lovers?" _That_ was unexpected. "But... that doesn't happen, does it? Don't you have to swear some serious fucking oaths to—"
"I would rather break a thousand oaths than Ji-hyeon's heart," said Keun-ju, slumping against the wall. "I've loved her for as long as I've served her, but never dared dream it would be more than... than what you said. The affection of a mistress for a slave. Then, the night of the Autumnal Equinox, after we fended off that giant spirit in the pumpkin fields, I was helping her undress for the night, and..."
"And _what_?"
"And she made her feelings for me abundantly clear," said Keun-ju primly.
"Uh-huh," said Zosia. "Talk is cheap for moneyed kids, Keun-ju. I hate to be the bearer of bad news, but if you'd actually tried going through with something she'd have dried up faster than you can say forbidden fruit looks better than it tastes."
"And if the ripe young Lieutenant Bang had weighed down her branch enough for you to reach it, I suppose you would have polished her on your sleeve, taken one bite, then cast her aside? I saw how you were savoring her with your eyes throughout the voyage."
"And we saw how well that worked out for me, didn't we?"
"Ji-hyeon loves me, Zosia, and I love her, and even if you're so base as to believe carnal consummation is required, well... rest assured my oaths have fallen like overripe pears forsaken by even—"
"I get it, I get it," said Zosia. "What gives with all the poetry, Keun-ju? You go the whole cruise without contributing so much as a song for music night, and now we get you talking about the princess and you're laying down the fruitiest verse this side of the Othean orchards."
"I would never debase her memory by taking part in a so-called _music night_ ," said Keun-ju bitterly. "And I will be mindful of my language in the presence of such a discerning critic as yourself. To answer your question, yes, there are sacred vows we must swear before taking on our duty, and yes, I have broken them, and no, I am not proud that I have broken them, but..."
"Yeah, I hear you," said Zosia, contemplating the many solemn oaths she'd bent, creatively interpreted, or just plain ignored over her storied career.
"It's ridiculous, you know?" Keun-ju sounded plenty pissed, which was due. "How many nights Ji-hyeon and I stayed up afterward, whispering in bed, and how often our talk turned to you—the Arch-Villain, the one woman in all the Star who refused to take what the world offered her, who lived life on her own terms, who died rather than compromise. And here I find out you're actually still alive, and come to think we're almost friends after everything we went through together on the boat... But you aren't anything like the stories. You're just a flunky of Ji-hyeon's dads, a coward who gives up rather than fights, a creep prying into the sex lives of strangers... Were you always so pathetic? Were all the tales about you false? Were you ever the woman they said you were?"
Zosia looked down at her scarred knuckles. The sea air had played hell with them on the voyage; what had been the odd ache back in her old life in Kypck now a daily nuisance of arthritic cramping. She deserved what the kid had said about her, but all the same she felt the impulse to give him a stomping. She set her teeth until it passed, then sighed and sat down beside him.
"That's fair. I was trying to rile the truth out of you, and got a sight more than I was looking for. I'm sorry, Keun-ju." Zosia felt like she meant the words as she was saying them, but had to wonder when she finished with, "And hey, since deflowering a princess is probably a worse crime than helping one run away, why not tell me the rest? I've always known you helped her, and now I know why, so let's get the full account. You tell me the truth now and I'll see that you're reunited with Ji-hyeon."
"I thought they were going to execute us any moment?" said Keun-ju, a watery smile showing at the hem of his veil. "And aren't you supposed to return Ji-hyeon to Hwabun?"
"I've been in tighter spots than this and seen my colleagues through," said Zosia, though at present she didn't have much in the way of ideas. "And as for taking her back to her parents, that depends on if she and Fennec can make me a better offer. So long as I have my army I'm not particular about who funds it, and I'll admit to having a romantic streak."
"Oh, you definitely strike me as the sentimental sort. _Fucking like rabbits_."
"Fair again," said Zosia, and found herself being as straight with this sad boy as she'd been with any proven friend. "I hide it better than you, but we're out here for the same reason. Love's what haunts me, Keun-ju, love for a man, a man and his people. Love for those I'll never be able to hold again, or kiss, or laugh with over a jug of strong drink." From his expression she could tell he believed, and that made her feel like he owed her now, owed her more than he'd ever know. "So that's me, and I swear on my husband's cairn I'll keep your secret till the devils take me. Now out with it, let's have the rest."
Keun-ju was silent for a time, then met her eyes. Held them. "All right, I'll tell you everything. Ji-hyeon—"
A door banged open just down the hall, and both Zosia and Keun-ju scrambled to their feet. Their iron-barred cell was one of several opening onto a narrow corridor in the rear of the customs house, and four figures strode to their door and stopped. The late afternoon light coming through the skylights made the pink of the officers' saris glow like fire coral. Zosia and Keun-ju were blindfolded and then taken from the cell.
Doors opened and closed on either side of them, and then they were on the city streets, the teasing scents of urban living hardly a match for the odors of the cramped _Crane's Bill_ but the riot of sounds far more jarring. Up stairs and down ramps they were blindly marched, past the smoke and din of a tavern or tubāqhouse, and then through another door. It was much quieter in here, though Zosia could still hear the ruckus through the wall, and after stumbling on the too-soft floor, she at last had the heavy cloth pulled away from her eyes.
Blinded by green-filtered light, she wiped her eyes with the back of her hand. They had not bound either her or Keun-ju, and, keeping her hand in front of her face to conceal her glances as her sight crept back, she took in the spacious room, looking for an exit. A stinghouse, pillows carpeting the floor, the wall-mounted terrariums teeming with cockroaches, centipedes, icebees, and a dozen other varieties of intoxicating insects. Between the glass cages were masked Raniputri women of decidedly shadier character than the customs agents who had delivered them and now quickly left out the back.
"I didn't believe it when I received Kang-ho's letter, but here you are," said a familiar voice, one that caused Zosia to drop her hand from in front of her face and stare at the rear of the room, where a figure reclined in a settee. Choplicker sat at the woman's feet, and she rubbed his head as she rose to her feet. "They're going to have to come up with a new handle for you, something like The Ghost Who Walks."
"Singh," said Zosia, taking in her old confederate. Keun-ju's jaw dropped as he realized they stood in the company of another legend, the Second Villain herself. "It's been a long time, Chevaleresse."
Whereas Kang-ho had gotten soft, Singh had hardened like a suit of sunbaked leather armor. Her black sari shone with golden moons and silver suns, and her nose stud and bangled wrists glittered in the terrarium light, but despite the casual attire an imperious ferocity radiated from the woman. Her hair was black as ever, though bound in two braids instead of a bun—Zosia wondered if Singh was widowed or divorced. Her once wild, waxy mustache had finally been tamed, the luxurious, upturned lip-weasel now maintaining its lilt by habit rather than force. Still handsome if haughty, with new scars glancing off her chin, cheeks, and bare feet, the knight brought a moist weight to Zosia's dusty throat. Singh looked damn good after all these years.
"I suppose I have you to thank for the more colorful charges against us?" asked Zosia, taking a step toward Singh. One of the guards melted off the wall and put herself between Zosia and her old friend.
"I thought you'd like that," said Singh, and to Zosia's chagrin she didn't call off her muscle. "I've been waiting for you all week. Kang-ho thought you'd make better time."
"Funny, Kang-ho claimed he didn't know how to find you," said Zosia.
" _That's_ what he told you? Typical. You should have looked me up first, sister; things would be very different if you had." Singh put her hand on the guard's shoulder and she stepped away, leaving Zosia to look up into the taller woman's kohl-ringed eyes.
Zosia sighed. There was no sign of Anklelance, who usually coiled herself around her mistress's neck like a dull-scaled necklace. If Singh no longer had her devil, that was something in Zosia's favor, at long bloody last. Yet of all the Villains to go up against in a barehanded fight, she would have picked any combination of the others over Singh. According to the songs, the knight had been in martial training from the time she left her cradle. Given Zosia's experiences, she'd chalk that up to understatement rather than embellishment. "Let me guess. Kang-ho didn't send you to help find his daughter?"
"Oh, Zosia," said Singh sadly. "He sent me to kill you."
"Yeah, that figures," said Zosia, and talked fast, before the knight could move on her. "I challenge you to an honorable duel, Chevaleresse. I win, you're back to taking my orders, and you'll help me track down the others, starting with Fennec. We're going to war again."
Singh cocked her head to the side, and Zosia gave silent thanks to the insane codes of Raniputri knights. "And if you lose, General, then what—"
Zosia swung on Singh. Surprise could only take her so far, but she didn't have much else to work with. It didn't take her nearly far enough.
# [CHAPTER
24](toc.xhtml#toc-chapter024)
Sullen and Grandfather had hoped that learning the name Uncle Craven had taken among the Outlanders would give their hunt a definite scent to pursue, but that wasn't how it panned out. It didn't help that neither Sullen nor Grandfather knew more than a few curse words of Crimson, and none of the folk they met spoke the Savannah tongue, so most of the time Sullen had to ask around until he found someone who spoke Immaculate. When he could make himself known to the Imperials, most of them had indeed heard of a powerful warrior named Maroto, but each and every taleteller sent them in a different direction. Inquiries after Hoartrap the Touch were even less fruitful, and met with anxiousness if not outright hostility. One trail took them up the cyclopean spires of Meshugg that clung to the sheerest eastern peaks of the Black Cascades like barnacles on a wrecked ship. Another brought them all the way down the Heartvein, to where the river opened onto Lake Jucifuge and spun the floating city of the Serpent's Circle in a perpetual gyre. Adventures were had, and skulls were split, and powerful foes vanquished, but if Sullen had wanted that shit he would have stayed in the Frozen Savannahs. Then, as summer gave way to fall and his spirits sank as low as the ground fog in the Temple of the Black Vigil where they again sought their quarry in vain, an unexpected lead...
While Grandfather dozed on a fallen column after declaring the mission a failure, Sullen wandered the hollow avenues, pondering the weirdness of the place. Sure, people called Emeritus the Forsaken Empire for a reason, but he still couldn't quite wrap his mind around the scope of the place. Take this temple, for example: that it was devoted to something called the Faceless Mistress had a queer ring to it, certainly, but was hardly that bizarre. Nowadays the Horned Wolf Clan bowed to the Fallen Mother, after all, which sounded close enough to beg the question of whether this Faceless Mistress was the same god as they had in Samoth and the Savannahs, just named something different. That happened a lot, according to the missionaries who had lugged the Burnished Chain up the Noreast Arm—turned out the Horned Wolves had been worshipping the Fallen Mother long before they'd converted, they'd just called her Silvereye and thought she was an ancestor of note who'd gone around slaying some giants and eventually ascending into the night sky to become the moon, instead of, you know, the One True God of All Things.
Far as the new faith went, there were some good stories, but a whole lot of it just didn't make much sense to Sullen. Inconsistencies and such, the sort of simple errors that cropped up from time to time in any tale, like how nobody could agree if the Old Watchers were gods or devils. Yet when he'd pointed out the Burnished Chain's contradictions to Father Humble, the priest had made him repeat a bunch of nonsense words and whip himself with a switch until his back bled. This was a marked contrast to how Grandfather would debate him for long hours on the particulars of any given saga or song, and thereafter Sullen kept his observations away from the ears of all but his ancient relation.
Anyway, faith was a fickle thing. You could be like Sullen, who suspected Grandfather was probably right when he said all tales had equal measures of wisdom, truth, and bullshit, or you could be like the true believers and erect whole empires to honor a single legend, like they'd done down here on the Soueast Arm. At the end of your trail, though, you all ended up rotting into the earth. Small wonder Old Black built her meadhall in the Land Beneath the Star, so that all worthy heroes might one day be reunited, or the Chainites said the Fallen Mother dwelled in a wondrous cave at the center of all things, or the Jackal Tribe worshipped the Noreast Gate, which had been carved by Rakehell when he'd escaped his infernal father-in-law. Obvious stuff, and the more stories you soaked up the more evident it became.
Anyway, they'd teased a few tales out of folk on their way down to Emeritus, but few had wanted to talk much about it at all. Odd, that, as usually people wanted to tell you all kinds of nonsense about their neighbors, but nobody wanted to talk about the Forsaken Empire, or how it got forsook, or what the deal was with their god. Matters only became stranger the day before, when Sullen and Grandfather had stumbled over an enormous, shattered statue of this Faceless Mistress. The ruined monument lay dashed in boulder-sized chunks across a four-block area, appeared to be made of charcoal, and gave off a faint buzzing that Sullen could feel in his teeth. Strange, but not unheard of.
Stranger yet was how every structure and street was drained of color, even the leaves of ornamental trees as grey as an old wolf's coat; if Grandfather hadn't displayed the same range of pigments as ever, Sullen would have assumed there was something wrong with his eyes. The crowning peculiarity about this place was the expanse of it—they called it a temple, but it was larger than most of the Outlander cities Sullen and Grandfather had visited... a temple the size of a capital, and totally deserted.
There was some bad swamp to cross at the southeast border of the Empire and the Emeritus Arm, and a few bog pearl divers had waved to them from a canoe as they picked their way along the wide, petrified boardwalks leading into the Temple of the Black Vigil. Now, after a week of scouring the empty buildings and desolate streets, there was no doubting that they were definitely the only ones alive in the whole place. No citizens nor squatters peopled this metropolis, nor beasts nor birds nor bugs. It might've been spooky, except it was the first place Sullen had ever set foot where he saw no trace of the devils that dogged him. Especially after becoming better acquainted with the fiends courtesy of that awful witch Hoartrap, this was no bad thing. Besides, Emeritus reminded him a bit of home, with the perpetual chill of the dull shadowed avenues offset by brilliant pastel skies and the orange sun of high summer; there was the world he walked through, grey and hollow, but a rich, colorful realm hovering above, just out of reach. He found himself wondering if he could talk Grandfather into prolonging their search another week, to better explore the sepulchral temple city.
Sullen had been raised better than to steal from the dead, if death was what had befallen the people who'd dwelled here. Surely there was no harm in admiring their abandoned hoards, though. Everything was in its place in the deserted storehouses and dining halls, apartments and palaces, offices and altars, with freshly prepared meals set out before shrines and waiting on many a table. The smells could be maddening, especially in one humble home where a warm pot of lentils waited on a cold stovetop, the long-absent aroma of berbere and pepper sending Sullen all the way back to his mother's kitchen... but Sullen was no thief. And besides, as disparate as the accounts of the fall of Emeritus were, the one constant was that the populace had vanished some five hundred years before. Whatever purpose kept those lentils hot and appetizing after all these centuries, Sullen doubted it was out of consideration for his homesick belly. For once, Grandfather agreed with his thinking, and they subsisted on the cold tack of the Imperials, wary of even kindling a fire from what fuel they might scrounge in this place.
Even so, exploring the temple nourished Sullen in a fashion he couldn't quite articulate. The world of the people who had dwelled in this place was obscure despite their every possession being laid out for his inspection, and long after Grandfather had relieved him on watch he would lie sleepless on the dusty street, contemplating the use of some gargantuan mechanical device or the symbolism in a lifelike painting of a weeping salmon. Grandfather seemed put off by the abandoned lives, which was why Sullen so looked forward to the old man's increasingly long midafternoon naps.
Today Sullen's wanderings took him farther and farther from their campsite in an orderly park where the great grey lawns and pregnant, pale orchards appeared carefully manicured, nary a weed sprouting in a single monochromatic flowerbed. Strolling for an hour, he turned down another nondescript boulevard, one he and Grandfather had not heretofore explored. He knew they had not come this way, for the faintly phosphorescent dust that coated every inch of the Temple of the Black Vigil here lay undisturbed by footprints. Even before he gained the intersection, he was somehow aware that this new road terminated in a great wall just a block or two down the way...
Huh. Striding out into the middle of the road, he sized up the dead end. The buildings on either side were the same austerely shaped white rowhouses that lined most every road in the temple, but instead of a wall this road ran straight into a high archway, and beyond the archway lay a Gate. Or maybe instead of ending at the Gate, this was where the road began—it was all a matter of perspective.
Sullen knew the oily pool of black mud that filled the carven-walled courtyard on the far side of the arch was a Gate because he had seen its twin, once, when he was but an unnamed pup. As he had dragged Grandfather home from the battle that had claimed his legs, they had passed within a mile or two of the Flintland Gate, a deeper patch of darkness on the horizon. The war had started because the Jackal Tribe had abducted and sacrificed several Horned Wolves, feeding them to that yawning mouth in the earth that they called the Ravenous God. Six nights later, when he was safely home in his bed, the devils had waited until he made the mistake of dreaming and then hauled him back to the Gate, carrying him as far as a plinth erected near its edge before he awoke. Horned Wolves weren't crazy savages who believed that if you died in a dream you died for real, but Sullen knew from the songs that devils could hurt you in your sleep, if they found a way past the charms hanging at your door and windows. For nine subsequent nights he had dreamt of the Gate, and each night the devils carried him closer and closer to the trembling lip of the abyss.
Then, on the tenth night, just before he fell asleep, he asked the devils not to take him back there. As a token of his earnestness, he had picked open the scabs he had acquired protecting Grandfather from a snow lion their first night in the wilds, and drifted off as the devils settled in to feed on his dripping arms. That night he dreamt of flight, but not the Gate, nor did he ever dream of it again. Strange, he hadn't remebered that in years, even after what had happened with Hoartrap on the plains...
Now he stood before a second Gate, and saw that his long-buried visions had shown true, for this portal in the earth perfectly mirrored that which he had dreamt as a boy who had never left the Frozen Savannahs. And here, in the wasted land of Emeritus, where only a Horned Wolf and his grandfather had dared to venture down many a lonely century, came all the devils he had not glimpsed since entering the temple.
Wide awake and unmolested by a witch as Sullen was, the devils materialized just the same, emerging not from the Gate but the puffs of dust rising beneath his battered boots. Up they rose, spiraling around him, the whisper of scale and fur tickling his skin and the muscles and bone beneath, and then they wheeled high into the air, winged toad and finned serpent, insectoid rodent and dog-legged crustacean, and a hundred thousand other flittering, slithering horrors. The devils came together into a squirming tornado that stretched from the dusty cobblestones high into the air.
"Aw, man," he said, not really having a lot of hope for his prospects here. Grandfather was wrong about some stuff, Grandfather was wrong about _a lot_ of stuff, even, but he'd been right about one thing: _Don't go wander off and get yourself killed in this dump while I take a nap_. Sorry, Fa.
The cyclone of devils contracted further, coalesced, the awfulness of their individual parts forming an even less wholesome whole: a humanoid figure twice as tall as the surrounding buildings towered above Sullen, its pendulous breasts, featureless face, and extended fingers all writhing with unending movement as it bent down for him.
"Don't do it!" he shouted, holding up his open palms to the nightmarish giant. "I don't want to hurt you!"
As soon as he said it he recognized this was a pretty silly thing to tell a titanic, devil-spawned monster, and right enough, it didn't give the entity pause. A palm half as tall as Sullen slammed into his side, fingers as wide as his legs closing around him. The ground fell away from him and the true expanse of the temple came into sight as he was lifted several stories into the air, the Gate now but a small pool beside the giant's foot... not that he was paying much attention to the cityscape laid out beneath him. No, his focus was on the enormous face the hand held him up to, a blank oval as richly dark as the Gate itself.
As he watched, queasy from the unique experience of being lifted so high so quickly, the abyssal darkness of the face spread down the wriggling, patchwork neck. It radiated down the chest and out across the shoulders, the individual devils going rigid as the blackness seeped over and through them. The devils comprising the hand that held him became agitated as the darkness began to seep down that arm, beaks and barbs desperately prodding against him. It was as though the devils were desperate to avoid the creeping darkness and sought to crawl over or through him to escape it, but were trapped, swimming in circles around the man they grasped. Were they a captive of something greater, just as he was?
"I'll... do something," he said, speaking to himself, to the devils who bound him, and to the enormous black face. The Faceless Mistress, obviously, she to whom this temple was erected, the god of the lost people of Emeritus. One of them, anyway.
" _What will you do?_ " Sullen hadn't really expected an answer, but as his ears popped and he heard his own voice pose the question, a distant constellation bloomed in the greasy depths of the giant's face. Even as these lights faded back into darkness came another question, and another flare of remote stars. " _What do you offer?_ "
What did he have? It already had his person, if it wanted it, and he wasn't foolish enough to think a god would desire what few possessions he owned. Grandfather? A low thought, that one, and Sullen frowned to think that moments before he went to his ancestors he had considered selling out his most beloved kin, if only for a moment. What would Old Black or Rakehell do, if they were in such a pinch?
"Don't have much," he said, not really scared so much as... awed, maybe? Awed, sure, but not so awed he couldn't think or speak. It was like dreaming, that way. "Whatever you want, I guess."
Sullen wasn't any better versed in the ways of gods than he was in the motivations of devils, but as soon as he said it he figured that was a fairly stupid offer to make. This time, though, it seemed he might've blundered into saying the right thing, because the encroaching blackness paused at the wrist of the arm that held him and the devils holding him all went still. The gargantuan head moved closer and closer to Sullen, and, eyes or no in its light-swallowing surface, he knew he was being sized up by the Faceless Mistress.
Then, a distant twinkle of light in the heart of the void. It flickered, expanded, crackled with energy. Exploded outward, to the very edge of the blackness, so close Sullen could feel the heat... and then it contracted again, sucking the warmth back in with it, so fast and so cold that beads of sweat froze half-birthed from his pores. An ebon mountain filled his vision, though like the god's voice he couldn't tell if it was really there, or appearing only in his suddenly aching skull.
The dark mountain was hollow as a drinking horn, and brimming with people. It reminded him of nothing so much as one of the dire ant mounds back home, swarming with bizarre life. And as he watched, flaming oil bubbled up from the depths, cascading through tunnels and melting the inner walls of the mountain, incinerating all of the teeming residents, and vomiting from the top in a great spume of ash and smoke. A city even greater than this temple, populated by an incalculable number of folk, obliterated absolutely.
"Nah, not doing that," said Sullen. "Can't. Won't, even if I could. I'm a Horned Wolf, not a witch nor devil."
" _No_ ," said the winking stars. " _Zosia will. Unless you thwart her_."
Zosia. Though it took a moment to sink in, Sullen recognized the name. His uncle's old boss from the first time Craven had sought his fortune on the Star, according to some of the songs they'd heard along the road. His uncle's bride, according to others, who'd died before Sullen was born. An utterly ruthless, diabolically clever, and intensely dangerous woman, according to all, a Queen of Samoth whom not even death could stop from sowing madness and sorrow, a phantom returned from the bowels of the grave to savage all of the Star.
"All right," said Sullen. "Preventing that kind of thing seems best. There's kids there, and such. Where is she?"
" _You shall meet her once you have found your uncle_ ," said the god. " _Under the snapping of Cobalt banners, in the Crimson Empire_."
"Oh," said Sullen. "Thanks."
A ring of stars flickered once, like a mouth of light smiling in the depths, and the face filled his entire world as it came in to swallow him whole. He closed his eyes, but instead of oblivion received a gentle kiss. Her lips were small and warm as those of Stoutest, before the girl had earned her name and stopped having anything to do with him. Stoutest was the only woman to have ever kissed him, and so he never had cause to doubt her counsel that one should always keep their eyes locked on their partner's when receiving such affection. Opening his eyes, he stared into the vastness of the god, and kissed her back. He felt it all the way down in his treasure, like the one time Stoutest had put her hand down there and made him feel nine kinds of heavens, followed by twelve kinds of embarrassment. This was nine thousand kinds of heavens, with none of the surprise or shame after.
And then his stomach dropped along with the rest of him as the devils holding him broke away from her black wrist, fading into the air as he fell. He landed a moment later on a steeply canted rooftop, the wind knocked out of him, and above him the Faceless Mistress went rigid. He heard the cracking of ice just before a glacier crumbled free of a fjord, and then, with slowness as impossible as the rest of her, she broke apart. The arm that had held him clipped the edge of the roof as it fell, sending splintered tiles flying into the air, but the bulk of her tipped back, crushing the building on the far side of the street. An eruption of dust and debris blanketed the temple for miles, and when it lifted nothing remained of the Faceless Mistress but another decimated statue. Sullen stared down at the wreckage and wiped his mouth on the back of his hand. It left a dark smear.
"By all the ancestors and the unborn, what happened to you?" said Grandfather when Sullen moseyed back into the park. It was the first time he could recall the old man genuinely seeming concerned for his safety, and the novelty made him feel worse rather than better. The last thing he wanted was to worry Grandfather. "Speak, boy, are you well?"
"I'm fine, Fa," he said, giving himself a once-over to make sure he hadn't hurt himself climbing down from the building. No visible damage, so how could Grandfather tell something had happened? "You heard the... ruckus?"
"The _ruckus_?" Grandfather put a hand to his mouth, kept gawping at Sullen. "What in all the... did you stir up a devil king, laddie? Find that Hoartrap again? What _happened_?"
"I found out where Uncle is," said Sullen, hoping that would distract Grandfather. It didn't. Better to get it said and over with, then. How would one of his ancestors have told the tale, once they'd had an adventure like that? With lots of sharp words and deft rhymes, probably, but Sullen's strength was in recollecting songs, not creating them. Let someone else tell it smarter, if they thought it worth a verse at all. "And, uh... I met a god. Or a goddess, I guess?"
"Oh," said Grandfather, relaxing on his pillar as though that settled the matter. A pause. "Was she nice?"
# [CHAPTER
25](toc.xhtml#toc-chapter025)
_T old you he wasn't a scout_." Maroto sneered at Purna, imitating the girl's snippy tone.
"I wasn't the one who let him go," she said, booting the stained wood of their cell door. It didn't budge. " _Durrr, he's got a Khymsari haircut, so he must be Khymsari_."
"It's a pretty terrible hairdo," said Maroto. "I couldn't see anyone but a cultist doing that to themselves on purpose. Lying little shit."
"Well, now what?" Purna turned away from the front of the sparse room to face Maroto. Even in the dimness he could see that her face was at the apex of its puffiness, lips split, cheeks bruised, one eye nearly swollen shut. The Imperials had really done a number on her before she'd gone down, but then Maroto supposed he must look even worse. He certainly _felt_ worse—it wasn't a competition, mind, but she clearly felt well enough to stand and pace the cramped cell and kick at things, whereas Maroto had no intention of rising from the hay-strewn floor anytime soon. "We just wait here for them to execute us?"
"Nah," said Maroto. "They'll definitely torture us first, get any information they can. Me, they'll probably try and use to get Zosia to open the castle—that'll mean more torture, public-like, where she can watch from the ramparts. _Witch, we got your Villain down here—open the gate or we'll cut him open!_ "
"Then what?"
"Then they gut me, because there's no way she's stupid enough to trust 'em—she opens the castle we're all dead, instead of just me."
"No, I mean, then what do we do, you and I, if they'll just torture us anyway—move on the guards when they come for us, or try to lure them in sooner? You look rough enough I could probably call them in now, say you've croaked and are stinking up the place. Then we snap their necks, steal their uniforms, and sneak out to rescue the others."
"Great plan," Maroto said dryly. "Assuming you even broke a neck properly, which I doubt, and we got out of here, which are longer odds yet, what better plan than risk it all to bust out those worthless scumdogs who couldn't even be bothered to fight back when the Imperials ambushed us? We might've stood a chance, they hadn't just let themselves be taken."
"What do you expect, we were all asleep! Except you, Sir I'll Take First Watch." Purna punctuated this with a withering look down at her mentor. "And maybe if we hadn't swung on them we could've avoided the whole thing, lied or bribed our way out, ever think of that?"
"Been thinking of little else," said Maroto, choosing not to remind the brat that she'd been the one to throw that fatal first punch when the Imperials had roused them—he'd been glad she had at the time, because then the Crimson soldiers had started coming at _him_ , and that meant he could fight back without risking his oath... for all the good it had done them.
"If we'd played it cool you and I would probably be locked up with Diggelby and the others, if nothing else. Wherever they are I imagine the accommodations are swankier than a tavern's closet."
"That where we are?" Maroto blinked into the dimness of the musty chamber. What daylight filtered its way into the cell came from above, the thatch or whatever comprised the roof in need of repair. Maybe they weren't so doomed after all...
"Yep, a real shitkicker establishment, too, judging by the stuffed fish mounted on the walls. Just how long were you out? I figured you were faking it so they wouldn't interrogate you right away."
"Yeah, they call that method acting—learned it from some rough-and-tumble Usban players I ran with for a while. A dozen of the troupe's been hanged over the years for getting too committed to their roles. They're not bandits or killers, but if they're _playing_ bandits or killers, well—"
"Rambling, Maroto."
"Listen: help me up, let's see if I can boost you to the ceiling. Maybe we can go up and out. They got the command stationed in here?"
"No, it looked like the important people were working from a temple a few blocks away. The others branched off there, but you and me got dumped in here." Purna was staring at the back wall as though she could see through the timbers and clay. "The tavern's a garrison, I guess you'd call it. Soldiers everywhere."
"Huh." Maroto's good ear couldn't pick up much. "Quiet enough now."
"There was a big to-do a few minutes ago, Snoroto. Sounded like they cleared out in a hurry."
"Doesn't get better than that," said Maroto, taking her extended hand and hauling himself upright. Not to his feet, even, just enough so he was sitting leaned against the rear wall, but even that development caused supernovas to explode in his vision and a volcano to erupt up his throat. Getting coldcocked never got easier; if anything, it seemed to be getting worse the older he got. Woof. Well, if nothing else he hadn't lost his knack for puking on himself.
"Sick!" Purna dropped his hand and danced back from him as another volley of bile came up. She grabbed the room's only furnishing, a chamberpot, and thrust it into his hands. It would have been too little too late, except the ripe contents of the pot summoned forth another devil from his belly. They must have been in here a while, for it to get so full.
Eyes shuttered from the world, icy sweat soaking his clothes, the stink of piss and shit and vomit curling his nose hairs, cooped up in a dingy, dirty cell—it was just like old times, all right. He swooned in place, thought he felt Crumbsnatcher crawling down his tunic but realized it was just a dribble of sick. The sheer abjectness seemed to transport him back over the years, into the last stinghouse he'd stumbled into, and a horrible realization broke way back behind his clenched-shut eyes, in the constipated bowels of his aching skull—none of this was real, not Purna nor the other fops nor Zosia being alive again, it was all just the bitedream of an old junkie. He'd wished away Crumbsnatcher, sure enough, but not to be free of the bugs, never that, but for something even more pathetic... and he almost remembered, could feel the rat's whiskers on his cheek as it kissed him good-bye, but then Purna intruded on his misery:
"Just... ugh. What's wrong with you? Are you ill?"
Maroto wiped tears from his cheeks. He told himself they were tears of joy at coming back to sweet, sweet reality after the waking nightmare he'd just suffered, but the sorry truth was he'd been crying before he came to his senses. Purna crouched beside him, put the back of her hand against his forehead, as though that ever did anything at all.
"Better," he said, because having the shakes and a splitting headache is undeniably better than having the shakes, a splitting headache, and actively vomiting while suffering a spiderbite flashback. He tried to set the chamberpot down gently but ended up just halfheartedly tossing it aside. Stupid numb fingers. "Been better. Been worse. Just give me a second."
More like a few hundred were eventually required, but at last Maroto was on his feet again. Purna looked skeptical when he told her to scale him, but they never had a chance to see if he could have supported her climb to the ceiling, for at that moment they clearly heard an outer door bang open and voices approaching their cell. Here came the torture. Maroto glumly supposed they wouldn't be fed first.
"Get ready," Purna hissed, snatching up the chamberpot. "I get the weapon since I'm smaller."
"All yours," said Maroto, wrinkling his nose and creeping to the side of the door. What a way to go—covered in your own puke, near blind from pain, and without so much as a half-arsed plan. He gave it a quick thought, whispered, "They'll be ready for this, so toss that pot in their eyes. Try to blind 'em before rushing out, or they'll just cut us down."
There. Now they had a half-arsed plan, or at least a quarter cheek's worth. They steadied themselves as they heard a rusty bolt slide, and then the door flew open. This was it.
On the other side were Diggelby, Din, and Hassan, all three falling back in squealing horror as Purna splashed the chamberpot in their faces. Din dropped her crossbow and pawed at her eyes, the weapon going off as it hit the floor and sending a bolt whizzing between Maroto's thighs to imbed in the back wall. If he were but a little shorter he'd have been a whole lot unhappier.
"Oh balls, sorry!" said Purna, hurrying to help their gagging saviors. Maroto followed her out of the cell, trying not to be sick again himself. Each step was hard-won. Looking past their retching companions, he saw that the repurposed common room of the tavern was empty save for dozens of bedrolls and mounds of equipment, the tables stacked up against one wall. A muted metallic clamor from just outside the tavern indicated that the soldiers had vacated their quarters just in time for some sort of entanglement.
"I told you we should have left them," Hassan told the recovering pasha and duchess, ripping off his stained lace ruff and throwing it at Purna. "Between his sleeping on watch and her provoking the Imperials when we'd already lost, they're about as useless as a eunuch at an orgy."
"I wasn't asleep, I just don't hear so good anymore," said Maroto. "And if you'd ever been to an orgy, son, you'd know eunuchs have a thousand and one uses, if you ask politely. But hey, thanks for busting us loose—how'd you do it?"
"Oh, it was ghastly, ghastly," said Diggelby, and now that the filth was either wiped off or ground into his already roughed-up finery, Maroto determined the old boy was blanched and quaking from more than the affront of Purna's attack. His lapdog Prince looked just as scared, shaking in his master's arms. "I've never... And I hope I never again!"
"An old friend of yours paid us a visit," said Duchess Din as Purna helped her up. "They took us to a Chain temple, to be interviewed by the commander. She wanted to know everything about you, and we were telling her, but then... I can't say what happened, exactly. Deviltry."
At the word the entire building trembled, the packed earth floor shivering beneath their feet. Maroto could relate. Most likely a substantial chunk of masonry had been dropped from the castle walls and struck ground somewhere close by, but even as the dust settled and everyone relaxed, he continued to shudder. _An old friend_. She was here.
"What in the cursed name of the creator is going on out there?" asked Purna, and then the oddness of it struck home—they were just outside the besieged castle, in the shantytown that had grown around its walls like dairy mites crowding on a rind of sheep cheese, so why in all the songs of Samoth would there be fighting here unless...
"They've quit the castle," said Maroto. "The she-wolf's left her den, bringing the fight to the hounds who ran her to earth."
"Madness," said Purna.
"Yep," said Maroto. "That sounds like her."
"The scout said she was badly outnumbered, and seeing the camp they brought us through, I believe it," said Purna. "Why sacrifice her only advantage?"
"Hardly her only advantage," said Hassan. "That witch—"
"Call her that again and I'll teach you some manners, Hassan," said Maroto, pointing a finger at the nobleman. "You've worked hard for my respect; don't be so quick to cast it aside now that you've earned it."
" _Her?_ " said Duchess Din. "The witch we're talking about is—"
"An old, old friend," said an all too familiar voice, a hulking figure emerging from a hall that led deeper into the tavern, the enormous pack on his back scraping the top of the doorframe as he entered the room. Beneath the cowl of his yellow robes lurked the withered face of a mummy, the forearms that emerged from the garment revealing impressive sinews bulging just beneath mold-white skin. One enormous hand clutched an oaken staff topped by a carven owl pointing its wing at them, and in the other he casually dangled Maroto's mace, as though the brass-and-steel killing tool weighed no more than a carpenter's hammer.
"Oh fuckity fuckers, he followed us," squeaked Diggelby, crushing his whining dog to his chest. "Look, we don't even really know the barbarian, so—"
" _Get a grip, Digs_ ," said Din, switching over to Falutin, the Imperial noblecant. As with most dialects of Star slang, Maroto understood them perfectly, and so did the pale monster grinning at him with black gums. " _Why would he kill all those Imperials and let us go if he meant Maroto harm?_ "
"Who..." Purna licked her puffy lips, obviously intimidated despite herself. No shame there, this was one scary motherfucker. "Who is he?"
"One scary motherfucker," said Maroto, putting every crumb of concentration into keeping his stride steady as he walked across the common room toward the terrible old wizard. "Hoartrap the Touch, as I live and breathe. They said some reeking old goatfucker had busted them loose, but that description was far too charitable for me to suspect it was you."
"We never said that," said Hassan. "I swear on my pals' lives, we never said it!"
"Maroto Devilskinner, the Barbarian Without Fear," said Hoartrap, flicking his wrist and sending Maroto's mace spinning up into the air. One of its small flanges loudly lodged in a rafter, and the heavy weapon stuck fast in the ceiling. "I'd heard you turned to bugs, so I _am_ relieved to see that was just a euphemism for volunteering your orifices to degenerate nobles. Added any new specimens to your menagerie of exotic genital poxes?"
"Sorry, friend—I know you like lapping up the discharge, but I've got nothing for you," said Maroto, looking square into Hoartrap's rheumy eyes. There weren't a lot of folk tall as Hoartrap, let alone who could meet his basilisk gaze, but Maroto wasn't a lot of folk.
"You look better than I expected," said Hoartrap, pursing his lips and nodding. "Tell you what, barbarian—for old time's sake, I'll let you cradle my balls in your mouth. Something needs to sweeten that awful breath."
Maroto couldn't come up with anything dirtier on the spot—he blamed the concussion—so he grabbed the nightmarish geriatric in a bear hug. Hoartrap creeped him out, because Hoartrap creeped everyone out, even his fellow Villains, but rather than keeping him at a distance like the others did, Maroto always just shrugged and got chummy with the wizard. If Hoartrap ever turned on them it wasn't as though proximity would save anyone; on the contrary, the only hope they'd have was if someone—and _someone_ always meant _Maroto_ —was close enough to lay the fucker out before he could pull one of his tricks. It had never come to that, thank the gods, and then there'd been that time in Emeritus when Maroto had pulled the sorcerer's fat from the fire and Hoartrap had loudly sworn on all his devils that since he owed Maroto his life, he would never take the barbarian's. There would be some who might point out that such a promise wasn't really much recompense, but knowing Hoartrap well as he did, Maroto had been glad to accept the oath.
Now, as the fierce old man returned Maroto's embrace with equal rib-aching vigor, the barbarian found that what had once been mostly pretext was now genuine affection. Damn if it wasn't good to see a familiar face, even an ugly one.
"Hoartrap the Touch?" Purna had slunk over while they were talking, and as soon as they broke their hug the girl bowed to the wizard. "It is an honor to meet you, sir."
"An _honor_ , is it?" Hoartrap raised the snowy branches of his brows. "That's not the welcome I usually receive when strangers recognize my name. Where did you pick this one up, Maroto, and what lies have you been feeding her?"
"He hasn't been feeding me anything," said Purna, but even as Maroto began to nod in approval she went on, causing him to flinch instead. "Much as he'd like to."
"Ah, I like this one," said Hoartrap. "I see she takes after you more than those other three. Yes, hallo, I see you trying to sneak away, but believe you me, that's a bad idea. The fighting's in the streets, and I'd strongly caution against wandering outside until it's over."
"We... we..." Diggelby and the others had frozen in front of the door.
"We're locking up, so no harried soldiers could flee back in here," said Din, directing a scornful frown at Diggelby. His belled collar had given them away. Hassan sighed and miserably dropped the heavy slat in place, securing them all inside the tavern.
"That's as chickenshit a scheme as I ever heard hatched by hero or hen," said Maroto. "Brace yourselves, we're going out there to help carry the day for Zosia."
"They may be chickenshit, dear Maroto, but your scheme is pure poppycock," said Hoartrap. "You and your assistant here are barely able to stand, and after my civil attempt to parley with the Imperial command went the way of the Sunken Kingdom, I, too, am in need of a bit of sit and sip, not stand and stab."
"I have to find her," said Maroto, raising up on his tiptoes to reach the haft of his mace. "I won't wait another moment."
The next thing Maroto knew, Hoartrap and Purna were helping him back up to a sitting position. Apparently he still hadn't shaken off his beating at the hands of the sneaking Imperials. From now on he was going to gag every scout he captured before they had a chance to open their mouths, then leave them tied to a tree—if he hadn't made that stupid vow he'd just as soon kick in their heads, but when you swear on your devil you have to play by the rules or risk Old Black knew what mischief. There was no lower form of martial life than a scout; professional cowards, better at spying and fleeing than fighting fair.
"Don't worry, she'll be here soon enough," said Hoartrap.
"She sent you to rescue us?" asked Purna. "Queen Zosia?"
"So she's _Queen_ Zosia to you, is she, girl? Silly old goat that I am, I thought she'd been dead and gone before you were born!"
Purna gave Hoartrap one of her imperious proclamations: "Even if she wasn't still alive, a queen like Cold Cobalt would keep her crown even in the grave."
"Oooh, she certainly sounds like you, barbarian, don't tell me you've sired another heir?"
"No, definitely not," said Maroto. Then, his head clearing by degrees, "Another? Call me an idiot, sorcerer, but don't call me a father—I've been too careful for that, unless the work I paid you to put upon my loins was naught but mummery? In which case I probably have a lot of heirs by now. And you have much to answer for."
"Trouble not your pretty head," said Hoartrap. "Like all gods, my works are eternal, so long as belief is strong. And as usual, you answer my questions without my even needing to ask them."
"And as usual, you answer every question with two or three more," said Maroto. "So let's have it straight, for a change, before I lose my patience—Zosia sent you for us? It's really her?"
"You don't know?" asked Hoartrap, helping Maroto onto a bench the fops had dragged over from the wall. With a wave and a mutter Hoartrap pulled one of the tables free from the stack and brought it skidding across the floor, kicking up a wake of bedrolls. The nobles squawked and Purna gasped, but Maroto was just happy to have something to brace his arm against.
"Don't know what, witch?" said Maroto, Hoartrap's shtick already tiresome. "I warned you about answering one question with another."
"I was earnestly asking," said Hoartrap. "I've just arrived myself, hot on your trail. I'd heard rumors of the return of the Cobalt Company, of course, everyone has, but assumed you'd caught up with her and seen for yourself. Don't tell me you were captured by the Imperials before you even reached the castle!"
"We were ambushed," said Purna. "It was ten against one."
"He was supposed to be on guard," said Hassan, he and Diggelby dragging another bench over so they could sit on the far side of the table. Din already had her cards out and was shuffling at the end of the board. "Mighty Maroto let those brigands stroll right into camp and get the drop on us."
"My hearing's not what it used to be," grumbled Maroto. "Caught an arrow in the ear while protecting these ingrates a few months back. So you haven't seen her either?"
"I was looking for you, as I said, and have been for ages. I did chance upon the pleasant company of some others who were seeking you out along the road, but I gather I've made better time than they. Here, you, deal me in—I have no great talent for such games, so pray go easy on me."
"I'll sit this one out," said Purna as the others set up their game, and asked Maroto's question for him. "Who was looking for him? Friend or foe?"
"Neither? Both? Who can tell?" said Hoartrap, winking at Maroto. "I don't think I'll spoil the surprise. They seemed... committed, so I imagine they'll catch up to you, sooner or later."
"Devils kiss me for ever missing your company," said Maroto. "Why were you chasing me down, Hoartrap, what business do we have?"
"We'll see soon enough. You've already answered most of the questions I had for you, so I suggest we just wile away the hours until our Cobalt Commander arrives. Then we'll both have our minds put to rest on a number of matters."
"Arrives?" asked Purna. "Why would she come here, if she's leading the charge outside?"
"Smart, yeah, just waiting here," said Maroto. "Whenever we'd won a town, she'd take the troops from tavern to tavern, rolling out barrels and serving the soldiers herself. If it's her, she'll come."
"I'll roll us out one to start," said Hassan, moving for the inner door Hoartrap had come through.
"Better let me help," said Hoartrap, nimbly dancing after him. Maroto couldn't decide which option was more unsettling, if Hoartrap's weirdness was cultivated or genuine. "I already settled accounts with the innkeep and his family, so it may be best if I accompany you."
As soon as the two were gone, the remaining three nobles started in on Maroto.
"Let's make a run for it," said Diggelby, and Prince yapped his agreement, maybe, or maybe he just yapped because he was one yappy fucking spaniel.
"Can we trust him?" asked Din.
"Should I cut his throat if I get the chance?" When Maroto swayed backward at Purna's question, she added, "I've heard the songs. You give me the word, and—"
A shriek came from the back of the tavern, and then Hassan staggered out of the door, paler than any foundation could ever lighten a man of his complexion. No one jumped to his aid, though most didn't have Maroto's excuse of not wanting to risk any sudden moves.
"What?" said Din, but Hassan just shook his head and wobbled over to the table. Maroto may have been the only one to notice that his tassel-toed slippers left dark wet footprints on the carpet of bedrolls.
"Some help you were," said Hoartrap when he returned shortly after, a hogshead floating after him. Most wizards kept their tricks in reserve instead of always showing off, but not Hoartrap. A train of mugs bounced through the air after the barrel, and while Purna and Diggelby stared openmouthed at the sight, Din focused all her attention on shuffling the cards. "What are the stakes, then? I only play for real wagers."
Purna helped Maroto to a drink as Hoartrap blathered at the petrified ponces. The ale was sour as tart cider, but cool on his ragged throat and feverish brow. As Maroto watched the game, Hoartrap pulled out the curved black pipe Zosia had carved for the sorcerer way back when they were all on an endless campaign against King Kaldruut, before she'd stolen his crown with little more than some well-spent silver and a whole lot of angry peasants.
What would a pipe like that be worth, Maroto wondered, hand-carved by the Stricken Queen before she conquered Samoth? Probably a whole devil-load more than he had pawned his for, back when he was suckling on the honeyed stinger—like so much from those days, he couldn't remember how he'd parted with it, only the day where he'd reached for it and found it gone, so he'd reached for another graveworm or scorpion instead. After all these months on her trail, he still harbored a tenderness over not being invited back to the Company, inventing countless scenarios for why she hadn't been able to find him... but all cards being down, it might could be she just knew what an inconstant son of a centipede he was, and thought herself better served by his absence.
"Care for a dip in my pouch?" Hoartrap said, and Maroto realized he'd been staring covetously at the sorcerer's pipe.
"Nah, I'm good." The tambo-stick Hoartrap had shaved into flakes and stuffed into his bowl was putting off a column of harsh dark smoke that smelled more like poison than tubāq, and even if he'd had his old briar there was no chance Maroto would have ghosted his bowl with that nastiness. "Looks like the duchess bluffed you, old man. You ought to pay more attention."
"Rare is the game that is made more enjoyable by being played more seriously," said Hoartrap. "A philosophy I have found applicable in literally all aspects of my existence. Ah, a worthy call, Count Hassan, a worthy call!"
Many hands later, somebody tried the door. Diggelby stood, Prince growling softly from his post under the table, but Hoartrap waved him back down without even looking up from his cards. Maroto's heart felt like he'd just provoked a bite out of a thunder wasp as he stared at the door, said aloud what he knew Hoartrap was also thinking: "If it's her, she'll force it."
The door shook again. Wood groaned. Metal began biting into it. The nobles stared along with Maroto, but Hoartrap coaxed Hassan back to the table by raising the already substantial pot three dinars.
Then the door gave. It was bright inside the tavern, Hoartrap having waved the lamps alight when the sun had set beyond the oilcloth-covered windows, but outside it was dark as a stinghouse basement, and the woman who stood before a crowd of heavily armed soldiers was silhouetted in the splintered doorway.
Maroto didn't stand so much as float to his feet, the one thing that could banish the agony in his battered skull at last before him. His vision tightened, his good ear pricked, and every inch of him tingled the way it did in the heat of battle, when all distractions fell away and the fight became everything. _Zosia_.
She strode into the room, imperious as was her due, and behind her came Fennec, the old crook. His fox helm sparkled, unblemished even after all these years, even after all the action it had seen, but Maroto's eyes passed over this in a twinkling to focus on Zosia's. It stopped his heart. A devil dog, snarling, with the twisted tendrils of a silver crown rising from the steel mask. How many hours had he spent helping her bend those tines back into shape after a battle, how many spikes had he helped replace after a close encounter with sword, ax, or hammer?
Zosia came to him, and Maroto gulped her down like a reformed drunkard tasting soju after a decade of sobriety. This was not the Zosia he remembered, this was Zosia from the portraits she had begrudgingly sat for in the Crimson Throne Room... just before their world had fallen apart.
Midnight blue riding boots came up to her knees, their cuffs banded with silver. Bare, dirtied, and perfect skin followed, her thighs shining with sweat despite the coolness of the night, nothing shielding her from assault or his eyes but a sheer loincloth of polished chainmail. Then her sculpted navel, her solid flanks, and another strip of silver links, her breasts barely constrained by the small outposts of armor. Beyond her helm and this briefest of defenses, so modest as to mock the dangers of combat rather than to offer any actual protection, she wore but a deep red cloak. Onto this burgundy cape spilled cobalt blue hair, the helm designed to let it flow wild—again, the spectacle was everything, her attire a laughing defiance of the suggestion that this woman had anything to fear in all the Star.
This was Zosia as Maroto had envisioned her ten thousand times, Zosia as she lived in his dreams long after all swore she had perished at Diadem. This was Zosia as he had always wanted her, how he had begged her to be.
In other words, whoever this masked, half-naked, blue-haired woman was, she definitely wasn't Zosia. He had let himself pretend for the last blessed months that his beloved was alive, but now, truly, he knew she was dead. Like so many others, he had been fooled by an impostor, taken in by an impossible dream. Maroto let the floor take him, as he had so many times before.
# [CHAPTER
26](toc.xhtml#toc-chapter026)
Diadem was built before the Haunted Sea swallowed the Sunken Kingdom and shadows devoured Emeritus. More than just the capital of the province of Samoth, more, even, than serving as seat of the entire Crimson Empire and anchor of the Burnished Chain, Diadem was the last stronghold built before the Age of Wonders ended, a monument to the ingenuity of mortals and the ability of the devils they bound. Even if all the world should plunge into darkness, Diadem's radiance would continue to shine from the crown of the Star, a beacon for mortals from every corner of the Empire, from every Arm and every isle, forever and ever.
So the Chain Canticles said, anyway. Sister Portolés had come to Diadem kicking and hissing, not even an anathema then, simply a young monster in desperate need of salvation. She had received it, Fallen Mother be praised, but even after they made her nearly human, even after she learned to pray for her exterminated family instead of weeping for them, she had never seen much of Diadem beyond the Dens built into the walls of the dead volcano that enveloped the city. Even when she had ridden out to war against or beside the Imperials, she had only ever passed through a tiny section of the city.
Now she had permission to go anywhere, to see everything, and before she left the capital on her mission she decided to get her feet wet closer to home. The expectation of simply wandering Diadem with impunity filled her with as much dread as it did joy, and the prospect of visiting the Office of Answers in particular made her squirm—but that was the only place the queen expressly suggested she investigate before departing.
According to the gatekeeper who gave Portolés directions, the most direct route from the warrenlike confines of the Dens to the smoother, orderly halls of the Office of Answers took one on a tour of the capital's tunnel system, traversing steeply arched bridges over ice-rimed sewer canals and causeways that dipped low through fungal gardens. Upon leaving the Upper Chainhouse, one descended five hundred and one steps, and while crossing the Forest of Eternal Sin replaced no fewer than thirteen of the candles that had invariably burned to nubs on the countless stalactites. Then a climb of precisely five hundred steps to the black rattan gate that separated the Papal territories of Castle Diadem from the Imperial.
Sister Portolés opted to deviate from this course at the first opportunity, offering the necessary salutes and signals for the wardens to let her pass out of the surrounding walls and into the city. This exchange of time-honored gestures was more or less a formality, as the wardens' purpose was to prevent citizens from getting into the citadel, rather than to forestall officers of church or state from leaving it. The outer door opened, and beyond it lay the bursting city of Diadem.
Wide as the caldera stretched, the five-hundred-year-old settlement had quickly spread from its heart to crowd the whole expanse, until there was nowhere left to build but up. Risky business, that, both practically and socially—climb too high too quickly and your better-born neighbors might sabotage your foundations in the night. No wonder even the fickle serfs here in the capital had rallied behind the Stricken Queen, after she'd opened up the dry, spacious caverns of Castle Diadem for public use. That reform had outlived the doomed despot for all of a week, before Queen Indsorith and Pope Shanatu ran them back outside into the gloomy city. According to the older anathemas in the Dens who had lived through those tumultuous times, it had taken months for the stink of false hope and abject poverty to fade from the interior.
Stepping down the black stairs into the black mud of the streets, Portolés smiled up into the black rain that fell onto the black cloth mask her kind wore when interacting with the pureborn. In the capital, anyway; the army put a stop to that practice as soon as they were a dozen miles outside Diadem's walls—allowing masked figures free range of your camp was asking for trouble.
Even after all these hallowed centuries since the first frame was raised, the walls of every tall, teetering building bled black in the rain, the ash of this sacred ground permeating every timber, brick, and shingle. The only color to be seen in the whole place was the steel blue scraps of storm cloud Portolés made out through chinks in the tightly clustered eaves far above her. From down here it was impossible to see the gay garments the upper classes supposedly wore to spite the grey heavens as they traversed their covered catwalks, and down here the hunched citizens thronging the narrow streets she passed through were draped in dark oilcloth robes not dissimilar from her habit. None but Portolés wore the mask of the witchborn, though, and passersby gave her a wide berth in even the tightest alley between listing estates that stretched close to a hundred feet into the air, the structures rocking ever so slightly in the keening wind. It was dimmer here, now, at midday beneath the open sky, than it ever got in the candlelit grottos of the Dens.
Portolés meandered through the ghettos of Raniputri and Usban, ate a flatfish tsire handpie she purchased from a Flintlander's cart, nodded her curt approval to a gaggle of shriven and branded Immaculate converts praying in the muck beside a line of penitents waiting to be admitted to the West Cathedral. Ashy mud plastered her sandaled feet until they resembled boots. At last, stuck to an announcement board on the covered porch of a condemned tavern, she found what she had sought: a bill printed on a drab sheet of rag paper. Two words that made the sister run hot then cold, her eyes flitting all about the dreary backstreet in nervous guilt, as though she had been the one to stick up the flyer.
_ZOSIA LIVES!_
There were several bundled figures lying on the porch, and once she was sure they were truly asleep Portolés reached for the bill with shaking fingers, as though it might scald her. It peeled back from the soft, damp board like an almost-ripe scab coming loose under a persistent fingernail. Folding and slipping the bill down her habit so that it was lodged in the binding that held her sweaty left breast, she hurried away. This was the sort of thing the queen had suggested she retrieve from the Office of Answers, but before she braved that dread department she had wanted to see for herself if the revolutionary propaganda was as prevalent in the wild as Her Majesty had suggested... And lo, it had taken only a bit of wandering around until she'd stumbled onto the bill, the search nowhere near so arduous as she'd expected.
Not that Portolés had possessed any cause to disbelieve Queen Indsorith on this matter, or any other, but ever since Kypck the war nun had been unable to stop herself from doubting virtually everything. This pervasive uncertainty was part of why she had agreed to honor the vows she had made to her queen, instead of those she had made to her church—Queen Indsorith alone had agreed with her that it was a sin to have executed those villagers and the disobedient soldiers, no matter who gave the order. Prior to this surprisingly liberating confirmation of Portolés's culpability, every single superior she had confessed to was primarily concerned that one of the Chain's anathemas had let an Imperial colonel die under her watch. Everything was backward, the Queen of Samoth quietly reflecting on spiritual matters while the Pope of the Burnished Chain raged over military failings.
In the end it was her doubt that propelled Portolés into the decisions she had made, decisions that had seemed so easy at the time but now stunned her with their enormity. Did her loyalty to her queen make her a traitor to her church? To the Fallen Mother? It was an unnerving experience, to trust in her intuition, as the queen had urged her, when all her life she had been taught that her impulses were not her own, that they came from the Deceiver to ensnare her soul. Yet here she had taken a first faltering step down that road, beginning her search out in the muddy streets instead of where the queen had suggested, and by giving in to her instinct she now had one less doubt to tax her cluttered skull. Curiosity, it seemed, might have its uses, despite how fervently the Chain derided that sin above all others.
She realized she had become lost, the anonymous streets giving up no hint as to which direction she stomped, and she paused at a mucky intersection. As soon as the panic of not knowing tightened her chest, though, she blew it out like so much bad air—Diadem was a ring, albeit an enormous one, and so long as she plodded forward she would find her way back to the castle in time. As if that wasn't the heaviest symbol ever to be wrought in stained glass, she thought with a smile.
Far in as she'd come, it took some time for her to get back out to the edge of town and reenter the castle. Several times as she passed higher and higher into Diadem's flanks she touched the bill that rested atop her heart; when offering the queen's writ to the guards who frequently barred her way she imagined giving them the flyer instead. She couldn't decide if those two words printed upon it were simply treason, or outright heresy.
When she was at last admitted to the open floor of the Office of Answers' Truth Chamber, the dozens of people undergoing questioning caused her stair-winded breath to catch in her tight chest. Considering there were far more individuals strapped to gurneys and chairs than there were Askers to tend them, the Office must be a bit understaffed at present.
"Raided a cell in Lower Leviathania," supplied the sweaty young clerk charged with chaperoning Portolés. "Usually we don't cram them in like this, but the holding pens are overfull, so we're making do."
Like all in the Office of Answers, he went naked while in the stiflingly warm Truth Chamber. The Askers had nothing to hide from their guests. By the light of the azure-flamed braziers reflecting off the polished floor of volcanic glass, Portolés eyed him for signs of deviltry, though she knew witchborn were forbidden from serving in the Office. That was not the way the state conducted itself. Portolés, on a real roll with thoughts both heretical and treasonous, wondered briefly if the Office would feel the same if those anathemas who could supposedly peek into minds could do so with strangers instead of only those with whom they were already intimate.
Regardless, everyone seemed to be predicting Portolés's thoughts of late, and it was making her paranoid. She jumped when an old woman's scream choked off into a gurgle as her tongue was removed with burnished shears that looked much like those used by the Papal barbers to heal the witchborn. Looking around at the other instruments in use or laid out on tables, and the dark swirling pools flowing into the numerous floor grates, she found much to compare with the operating theater where she had been rendered as pure as the church could make her. Bad memories surged up in her gorge... or maybe it was just the peanuty flatfish she'd eaten.
"They were all caught in the act?" she asked.
"A few ringleaders, and a lot of folk just looking for easy work or a dry bed." The clerk sighed. "It's always like this. Don't worry, sister, most of them will be turned over to your people soon enough."
"And all this was found in their quarters?" Portolés's heart tapped at the bill resting above it as she surveyed the table piled high with identical leaflets and several aged, weatherworn folios. "Propaganda?"
"That's one word for it," said the clerk. "I'm sure you'd call it something else. Was there someone in particular we could help you find? Even if they are not here we could have them to you in hours, I assure you."
Portolés picked up one of the folios, flipped through it, tossed it down, and picked up another. Beneath the mask that limply clung to her sweaty face she could feel her cheeks burn from more than the heat. The name of the Stricken Queen, appearing over and over, on every page... Surely the authors had known their words could land them here, and yet the text spoke to their fearlessness. Fearlessness, or a need to put it down in ink, regardless of the cost. The vellum folio in her hands was only half written, waiting to be completed in the cramped yet precise script—did the author still have her fingers, or were they already in a vise?
"I'm taking this," she said, as much to herself as to the clerk. "Do you need to make note of that before I take my leave?"
"Revered Sister, you can't—" the clerk began, then amended himself when she glanced up from the book. "That is, the Office, under direct orders of the queen, has immediate need of it. I will personally copy its contents for you and—"
"Do I need to show you my writ again, boy?" said Portolés, flushing anew with the overconfident words.
"No, Revered Sister," said the clerk, looking at his bare feet.
This was the extent of the power her queen had granted Portolés. It was staggering. She might die on the morrow, but for today she, an anathema, had authority unrivaled by any save the Crimson Queen or the Black Pope. By any means necessary meant by any means she wished, and pity the pureborn who questioned her will. Out of habit she tried to choke down her smile, but then reminded herself she was entitled to grin from ear to ear.
"I also wish to speak with the author. Someone here wrote it, yes?"
"We won't know that unless we are permitted to use it in our questioning, will we?" said the clerk with a bit more attitude than Portolés expected. It was a fair point, though.
"I did," called a teenage youth strapped to a nearby gurney. He had the ferret-eyed, rawboned look of a natural born thief to him. He leered at her. "You like my tract, witch-nun? It's all the Fallen Mom's honest truth, every blessed word of it, and—"
"That's quite enough of that," said the Asker who had been quietly talking with the woman in the next chair over. He was a scrawny man whose shaven genitals were blurred by bright red tattoos of Cascadian script, and he jabbed at the gurneyed man with his dripping three-pronged prompter. "I already have quite a few queries for you; no sense in raising more questions before we've even started."
"Believe!" said the boy. "Take off those blinders they force your kind to wear, witch-nun, read the truth and decide for yourself!"
"I'm very sorry, we'll have to continue this later," the Asker quietly told the semiconscious woman he'd been interrogating. "As for you, young man—"
"What harm would it be were it false?" cried the boy, his eyes still locked on the slits in Portolés's mask. "When's a lie ever called down such consequences, answer me that!"
Portolés had no more expected profundity in the Office of Answers than she had subtlety, but she found herself deeply moved by the boy's appeal. In this roomful of tortured dissidents and Askers employed by the Crown, only she knew that what the flyer said was true: Zosia lived, and what was more, Portolés had probably met her face-to-face in Kypck. In twenty years of rule, Queen Indsorith had told no one of the deception that had fooled the world, and only confided in Portolés because she believed that doing so could prevent another war. These rebels couldn't actually believe Zosia had survived her two-thousand-foot fall from the Crimson Throne Room and was biding her time until she launched a second Cobalt War. Their slogan of _Zosia Lives!_ was just that, an anthem designed to fill their fellows with hope and their enemies with hatred... But like the boy said, if the Empire knew their rabble-rousing came from baseless beliefs, why suppress it so viciously? The queen knew there was more than a kernel of truth in their message, and this was how she dealt with it—the same way the Burnished Chain dealt with anathemas. Doubt blossomed anew in Portolés's heart as she realized that her new master could be every bit as brutal as her old one, when she felt threatened. Queen Indsorith had claimed that the mission she entrusted to Portolés would save countless lives across the Star, but even if that proved true, Portolés couldn't save the poor, naïve sinners in this room.
"You seem to be confused on the etiquette of polite discourse," the Asker told the outspoken prisoner, looming over his gurney and softly applying the points of his prompter to the ball of the youth's throat. " _I_ ask, _you_ answer, not the other way around. But since you're so eager to converse, why don't we just dive right in?"
For all his bluster, the young man closed his eyes and let out a whimper. He would be making a lot more noise before long. Portolés had screamed and screamed when the barbers had carved the sin out of her, screamed until they had seized her forked tongue and stitched it together, blood gurgling in the back of her throat. This heretic was going to scream, too, but with no physical signs of corruption, how would the Asker know when his work was complete? As the steel prompter reflected the brazier light, Portolés felt a flashback of fear, and just as soon a pulse of relief that it was someone else who was going to be cut instead of her. Back in the Kutumban mountains, she had executed men and women who refused to massacre peasants, and then she had overseen the purge of Kypck, and then she had watched as an Imperial colonel burned alive, but she was going to turn around and walk out of here, and this boy who had only written a political treatise probably wouldn't. Perhaps the Crimson Queen's justice wasn't so different from the Black Pope's.
"Sister?" said the clerk, reaching out for Portolés's elbow but thinking better of actually touching her.
"Mmmm," said Portolés, picturing Brother Wan strapped down where the heretic was, imagining the sounds he must have made when they removed his half-formed beak. Just like that, it happened, the anticipation of a new sin warming her chest.
"It would be best if we left Asker Vexovoid to do the queen's work. I can escort you out."
"Certainly." Portolés nodded, savoring the sensation of delay until it became unbearable. "As soon as you unstrap that heretic. He's coming with me."
Of all of them, the heretic seemed the most surprised. Asker Vexovoid ground his jaw so loudly that Portolés could hear him, but sheathed his prompter and began loosening the boy. The clerk just scowled at her. As the shock wore off, the heretic giggled nervously.
"It's no laughing matter," the Asker told him. "You'll be wishing you'd kept your mouth shut before the end. Our Mother Church has a very different methodology for gathering intelligence than this office."
"I'm not going to strip before I torture you, is what he means," said Portolés, pleased to see Asker Vexovoid's sour expression now matching that of the clerk. Already she doubted her snap decision, as she always did when she had crested the trespass and was left with nothing but the promise of penance. "I'm in a hurry, so let's get a move on."
"Would you like him like this, or is there something more the Office can do for you, sister?" asked the clerk as the heretic clambered down from the gurney and Asker Vexovoid turned away without a polite farewell.
"I would like some pants, if it's not too much trouble," said the heretic, cupping his shaking hands over his groin.
"Manacles on his wrists and ankles, connected to each other, and to a collar. Three extra locks. The same key for all of them. A long chain tether fixed to his collar. A gag in his gob and a blindfold under his hood. Plain robe," said Portolés, and then decided to be charitable. They were going to be riding for some time. "Undergarments, I suppose."
The heretic might be useful. Even if he'd been lying about writing the tract and just taken the credit to get her attention, if he'd been brought to the Office of Answers he surely knew more of the cultish veneration of the Stricken Queen than Portolés did. Any knowledge he possessed might prove valuable as she embarked on her quest to track down the woman who had escaped Kypck, the woman Queen Indsorith believed to be Cobalt Zosia. Besides, Portolés could always kill the man if he turned out to be of no use to her. She could kill him for no reason at all, if she wanted—that was the power of the authority the Crimson Queen had given her.
So she told herself, but these thoughts only took form after she had saved him from the Office of Answers.
It was after sunset and still raining when Diadem's southern gate opened for them several hours later. There was something sublimely absurd in the hundred-foot-tall, ten-foot-thick iron-banded gate rolling back just for two riders and a pack mule. The thousand soldiers who worked the winches doubtless agreed—not for nothing was the southern gate normally opened but once a day, to admit travelers during the noon hour.
The heretic had to ride sidesaddle since Portolés refused to unlock his ankle chains, but any protest he might have leveled failed to clear the gag. Their way was lit by sputtering sapphire flames of burning gas that rose from the mountain via tubes of carven obsidian flanking the wide road, torches that had never gone out since first lit at the dawn of Diadem, even in blizzard or hurricane.
Midnight found them at the last torch, and Portolés hitched their animals at the way temple beside the final beacon. It was a humble yet large one-room chamber carved into the dead rock. Only the clergy were permitted to use the refuges that spotted the Imperial highways, but based on the bashed-in door and heaps of excrement on the broken penitence bench, others had sought shelter here. Tonight, however, they had the place to themselves, and intending to keep it that way, Portolés used the ruined bench to bar the door.
"I could've died!" the youth said as soon as the gag was out, shaking his manacled hands at her. "Can't breathe good through my nose normal-like, say fuck the devils with a wet hood over my face!"
"Say fuck the devils again and I'll put it back in," said Portolés, pulling her own damp mask off and tossing it carelessly on their heaped provisions. She returned to the fire she'd kindled in the potbellied stove before tending to her prisoner. The wood let off the strong odor of urine as it burned. "My name is Sister Portolés. You will address me at all times with the respect my station commands."
"Sure, sister, the respect of your station," said the heretic, scooting on his butt over toward the fire, the chains around his ankles and wrists jingling. "Not that you asked, but my name is—"
"I will call you Heretic," said Portolés, deeply unhappy with herself for the mad compulsion that had led her to take him along. "Count yourself blessed I can call you anything other than the memory of a doomed man I left behind in the Office of Answers."
"Whatever you say," said Heretic, warming his hands. "You're the boss, I'm the heretic. Got it."
Heretic had the sense to stay quiet while Portolés boiled water to soak seaweed and beancurd in, and then they ate in silence, slurping from plain wooden bowls. Camping like this reminded her of being out in the field on campaign, first against the Imperials and then alongside them. The marked difference was that it was just her and a single other soul settling in for the night, instead of a whole regiment, and she felt an unexpected tremor of lonesomeness—she was often alone in her cell, of course, but she could never remember a time when there weren't legions of other people within shouting distance, either in Diadem or on campaign. Now it was just her and a proven criminal for miles and miles.
After they'd eaten, she looped Heretic's chain leash around the base of the stove, back through his manacles, and then secured it with one of the spare locks. He wouldn't be comfortable, bent up like that, but he would be warm.
"This isn't necessary," said Heretic. "Really!"
"The sooner you stop hoping I'm a fool the sooner you will find peace in your fate," said Portolés, stretching out to her full length on the other side of the stove. Well, he might think her a fool, given her decision to take him into her custody. When Queen Indsorith had given the war nun permission to enlist anyone she felt would help her find Zosia, so long as she kept the nature of her mission a secret, Portolés rather doubted Her Majesty could have foreseen this ill-advised conscript. This was the exact sort of thing that had always landed her the worst penance, snatching at forbidden fruit just to see what it tasted like. Mother Kylesa and Abbotess Cradofil and even Brother Wan had always warned her there would come a day when she fell too far to climb up again.
She pulled out the heretic's book to distract her from the relentless guilt that constricted her throat. No matter how convinced she was at the time that her actions were correct, within in a few hours she always arrived at this place, craving confession even worse than she had craved whatever temptation she had succumbed to. Except now she no longer even had the prospect of confession to assuage her fears—Queen Indsorith had convinced her that once she left Diadem, it would be incredibly dangerous for her to meet with any other clergy, lest word of her location reach the Black Pope and arouse her suspicions.
"This isn't what I expected," said Heretic. "You hear a lot of stories, sure, but I never... I mean, where are you taking me? Can I know that? Are you gonna publicly execute me in some dismal corner of the Empire? As an example, like?"
"Hmmm," said Portolés, opting to put another log on before settling in with the folio.
"No, that don't make sense," Heretic decided. "Maybe—"
"Heretic," said Portolés, sitting back on her bedroll and glaring at the scruffy embodiment of all her questionable decisions.
"Yes, Sister Portolés?"
"If you say another word without being spoken to I'll put your gag back in, and leave it there all night."
"Mmmmmmm," said Heretic peevishly, but he spoke no more.
As she finally settled in to read, Portolés felt some of her anxiety burn off into giddiness. Reading the contents of this tract was obviously a crime against both Crown and Chain, and it was hers to savor. What an ominous pair of days she had lived through. Who knew letting that nasty Colonel Hjortt burn to death would upend her life in such a radical direction? The Fallen Mother, obviously, and the Deceiver, surely, but not Portolés. She opened the book and read the first two pages, pages that held more heresy than she had ever thought possible to contain in such a scant space.
_Look! Listen! Harken! Your Very Life is at Stake!_
_Look here, You! Look with Your Own Eyes! And if You be Blind, put then Your Ears to the Lips of the Wise, and Listen! Listen! However you Come to this Truth, the Only Truth in Diadem, Ponder Upon It, and do so with Your Mind. The Mind that is Yours and Only Yours. Feel the Truth with Your Heart, the Heart that is Only Yours._
_Decide for Yourself. You Must Decide for Yourself._
_You Bow before queen and pope. You Believe Them. You Sacrifice Yourself to them, You Sacrifice Your Children to them, Your Spouses, Your Animals, All Your Worldly Possessions. They Say this is the Price. The Price for what, We ask you? Protection of Your Body, Protection of Your Soul, that is their answer. This is The Lie._
_It was Not Always So. The Burnished Chain speaks of a Deceiver in Heaven. There is a Deceiver, but he is not in Heaven, but Here, on the Star, in Diadem!_
_The Burnished Chain speaks of a Savior in Hell. And this is the Lie, coached in The Truth: our Savior came to liberate Diadem, and it was the Burnished Chain who cast her Down._
_Queen Zosia Believed in a Diadem Free of Chains. Queen Zosia fought the Devils we now Bow before. Queen Zosia fought to Free Us. If we are Worthy of Freedom, should we Accept the Yoke of Corrupt Church and Illegitimate Queen?_
_If You Deserve Freedom, True Freedom to Live As You Wilt, Why Do You Wear the Collar of Your Oppressors?_
_Fear is the Answer. Fear for Yourself. Fear for Your Family. Fear for Your Soul._
_Fear is the Sword and Scepter of the Church and the Crown. Fear is the Shackles Upon Your Limbs. Fear is the Blindfold You Wear. Fear is the Poison in Your porridge, making You Sick. Making You Die. The pope Laughs as You Weep. She drinks Your Tears. The queen smacks Her lips as You Work Yourself to Death. She drinks Your Blood._
_All they Bring Us is War. War Against Whom? Barbarians to the East? Immaculates to the West? Raniputri Dominions or the Free Cities of Usba? No. They Bring War Against Ourselves. They Say Peace has been Bought, At Last, but how Many lie Dead from a Childlike Squabble between queen and pope? You Know Innocents Who Died in this War, do You not?_
_You, reading This Truth. You, Hearing This Truth. Answer True: how many of Your Loved Ones Perished in a Senseless War? You Tithe and You Tithe and You Tithe, All to Fund a War Against Your Own Family._
_This is The Lie. The Same Tongues who spread The Lie also Claim that Queen Zosia is twenty years Dead. Do You Believe? Do You Trust the liars who Grind You to Dust? Do You Believe Queen Zosia and All She stood for can Ever Die?_
_There are Those Who Believe. There are Those Who Do Not. The Truth is Not that One is Right and the Other Wrong. The Truth is that Queen Zosia Lives On. Her Breath Stirs the Coals of Freedom. The Fire She kindled when She took the Throne is Dying, but is not yet Extinguished._
_Does Zosia Yet Live? some ask. Did She Ever? say others._
_This is not The Truth. The Truth is that She is With Us, and if We are Strong, She will Aid Us. But We must be Strong before She Returns._
_There is Time. To Save Our City. To Save Our Empire. To Save Our Souls._
_Stand Against the Dark. Fight Against the Dark. Stand Against the Dark._
_Listen! Listen, Think, and Prepare. War is Coming, and Not the War They Wanted. We Will Not Stop Until The Cause Our Parents Died For Is Saved. Zosia Exists Forever in Your Heart—Will You Set Her Free?_
Portolés closed the book and reflected for a very long time on what she had read. Then she took out the bill she had removed from the tavern wall and carefully unfolded the damp paper by the low light of the dying fire. She had seen hundreds of duplicates stacked on the table in the Truth Chamber, but still the sight of the poster sent shudders coursing through her. Even after all the queen had told her, even after seeing how plainly the Deceiver's wiles were at play in the text she had just read, these two words filled Sister Portolés with a churning, burning mixture of dread and, Allmother forgive her, excitement.
Could it be true?
Could it not, given what she now knew? A week ago the Stricken Queen had meant absolutely nothing to Portolés, a blot that both Crown and Chain agreed should be scrubbed from Imperial history. She had never suspected that peasants the Star over apparently clung to the woman's memory, praised her as a holy symbol of resistance, and were tortured for it whenever they were caught. And most incredible of all, these dissidents were right, more right than even they suspected. Even when the fire died completely the words on the flyer floated before Portolés's vision, tattooing themselves upon her eyes:
_ZOSIA LIVES!_
# PART II
# AND THE DEVILS TO GRANT THEM
I wish to leave the world
By its natural door;
In my tomb of green leaves
They are to carry me to die.
Do not put me in the dark
To die like a traitor;
I am good, and like a good thing
I will die with my face to the sun.
—José Martí, "A Morir" (To Die) (1894)
# [CHAPTER
1](toc.xhtml#toc-chapter027)
In the plush backroom of a Zygnema stinghouse, Zosia battled Chevaleresse Singh. Neither Keun-ju nor Singh's crew were foolish enough to intervene, the Virtue Guard and the masked women sidestepping when necessary to avoid the fray. Zosia wouldn't have bet on herself in a fair fight, dead gods knew, but when a combatant is a devil up on her foe, well, that changes things. Or at least it ought to. The question was whether Singh had actually set Anklelance free in the decades since they had last seen one another, as Zosia hoped, or if the woman's devil was secreted beneath the pillows strewn around the room, waiting to strike her calf. Of all the ill-starred luck, to be saddled with a dingo of a devil when your second in command lands a carrion viper...
Singh fought like a devil, but Zosia fought like a witch trying to bind one. After Zosia's sucker punch failed to drop her, Singh tried to keep her at a distance, pummeling the older woman with her longer limbs. Zosia careened through the onslaught, deflecting what she could with her ropy forearms and shrugging off what she couldn't. She got in close, firing a chain of punches right into Singh's stomach, chest, and throat. It felt like hitting a shield, only harder.
Singh popped her knee up between them, uppercutting Zosia's left breast. Then she tackled Zosia to the ground, legs and arms coiling around her like a funnel python's rubbery tentacles and locking into place. The crook of Singh's elbow choked her, and through watering eyes Zosia looked for Choplicker. This was it. Her devil was nowhere to be seen, and no matter how she contorted herself or how viciously she jabbed with her elbows, Singh only bore down harder.
Zosia panicked. This sort of end had always been a possibility, and she'd always imagined herself going with dignity, maybe a wry last word to her executioner, but now that it was really happening she couldn't help herself. The more the strength went out of her the harder she raged, choking herself even worse in the process. What a way to go—throttled by one of your best friends, universally reviled to such a degree that even the devil bound to you would rather suffer an eternity of imprisonment over your grave than intervene to save you. Perhaps Choplicker knew she would never set him free, even if he helped her now, and so sought to get it over with rather than prolonging the inevitable...
Zosia realized these were dream musings, that her throat no longer burned, that she had floated away from Singh, from the stinghouse, from the Star. Untethered, she drifted through a moonless, starless sky... or the depths of a lightless sea. As soon as it occurred to her that she was dying, or maybe even already dead, the Diadem Gate appeared before her, the alabaster rim luminous even without sun or moon to reflect upon its etched surface. Beyond that border a deeper darkness rippled, and something colder and more primal than even the fear of death filled her lungs, stopped her heart, and caused her to impotently claw and kick the void around her as she floated inexorably toward the Gate.
Singh slapped her awake, gently-like. "Ups time, Queenie. This isn't that sort of fairy tale."
"Buh!" Zosia rasped, sitting up and shivering. They were still in the bugroom, Singh's lined face highlighted by the chaotic dimming and brightening of the firewings in the terrarium above Zosia's pillowy bower. Keun-ju and Singh's guards had left, but Choplicker remained, the furry piece of shit lying on the far side of the room, watching them. She spit blood at him, and said, "Didn't think it was possible you could hate me as much as I hate you."
Singh followed her gaze. "Devils see further and farther than mortals, you of all people know this. He wouldn't have let me kill you. No devil is _that_ stubborn."
"That's what you say," said Zosia, blinking the cup in Singh's hand into focus and taking it in her own shaking fingers. Honeyed water. Warmer than she liked, and it hurt to swallow, but it soothed her raw throat. "You ever heard of a devil turning down its freedom?"
"Never," said Singh. "But they are not gods, Zosia—if a devil cannot fulfill a wish, it cannot fulfill a wish. Have you thought about why it might not have been attainable?"
"If I knew why, I'd be long shy of him," Zosia said darkly, raising her voice to make sure he heard. "Whatever his reasons, I don't think my wish was asking much at all, powerful as Hoartrap said he was. I'm starting to think the fucker's got a high opinion of himself, is holding out for a request worthy of his regard. Joke's on him, because the more I think on it the more I've come to realize the thing I want most in the whole wide world is to pay him back for all the heartache he's given me. I hope he's there when I go, so I can look him in the eye before leaving his worthless hide to rot for all time in a hell of his own making."
The silence stretched on after this pronouncement, kept stretching as if it might extend forever. Singh broke it by reaching over and hugging Zosia, saying, "Oh, sister, how I've missed you. I wore white for the week after I heard about Leib and your people, and had my sons prepare them a banquet in the Kitchen of the Gods. I am overjoyed to see you alive and hale, but would have preferred to think you dead, so long as you and yours were living happy lives."
"Thanks," said Zosia, wincing as she straightened up on the pillows. Singh had really nailed her in the tit. "Good to be missed, especially if this is the welcome I get when I visit."
"You struck me, Zosia, and in front of my children—I should have taken it, thanked you, and asked to kiss your bottom?" Singh stood and went to one of the terrariums built into the walls. "I'll get you something for the pain."
"No thanks," said Zosia. "You said Kang-ho sent you to kill me, Singh, what should _I_ have done? Next time, open with 'I'm not going to do it, but here's what's up.' Save us both some bruises."
"I'm not bruised," said Singh, shuddering on a long, fine-mailed glove and sliding open a panel above the glass cage. "And I would have hoped you'd trust me, after all we've been through. I owe you my life, General, a dozen times over."
"So does Kang-ho, and he still tried to get me dead. Maybe to his thinking if you did the backstabbing for him it wouldn't count." Talk Singh into helping, track down Fennec and Princess Ji-hyeon, ransom the girl back to Hwabun, screw Kang-ho over in the process, and then hit Samoth and its evil queen with everything she had. That order. Oh, and Bang—that punkass pirate needed to get hers, too. "I told you I don't want any bugs, Singh, don't make this weird."
Singh had reached into a narrow terrarium and, tapping her mailed pinky on the leaves of a nettle, enticed a sinuous insect from its hiding place on the plant's stem. The centipede darted forward, burying its head in the mail and coiling itself around the finger. Singh cautiously raised her hand from the glass cage and held the centipede-wrapped pinky up to her pursed lips. She slowly brushed the creature's downy back against her mouth, her lips puffing out in bright magenta blooms as she returned the insect to its enclosure and gently thumbed it off its perch. "Mmmmmm. That's much better."
"And here I'd heard Maroto was the one who'd gone buggy."
"Oh gods, Maroto! That's a tragic case, all right—Kang-ho told you what happened to him, then?"
"Only that he didn't stay on with the new queen," said Zosia, still marveling that of all her Villains Maroto had been the one to ignore her will and thrown down in her memory. "Kang-ho said you and Hoartrap were the only ones who followed orders on that count."
"Don't remind me," said Singh, swaying back over to where Zosia sat and plopping down in the cushions beside her. She rooted around and retrieved a pillow that turned out to be a thickly padded pipe-purse. "You want to borrow one of mine? I sent your things off with your boy, and I'm guessing you don't want him listening in, if he's one of Kang-ho's."
"Definitely. On the pipe, I mean, not so sure about the boy working for Kang-ho," said Zosia. "Whatever you're puffing is good—too much to hope you still have that devil I whittled you?"
"Keśi rides," said Singh, passing over the pipe Zosia had carved her during the Siege of Rondio. Whereas most of the pieces Zosia crafted aspired to beauty, Singh had expressly asked her to carve an eyesore; a pretty pipe was both provocation to pride and a target for thieves, but a beater would invite no such attention. Zosia obliged the knight, first shaping the finest billiard she had ever wrestled from the briar, and then scuffing and scratching and chipping away at it until it looked like an animal had chewed it. Instead of leaving it natural or giving it a traditional stain, she colored it sickly yellow, highlighted with splotches of green and white. The finishing touch was a short, slightly crooked stem whittled from the tusk of a devil horse they had brought down together in the acid-dripping jungles of the Forsaken Empire.
"I made the walls too thin," said Zosia, inspecting the pipe. "This must smoke hotter than a devil's fart."
"Reminds me to pace myself," said Singh, retrieving a handsome meerschaum pipe from the purse for herself. The bowl was intricately carved in the shape of a woman's face. Peering closer, Zosia saw it was modeled after Singh right down to the mustache. Heavy usage had darkened the white clay, browning it like good toast and making the resemblance uncanny. So much for chivalric humility. Singh waved it at her. "Outlandish, isn't it? The kids got it for me when I turned fifty, and I'm ashamed to say I've been relying on it of late. You don't have to rest it like briar, so on days when I need a few bowls to see me through she's a welcome sister."
Singh sliced medallions off a tawny rope of palm-wine-infused tubāq and tossed two of them to Zosia, who rubbed hers out before packing Keśi. Singh simply folded hers into the meerschaum bowl. If Zosia had been smoking with any of the other Villains she would have insisted they switch pipes now, given the trick Kang-ho had pulled on her, but Singh would never stoop to such treachery. Not if she didn't have to, anyway, and if she'd wanted to drug Zosia she could have shoved her nose full of icebees while she was choked out.
Zosia gladly accepted the glass lamp and whangee tamp Singh offered, and once they both had their pipes well lit they relaxed back in their pillow piles and smoked in contented silence. Zosia knew sooner or later they would talk, and when they did she might not like what Singh had to say, so it was better to prolong this rare happiness as long as possible. The back of her mind roiled with a dozen questions, a hundred suspicious, but she shut them out to again bask in the companionable quiet she and Singh always found together. Not even the throbbing ache in her breast could detract from the experience. When her thirst got the better of her and she sat up to ask her host to send for a draught, Singh seemed to read her thoughts and before she could speak tugged on a bell rope. They grinned at one another through the spicy fog, it becoming a competition to see who would crack first, but it wasn't until a turbaned woman brought in a low table and a bareheaded, bun-wearing man followed with a laden tea tray that Zosia broke the silence.
"Thank you both, truly." Looking to Singh, she asked, "Yours?"
"Sriram, my second son, and Udbala, my third daughter."
"You honor me, Mahārājñī Zosia," the two said in unison, each taking a knee.
"Your kids, all right," said Zosia. "Enough of that, you two, no bowing to me. Not unless your mother does first."
The son looked confused by this, the daughter looked insulted, but Singh just waved them off. "Make sure our other guest is being looked after. And if I see you chewing betel in my house again, Udbala, I'll really make that mouth red."
Zosia waited until the children had left before saying, "I thought your teeth looked pretty clean."
"Quit gnawing that trash years ago," said Singh, pouring the chai and retrieving the pipe from where she had propped it against the tray. "Even now, though, I see them spit and I get the old craving. Hard to believe I used to have more spittoons than pipes."
"Good-looking kids—there were four girls in here when Keun-ju and I arrived; they all yours?"
"Only Udbala, the other three are nieces. My twins aren't speaking to me right now—I wouldn't support a harebrained campaign they were launching against a nearby Dominion. Even though I tried to talk them out of it they blame me for their failure. It's just too stupid for words."
"Free counsel can be pretty expensive, if you don't heed it," said Zosia.
"Hmmm," said Singh, relighting her pipe while Zosia sipped the buttery tea. "That sounds like a wise saying, but I'm not sure it actually makes much sense. Anyway, the girls are good, other than being brats. I also have a pair of sons who haven't done anything too idiotic of late. My eldest, Masood, is fomenting a rebellion in Thantifax, the capital of the next Dominion over. That's another reason Umhur and Urbar are mad at me; they think I'm playing favorites by casting my lot with him but not them. Ugh. This stinghouse belongs to the other one you just met, Sriram. It's a cover to launder money for the Dull Kriss, a revolutionary faction that we're steering away from Zygnema by offering them stakes in Thantifax."
"The nut doesn't fall far from the bush, I guess," said Zosia, biting into a biscuit. "Five kids sounds like a lot. How do you find time to work?"
"The grandchildren are where things get complicated," said Singh. "When it was just my brood, it was easy—I rode an elephant into Daar with a twin on each tit, and their father looked after them when I rappelled down the side to accept a challenge from the raja we were unseating. It's a hassle to duel with a big belly and your dugs all sore and leaking, to be sure, but it's better than fighting with a broken leg or arm, and we've both done that well enough. The grandchildren, though, for some reason I get nervous around them, more nervous than I ever was with mine. They stay with a nurse rather than riding with us into battle, and the whole blessed time I'm worrying about what might go wrong back at home—what if the nanny doesn't let the milk cool, that sort of thing. Stop smiling, it's embarrassing!"
"I'm glad you've done so well for yourself," said Zosia, and though she meant it with all her heart there came hot on its heels another thought, a darker one. Why were Singh and Kang-ho allowed to start over, in plain sight and with any riches they'd plundered from the Crimson Empire, when she and Leib had forsaken everything, even her name, and were still punished absolutely?
This wasn't a rhetorical question— _woe is Zosia, where is the justice in the world_ , that kind of shit. Zosia had been queen for a full year before becoming so depressed with her ineffectuality that she preferred to fake her own death rather than continue to rule, so she would never begrudge the devils for her ill fortune, or an old friend for her better luck. No, the question of why Kang-ho and Singh were doing so well, living under their own names, demanded an answer. If Zosia had been in Indsorith's position, she would have targeted each of the Five Villains first, and only when they had all been brought down would she have gone after their leader. The captains would be easier to find, for one thing, and if the assassination of their general failed, as it had, she would not have been able to fall back on her Villains for aid. It was so obvious an oversight that it gave her pause, until she remembered what Kang-ho had said about the aftermath of her abdication—Singh and Hoartrap had helped Indsorith solidify her rule. Odds were Kang-ho had been less than forthcoming about his own involvement in aiding Indsorith...
"Kang-ho wants me dead," said Zosia, grimacing at the thought. If she couldn't trust him, how could she trust any of the Villains? Other than Maroto, anyway—it sounded like he had kept the faith... but even if he hadn't fallen off the way the others claimed, she would prefer to go it alone than waste time hunting him down for dubious reward. And really, if Singh was working the same angles as Kang-ho, Zosia would already be dead. "Chevaleresse, give me your word of honor you're not working for Queen Indsorith."
"Given," said Singh. "I left her employ some fifteen years past, and only stayed on as long as I did because it was the dying wish of my fearless leader that I do so. Remember?"
"Oh, I remember, all right," said Zosia. "But Kang-ho's working for her, that seems obvious now. I wonder if he even has a daughter—maybe everyone from Hwabun has been playing me, even the Virtue Guard."
"Zosia, Zosia, Zosia," said Singh. "You sound paranoid. The daughter's real, I assure you, although I will remind you that just a few minutes ago I cautioned against trusting the Virtue Guard. As for Kang-ho, he made off with a substantial portion of Diadem's treasury shortly after your fall—the queen must hate him even more than she hates Fennec and Maroto. I cannot imagine she is terribly pleased with Hoartrap or myself, either, considering how we left things with her. So the queen found out you were alive and went after you—that's a bad break, no question, but I wouldn't make the matter worse by imagining conspiracies."
"All right then, Singh, did Brother Kang-ho give you any other motive for ordering my assassination?" Choplicker had picked himself up and padded over to beg for a biscuit. He'd be begging for a while.
"I'm sure it has something to do with this," said Singh, hopping up from the pillows with enviable ease and retrieving a large piece of parchment from a drawer in the base of a terrarium. She shot out her hand, launching the paper through the air, and Zosia snatched it as it floated down to her. The chai curdled in her mouth as she saw what it said, and she crumpled the bill in her fist.
"What the devils is this? Kang-ho sent it?"
"No, that one I found down at the customs house—there's a board out front for flyers. They're less common in the Dominions, but I hear in the Empire they're showing up on every corner."
"What's the angle?" said Zosia, unballing the poster to make sure she hadn't missed anything. She hadn't—hard to miss much in two little words. "I don't get it. The queen's the only one who knew, so why... this? She wouldn't put them up; a bounty poster, maybe. Who's announcing my return, and why?"
"Oh, those have been around for years," explained Singh, digging through the drawer for something else. "You've heard that Indsorith banished your name, likeness, and everything else, yes? The Stricken Queen is how you're referred to, when bringing you up at all is completely unavoidable. So that was a popular slogan for your supporters when Indsorith took over, a petty defiance. Graffiti, nothing more. Over the last year, though, it's become something quite a bit different. A rallying cry."
"My supporters," said Zosia quietly. She hadn't really believed she would be missed at all. Yet over that last year before she overthrew King Kaldruut and crowned herself the Last Queen of Samoth, they must have had fifty thousand peasants behind them, people who abandoned their farms and trades to join her cause—was it so surprising that they had really believed in her? Some of them must have known her failure to institute the Empire-wide equality she had promised stemmed not from selfishness or hypocrisy but the sheer magnitude of the task, with all her efforts snagged in the razor-sharp gears of Imperial bureaucracy. Despite her promises, despite her becoming the _fucking queen_ , for the love of the Deceiver, every reform she attempted backfired, her unstable rule further weakened by sabotage from every quarter save the lowest classes—nobles, merchants, and the Chain rallied against her, ancient enemies coming together against the common threat: her.
And what of the peasantry, then? All those people who had needed her to succeed, who had bet everything on her cause, those same citizens now shouted her name in defiance, even though it might cost them their lives, even though she had failed them. All those people whom she had abandoned so that she could hide out in the hills with her favorite hooker... Zosia let herself fall back on the pillows and stared at the insectoid figures carved into the lintel over the door. Just when she thought she'd run out of reasons to be disappointed in herself.
"I didn't do it to be a martyr," she said. "I did it because I was a coward."
"You're many things, sister, but you're not that," said Singh. "Here we are. Take a look at this."
"What is it?" asked Zosia, sitting up and accepting the dossier Singh handed her.
"Everything I have on the Dull Kriss," said Singh, dumping out the dottle from her meerschaum and sitting down to repack it. "All the elements are here—we have the arms, we have the hands to wield them, and we have, at the moment, the support of several powerful cults. But we'll only have one go at it, and if that one push fails, then it will be years before the revolution recovers enough to try again. Assuming we aren't all caught and hanged."
"Sounds like old times." Zosia fingered the ribbon wrapped around the dossier. "Kang-ho wants me dead for reasons you aren't willing to spill, but you want me alive to help you plot your rebellion."
"You possess the greatest mind for tactics I've ever known," said Singh. "Sharpen the Dull Kriss with your advisement, and the Dominions will be all but united. I wonder how useful you would find it to have an entire Arm of the Star in your debt before launching an attack on the Empire?"
"Pretty useful," said Zosia, looking from the dossier to the crumpled flyer on the floor. "But even the best plans go awry."
"You have my word of honor, I will assist you in every way I can, regardless of the revolution's success."
"Well, that's something," said Zosia. "But since Kang-ho's obviously told you all about my plans, you can understand why it makes me nervous that you aren't willing to tell me why he sent you after me. He had me knocked out on his island; why not whack me there and be done with it?"
"I suspect Kang-ho and his spouse are at odds," said Singh. "Who was it that sent you after Princess Ji-hyeon?"
"Huh," said Zosia. "Kang-ho doesn't want his daughter found, does he? All that talk on Hwabun was for the benefit of he who holds the purse strings—Jun-hwan doesn't know his husband helped their daughter run away, does he?"
"If he did I expect the sweetness of affluent domesticity would sour substantially for our old friend."
"So Kang-ho helped his daughter run away, but blamed it on Fennec." Choplicker had surreptitiously scooted closer to the low table with its plate of biscuits. Planting a foot on his shoulder, Zosia smoothly shoved him back to a safe distance. "Clever enough. I wonder if the old fox was even involved."
"Definitely," said Singh. "I met with them both when they arrived here."
"Fennec and Kang-ho?"
"Fennec and Princess Ji-hyeon. There was a third with them, a wildborn woman. They wanted my help, but even if the scheme had seemed tenable, I was then as I am now occupied with my own affairs."
"And what's the scheme?" asked Zosia, relighting her low-burned pipe and taking a few embers to the tongue for the effort. That's what you got for scraping the bottom of the barrel.
"Isn't it obvious?" said Singh as her former general coughed on a mouthful of hot ash. "Zosia lives."
# [CHAPTER
2](toc.xhtml#toc-chapter028)
Everything had been progressing smoothly until the Siege of Myura, when a couple more of Ji-hyeon's second father's old friends showed up to complicate things.
Choi's strategy had worked perfectly, the Myuran regiment never expecting Ji-hyeon's troops to charge straight out of the castle and swarm the town. The Red Imperials were caught with their codpieces down, and were routed before they'd had a chance to lace them. Ji-hyeon's pride in yet another decisive victory mingled with unease at just how little fight the Myurans had mustered—she'd barely cut down a dozen enemy soldiers before the whole lot of them fled the town. This unease deepened substantially when Choi regrouped with her after the day was won and insisted Ji-hyeon accompany her through the dusty streets to an old temple where the Imperial command had been centered.
Had. Everything seemed perfectly preserved, the beech pews neatly pushed against the walls to make space in the central chamber for two long tables. The boards were stacked with papers, maps, a small diorama of Castle Myura, and several black bottles. From the look of things, they had been no more than a day or two out from sapping their way inside—the clever bastards had dropped a tunnel straight under a shallow stretch of the river that abutted the castle's northern wall.
Ji-hyeon stepped over impossibly bent and broken weapons to get a better look at the uniforms and boots scattered around the temple. The crimson cloth and light grey kidskin were shredded by wide gashes, curious burns, and tight clusters of countless tiny holes. Instead of incense, the chamber stank of dank, deep earth, freshly tilled. Despite the obvious violence, there was no scrap of the missing officers themselves, what Ji-hyeon had thought to be a lone blood splatter on the gritty tile revealing itself to her fingernail as wax.
Choi seemed as confounded as everyone else, and even without the rest of it, seeing her usually unflappable wildborn ill at ease would have been enough to make Ji-hyeon sweat. She should have known things were going too good to last.
"What a rout! Time to add another verse to the Ballad of..." But whatever song they were to expand with their deeds went untitled as Fennec came in from the street and saw the state of the enemy command. If Choi looked on edge, Fennec appeared to have fallen clear over the side, all the color draining from his tan features and both hands shaking as he reached up and slid his visor shut, as if to insulate himself from further fright. "Oh... oh dear."
"What happened here?" Ji-hyeon asked him, staring up at where an empty scabbard had caught in the exposed rafters.
"I was... That is... Um." Fennec didn't rattle easily, either, and that both he and Choi were so uneasy did not bode well. "I supervised the left flank from the rampart, as you ordered, so this is the first I've seen of... this."
"No it's not." Ji-hyeon had learned that bluntly smashing through his lies was far more effective than trying to outfence her former tutor. "You've seen this before, haven't you? If not here, when? And who?"
"Bide." Choi had a palm up, and knowing the wildborn would never spare Fennec from an unpleasant interrogation without strong cause, Ji-hyeon did as she was asked. Choi's other hand went to the hilt of her sword, and she moved quickly but carefully across the temple floor, as though stepping on the wrong tile would trigger a calamity. Tugging her ear at Fennec, Ji-hyeon followed.
On the street, Choi huffed the air with her narrow nostrils, and immediately led them several blocks to what appeared to be a tavern or inn. The door was barricaded from within, but not for long. A hundred of her best troops backing her up, Ji-hyeon borrowed an ax from an obliging soldier and hacked down the door.
On the other side were a bunch of her dad's old gang. At first, Ji-hyeon thought the old barbarian had died right in front of her, the potbellied, high-haired ruffian staggering away from the table where his fellows sat and then biting the floor right in front of her. He looked in a rough way, to be sure. As soon as he hit the ground a small yet sturdy woman hurried to his aid, her face too freshly battered to determine much about her, save that she was no dark-skinned Flintlander like her friend.
"My my my," said another old-timer as he looked over his shoulder, unwilling to abandon his card game despite the fact that the other three players had all stood and backed away from the table. These standing players were younger, hard-looking rogues mockingly dressed in shoddy imitation of the Imperial noblesse. One even held a tiny dog to complete the charade. The seated speaker resembled an ogre crafted out of porcelain, only bigger, paler, and uglier. "Fennec, old boy, you never fail to disappoint. This is so much better than I expected!"
" _Captain_ Fennec is not in charge," said Ji-hyeon, her irritation at being ignored by this ancient ox supplanting the definite apprehension he inspired. "I am."
"Cold Cobalt," breathed the beat-up woman kneeling over the fallen barbarian, her blackened eyes wide. "Blue Zosia, the Banshee with a Blade—it's really you!"
"The devils it is," said Ji-hyeon, yanking off her helm, but rather than coming off clean it caught in her blood-matted hair and she had to wrestle it free. Hardly the dignified entrance of the future ruler of the Crimson Empire. She hated this stupid helmet, and hated Fennec for insisting she wear it. Scheming Fennec and his... his... _schemes_. "I am General Ji-hyeon, Commander of the Cobalt Company, Heiress to Glory, and the next Queen of Samoth."
The geriatric giant snorted and everyone else just looked perplexed. Choi's whisper ruffled Ji-hyeon's hair as she said, "That one is a poison. Do not let him touch you."
"Good to see rumors of your demise are only slightly exaggerated, Maroto," Fennec said to the unconscious barbarian as he stepped past him and advanced on the ogre. Ji-hyeon blinked, trying to reconcile the comatose old man on the floor with the Mighty Maroto of all the songs. "Whatever hive you dug him out of, Hoartrap, I expect it will be a wasted effort. I think he's had a heart attack, but even if he lives, what good is an old stinghound?"
"He found you, Villain," snapped the woman tending Maroto. "We've been chasing you down all summer. The Touch only caught up with us today."
"Hoartrap the Touch," said Ji-hyeon, remembering her father's stories about the sorcerer. Stories he only told when his daughters were misbehaving and he sought to frighten them into obedience. So two of the original Villains had come looking for her... but why? "The command temple, that was your doing?"
"Ah, yes," said Hoartrap, as if remembering a chore he'd taken care of the previous week. "You appreciated my help, did you?"
"What did you do to them?" asked Ji-hyeon, and at the question one of the cardplayers lurking in the background doubled over and vomited on the floor.
"There, there, Diggelby, it wasn't as bad as all that," Hoartrap told the man, then finally clambered to his feet. Even with Fennec standing between them, he easily looked over the man's head and stared Ji-hyeon in the eye. His gaze made her queasy, but she held it, told herself she was doing so because she wanted to, and not because she lacked a choice in the matter. "Do you really want to know, little general? I'd be more than happy to show you..."
"She does not," said Choi, putting herself in front of Ji-hyeon and breaking the nauseating glare. Even with a dozen of her best—and best-paid—mercenaries crowded into the tavern behind them, Ji-hyeon began to feel as though she had blundered into a dire showdown. Of all the Villains to face head-on, it had to be the sorcerer...
"Greetings, oh witchborn thug," Hoartrap told Choi. "If you will excuse us, your mistress and I were having a discussion."
"No," Fennec said firmly, having rediscovered some of the mettle he had misplaced back at the command temple. "You and I talk first, Hoartrap. We are delighted at your having assisted us this afternoon, and would discuss terms about the future before—"
"Captain Fennec, I think in your excitement at seeing old friends you have forgotten yourself," said Ji-hyeon. Each day he got bossier, and if she let him determine how things went with his old chums now she might as well resign herself to always doing what he ordered. Besides, if he had set this up, this reunion on the sly, she aimed to find out about it before the Villains could get their stories straight. "I believe a better use of your time will be to convene with Sasamaso and Kimaera. Determine how light a contingent we can leave in Myura and still hold the castle for a reasonable time when Imperial reinforcements arrive. I want the bulk of our forces marching on Cockspar two days hence."
"General," Fennec began, sliding up his vulpine faceplate. The nine months of hard campaigning had planed off most of the joviality—and double chin—he had worn as Brother Mikal. "I cannot stress how important it is that at a minimum you and I first discuss certain particulars."
"Don't, then," said Ji-hyeon, and when he clearly didn't get it she sighed and spelled it out. "If you cannot stress the importance, then don't, was the meaning. Just forget it."
"Oh, don't mind me," said Hoartrap, nudging Maroto with his bare foot. "All this fretting is unbecoming of commanders, and I don't really think there's anything to talk about until this one is up and about. For my part, I'm always delighted to assist an old friend, or an old friend's family—you _are_ kin of Kang-ho's, General?"
"His second daughter," said Ji-hyeon, which caused Choi to hiss in irritation, but Ji-hyeon didn't see any utility in denying what the evil wizard already knew. She added a good line she'd been waiting to use for some time. "In another life, I was Princess Ji-hyeon Bong, betrothed to Prince Byeong-gu of Othean, fourth son of Empress Ryuki, Keeper of the Immaculate Isles, but I sought my own path. Instead of giving my hand to another I shall make it a fist to crush my enemies."
"Hey, me, too!" said the woman who had gone to Maroto's aid. She was a fighter, no doubt about that, though given the state of her face maybe not a very good one. "I mean, a second daughter seeking her own way, not the rest of it, obviously. And so are Diggelby, Din, and Hassan there—get over here, you lot, the general's just like us!"
Ji-hyeon rather doubted that was the case, but had gotten used to biting her tongue for the greater good. She nodded as the three weasely rogues came around the table, the man who had thrown up when she'd asked about Hoartrap's activities at the command temple offering her a curtsy of his battle gown and the other two bowing as they introduced themselves. The beat-up woman kneeling over Maroto rose to join her compatriots, the low dip and cocked elbows of her bow identifying her as a member of the Ugrakari noble caste... which meant if you went back far enough, she and Ji-hyeon might be related, on her first father's side.
"Tapei Purna," the Ugrakari said. "And like the Touch said, the big guy here is Maroto—you know, Maroto Devilskinner from all the old songs. He brought us here because he thought you were Queen Zosia, but you're just dressed like her, huh?"
"Yes," said Ji-hyeon icily. Legions had flocked to her blue banner, just as Fennec had said they would, but more than a few had deserted as soon as they found out that the Cobalt Queen had not actually risen from the tomb to lead her old Company. That was the worst feeling, seeing so much disappointment that she wasn't someone else. "Think of me as her successor."
"So you're after the same thing as her, too? Taking back the Crimson Throne? Well, not taking _back_ , in your case, just snatching it..."
"I will succeed where Zosia failed," said Ji-hyeon. It was beginning to feel like a script, the words a variation on a dozen speeches she had given during the campaign. "No more Chain, no more Empire. I will wear the Carnelian Crown only long enough to destroy it, and then all people of the Crimson Empire will be set free."
"Sounds like a plan," said Purna. "But before I vow my allegiance to your cause, I need to clear it with Maroto. I'm sure it will be fine, though."
"A _hem_ ," said the woman called Din, straightening her listing wig. "Overthrowing the current regime is fine and dandy, and we are all in favor of _that_. But what's this about destroying the Empire?"
"Din... that's a Cascadian name, isn't it?" said Fennec, who had not pissed off like Ji-hyeon had told him to. "Rest assured, my lady, that those who assist the general in her quest to bring justice to the Star will not be forgotten when she is queen, regardless of their lineage."
"Then there's the niggling fact that you've just overheard enough to ensure they'll never let you leave their camp," Hoartrap supplied. "We're all with them now, friends, so why don't you come back over here so we can finish our game?"
"That's not true, is it?" said Purna, squaring her shoulders as she appraised Ji-hyeon. "You wouldn't keep us prisoner if we wanted to leave? Not after we messed up a bunch of Crimsons just to get to you?"
"No, never," said Ji-hyeon, very much wanting to lie down all of a sudden. She hadn't slept for two days, and the adrenaline that had propelled her through the day's fight had slipped away, leaving her exhausted and in the most dread of circumstances—social interactions with foreign nobles. Yawning, she waved Fennec over. "We don't have the means to properly care for prisoners, so any who would stand against us or desert our cause are hanged. Fennec, escort me back to the castle so we can have a word, and Choi, see that our new recruits are well looked after. Make sure there are plenty of guards at each entrance to their bunkhouse here, so nobody can sneak in and do them a mischief. Night, all."
Most were respectfully silent, but Hoartrap laughed and laughed as Ji-hyeon wheeled away, her silent soldiers parting for her as she stepped back out into the road. Scant protection as her armor granted her in battle, it gave her even less from the night wind, and she pulled her cape tight as she stalked back to her most recent conquest. Fennec followed after, giving her measured advice for a change instead of chiding her for this, that, and the other thing. He claimed to have no idea why they had sought her out, other than the too-convenient explanation that they, along with so many others, had believed the rumors and thought their old leader returned from the grave. That might explain why Maroto had fainted at her appearance in the doorway of the tavern, given Fennec's description of the barbarian as a sensitive soul. When they arrived in her chambers, they were agreed on the most important matter, if very little else—Hoartrap the Touch could not be trusted.
Fennec left her without even making a pass, which was another welcome development, and with a happy groan Ji-hyeon unsheathed her sweaty feet from the high boots. The Duke of Myura's bedroom had a drysink as long as an inn's bartop, and with just as many bottles cluttering it, and before allowing herself to rest Ji-hyeon called in a pair of handmaids to help her bathe. If she'd been a good little princess and married Prince Byeong-gu like her first father had wanted, she would have had a dozen maids by now, and a castle far more luxurious than Myura to call home. Instead, she had a pair of wide-eyed camp followers tending to her with stained rags and a warm bucket of soapy water in a drafty stone pile on the ass end of the Crimson Empire.
Once she was as sweet as she was liable to get without a proper tub, she sent the boy and girl away and lay back on the enormous bed to take a much-needed sabbatical from the waking world. This proved harder than she'd expected. The arrival of two more of the original Villains seemed far too convenient to be chance, and so the only question was whether her father had sent them independently of Fennec, or if the old fox was lying about what he knew. Neither possibility strained credulity. Although Chevaleresse Singh had initially declined Ji-hyeon's invitation to become a Villain in the new Cobalt Company, how long would it be until the Raniputri knight arrived at an opportune moment? Pretty soon all of the Five Villains would be riding alongside her, at which point it would scarcely matter if the woman leading them had blue hair or the right helmet. They could just stick a tame raccoon dog on a horse and call it General Fatface for all the difference it would make—people would still assume it was the reincarnation of Zosia.
After tossing and turning for a while in the moonlit tower room, she forced her mind away from the imponderable worries and onto the much nicer subject of sex. Gods, spirits, and devils, how she missed Keun-ju. Not only for that, of course not, but in trying to distract herself with pleasant memories she just reminded herself of how many months it had been since she had kissed her Virtue Guard. It was not so long ago that she would have ranked Choi as her favorite guard, followed by the funny and charming Brother Mikal, with the stiffly formal Virtue Guard coming in dead last... but then she had grown up.
She couldn't really talk to Choi, not about her heart, and though she used to find Brother Mikal a wonderful listener, she had come to discover that Fennec would use any secret to his advantage. If only Keun-ju had not abandoned her she could have had someone to talk to, someone to confide in, someone to laugh with. Among other things one can do with her mouth.
It was lonely being the Arch-Villain.
# [CHAPTER
3](toc.xhtml#toc-chapter029)
The walleyed anathema stared at Domingo from across the sumptuously laden folding table erected in his tent, the monk's exposed, pale gums and stained wooden teeth enough to put a billy goat off his breakfast. During that winter campaign, what, twenty-three years past, Cold Cobalt's peasant army had cornered the Fifteenth on a peninsula jutting out into the toxic swamps at the border of Emeritus and they'd had to dig in and wait for reinforcements to come break the siege. Domingo had been obliged to take two weeks of meals in a fetid miasma. Black flies had swarmed the whole camp and delivered an especially virulent pox that caused gangrene to spread through the regiment like crotchrot through a Geminidean brothel, and attempts at digging latrines on that miserable spit of marsh only resulted in bubbling pools of slime that reeked worse than their intended cargo. He didn't have many fond memories of that noisome ordeal, but it had toughened his stomach from such relatively minor distractions as a hideous witchborn monk, so he tucked into his venison with little more than a passing wish that the anathema would drop dead. Preferably after suffering unimaginable agonies.
"My thanks for the invitation to dine with you, Baron Hjortt," said Brother Wan, carving his tender meat into tiny mouthfuls and spearing one into his mouth with the tip of his knife. From the rapturous expression on Wan's face as he chewed, Domingo supposed even the pope's favorite monsters didn't eat this well in the Dens. Good that someone would enjoy it, then—the doe was far gamier than Domingo preferred, but they were still a long way out from Cockspar and its kitchens. He supposed he ought to reacclimatize himself to such rough cuisine, for they would only be in the capital for as long as it took to ready the regiment for departure.
"It's Colonel out here, not Baron. And it won't do for you to dine anywhere but in the command tent once we have the Fifteenth on the move." There was a pleasant thought, weeks upon weeks of staring at that rank parody of humanity while he choked down increasingly bland fare. "Might as well get used to one another. Make sure your... subordinates are mindful never to enter without permission, nor address me directly. I know the chain of regimental command is not the leash your kind are used to, but I won't be able to excuse any oversights once we're officially in motion."
"Quite so," said Brother Wan, perhaps smiling, or perhaps not—it was damnably hard to tell, with the man's lack of an upper lip. "But the war nuns and monks under my authority have far more military experience than I, so I assure you they will not cause any embarrassment."
There was a howler if Domingo had ever heard one—three dozen robe-swinging servants of the Chain joined up as a special attaché to the Fifteenth, most of them anathemas to boot, and he shouldn't be embarrassed? Why not just let this untrained, inexperienced mutant wear his helmet and give the orders? The Fifteenth would be eating crow along with their usual rations, to be saddled with the same elite unit of witchborn clerics they'd spent many a long campaign battling all across the Star, whenever old Shanatu got it in his head that this time his brilliant coup would work.
Well, he must be the only one in the regiment not accustomed to their presence—shortly after he'd proudly passed on his command to Efrain, peace had yet again been brokered, and the Fifteenth, like all Imperial regiments, had begun employing agents of the Chain. They were probably damn useful in a bind, Domingo had to admit—given the havoc they'd caused when they were the enemy, a few powerful war monks and nuns could come in handy now that they were allies...
And then there was the dread weapon Pope Y'Homa had entrusted him with, which rolled along at the back of the caravan in a long covered wagon. For all the Black Pope's talk of it being worth more than ten thousand soldiers, it looked mundane enough to Domingo, and he knew a sight more than a teenage pontiff about war. And even if it proved as devastating as promised, it sat extremely poorly with Domingo that in order to employ it he apparently had to take Brother Wan along. When he'd been told that only one of her most trusted servants could activate the weapon, he had assumed she meant a war priest, and a pureborn one at that, given Y'Homa's outspoken revulsion for the anathemas. Instead her liaison turned out to be the monstrous assistant to one of her cardinals—she would have apparently preferred to send the cardinal himself, but attaching such a high-ranking official to a military unit would risk attracting the attention of Queen Indsorith's spies. So instead of a human fanatic who had the sole key to a weapon capable of murdering the whole Cobalt Company in one swoop, Domingo received an abominable one. Well, so long as it did what it was supposed to and carried the day with a minimum of casualties for the Fifteenth, he would take all the secret weapons he could get.
Most of them, anyway; devils would be useful in a war, too, but nobody outside the old maniacs of the Cobalt Company seemed keen on using them. Yet. Who the hells knew what the Black Pope would try next, if this debacle ended in Queen Indsorith being supplanted by some papal puppet. That thought was enough to spoil his appetite, even if the ugly little monk wasn't.
"Sir!" a voice barked from beyond the tent flaps Domingo had tied shut to keep out the wind whistling down from the northwestern extremity of the Kutumbans. "Permission to enter, Colonel?"
"Granted, granted," Domingo called, pushing his plate back on the table. "Hold a tick, Brother Wan here just needs to untie the door."
Was that narrowing of the anathema's beady eyes an invitation to dance? Domingo imagined flipping the table on top of the frail wretch and then jumping up and down on it until the mutant deflated...
"Colonel Hjortt, sir." Brother Wan admitted Captain Shea, the young woman's lean features reminding Domingo of the substandard venison congealing on his plate, and her grim expression mirroring the colonel's assessment of his meal. Her salute was as sharp as her nose, but considering that Efrain had promoted her from the ranks during his short tenure as steward of the Fifteenth, Domingo wasn't inclined to optimism where her credentials were concerned. Especially with that third button of her uniform ajar, like she was some navy hump swaggering about on shore leave... "Sir?"
"Hmmm?" Both Shea and Wan were just standing there, waiting, and Domingo cleared his throat, waved her on. "Report then, out with it."
"We have..." Shea glanced at Wan, who was watching her with the interest a gecko pays an ant, and amended herself. "That is, the witchborn outriders, who continued on while we broke for camp?" Great devils of the sea, if this captain of his framed everything as a question he'd have worse irritations than his piles to worry about on this campaign. "Well, they saw a campfire in the hills, north of the road? And they..." A ruckus was coming slowly toward the tent now, raised voices and stamping feet, and Shea spilled the rest in a rush. "They've taken prisoners, sir. Immaculate scouts, dressed for war."
Well, _that_ was something! Domingo felt the old shivers at the thought of enemy spies creeping across his camp, but the ripples did not betray his delight by carrying through to the puddinglike surface of his features. Mulling it over and putting his green captain on the defensive at the same time, he said, "Why the devil would there be Immaculate scouts out here, Captain?"
"We _are_ reasonably close to Linkensterne and their wall," Wan said thoughtfully, as though Domingo hadn't been the one to detour them up to this blasted northern road upon hearing the pass to Lemi was avalanched under, as though the Baron of Cockspar didn't know where the nearest foreign city lay in relation to his province's borders, as though the Immaculates' theft of Linkensterne didn't weigh down his bowels nearly as much as the death of his son.
"Yes, well, thank you very much for that brilliant intelligence," said Domingo. "But next time don't speak out of turn—I was addressing Shea. Furthermore, Brother Wan, in the future your agents will report back here to me before carrying out any military actions at all, is that clear?"
"As you say, sir," said Wan. "Only..."
"Only?"
"Only you said my troops were to report to me, and that I would then relate any pertinent information to you. Sir." There, that was definitely a faint smile on the monster's face; Domingo could tell by the way his cheeks moved. An awkward pause followed as the colonel began envisioning another violent fantasy, but he pulled himself back before it got too involved.
"I suppose I won't lecture a Chainite monk on semantics so long as he doesn't seek to advise me on swordplay. What about you, Captain, care to point out that the moon rises in the east?"
"Yes, sir?" Shea looked back at the canvas flaps that were snapping in the wind now that Wan had left them open. "I mean, no, sir. I mean, the Immaculates' wall is still under construction, so they may be doing reconnaissance to make sure we're not rallying to take their wall and reclaim the city before they can finish their fortifications."
"Not bad," Domingo nodded. "Not the best theory, but not bad."
"It's time to put our theories through the crucible," observed Wan, as the voices outside reached the tent, followed hotly after by the stomping boots that carried them. Definitely an Immaculate whining out there, and Domingo unhappily rose to his feet to meet the prisoners. That Captain Shea's company had ridden all the way up here to meet their returning colonel at the Azgarothian border only to let these puffed-up anathemas steal the show by capturing some scouts was unfortunate. What was unforgivable was that apparently not a one of his trained officers or soldiers had told those goons to detain their prisoners elsewhere instead of bringing them to the command tent. Who to horsewhip, though, that was always the question... Looking from the sheepish Captain Shea to the reptilian Brother Wan, Domingo found himself spoiled for choice.
"Baron Domingo Hjortt," the lead war nun called into the open door of the tent, her sonorous voice at odds with her slight profile. "We have taken captive three Immaculate scouts"—there came an outburst in Immaculate from the dark silhouettes bunched behind the small woman at the word _scouts_. "One claims to be a nobleman with writs of passage, and so I deemed it best to bring them before you."
Deemed it best, did she, to ignore protocol? This anathema had cut straight to the front of the horsewhip queue, but first there was the niggling problem that an armed posse under his command seemed to have abducted a foreign dignitary. "Bring them in at once."
The war nun entered, followed by two Immaculate women and a man, and then another three anathemas, just to make sure the formerly spacious command tent now felt as tight as the Chain's confessionals. Both Immaculates and witchborn were in a bad way, faces flushed, armor smeared with dirt and blood, but the anathemas still had weapons in their scabbards, while the only metal close at hand for the Immaculates were the chains around their wrists. From the way the two Immaculate women instinctively flanked the younger man, it didn't take a clairvoyant monster to guess the pretty boy was the supposed nobleman.
"Baron Domingo Hjortt, is it?" snapped the young Immaculate fellow in stiff but precise Crimson. It seemed he trembled out of rage, not fear. "How dare you, sir, how dare you!"
"I don't quite know," Domingo drawled, "but we'll find out soon enough. And Colonel Hjortt will do fine in this tent, lad."
"Lad? _Lad!_ " The handsome lad had colored the shade of the seared venison on the table between them. "I am Prince Byeong-gu of Othean"—the twin winces from the boy's bodyguards implied that his accounting himself thusly was a habit they had vainly tried to curb—"fourth son of Empress Ryuki, Keeper of the Immaculate Isles, and you dare shackle me like one of your hounds! You dare, when I have writs of passage stamped by my mother! You dare, sir!"
If there was one thing worse than a twit like Captain Shea who put everything as a query, it was a blowhard who phrased questions as proclamations. This prince was like some hammy actor overselling the role of spoiled fop.
"With due respect, Your Highness, you have no notion of what I dare, so I'd take a deep breath if I were you," said Domingo. "Now, if my guests would make themselves comfortable by sitting on the floor, we can clear up what I am confident is all just one big misunderstanding."
"Sir," said one of the witchborn in the rear as the prisoners begrudgingly lowered themselves to the ground. "We found this in one of their satchels."
"Oh? Must be this writ of passage his highness spoke of." Domingo kept his eyes on the prince as the folded cloth was passed from war monk to nun, from nun to Brother Wan, and from Wan to Captain Shea. The little jackass was squirming now, and his bodyguards stiffening. The captain unfolded the pennant on the edge of the table. A blue flag—cobalt, really—with rather obvious heraldry. "Oh. I see. It appears his highness is scouting a long way north from the rest of his company."
"You dare defile the private belongings of a member of the royal family?" A lot of the bluster had left the boy now, and he looked almost as worried as his two handlers. Almost as worried as he should be. "You have the nerve to imply we—"
"Shut up!" Domingo barked, the bodyguards twitching, the boy flinching. That was good, they were all on edge... maybe so on edge they couldn't see how rattled Domingo was. If the Immaculates were supporting the Cobalt Company, then the Crimson Empire was in a great deal more trouble than Pope Y'Homa supposed. "We catch you skulking _on my lands_ , with the flag of brigands who are _terrorizing_ the Empire, and you _dare_ talk down to _me_? I could have you all hanged as spies and your coddling mother couldn't do a damned thing about it, Headwoman of the Aloof Isles or no!"
"We are not affiliated in any way with the Cobalt Company," the prince said firmly, meeting Domingo's glare and making no move to wipe away the spittle that had landed on his bruising cheek. "We are not spies, nor are we scouts. We are returning to the Isles, after a very long and trying journey across the Star. The flag is... evidence we recovered, not a token of our sympathies."
"Evidence of what?" asked Brother Wan, and Domingo gave him a scowl to stop his deformed heart, or at least impress upon him the importance of letting his colonel do the talking here.
"Evidence of a crime. It is a private matter, of no consequence to Azgaroth, nor the greater Empire."
"I think I will make a far better judge of that than you," said Domingo, and when the prince looked down instead of elaborating, he whipped his saber from its scabbard with a steel hiss. The bodyguard on the left nimbly hopped from her knees to a squat, but before she could move farther the flat of a witchborn's spear had slapped against her throat, freezing her in place. A trickle of blood crept down the face of the blade where it had nicked her, the other bodyguard leaning close to her prince's ear and murmuring in some unintelligible noblecant. Domingo stepped around the table and approached the prisoners, leading with his steady saber until the tip of the blade hovered an inch from the prince's left eye. The whispering bodyguard went silent, easing slowly back into a stiff-backed posture, glaring at Domingo with all the hatred a vixen bears the hound who treed her. "I'm asking you as a courtesy, Your Highness—if you don't tell me of your own accord, I'll have my Chainwitch here peer into your brain and get the truth in nothing flat."
Brother Wan cleared his throat but made no further comment. Domingo didn't have the foggiest if the Black Pope had been telling the truth when she'd said the anathema could only glimpse the secrets of those with whom he was intimately familiar, but if Domingo himself was unsure about the limits of a witchborn's power, then how certain could this princeling be? The stoic little cuss scowled silently up at Domingo, and without breaking the boy's gaze, the general moved the point of his sword closer and closer...
"All right, all right!" The prince had his eyes shut tight, and Domingo realized he'd just drawn a drop of blood from the lad's lid. He flicked his saber up so that its curved back rested casually over his shoulder, his whole body humming at how close he'd come to putting out the runt's eye. "If the wildborn can read my very thoughts, he can confirm that I am telling the whole truth as the words leave my lips. And once I have told you the sum of my account, you will release us—agreed?"
"In war, there are certain codes that all true soldiers abide," said Domingo, leaning back against the table as he considered his prisoners. "The ignorant speak of war as savage, chaotic. In truth, when open war is declared between two peoples, it is a thing of meticulously obeyed law and absolute civility. The Crimson Codices are one such guide, and having read your own Ji-un Park, I know the Immaculates view war in much the same way. Without such rules of conduct, there is no war, only theft, arson, and murder on a grand scale. The Empire does not acknowledge the Cobalt Company as a legal army, and so if you are their agent I am not bound by the usual provisions in how I treat with you. Conversely, if you only represent the Immaculate Isles, Prince Byeong-gu, than I must uphold certain standards with how you are treated in my camp... and most pertinently, if you are not working for the Cobalts I will have no reason to detain you."
"Very well," said the prince, his eyes still as low as his voice. "My Martial Guards and I came to the Crimson Empire last winter, just after the New Year. We were searching for my fiancée, the Princess Ji-hyeon Bong. We believed she was kidnapped by a missionary of the Burnished Chain."
Domingo glanced at Brother Wan, but couldn't get a read on the freak. The Black Pope had mentioned this royal abduction to Domingo in the confessional, but how much had she not told him? If Wan had the trust of not only a cardinal but even the pontiff, how much did this anathema know?
"She... she was not," the prince went on, and, returning his full attention to the noble, Domingo thought the lad's voice was on the edge of cracking. "We sought her all over the Star, at first suspecting an Imperial plot, and then a Raniputri one, until the rumor we heard more and more frequently became impossible to discount. She is with the Cobalt Company now, which is why we have that flag—it was still flying over the city when we reached Katheli, even after the Company had ridden out before your armies could catch them."
"They took a princess hostage..." Domingo mulled it over—this could be a godsend, if it provoked the Immaculates into war against the Cobalt Company, or it could be a total fucking fiasco if it convinced them to sit out the war entirely, or, worse, aid the rebellion in exchange for the return of their noble...
"Not a hostage," said the prince, his voice thick with sorrow. "A general. I interviewed dozens of survivors, and many told the same story—Ji-hyeon helped lead the charge on Katheli. We'd heard such songs before, the closer we got, but after that I could deny it no longer. I took the flag as a... memento. No, that's not the word. In Crimson I should say... a reminder, a reminder to be more cautious with my heart. To not ignore the truth simply because I abhor it."
"What about Zosia?" Domingo asked, unable to help himself though the invocation of the forbidden name definitely raised the brows of every witchborn in the room. "If your princess was the general leading the Cobalts, where was Zosia?"
"Ah, the phantom of your Stricken Queen," said the prince, shaking his head. "Yes, she was there, too, if you believe the word of a few terror-stricken peasants who swore they saw her. I was more interested in finding my fiancée than listening to ghost stories."
Domingo tried to contain his excitement; further corroboration that Zosia had returned was as welcome as it was unsettling, but a wise tactician wages one battle at a time. Prince Byeong-gu's story was interesting for more than the mention of Zosia.
"And so after finally finding your intended after all that time, you expect me to believe you just turned around and ran back home?" The prince didn't bow under Domingo's gaze. "You didn't catch up with your beloved general and have a friendly chat about old times? Maybe speculate on how your people's relations with the Crimson Empire might improve once an Immaculate noblewoman helped the Cobalt Company seize the throne?"
" _No_ , I did not." The prince sounded about as warm as the waters of Desolation Sound. "She could have been my first wife, but she ran away to be a petty criminal. I have nothing to say to a lying, scheming traitor like Ji-hyeon Bong. We should have listened to my uncle when he advised Mother against the engagement, but fool that I was, I convinced her to allow it. Taming the daughter of Kang-ho Bong seemed a challenge worthy of my talents, but I see now—"
"Kang-ho?" Domingo shivered, couldn't help himself, as he imagined that smarmy Immaculate scum coming apart under his bare hands. It was one thing to face an opponent on the field and then face him across a banquet table at court, that sort of thing happened all the time with members of the inconstant clergy. Kang-ho, though, Kang-ho had never, ever even attempted to be civil to his old enemy, only taking time out of laughing behind his back to laugh in Domingo's face. He always pretended to forget Domingo's name, which was not the sort of thing that becomes amusing with repetition. "The _First Villain_ , Kang-ho? Everyone knew he'd fled back to the Isles, but how in all the heathen hells of your people did that crook sire a princess?"
"He is royal by birth as a child of Hwabun, and he married into the Bong family, who are beyond reproach." The prince seemed relieved, now that they had found some common ground in hating Kang-ho with the wrath of devils. "His husband is King Jun-hwan Bong, and with the aid of a wetmother they... well. Ji-hyuen calls King Jun-hwan Bong her first father, since she resembles him more, but given her deceit I am inclined to believe it is the blood of Kang-ho that—"
"I know how babies are made," said Domingo, a glorious stratagem blossoming in his brain like a crimson lotus. And here he'd been cursing this far-flung detour but an hour before. "Kang-ho's daughter is one of the Cobalt leaders, you're sure of this?"
"Sure enough to abandon all hope of saving her from herself," said the prince forlornly. "We should have been married last spring, and by now she could be fat with our—"
"But nobody on the Isles knows what became of her, that's what you're telling me?" Domingo tried to keep the excitement out of his voice. "You found out her secret, and are going home to inform everyone—yes?"
The still-seated bodyguard's eyes opened infinitesimally wider, but the prince obliviously carried on. "By now my message will have reached Mother. I requested her to remove the white from my palace before I returned, for there is no longer cause to mourn my fiancée."
"Nothing else? Before I let you go, I would have every detail—for the safety of the Crimson Empire, what else did you tell Empress Ryuki about the Cobalt Company?"
"Your Highness," the seated bodyguard hissed, but the prince waved her quiet, all confidence now that his tale was nearly told and his captors impressed with his innocence.
"I told her everything—that I had found Ji-hyeon and that she was not kidnapped, but must have run away to become a general in this Cobalt Company. Oh, I advised her that Kang-ho ought to be questioned about his involvement in her disappearance. It hardly seems a coincidence, that she would join a mercenary army with the same name as her father's old company." The prince pursed his lips, and then decided to tell all. "I also asked Mother to ask Uncle to call the matchmakers back to Othean, since I am apparently in need of a new fiancée. And that, Baron Hjortt, is everything there is to know—you cannot fit many High Immaculate characters on an owlbat scroll, and Mother insists I never write to her in the baser tongues. I hope this intelligence has been helpful?"
The prince smiled cautiously up at Domingo, and Domingo smiled back. Then he whipped his saber down into the lad's throat. The squatting bodyguard cried out, belatedly trying to lunge in front of her lord even as the witchborn who held a spear to her neck wrenched the blade with such force it nearly decapitated the woman. The seated bodyguard bellowed at Domingo as the colonel wiggled his blade free from the shocked, dying prince's collarbone, the other bodyguard falling dead at Domingo's feet. Then one of the witchborn punched in the screaming woman's skull with a pick. It went very quiet in the command tent, save for the sound of blood running off of Prince Byeong-gu's silk robe to pat-pat-pat on the face of the dead bodyguard beneath him. After a moment, the prince toppled over to sprawl with his countrywomen on the ground.
"Fallen Mother have mercy," Captain Shea finally managed, staring at the carnage. "The prince... you...?"
"I didn't do anything," said Domingo, hardly surprised to see that every witchborn in the room wore the same stoic face, save the grimacing Brother Wan. But was it a happy grimace or a sad one?
"The codes of war," Shea whispered. "You told him—"
"I told him the truth," said Domingo, taking Brother Wan's napkin from the table to wipe his saber off. "I chose to take him on his word that he was not an agent of the Cobalt Company, and therefore not an enemy combatant deserving of all those complicated bylaws cluttering up the Crimson Codices. What a happy day for all the Empire that we have not been at open war with the Immaculate Isles for many years, despite the recent Linkensterne debacle."
"Nor will we be again anytime soon," said Brother Wan, his sharp, blue-grey tongue playing over the dry pegs in his upper jaw as he fished around under his robe. He removed a long, black-pommeled dagger and offered it to Domingo. "Next time you need to execute an enemy of the Empire, Colonel, pray use this gift of the Chain."
"I told you, Brother Wan, don't lecture me on what to do with blades and I won't lecture you on how to carry out your pagan worship." Domingo sheathed his saber and waved away the offered knife, turning his full attention to the still-shaking Captain Shea. "Captain!"
"Sir!" She stood straighter at that, but her eyes were still on the corpses. "Sir?"
"Captain, it hardly needs saying, but you are to speak to no one of this... interrogation. _No. One_. Is that clear?" She nodded, but too quickly for Domingo's liking, so he added, "As this is a matter of Imperial security, these agents of the Chain will be monitoring the camp to ensure no baseless rumors start flying around. As senior officer until we reconvene with the rest of the Fifteenth, it is dependent upon you to make sure any gossip is quashed long before it reaches the keen ears of these witchborn, or less friendly company. There is to be no gossip because there was no incident—no Immaculates were ever brought into camp. Am I clear?"
"Yes, sir!" That was what Domingo needed—a statement, not a question.
"Now, leave me with Brother Wan and his subordinates so we can clean this mess up." As Captain Shea nearly tripped over the bodies in her haste to be away, Domingo looked up from the Cobalt flag strewn over the dirty table and called after her, "And send in another round of this venison. I think I've found my appetite at last."
# [CHAPTER
4](toc.xhtml#toc-chapter030)
Goatsdamn, but Grandfather was a pain in the arse. Or rather, the small of the back. Shrunken as the greylock was, lugging him over hill and dale for days and then weeks and finally months without end had put a whiny kink in Sullen's spine, one that troubled him even after he'd shrugged off the old man and settled in atop the mountain's ridge. Family, man, what can you do?
"Leave me to die in the mud like a common animal," grunted Grandfather as Sullen lowered him down to sit on a slab of brown stone protruding from the lichen-draped mountainside. "That's what they wanted you to do. Born-agains playing at being heathens. It's enough to make a horned wolf puke."
"Yeah, Fa," said Sullen, knowing the prospect of meeting an army was stirring up memories for the old man. "You sure this is far enough off the path?"
"It'll do," said Grandfather, closing his eyes as he panted. As though he'd been the one to haul Sullen up the steep, treeless mountain. The two men looked back down the way they had come, the crust of frost on rock and moss sparkling in the dawn. Far below, a road cut through the evergreen bamboo and browning saam groves that thrived in the valleys here, a ribbon of bare earth wound through the hair of the mountains. "They'll make through yon pass and camp in that meadowland beyond. Creeks coming down to water the animal, flat enough for tents—too posh for lambs like them to pass up."
"I still think it's best if I go myself, just at first," said Sullen. Grandfather cracked one eye at his grandson, and Sullen blundered on, knowing full well that reason never carried him nearly far enough with the stubborn old wolf. "I'm faster and quieter, and—"
"And you don't know what your uncle looks like," said Grandfather. "And even if you are a little quicker without me, so what? If some half-wit sees you creeping and gets lucky with a weakbow, where does that leave me? Up a damn mountain, waiting for a vulture to peck out my liver, or whatever mercy the Old Watchers give me for sitting out a fight. We stick to the creeks it'll cover your racket, and if they catch us 'fore we find your uncle you can always toss me on the enemy to cover your escape, you're so worried about getting away."
"I wouldn't," said Sullen. Grandfather had adamantly refused to hear his account of his encounter with the Faceless Mistress after their brief initial exchange on the subject back in Emeritus, saying if the gods wanted to involve him they'd call on him themselves, instead of sending Sullen. As a result, Sullen hadn't told the old man about his need to thwart this Zosia character from murdering an entire people, a need far more pressing than reuniting Grandfather with his ne'er-do-well son. Since that Faceless Mistress implied the two of 'em ought to be in the same camp, though, maybe it did make more sense to find Uncle Craven first. "Never mind. We'll go together."
"Oh, I hope that's not true, laddie," said Grandfather. "I hope you've got more thaws than me ahead of you yet."
"No, I mean... you know what I mean."
"Oi, there we are—not a breath too soon! Ha!"
Following Grandfather's gaze, Sullen made out a distant glint that might have been morning light striking a patch of early snow in the dying saam forest. It bobbed up the road, disappearing for stretches and then reappearing, and at last it came close enough for Sullen to decide what was what. Four riders in dark blue, the occasional twinkle coming from their bridles, which seemed to be the only edge of metal not obscured to prevent just such detection. The scouts passed far beneath them, and though Sullen knew he and Grandfather must be invisible at their perch among the high rocks, he still pressed himself flat to the frozen earth.
More shimmers and sparkles came quickly after, and then, as though the first few were but the trickles heralding a flash flood, a column of reflected light poured up the wide road. On and on the caravan came, Sullen quickly losing count of individuals, and then losing count of wagons, and finally turning to Grandfather when the stream showed no sign of stopping after close to an hour.
"Didja know there'd be so _many_?"
"One good wolf is worth a thousand sheep," said Grandfather, but even he looked rattled by the sheer size of the Cobalt Company.
Grandfather had always just looked like Grandfather, but now with the chill light of dawn striking his leathery features and the few wisps of hair left on his head and chin, Sullen had to be real: Grandfather had gotten... well, _old_. Maybe it was being away from the Savannahs, chasing rumors and false leads all across the Body of the Star, dealing with crazy Outlanders and exploring desolate ruins—Sullen felt five years older, so imagine what toll the quest must have taken on Grandfather.
Then again, Grandfather hadn't been the one touched up by a god. The old man clearly slept like a babe whenever he wasn't taking watch, and probably sometimes when he was, too, whereas Sullen hadn't gotten a good night's sleep since his encounter with the Faceless Mistress. During the months since, he had yet to unearth any information at all about her worship, the faith of the Forsaken Empire as obscure as its fate, but he did learn much of the woman she had charged him with hunting down: Cobalt Zosia. They called her the Stricken Queen now, but in her day she'd brought this land to its knees, leading an uprising of peasants against the Crimson Empire and becoming queen, only to die at the hands of her successor, Indsorith. Yet now she returned from her twenty years in the earth, and brought fresh war against the rule of her assassin.
And Sullen, armed only with his mother's spear and his father's knives, was supposed to stand against a woman whom not even death could stop, on behalf of a long-forgotten god he'd never once prayed to. If he failed, more people would die than he could even count. It was enough to get anyone down.
Sullen and Grandfather were spotted before they'd even cleared the second perimeter of sentries. They would've made it farther had it been darker, but the Cobalt Company kept the edges of their camp brightly lit and tightly patrolled. The shadowy creek Sullen slunk through suddenly flashed with firelight, and shouts encircled them. He wheeled about, blinded by the unhooded lanterns directed at his face, and was about to make a run back up the stream when two arrows struck the shallow water on either side of him.
" _Move_ something something _you be dead_ , something!" came a voice from just up the slope, and Sullen gave thanks their search for Uncle Craven had taken so long—when he'd first left the Savannahs he hadn't spoken a word of Crimson, but now he was conversant enough to get the gist of the order. He planted his spear in the creek bank and raised his empty hands as the same voice called, "Something something _wrong you back_?"
"Tell them we're here for 'Maroto,' " sighed Grandfather. "Our only hope is he's got some pull with these Outlanders and isn't just taking orders."
" _Devil!_ " cried another unseen sentry.
" _No!_ " said Sullen in childish Crimson, pointing at Grandfather. " _Not devil! Grandfather on back! Grandfather no walk! Not devils! Horned Wolves! Here look Maroto! Maroto family!_ "
"Something something _figures_ ," said the first sentry. "Something _Maroto_ something something?"
" _I speak small Crimson_ ," said Sullen, wishing for the hundredth time that the Imperials did as much trade with the Immaculate ships as the Flintland clans did—he was near fluent in Immaculate, but that hadn't come in as handy in the Empire as he'd expected. " _Maroto here, we talk Maroto. Take us Maroto._ Uh _, please?_ "
" _Wait_ ," said one scout, so wait Sullen did, despite the icy water running into his worn-out boots. Walking the Frozen Savannahs could make your feet cold, but hanging out in this mountain stream was something else entirely. The lantern light didn't flicker or leave his face, so he closed his eyes and ignored Grandfather's sour mutterings about how Sullen couldn't sneak up on a deaf turtle. Oh, if the Faceless Mistress could see him now...
"Told you we shoulda just grabbed that first scout and snapped her neck," Grandfather grumbled. "Could've worn her cloak and snuck right through the lines."
Sullen didn't talk back, but really, how would _that_ have worked, with Grandfather jutting up over his shoulders? Maybe if they were sneaking into a camp full of hunchbacks...
"Horned Wolves?" said a new voice in the root language of Flintland that most of the clans used for local trading. "Let's see some horns, then."
It felt so good to hear the true tongue that Sullen broke into a wide grin and flashed the secret hand signals of his people. As soon as he did, Grandfather clocked him upside the head, whispering, "That's a damn Eagle accent if I ever heard one, no kin of ours."
"All barbarians are kin out here in the Empire, cousins," said the voice, and, feeling the brightness diminish, Sullen opened his eyes again. The circle of sentries had tightened up close, but the lanterns were now directed low enough on the ground that Sullen could see the woman still wore the plumed headdress of the Crowned Eagle People, as well as a cobalt cloak. "How many more of you are up in the high country?"
"It's just us," said Sullen. "Me and Grandfather are Maroto's kin."
"Maroto didn't tell us to keep an eye out for any of his people who might sneak down under cover of night," said the Crowned Eagle. "So may I ask just what in the holy fornication of the gods you two are doing out here? If you're friendly why not enter our camp by day?"
Meeting the scouts on the road that morning, openhanded and all, was just what Sullen had wanted to do, but Grandfather wouldn't hear any of it. Sullen wasn't about to say that in front of strangers, though. "My Crimson is bad and most Imperials we've met don't speak Immaculate so good. We thought this would be a surer way of finding my uncle. I swear on my knives we mean him no harm. We're his family."
"And how can we know that?" asked the Crowned Eagle.
"Our talk is with Maroto, fledgling," said Grandfather. "Don't tell me that pup sends a bird to do his business these days? Bring him out, and then we'll hear what he has to say on the matter."
"Fa..." Sullen began, but Grandfather was in a testy mood.
"If he's not wolf enough to face his kin we'll just turn around now and have no more to do with him. Would give him a second chance, but if this is the welcome he offers, well, they can keep him and we'll just head home."
"We'll see what's what when Maroto returns," said the Crowned Eagle. "But until then you two aren't going anywhere. I've got a dozen of my best checking the countryside as we speak, so if you forgot to mention any other of your kinfolk who might be hiding up there, now's the time to make it right."
"Call us liars again and I'll bend your beak all the way back to your cloaca, see if I—"
"Just us." Sullen spoke quick and loud, talking over Grandfather. "You go north up the ridge to the first saddle, our gear's stowed under the glacier lip there, behind some rocks. Be obliged if your people could fetch it for us."
"That's just great," said Grandfather, probably pissed at Sullen. Again. "Take us to whoever's in charge while Maroto's away, then."
The woman laughed. "I'll be in charge of you till he returns, and we'll leave it at that. I am Chevaleresse Sasamaso, acting captain of the general's bodyguard."
"I'm Sullen," said Sullen. "And my grandfather's Ruthless."
"There's a joke in there somewhere, I'm sure," said Chevaleresse Sasamaso. "I'm going to come take your weapons now, all right?"
Sullen worried that Grandfather was going to make a stink about it, but the old man stayed quiet as the Crowned Eagle took Sullen's spear and knife bandolier. Had the woman tried to disarm Grandfather of his toothpick there might have been trouble, but she pretended not to notice the sheath poking out of his harness. Finally, she stepped back and invited Sullen out of the creek. The night air of the mountain felt colder on his damp ankles than the water had.
"A chevaleresse's what they call a warrior out here, right?" asked Sullen as she led them into the camp proper, a few of the sentries accompanying them but most hooding their lanterns and returning to patrol. "But you're a Crowned Eagle."
"A chevaleresse is more than just a fighter," said their friendly captor. "It is a title with much honor among both the Raniputri Dominions and the Imperial provinces, one they rarely bestow on foreigners. It signifies nobility of spirit as well as martial prowess."
"Is my uncle a chevaleresse?"
"Maroto? No, he's no knight, though it's said they offered him the privilege many times over, had he wanted it. Turned it down every time."
"Why would he?" Sullen tried not to gape as they were led through the thronged camp, regal-looking folk in spotless metal armor sitting around fires with bare-chested soldiers so grubby and disheveled they looked like beggars.
"They have rules, don't you?" said Grandfather. "Calling yourself _knight_ means no more fighting dirty, no lying or cheating, eh?"
"To name but a few of the codes of conduct," said Chevaleresse Sasamaso with a smirk.
"There's your answer," said Grandfather, settling back in his harness. "He'd have no part of _that_ , not our Craven."
"Craven?" Chevaleresse Sasamaso looked delighted. "I knew Maroto wasn't a Horned Wolf name. _Craven_. Well!"
"These are the spies?" A new woman strode toward them through a break in the tents. She addressed them in Immaculate rather than Crimson, thank the Old Watchers. The guards flanking her were impressive enough, with their crablike plates of armor and steel helmets shaped like dog skulls, but as the prisoners stopped to meet the woman by the shifting light of a bonfire and Sullen caught better sight of her, he felt his throat close and his hands sweat.
It wasn't that he was knocked off guard by her scant attire, though her sparse patches of chainmail did catch his eye—despite enjoying warmer climes than Flintland, most Outlanders swaddled themselves in more sweltering layers than a newborn with pneumonia. It wasn't a stirring at her beauty, though she was decidedly fleet. No, it was the rich blue of the long hair framing her face, the severe slash of her bangs casting her dark eyes in shade that not even the bonfire could banish. She was exactly as the stories of Cold Zosia had described her, a ferocious swordswoman with cobalt hair who led devils as well as armies.
This was who Sullen had to stop, before she used her witchcraft to destroy an empire. Zosia. As if punctuating his realization, a small owlbat flapped overhead, its wings shining ebon in the firelight.
"We look like spies to you?" said Grandfather, conversant enough in Immaculate despite all his shit talking of their shipwrights, rice spirits, and general style. "We're here for Maroto."
"Kinfolk of his, they say," said Chevaleresse Sasamaso. "For what it's worth, I believe them." Switching over to Crimson, she added, "Something something _foolish enough_ something something."
"I'll take Maroto over the rest of the old guard," said the blue-haired woman, again in Immaculate. Then, bafflingly, she bowed. "Welcome to my camp, kin of Maroto. I am General Ji-hyeon Bong, Commander of the Cobalt Company."
"I'm Sullen," said Sullen, though at present he felt anything but. No, he was happier than he'd been in a very long time that he wouldn't have to throw down on this woman. Especially since he was positive the owlbat wheeling overhead was a devil that was looking out for her. Not sure how he knew it was bound to her, but he did. "And my Grandfather's called Ruthless. We're Horned Wolves. Or we were, aren't no more. Might be again someday, I guess. Depending." Sullen was many things, but he had never before found himself a babbler, so he cleared his throat and finished with, "Anyway, we come down from the Frozen Savannahs."
"The tundra of Flintland?" asked this Ji-hyeon.
"Did he stutter?" said Grandfather. "It's called the Frozen Savannahs, girl, and you'll show it the respect it's due by calling it such."
Sullen blushed, but to his relief Ji-hyeon smiled at the admonishment. "My apologies, Master Ruthless, I meant no disrespect. Quite the contrary, that's a long way to travel with no steed but your grandson."
Sullen's blush heated up, and he weakly explained, "Wolves don't ride."
"I would like to accept your apology," said Grandfather. "But so long as we're your prisoner I don't think I will."
"Old wolf, you ought—" began Chevaleresse Sasamaso as one of Ji-hyeon's guards took a step toward them, but Sullen got to it first. There would be hells to pay later, especially since he said it in Immaculate, but the words were out before he could stop them.
"By the heathen god and the true ancestors, Fa, just say thank you! They caught us sneaking in here like lions trying to carry off a baby, and you expect 'em not to be wary? What would you do if you nabbed a Jackal man coming through our window some night? Offer him a cup of snowmead?"
Grandfather went rigid on Sullen's back, but did not speak. Again Ji-hyeon smiled, and as the wind stirred up the fire he saw her eyes better, and found they were not so dark as he'd first thought. While those shining gems stayed on Sullen, she addressed Grandfather. "Ruthless of the Horned Wolf Tribe, if I have your word that you and your grandson will cause no evil, you are welcome to stay as guests instead of prisoners."
"Given," sniffed Grandfather, relaxing a bit in his harness. "And I warmly accept your gracious apology, General."
"Excellent," said Ji-hyeon. "Chevaleresse, see that a private tent is erected for them. When Maroto returns from his expedition I'll see that he is sent to you at once, whereupon you will have to make the decision to move on or swear allegiance to our cause. Much as I might like to provide for you indefinitely, with winter fast approaching I can only afford to supply those who are in my employ. Welcome to my camp, gentlemen."
General Ji-hyeon gave a clipped nod and walked past them; likely she had not actually been looking for them but on her way somewhere else when they had crossed her path. There was no parting smile for Sullen, not that he expected one... but he missed its absence enough to risk acting the fool, and pivoted around.
"Hold up now," he said, feeling pretty confident for a change. That confidence evaporated as the general turned back and he saw how annoyed she looked. "I, uh, was going to say we ought to burn one together. You and me."
Her expression didn't make it seem likely, and Grandfather snorted on Sullen's back, but he plunged ahead, trying not to sound as desperate as he felt right then. "I can tell you're a busy woman, so there's no need rushing it. In your own time, then, in your own time."
"I don't smoke tubāq," said Ji-hyeon, and Sullen could tell she'd be gone in an instant if he didn't say something witty. Wit, though, was no kin of his, so he just spoke the truth, as he always did. For all the good the truth had ever done him.
"Me, neither, nasty stuff. Fa rolls the beedies in it sometimes, but I've got no stomach for it straight. I'm not some sheep, to be living off poison weeds. I was talkin' about saam, yeah?" There it was! All cautious-like, just peeking out the corner of the general's lips like a wary fox testing the air outside her den, the faintest hint of a smile.
"You want me to smoke drugs with you, is that what you're asking me?" Fast as he'd seen it, that smile was gone. "You want me to take time out of war-waging to get high with you, barbarian?"
Chevaleresse Sasamaso covered her mouth with a mailed hand, and Grandfather rocked on Sullen's back with silent laughter. This was a disaster.
"Saam isn't a drug, it's a medicine," said Sullen lamely.
"And what malady does it treat?"
"Bad moods?" he said. He'd never really thought about the practical applications before, but knew mudworkers and poison oracles used it. Admitting that he had in fact just been asking if she wanted to get high with him seemed a bit low, though.
"Master Ruthless, I have a request to make regarding your grandson," said Ji-hyeon, and while that almost-there smile was back, she was giving Grandfather her full attention now. Sullen had really stepped in it this time.
"He's a good lad, General, just not used to conversing with warlords," said Grandfather. "So long as you don't aim to flog him for his impudence, though, I could see my way into letting him take a little discipline for his cheek."
"Good," said Ji-hyeon. "With your permission I would like to take kaldi with him sometime in the next few days. In private. I hope you understand?"
"Oh, I understand," said Grandfather, which was good, because Sullen certainly didn't. "I'll give you leave to talk to the boy, but nothing more than that. He's still a virgin, and I aim to keep him that way—big, smart lad as he is, he'll catch quite the groomprice if I can arrange a marriage somewheres along the line without him—"
"Great fucking devils, Fa, shut the fuck up!" Sullen wished the old man had straight up murdered him, instead of talking this shit. "I don't... She doesn't... devildamn it!"
"I assure you his chastity will be preserved," said Ji-hyeon, giving them a final bow. Her smile was out in force now, but Sullen was no longer so delighted to see it. Fucking Grandfather, man...
# [CHAPTER
5](toc.xhtml#toc-chapter031)
This is bullshit," panted Duchess Din, plopping her mohair-swaddled bottom down on a boulder near the one Maroto and Purna occupied. The pass they had reached was less than a dozen feet wide, the rugged peaks on either side wasting no time in jabbing straight up to poke heaven in the eyes. With the whistling wind delivering a slurry of early snow and rock dust, it was hardly an ideal picnic spot. On either side of the narrow saddle, rough talus slopes sharply dropped a thousand feet before leveling off a bit, and if anything, the side they were to descend looked even steeper than the way they'd come up.
"Testify, sister!" said Purna, raising a fist and lowering her head. "If I'd known this was the work we'd be doing I would have just had the Cobalts execute me as a traitor. If I wanted to play marmot I never would have left Ugrakar."
"Puhhhhhh," gasped Diggelby as Hassan helped him up the last jagged rise, even his mean little dog wheezing as it scrambled up the rocks ahead of them.
Yet Maroto was pleased, which he hadn't been in... weeks, maybe a whole month. Old Black knew, he probably hadn't cracked a smile since he'd found out the blue-haired girl everyone thought was Zosia was just Kang-ho's brat, with Fennec her faithful puppeteer. Now, though, he felt genuinely happy. The reason was propped up against another boulder, as though the three scouts were huddled into a windbreak, and not, you know, dead. Maroto wasn't such a baddie as to rejoice at seeing random corpses—hells, if he were that sort of man he'd rarely stop smiling, living the life he'd lived. No, his bliss—and bliss was really the only word for it—was that he recognized one of the scouts Choi had dispatched just before dawn, when he and the others were still way down at the misty bottom of the pass. It was Lukash the Nearly Noseless Scout, that lying fucker who had repaid Maroto's mercy by bringing a whole platoon of Imperial toughs down on them outside Myura, just before they'd finally found the Cobalt Company. Maroto only wished he had been here to watch Choi do the deed. Maybe advise her to be a bit slower about it. His oft-regretted vow prevented him from torturing agents of the Crimson Empire, sure, but that was no reason why he couldn't offer his professional oversight to such activities. Same reason he could guide a scouting party to spy on the Imperials but not lead an open charge against 'em—a man has to keep his word to his enemies, if no one else, but that's no reason not to get creative with interpretations.
"Don't get comfortable," he called to Diggelby and Hassan as they collapsed onto the harsh brown summit of the saddle. "Soon as Choi shows herself we're moving out, and fast. Too exposed up here."
"They need a rest, Maroto," said Purna, her own face ruddy and sleek with sweat. The fops had learned to leave the makeup in its case on mornings that started with a steady climb up an exposed mountainside. "Look at them. You think we're going slow now, wait until someone snaps an ankle because you're pushing them too hard."
"Take it up with Choi," said Maroto, eyeing the alpine meadows into which the slope poured its talus like a waterfall of sharp stones. Somewhere down there the weirdborn was creeping around, and as soon as they got her signal they could—
"Stay here until dark," came Choi's voice from above them. Except for her modest horns, which were mostly hidden by her mesh hat, the white-haired weirdborn looked enough like a normal woman, sitting around camp with the rest of the crew... but nobody watching her melt down the sheer peak beside them could mistake her for human. Too fast, too surefooted, too damn devilish. "There's a regiment nesting in the next meadow, and they will have more scouts down there watching the descent from this pass. If we come down now we will be witnessed."
Duchess Din whistled appreciatively. "So much for Maroto's assessment of the Imperial colonels being, what was it, 'too damn thick to cover their front, let alone their arse'? I've lost track of how many times you've proven him wrong, Choi."
"Things have changed," grumbled Maroto. Which was true enough, whether it referred to the Imperial brass sharpening up or Maroto growing dull from neglect. "A lot."
"Since the days when you were one of said colonels, you mean?" asked Purna, and even though Diggelby and Hassan were too far away to hear what she was saying, the contrary bastards tittered right on cue. Then again, they both had two working ears, so maybe they heard her perfectly.
"Get down from there, move around back," said Choi, walking past them and squatting down on the far end of the boulder, overlooking the way they'd come. "If a change of guard comes we do not want them to see us until they reach the top."
Maroto joined Purna and Din in groaning theatrically as they clambered down from their sunny perch and dug in against the cold backside of rock. Quick as Maroto's good humor had been restored, it was gone again. He'd felt like a dead man, wandering the Cobalt camp like an unwelcome ghost after meeting General Ji-hyeon and Fennec in Myura, unwilling to take the oaths of fealty that the rest were falling over themselves to swear. Well, not so much unwilling as unable—that was the thing about oaths, you swear one and all of a sudden it becomes a lot harder to swear any more—but in the end he'd found a sort of compromise. He hadn't relented out of any long-dormant loyalty to his old comrades and their ascendant offspring, but due solely to Purna's pestering—she wanted to offer her services to General Ji-hyeon, but wouldn't until Maroto agreed to do the same.
"Here's the rub," he'd told her. "I can't raise a sword against the Queen of Samoth."
"Whaaaaaaat?" she'd said. "Why the devils not? You hate the Crimson Empire, you've said it a hundred times! And you dragged us all over the Star looking for this army, who are obviously _at war_ with the Empire, and you can't be at war with an empire without also being at war with its capital providence, can you? 'Fighting the good fight,' you said it a _thousand_ times! Now, I know the Cobalt leader isn't who you expected, but we're here, and we can help, and what else would you do—go back to hosting hunting parties in the Panteran Wastes?"
"I swore an oath," said Maroto, as unhappy about the situation as he'd ever been. More so, probably. "Long ago, to Queen Indsorith, and I won't break a vow, not even one I regret. I came here chasing a dream, Purna, and now it's time to wake up."
"So swear a new oath," Purna had said, knowing him well enough not to dig at subjects he didn't want dredged. "To help me! If you're defending me from Imperial swords, that's hardly the same as, um, raising a blade against the queen."
"Hmmm," Maroto had said, because he had no intention of going along with any more of her brilliant plans but knew _her_ well enough not to say no outright.
And yet here he was, weeks into a scouting expedition ordered by General Ji-hyeon. Maroto's insider knowledge of the Imperial military made him an obvious choice, and anywhere he went there went Purna, and wherever Purna went there went Din, Hassan, and Diggelby. Choi had been assigned to the mission because General Ji-hyeon evidently had the sense not to trust any of her new recruits further than she could have them shot, and so the weirdborn was put in charge of their band. Maroto hadn't thought anything could reduce the nobles from a merry band to the regular kind, but the sharp-toothed Choi had done wonders to dampen everyone's spirits: no fires, no feasts, no fighting, if they could help it, and, cruelest of all, no singing. It had been a long, joyless slog through the mountains, and while they had gained quite a bit of information on the Imperial forces moving in to surround the Cobalt Company, Maroto hadn't been properly drunk since leaving Myura. Worse things than not drinking, though—he could barely remember the last time he'd gotten laid, to think of one. It'd been before he'd taken on the lordlings; devils' delight, what had happened to the Mighty Maroto, that he'd go the better part of a year without so much as a suck? Getting old beat getting dead, but not much else, and not by much.
And at last they were almost back to the Cobalts, but of all the idiot fates, another Imperial contingent was smack between them and a proper drink, and if Maroto was lucky, a roll with a campwhore. Not that he was all that lucky, these days...
"Hey look, a goat!" said Purna, spoiling Maroto's nap. You'd think an Ugrakari girl would be long over the novelty of seeing the animals universally regarded as the second-biggest arseholes on the mountain, but apparently not. "What a beard! He must be older than Maroto!"
"Not as horny, though," said Hassan, leaving Diggelby and his dog to doze on the smaller, sharper stones while he climbed the last dozen yards up the slope to join Maroto, Purna, and Din in the lee of the boulder. Now that the flurry had blown over, the afternoon brightness of the mountain sun made Maroto's eyes water, and every bone in his arse ached as he sat up straighter and wiped drool from his stubbly chin.
"Choi keeping an eye on the other side of the pass?" he asked. "Or did she run off again and you clowns decided we didn't need a lookout of our own?"
"What's to watch for, at the top of a bloody mountain?" grumbled Din, whetting the ornately hooked heads of her crossbow bolts.
"That's probably what the last scouts to hold this post thought," said Maroto, jerking a thumb in the direction of Lukash the Nearly Noseless Scout and the other corpses. "Don't all volunteer at once."
"Man, that old boy is making straight for Diggelby," said Purna. "I've got five dinars that says it's on top of him before he wakes up!"
"I'll pledge six thousand rupees that Prince wakes up first," said Hassan.
"No fool's taking that bet," said Din. "The dog wakes before Diggelby, whatever else the outcome... but I see Prince waking and rousing his master before the goat is within pissing distance. So I take your wager, Purna."
"Damn," said Purna. "Hadn't thought about the dog. As far as a goat can spit, or as far as a person?"
"As we determined in the Wastes, dromedaries can spit some distance indeed," said Hassan. "But I am unversed in the range of goats."
"Where's an avalanche when you need one?" said Maroto, his joints popping as he rose to a crouch. "I'll take first watch, then, so as..."
Idly glancing down the mountainside they had earlier scaled, he saw the so-called goat in question. Maroto felt his guts turn to iron, the weight threatening to rip out through his taint. He blinked, licked his lips, willed his suddenly trembling legs to be still. They ignored him. For the first time since waking he noticed that the wind had died completely, and the sun now buried its face in a tuft of cottony cloud. In the stillness it must have picked up the scent of their trail, and in the shade the creature's eyes would be as sharp as its teeth. And it was only a hundred yards down the steep slope, clip-clopping straight toward the snoozing Diggelby.
"... five that it wakes the dog from the distance of a practiced human spitter for Hassan, then, and five for Din that it's a camel's range before—"
"Shut your fucking mouths," said Maroto, dead calm in the way he only got in the heat of a battle and other mortal-fucking-circumstances. "Crawl around the rock. Now. Purna, you open up the belly of one of those dead scouts. Then you all go down the other side, quiet as you can. Now."
"Are you serious?" asked Din. "Is he serious? What is it?"
"Fucking go," growled Maroto. "I'll crawl down and grab Diggelby. Be right behind you."
"Is it Choi?" asked Purna, looking everywhere but at the beast meandering up the mountain.
"What are we looking for?" asked Hassan. "Is it near the goat?"
"That's not a goat, damn your eyes," said Maroto, shuddering. "It's a horned wolf."
The other three went quiet, and Maroto snatched up a sizable pebble. Shying this off Diggelby would be safer than crawling out in the open, but just as he flicked the stone at his target, Din and Hassan burst out laughing. His missile went wide, clattering loudly across the stones. Their guffaws would echo, he knew, and the horned wolf went stock-still, cocking its snout in the air.
"You had me, Mar—" Din began, but Maroto lunged over and clapped a hand over her mouth.
"Maroto, have you ever actually _seen_ a goat before?" whispered Purna, pointing at the creature. "Because I'm telling you, _that_ is a goat."
A bark brought them up short, but then Hassan was snickering again as they all realized it was just Prince. Diggelby's dog scrambled up in a cloud of dust as though he'd been stung by a bee, yipping in earnest now. His nominal master groaned and swatted at him but didn't rise. Then Prince stopped yapping, took a big sniff in the direction of the horned wolf, and turned tail on master and monster, his leash bouncing along after him.
"Prince! Prince!" hissed Din, but the dog ignored her, shooting past their boulder and disappearing down the other side of the pass. The horned wolf had stopped moving when Din and Hassan had made their racket, and had stayed rooted to the mountain the whole time Prince yapped at it, but now it was on the move again, dropping its belly close to the ground and quickly slinking up the mountain in a decidedly uncaprine fashion, its legs now splayed out at right angles like the scuttling appendages of a spider. That must have got Din to appreciate the severity of their situation, as she carefully set down the bolt she'd been sharpening and started to string her crossbow with equally deliberate slowness.
Purna had also come around, although to predictable outcome: "Oh devils yes, let's take this beast! Should we flank it, or—"
"Shhhhh," whispered Maroto. "I told you, we run. He's too fat to be sick and too fast to be old, and that means he has a pack laid up in some cave around here. We go, now, and hope the dead scouts keep him happy."
"Diggelby," said Hassan. "We can't just leave him."
"If you'd listened to me, I would've had him over my shoulder already," said Maroto, the bottom threatening to drop out of his bowels as he watched the horned wolf slither up the steep mountainside. There was no way he could grab the dozing noble in time.
"Sacrifice," said Purna, which even Maroto thought was harsh. "No time to talk, come on. Trust me."
Purna squirmed around the edge of the boulder, Din and Hassan following tight on her heels. The horned wolf was close enough now that Maroto could see it had two pairs of horns, one going out and up and the other curving in and down. This was no mere animal, this was a monster out of legend. Sacrifice, Purna had said, but while he knew he'd saved Diggelby's hams a dozen times over since meeting the callow twerp, he couldn't shake the memory of throwing open the cell door when he and Purna were locked up in Myura and seeing that chump on the other side...
So maybe it was gratitude that took Maroto to his feet, or maybe it was a deep-seated refusal to just hand this rich kid the best death a warrior could ask for, while he snuck away to find an inferior demise. Craven, they had called him, when he'd guiltily returned to the clan after all his adventures with Zosia, and a different Maroto had deserved that name... but he was no longer the sort of Horned Wolf who turned tail rather than bearing fangs at the avatar of his people. This was it, then—it was time for him to come home. It was enough to drip glacier water down a man's crack; as far as he'd journeyed, from the Frozen Savannahs and back and then away again, to here on the southwest edge of the Crimson Empire, it still came down to a horned wolf catching his scent on a still day.
For just a moment, Maroto let himself pretend this monster was Dad, returned from the dead in the guise of the Old Watchers to retrieve the son who had abandoned him twice. The first time he'd forsaken his father Maroto had been but a boy, so desperate to hide his shame at fleeing from a horned wolf he'd seen by the fields that he'd kept running until he reached Samoth. The second time had been even worse, with his wee nephew there, watching him go...
But no, the past is a trap as sharp as a horned wolf's tooth, and Maroto shook himself free of the guilt that had stalked him for years. Going back to the Frozen Savannahs after Zosia's death had been a mistake; he would not compound the error by revisiting it in his mind. All tolls would be paid in the end.
He stepped out of the shadows of the boulder, the great big world spread out as far as the eye could see. Mace up, head down, he made his peace, such as it was, with whatever invisible ears still cocked in his direction, be they divine or infernal, so long as they were listening. Then he pursed his lips to whistle a challenge, when clattering rocks to his side made him spin around—he'd been flanked by the monster's pack-mate!
No, it was Purna, Din, and Hassan crabwalking across the saddle, the body of Lukash the Almost Noseless Scout in their arms. Before Maroto could step forward to help, they had stumbled past him, and with a muttered "heave!" they did just that, launching the corpse over the lip of the ridgeline. He landed a short way down with a snap and a crunch, but slid to a stop on the jagged earth rather than picking up momentum and rolling on. The horned wolf stopped in its tracks, looking not at the broken body that had landed a scant dozen feet from where it crouched, but at the humans who had thrown him one of their kind.
It was so quiet on the mountain that they could hear a distant wheeze from the creature's throat, the patter of its drool landing on the rocks. This close, it was easy to see why Maroto's heathen ancestors had thought these beasts were devils, if not outright gods: there was a regal bearing in its pale woolly shoulders, something otherworldly in the twin rows of black teeth gleaming in its nightmarishly long mouth. Finally, those disturbingly bright eyes looked away from the four breathless people standing above it, passed over the sleeping shape of their comrade, and settled on the offering. It extended one sharp, splayed hoof toward the corpse...
"Will you shut _up_!" said Diggelby, sitting straight up from his rocky bed. "Oh, a goat!"
The horned wolf's hackles flew up and it ducked back into a crouch, growling low in its throat, eyes fixed on Diggelby. All of Maroto's relief rushed out of him in a cold sweat. The wind came back, now that it couldn't help them by smearing their scent, and Diggelby scrambled to his feet in a foolishly hasty fashion.
"What do _you_ want, goat? I don't have any old cans, if—" Diggelby began, but then the horned wolf was flying up the rocks toward him, and his chiding rose to a panicked, "—Eeeeep!"
Usually time didn't seem to slow and then crystallize, like honey settling at the bottom of a jug, until Maroto was in the thick of a fight, with a few blows already traded. This time, though, everything was already in focus, the action blocked even before he swung. Purna's hands were fluttering up, pistol and kakuri a second away from being useful; Din was dropping to a knee before shooting her crossbow, but her foot was on loose rocks and it would take her a moment to stabilize before firing; Hassan's saw-toothed sword was cocked back, but in taking a wide charge to not interfere with the girls' shots he would never reach Diggelby in time. None of them would... but Maroto launched himself anyway, bounding over and down, his only hope that the beast would see him coming and redirect its attack toward the bigger threat...
It did, but not at him. Choi appeared like a devil in a summoning circle, shoving past Diggelby and down to meet the beast's charge, her limbs too quick for even Maroto's eye to track. Yet not too quick for the horned wolf, the creature dipping to the side to avoid her jabbing sword and then slamming its skull into her wheeling legs. One of its upper horns gored her thigh, upending her even as its slavering mouth closed on her ankle. It caught her out of the air and flipped her onto her back, more like a Raniputri wrestler than an animal.
Maroto smelled Purna's gunpowder, and then the report rattled the stones beneath his floating feet, and a tiny puff of white hair bloomed on the creature's arched back where the ball grazed it. Din's missile fared better, a quarrel gliding softly into the horned wolf's haunch as it furiously banged Choi against the rocks by her bloodied boot. It didn't take notice of the bolt quivering in its flesh, even when the red began to pulse out and stain its leg. Choi must be dead, she must be, but even as Maroto watched her limp body flop up off the steep ground she reared forward, as though trying to touch her toes, and stuck the creature in the muzzle with the sword she still clung to. It slammed her back down even harder, and the sword clattered away down the mountainside.
The rocks came up to meet Maroto, and he made his final bounce off a granite springboard, this last bound taking him directly on top of the horned wolf... which suddenly jerked its enormous head and released Choi, flinging the bloodied woman directly into Maroto's path. Just before they collided he saw the horned wolf tense, and then Maroto and Choi crashed into one another. Something cracked in his right elbow as he landed on the merciless slope, pain jolting him alert even as his left knee was flensed near to the bone by a sharp stone edge. They tumbled a bit, Choi tangled in his arms, the mace dropped lest he bludgeon one of them in their slide, a soft whine coming from either him or the woman, he couldn't tell which. Snarling drowned out the whine, and he slapped out the one hand that was still doing as he asked, wedging his fingers in a rocky crack to arrest their slide and loosening a few fingernails in the process.
His plan was to roll away from Choi, dividing the horned wolf's attention, but even as they jerked to a stop the woman sprang away first. Well, shit. Just lifting his surprisingly heavy head took more work than he'd expected, and when the swirling mountain slowed its orbit in front of his vision he saw that neither Choi nor himself were in immediate danger: the horned wolf had mounted the saddle after the nobles, rather than following Maroto and Choi down the mountain. From here he couldn't see anything but the lip of the ridge and hear the screams. That explained why the horned wolf hadn't charged them from the first, then; from just a short ways down the slope one couldn't see much of the summit.
"You can move," said Choi, hunched over him. It didn't sound much like a question. Looking up at the weirdborn, he saw that her whole face was bloodied and raw, and one of her horns had snapped off near the tip, marrow and blood running down its length. One arm hung limp, while the other caught his good elbow and helped him up. Putting weight on his skinned knee, he felt queasy and terrible, but he didn't fall over or pass out, so it wasn't shattered. Hopefully. "Move!"
Move they did, though not nearly as fast as either of them probably wanted. Retrieving his mace and using it as a short, clumsy cane, Maroto hobbled after the limping weirdborn. They both left bloody tracks as they scaled the saddle for the second time that day, Maroto glancing behind them every few steps and thanking the old gods and the new every time he saw nothing but a lonely mountainside at their backs. Choi strafed to the side, plucking her chipped sword out of the rocks. Then, a dozen feet beneath the summit, a tooth-rattling howl overpowered the screams and grunts of the nobles. It trailed off, and when it was gone not even the low groans of the dying lordlings could be heard. Choi and Maroto both stopped, braced themselves for the inevitable attack.
"Not a bad death," he told himself, and though he wasn't sure he'd even said it aloud, the weirdborn seemed to hear him.
"None of them are," she said, and, glancing over at the battered barbarian, grinned at him despite the oozing sockets where her sharp teeth had been knocked out. Maroto saluted her with his mace. Worse ways to go, certainly.
"That," came Diggelby's voice from the saddle above, "is _definitely_ not a goat."
"Maroto! Choi!" Purna appeared like one of the Burnished Chain's angels, shining from on high. "They're alive!"
"More than can be said for me," said Hassan, stumbling into view and dropping his bloody sword with a shudder. "I think it's killed me."
"Get down there and help them," said Din, for once following her own counsel and nimbly climbing down to Choi. "They've had the worst of it."
"Where's Prince?" said Diggelby. "Prince? Priiiiiiiince!"
"Shut it," Maroto gasped. Every time he thought he was done for, too tired to move, these nobles did something so idiotic it pumped him full of nervous energy. As the fop's voice echoed out behind them, Maroto staggered on with newfound strength. "For the love of devils, shut the fuck up!"
"Don't worry, boss, it didn't get away," Purna said smugly as she helped him the rest of the way up. She was a hard one, all right: the horned wolf had taken a mouthful out of her forearm, her leather gauntlet sheared through as though it were silk and a dark bandage already leaking. "Put one in the brain, just like you always say."
"No such thing..." he panted, teetering on the edge of the saddle even with her support and then collapsing onto the summit. He stared at the limp mountain of fur and horns splayed out in the dusty pass, rivulets of blood extending in a mandala around it. "No such thing... as..."
"As a carnivorous goat?" said Hassan. "I would have agreed, if not for our little fete with this fellow. We appreciate your softening him up for us, Choi. Diggelby never could have laid him out if not for your opening salvo."
"I could, too!" said Diggelby. "But more important, where's my dog?"
"The other side," said Choi, all action even after tangling with a monster. "Go and spy. Now. The Imperials will have heard Purna's attention-getter."
"Run," said Maroto, waving them all away before it was too late. "Go. Down the other side. Hoof it, you fucking fools, hoof it!"
"But the Imperial camp—" began Hassan, when Din, having heeded Choi's order, called from the other end of the boulder:
"Are coming up, maybe a dozen of them! They're just at the meadow now, but as soon as we take a step down they'll see us."
"Retreat, or dig in?" asked Purna. "But if we stay and take these ones out, the main body will still know something's afoot, won't they?"
"Retreat," said Choi, crouching over a pack and rooting through it with her good hand. "Even wounded we'll be back down before they're up. You, help me tie a sling, and you, bandage Maroto's knee. Then we retreat."
"But Prince!" protested Diggelby.
"Fuck your stupid dog," said Hassan, retrieving his sword and wiping it off on his friend's exposed back. "Pack us up while I tend to our wounded heroes."
"No," said Maroto, shaking his head and feeling his brains slosh around, as though his skull were so swollen the grey stuff had more room to breathe. "Straight down on top of them. Two of you put on those scouts' uniforms, might buy us some time until they're close enough to see you're impostors."
"Why—" Purna started, but then a distant howl silenced her. Followed by another, and then another, and then a dozen more. From back down the way they'd come. Far off, but not nearly far enough.
"Because there's no such thing as a lone horned wolf," said Maroto, flopping back on the coarse stones and staring at the clouds. They were tinted with red now that the sun was brushing the far peaks. "A pack'll have a dozen of the monsters, maybe even two. And that one you killed? Either a pup or a runt. His parents will be bigger, faster, smarter, meaner. We're all dead."
Nobody had anything to say, which was nice—he could hear the howling of the horned wolves better this way. Then Purna crouched beside him, slapped a bandage on his seeping, grit-stubbled knee, and began wrapping it tight. Hassan came to his other side with one of Din's bolts, broke off the head, and set to strapping it against his sore, pulsing elbow.
"I'll see to myself," he heard Choi tell Din. "You and Diggelby put on those dead women's uniforms. Fast. We're going down."
"Better to make a stand here," said Maroto, sitting up as best he could. "You don't know horned wolves, weirdborn. They'll be on us—"
"Her name's Choi," said Purna, cinching the bandage painfully in place. "Don't be an asshole, Maroto, you know better than to call her anything but her name. Now, if you want to be soft as a firstborn royal and wait up here for the easiest death you can find, you're welcome to it, but the rest of us are going to bring hell down on those Imperials before we go. The least we can do is lead a pack of pissed-off goats straight to their camp."
Looking around, Maroto saw Choi nod, lick blood off her lips, smile at him in a way what got him eager to stand, if only to be the closer to a fit woman with red smears on her cheeks and a red sword in her hand. Saw the fucking ponces he'd led both ways across the worst desert of the Star watching him, crazed grins playing on faces painted with grime and blood instead of makeup. Hassan put one hand under the armpit of his jacked-up arm, and Purna took his other. Together they hoisted him up.
"So what's it going to be?" asked Purna, as if it was even a fucking question.
Maroto put his head back and howled like the horned wolf he was.
"That's more like it," sniffed Diggelby. "Now let's find Prince!"
# [CHAPTER
6](toc.xhtml#toc-chapter032)
Zosia lived, all right, as a saddle sore on the thigh of every rider in the Imperial regiments tasked with pursuing the Cobalt Company. The timing was right for it to be the mayoress that Sister Portolés had met, the Cobalts showing up in regional complaints and then official reports just a few months after the massacre at Kypck. Depending on who you talked to, they were a band of mercenaries hired to stir up trouble, unusually effective revolutionaries, or bandits who'd gotten organized. Considering they had gone from raiding outposts and border garrisons to sacking whole castles and pillaging provinces, the threat the Cobalt Company posed to the newly won tranquility of the Crimson Empire would have been immediate and severe regardless of their leader, but if it was truly the Stricken Queen returned, well, Fallen Mother have mercy on them all.
Portolés did her best to keep her mind on these more practical, definitive problems, rather than on the slippery questions of why the story Queen Indsorith sang her in the throne room was so different from everything she had grown up believing. That she was sworn to secrecy on the truth of how Cold Cobalt lost her crown, even where her superiors in the church were concerned, did little to relax her worries. Nor, for that matter, did all the finer points in Heretic's propaganda that supported some of what Queen Indsorith had told her. Baiting her companion into sharing even more minutiae on Blue Zosia turned out to be as simple as not beating him silent whenever he opened his mouth, which was often.
"... which makes a lot of sense, when you put it all together," he said as their boat bobbed across the waves toward the gleaming cliffs of Hwabun. "You can just murder a woman, but then you make her a martyr. But by concocting a version of events where she's meeting your marionette in a fair fight, and loses, then you've stripped her of one of her key strengths: her skill in combat."
"So you don't think it was a fair fight?" asked Portolés, fanning him on. "That Indsorith, what, poisoned Zosia before the duel?"
"That the duel never even happened!" said Heretic. "Whose word do we have that it did? The letters signed by Zosia that confirm it are just that, letters, easily forged. Open your eyes, sister, you've been duped, just like the rest of the Chain, the rest of the Empire."
The Immaculate escort they had been assigned at the border didn't even try to conceal his amusement as he directed the two sailors to bring them into Hwabun's harbor. Let Heretic and this infidel have their smiles. Portolés was discovering that by checking her pride she was gaining far more insight into popular sentiments than she ever would have by checking his cheek. With any luck, she was about to discover a lot more about the Stricken Queen.
Hwabun. The Immaculate Isle where Kang-ho had fled two decades past was the sensible first stop on their search. According to Queen Insdorith, she and Zosia had agreed that the plot could only work if not a single other soul knew the truth, and so even her most trusted captains thought their Cobalt general dead. Upon coming out of hiding she would likely reveal herself to her Five Villains in hope of enlisting their aid—if nobody suspected Zosia was alive, how could she have raised an army so soon after the attack on her village without the help of some old friends? The timing was too close for Zosia to have done everything on her own.
Most of the other Villains would be hard to find, if they were even still alive; Chevaleresse Singh bounced around the Raniputri Dominions, and the rest could be anywhere. Kang-ho was the easy one, having settled down here, and if Queen Indsorith knew that, it was a safe bet that Zosia did, too. Not that Portolés expected to get the truth out of any of the Stricken Queen's cohorts, but considering the Cobalt Company would be as tough to catch up to as any of the other Villains, she might as well start close to home.
If the woman from Kypck had been Zosia, of course, and if the same woman was indeed leading the mercenary company that currently terrorized the southern end of the Empire... but Queen Indsorith had been convinced by Portolés's description of the woman and the concurrent appearance of a new Cobalt Company. Convinced enough to risk her throne by bringing Portolés into her confidence. When the queen had asked Portolés if the mayoress had a scar on her chin, the war nun had remembered that detail, vivid as she remembered the first time she had convinced Brother Wan to touch her... but now the old worm of doubt was gnawing at her, making her question if she had actually remembered the telltale scar, or if she just thought she had, prompted by Queen Indsorith's obvious need for the suspected woman to have had such a mark. _If_ she had the scar, and a strange dog, and had seemed far too educated for a country mayoress in the Kutumbans, then she might be Zosia, and that possibility was too dire for Queen Indsorith to dismiss out of hand. That Portolés was the only person who would be able to recognize Kypck's mayoress at a glance made her the only candidate for hunting her down before the Crimson Empire found itself embroiled in a second Cobalt War.
Portolés would soon find out if it was truly Zosia, or at least have more to go on than the speculation of a lone woman. Even if said lone woman was the Crimson Queen, one of the most powerful individuals on the Star, a little corroborating evidence never hurt.
As Portolés, Heretic, and their Immaculate escort were led across the isle and into the manse by a coterie of servants, the first thing the war nun noticed was all the white lanterns and candles—the family was in mourning according to her guide. Her request for an audience with Kang-ho was met with less surprise and stalling from the majordomo than she might have expected a foreign cleric to garner, even with all her diplomatic writs, but the gentleman who came out to greet her was regally attired in Ugrakari fashion, not Immaculate. Kang-ho's husband, King Jun-hwan Bong.
"To what do we owe the pleasure of this visitation?" he asked straightaway, cocking his high-domed skullcap at the road-weary Imperial nun and her scuzzy assistant. The glossy bird-of-paradise feathers set in the hat were probably worth more than the heavy silver bracelets around his wrists. "Surely my husband did not anticipate your arrival, or he should have made himself available."
"My name is Sister Portolés, and I seek an audience with you, King Jun-hwan," said Portolés, and, knowing every lie goes down smoother with a dollop of truth on top, added, "Your husband is not expecting me."
"I see." This monarch's sovereign nation might be a single island that was substantially smaller than the Queen of Samoth's summer castle, but he was still a king, and if he decided to send them away there wasn't a thing Portolés could do about it... "Shall we take kaldi? I have business this evening, I am afraid, but can certainly spare an hour for a representative of our Chainite friends."
"An hour is fine," said Portolés, trying not to reveal her relief. "If your servants can entertain my escort and keep an eye on my prisoner here I would be obliged."
Eyebrows went up all around at that, and Heretic laughed, shaking his manacled wrists at them. "That's right, I'm a desperate criminal. These irons won't hold me for long, so mind a tight watch or I'll plunder your pockets to the seams."
"This way, Sister Portolés," said Jun-hwan, and she followed him through several corridors vaulted with delicately painted rafters until they emerged on a long balcony. From up here the crashing waves sounded faint as a whispered chant, and off to the north, Portolés saw the spectral fogbank that must mark the farthest extremity of the Haunted Sea. To think, during the Age of Wonders she could have looked from this very spot and gazed upon Jex Toth, before it became the Sunken Kingdom. As distant as she now felt from the church itself, its teachings would always be at the front of her mind, and she felt a joyful tremor at beholding such a hallowed place. Some said there was a maelstrom at the heart of the Haunted Sea, others spoke of a leviathan that patrolled its depths. Neither seemed beyond the realm of the possible to Portolés—you wrap your kingdom up in devil worship and black magic, and you could hardly claim surprise when the ocean swallowed you whole, belching up further darkness where your land had once been.
Yet even the foulest pit could nurture a seed of goodness, like a rosebush springing from a midden heap; who knew that better than Portolés? And just as the Fallen Mother found purchase in the corrupted flesh of an anathema, so, too, would she transform the iniquitous Sunken Kingdom into a garden of the blessed, once the Star had proven itself worthy of the honor. When that happened, the storms would cease and the fog would clear and the Haunted Sea would part, a host of angels raising the Sunken Kingdom back to the surface, the holy land scrubbed free of its ancient sins and ready to welcome those deserving of its bounty. The Chain Canticles said on that Day of Becoming, the faithful pureborn would be called home, the few deserving anathemas would be healed, and all the sinners and devils would inherit the ruined Star. On that day, even a monster might finally see the face of the Fallen Mother, but even if she was deemed unworthy, she now knew there was a place upon the Star where the damned could look out upon the habitation of the saved and reflect upon their fate...
Then again, the Chain had foretold the return of the Sunken Kingdom for over a hundred years, and here was proof with her own eyes that nothing lay out there but rough seas and bad weather.
"What does the Burnished Chain believe happened there?" King Jun-hwan asked, following Portolés's gaze. "Witchcraft? A ritual gone awry? The wrath of the gods?"
"Something like that," Portolés croaked, her momentary elation transmuted into dejection as she turned to the low lacquer table. "The Sunken Kingdom is often in our prayers. And what do the Immaculates say?"
"Witchcraft. A ritual gone awry. The wrath of the gods." Jun-hwan smiled. "Superstition is universal, sister."
Portolés hated the word "superstition," hated how snidely it dismissed the miraculous and reduced the faithful to the feebleminded. "And what does a learned gentleman believe, living so close to where it all happened?"
"A weapon beyond our ken," King Jun-hwan said in the easy manner of one discussing the weather. "There was a war between the ancient kingdom Jex Toth and the Star. Surely I cannot conjecture on the source of the conflict, but whatever the cause, both factions lost. They sought to control the uncontrollable. Jex Toth sank into the waves, and even from this great distance they dragged the people of Emeritus down with them. An end to war, and an end to the Age of Wonders, at a cost greater than anyone living or dead could conceive. The tragedy of our ancestors."
"Don't the Immaculates say time is one big mill wheel?" asked Portolés, trying to get her mind back on track—she was here for answers about the present, not the past. "What do you think that bodes for the Empire's current trouble?"
"Another matter beyond my ken," said Jun-hwan, and Portolés realized she was expected to sit first. Very well. Pulling out a cushion, she made herself comfortable on the floor as more servants flitted out of the screened door like so many drones leaving the nest. Kaldi was, of course, forbidden, but with a writ of absolvence in her pocket, she savored the heady smell of the decoction in her porcelain bowl. Besides, it didn't do to be rude.
"Besides," Jun-hwan went on, "you have your pagan heresies mixed up. It is the Ugrakari who think of time as a mill wheel. The Immaculates envision it more as a river, rushing along, with eddies and pools and a very strong current."
"It must have been your bracelets that threw me," said Portolés. "Do you ever miss the mountains of your homeland?"
Jun-hwan smiled, touching the silver serpent that guarded one lithe wrist. "Here I have both stones and sea. Furthermore, I was born on the Isles, to an Immaculate father. My mother was Ugrakari. These belonged to her. But did you come here to discuss genealogy or theology, sister?"
"Everything is theology," said Portolés, sipping the kaldi. It was far more bitter than she'd expected from the smell. "I came here because I'm looking to stop another war. Ugrakari, Immaculate, or Imperial, surely we can agree war does little good."
"It depends upon the war, I suppose," said Jun-hwan, stirring cream into his bowl.
"Spoken like a general," said Portolés. "Well, we need generals as much as nuns, I suppose."
"Mmmmm," said Jun-hwan, daintily sipping his kaldi.
"I will speak frankly, King Jun-hwan," said Portolés, and played her bluff. "I am here on the express orders of Queen Indsorith. She is curious to know what came of your husband's meeting with a woman claiming to be Blue Zosia, and whether Samoth ought to be concerned."
Some stiffening there, in the hand that held the king's bowl, but no other trace of acknowledgment. It was enough to convince Portolés she had struck true, she was sure of it—Brother Wan was always talking about how if you paid close enough attention, you didn't even need to have the second sight to know when people were lying. Jun-hwan tried to play dumb, but it was too late. "You speak of my husband's former commander, the woman your queen personally executed two decades ago?"
"That is she," said Portolés, and decided to add some details to her wild speculation—so long as she didn't overdo it, she had him, she could feel it. "Sharp a fellow as you are, King Jun-hwan, surely you deduced the identity of your husband's guest? Forgive any seeming impertinence, but it will help to avoid an international incident if you are forthright with me on this matter. We know she met with Kang-ho, what we don't know is what came of this conversation. That the man himself is absent when I call, well... surely you understand our concern. Especially considering that Hwabun sent no word to Diadem following Zosia's visit. The Crimson Empire has always counted the Immaculate Isles as dear and faithful allies, but first you exploited our recent domestic troubles to illegally seize Linkensterne, and now this matter... Suffice to say, Queen Indsorith is curious what exactly she has done to offend."
"And for such a critical diplomatic mission, the Queen of Samoth sends a lone wildborn war nun as her envoy? And this envoy is sent first to call upon my husband at Hwabun, instead of to Othean to meet with Empress Ryuki?" Jun-hwan carefully put his bowl back on the table. "You are fishing, Sister Portolés."
So much for her cunning ruse. "I am. And I shall catch something, here or elsewhere, but I have no intention of returning home hungry."
"Well, never let it be said the Immaculate waters are barren," said Jun-hwan. "Perhaps your bait is lacking, sister. What if you tried another lure?"
"Forgive me, King Jun-hwan, but I am no more a courtier than I am a fisher. Talk in riddles if you must, but don't expect a humble nun to decipher them." Portolés drained her bowl and stood, hoping she had aroused the man's curiosity enough that he'd try to talk her back down. During the card games Heretic had taught her around their campfires, he had chided her for following up one bad bluff with another, but Portolés didn't have any other strategies here. "I was sent here to ask a question. You've given me one answer, and I expect to receive a different one from the Empress of the Immaculate Isles when I meet with her two days hence. Both shall be returned to the queen, unfiltered by the simple mind of the messenger."
Jun-hwan stood as well, not nearly as ruffled as Portolés would have liked. "May you find better luck casting your line in Othean. The Autumn Palace has many pools for you to plumb."
"If you or your husband do happen to run into a dead woman who goes by the name of Zosia, let her know that I'm looking for her," said Portolés. "It's important. Tell her..."
Tell her what? That Queen Indsorith had nothing to do with the slaughter at Kypck, that this was an obvious plot to set Zosia against the Crimson Empire? That Queen Indsorith suspected the Burnished Chain had found out about Zosia and sent Colonel Hjortt to kill her people to create this very situation, where Stricken Queen sought vengeance against Crimson, and the church could rule absolutely after they had destroyed each other? That the Crimson Queen had sent Portolés to alert Zosia to all this, so that another needless war could be avoided? The only thing more insane than the truth was the notion that Portolés say anything more to Jun-hwan on the subject; already she had given too much away. "Just tell her Sister Portolés needs to parley."
"I say again, I believe you are confused, Sister Portolés—I do not know this woman you speak of."
"Thanks for the kaldi." Portolés looked back to the distant fogbank, and Jun-hwan stepped around the table. In a low voice, so low Portolés barely heard him, King Jun-hwan said:
"There are others you could ask, sister."
"I told you, I'm no good at riddles," said Portolés, holding his gaze. Now, at last, there was something more than an impenetrable mirror meeting her eyes—eagerness.
"The schools of harpyfish swim farther and deeper than any creature in the Isles," Jun-hwan said as he leaned down, popping open a hidden recess in the center of the table and retrieving a tiny, pink-lidded cream pitcher. "As deep as the Sunken Kingdom, some say. Those who drink of their essence are granted a deep communion with friend and foe alike, and stranger folk still. There is no deception in the realm of the harpies—we could share everything with one another, and know that our exchange was equal."
Portolés took the miniature carafe and opened the hinged lid with her thumb. The oil within shimmered as black as the Gate in Diadem, into which all anathemas had to cast any devilish scraps the Papal barbers had removed from their malformed bodies before first being admitted to the Dens. It smelled of kelp turned up on desolate spits of rock, and the draught sang to Portolés's scarred tongue, setting her blunted teeth on edge...
"But would I remember a damn thing afterward?" Portolés smiled as she poured the harpy toxin over the balcony, into the sea far below. It hurt so good to refuse the temptation. "I've heard of your devil milk, King Jun-hwan, and politely decline the invitation."
Jun-hwan hissed through his teeth; even for a highborn gentleman of the Isles that stuff must be worth a fortune. "I had hoped one of your descent would have a more enlightened view."
"Hope isn't really a dependable purview," said Portolés, shaking out the last few drops before gingerly returning the ceramic vessel to the table. "Faith, well, that's something you can fall back on, when hope doesn't pan out."
"There is war coming, sister, but not the one you're expecting," said Jun-hwan, his smile just a hair too wild for Portolés's liking. "Your superiors in the Chain are busy as wastewasps with their preparations, even if they keep their plotting far from the ears of the wildborn they convert through mutilation. Or the queen, for that matter. You could have learned much, if you hadn't stopped your ears with divine mud."
"Divine mud, huh?" she said, already aching inside at her decision to dump out the drug—she always regretted the sins she had passed up more than those she had indulged. But she couldn't risk revealing the weapon Queen Indsorith had entrusted her with, even for something as tempting as a taste of the black brine that flowed through the Sunken Kingdom. "Mud's dependable, too. I put stock in the ground beneath my feet, even when it's soft, rather than jumping over yon railing and _hoping_ the sea air is more to my liking."
"Good afternoon, Sister Portolés," said King Jun-hwan, and two servants sprang out of the door like wooden dolls on a Cascadian cuckoo clock. "See that our guest and her, ah, prisoner are escorted directly back to their ship. They are in a haste to be away on other business."
"Thanks again," said Portolés, following the servants.
"And do give my regards to Empress Ryuki," Jun-hwan called after her, which put Portolés in half a mind to actually sail straight to the capital—with her paperwork, she might actually be able to finagle an audience. But that wouldn't do her any good, and would show the queen's hand more than Portolés already had. Ah well, if nothing else she'd finally gotten to try kaldi, though as far as sins went that one hardly ranked.
# [CHAPTER
7](toc.xhtml#toc-chapter033)
Plotting and executing a coup isn't the sort of thing you can rush into willy-nilly, but Zosia thought she'd done an impressive job given her tight time frame. Better still, she got to spend some time catching up with Singh and properly meeting her children. The reunion almost made her happy to ride a week in the wrong bloody direction to get the revolution started in Thantifax, the targeted Dominion even farther out on the Souwest Arm than Zygnema. Almost.
Now, though, it was time to escape the city and let the Dull Kriss revolutionaries do all the heavy lifting. Past time, if she wanted to be pedantic.
Outside, in the narrow warrens of Thantifax's streets, the fighting was well under way, the wattle walls of the temple shaking as another explosion tore through the city. Inside, Zosia took one more hard pull on the familiar pipe Singh had scared up for her, a poker-shaped briar piece she'd meticulously rusticated and stained to resemble a piece of Flintland frost coral. That had been a quarter century back, and it'd apparently been gathering dust on Singh's pipe rack for the better part of a decade.
It hurt to know Maroto had pawned the pipe she had spent so many hours carving for him, but she was relieved he'd had the decency to sell it to another Villain. Knocking the bowl out against her thigh to make sure she didn't set her purse on fire, she stowed it and shouldered her pack. Choplicker whined and scratched at the hollow altar in the back of the temple, no doubt peeved he wasn't permitted more than a taste of all the desperation wafting off of the hidden orphans Zosia and Singh had led here just before the rebellion began in earnest.
"I'm going to stay and help," said Singh, cinching her breastplate tight. "I understand if you'd prefer not to, and we can reconvene in—"
"I'm not hearing this, Chevaleresse," said Zosia, expecting this bullshit but nevertheless perturbed at the aroma. "A deal is a deal is a deal, here as anywhere on the Star, or beyond, as far as I know. Don't tell me Raniputri knights started reneging on their oaths while I was away."
The barricaded doors shuddered, and not from another bomb. Idols teetered on their shelves, and the priestesses prayed all the louder as they lifted their writhing snakes toward the graven rafters. Singh tried to stare Zosia down. As fucking if.
"My oath was to help you only after you helped me, and until we can be sure Thantifax falls you haven't fulfilled your end of the bargain." Singh tucked the ends of her mustache under the chinstrap of her spiked helm. "My children—"
"Will win this war with their own blades," said Zosia. "Or lose it, I don't really care. I spent weeks planning the attacks with Masood, and wheedling your daughters' allegiances to boot, which wasn't part of the original agreement. Nor was laying the explosives myself, nor was herding up all those brats and shepherding them to this safehouse. Don't think I'm too thick to realize we're in the worst loyalist quarter of the damn city, either. Just getting out on the road to the Empire is going to involve a whole lot of killing. I haven't bellyached once, Singh, so don't you dare try this shit on me now, just so you can gloat over the success of your brood."
"It's not gloating," said Singh sternly, then softened. "Well, maybe a little. It's just so good to see the family come together for once. Give me this boon, Zosia, and I'll see that a hundred riders accompany us to the Crimson Empire—surely that's worth dallying another day, to do what you do best?"
"If you'd asked me outright..." said Zosia, looking to Keun-ju. The Virtue Guard shrugged, and with shaking fingers cupped one of Singh's wasps to his neck, shivering as it administered its dreamy kiss. He still looked peaked from the bloodbath of the morning. Apparently for all his fighting of cantaloupe devils or whatever back home, shedding human blood wasn't something he was used to. Give him time. "Curse me for a sentimental old fool. Two hundred Raniputri dragoons, Singh, and not a hump in the bunch—we'll need real riders where we're going, not loafers or greenies still figuring out their straw foot from their right."
"You didn't even make me say please," said Singh as the doors began to buckle. "Soft as a kitten's belly, as I've always said."
"Softer than that, but only for you, sister," said Zosia, whistling to Choplicker. The dog looked up at her but made no move to leave the shrine. "Hey there, old buddy! Hey! You ready to be a good doggie? Maybe not just sit there and watch me get knocked the fuck out for the third time in a row?"
Choplicker beat his tail on the floor in time with the wailing of the snake-handling priestesses, his thin canine lips pulled back to show his full array of slimy yellow teeth.
"Yeah yeah, what's in it for you?" Zosia brandished her war hammer and strutted to the rattling door. "Come on, then, might as well feed the dog if we're not leaving right away."
"Thank you, sister," said Singh. "We'll be on the road in two days, at the farthest."
"You hear that, Keun-ju?" said Zosia. "You want to see your Princess Pumpkin again, you'll get off your bee-stung ass and use that two-tiger of yours."
"Four-tiger," said Keun-ju, all energy now that the wasp was in him. "Let them bring their sharpest steel and their fiercest devils. Nothing, not even their pagan gods, will stop me from meeting my bride."
"Yeah, well, pagan gods have their ways of reuniting lovers that aren't reliant on all parties being alive," muttered Zosia. "First things first: we fight until the fighting's done, have a victory feast with the chevaleresse's family, ride out with our new cavalry, and deliver you to your girlie. That order."
The doors splintered wide, an arm wriggled through and shoved the bar open, and then raging loyalists poured into the temple even faster than the sunlight at their backs. Time for Zosia to do what Zosia did best.
If the Thantifax loyalists had been sensible and led their attack on the temple with a volley of arrows or simply rolled in a bomb, things might have turned out very differently. To be fair, they only expected to find a gaggle of priestesses and refugees, so Zosia could forgive them their rash tactics. Most of the charging loyalists wielded short katars, but a few had khandas much like the heavy serrated sword flashing in Singh's hand.
None wielded their blades as well as the chevaleresse, however, as was made intensely clear when the first man was deftly deflected by Singh, her sword bouncing off his and cleaving neatly through his finely ornamented helmet. When one of his fellows tried to seize the moment and hack into Singh's exposed armpit he discovered that Keun-ju's thin four-tiger sword might not pierce a bronze helm but could certainly glide through an eye-slit and skewer a skull. Zosia covered the chevaleresse's other flank, the insatiable pick on the back of her hammer punching through a breastplate and sending the woman who wore it tumbling back into her fellows. Despite their superior numbers, the flood of raging loyalists broke upon the three defenders and then fell back like a retreating wave rebuked by a seawall.
They were well armed and armored, these warriors, most wearing the deep purple and violent green of minor Thantifax nobility, and not as foolhardy as they'd initially seemed—with Zosia and company pressing their advantage, the bulk of the loyalists quickly pulled back to the street. Their fallen and falling comrades slowed Zosia, Keun-ju, and Singh just long enough for the loyalists to pass around a stack of chakram, and as the three rebels burst out of the temple doors they were greeted by half a dozen grinning bastards brandishing the wide, razor-edged rings. An especially cocky fucker was twirling one on her finger.
Keun-ju and Singh ducked back around the ruined doors as the loyalists launched their missiles, but with Choplicker at her side Zosia stood proud, raising her arms in a shameless display of bravado. Well, what was the point of putting up with a devil if you couldn't show off? The chakram aimed at Singh and Keun-ju embedded in the doorframe or flew into the temple, but even as Zosia heard them bouncing through the building the ones thrown at her continued to float slowly toward her, their speed undone by Choplicker. All but one abruptly dropped to the street, but the final chakram drifted into Zosia's reach. Jaws dropped, as well they fucking might. Passing her hammer to her off hand, she plucked the deadly, lazily spinning circular blade out of the air with her right... yet as she closed her hand on it, Choplicker released it from his wiles, and it sped up enough to cut her palm before she'd held it fast. Dirty fucking devil.
"That's right, children," Zosia said, hefting the familiar weight. "You've gone and fucked the pooch but good this time."
Zosia pitched it back into the crowd, and Choplicker must have put some extra spin on it, as it took off the forearm of the girl who raised a hand to shield herself and carried past her, bisecting the face of a man behind her. Then Singh and Keun-ju were following Zosia as she led the charge, a pair of sensible girls in the back turning tail before the trio even reached the front-runners. Steel met steel, and steel met flesh, and pretty soon all parties were sliding around on the bloody cobblestones. The bravest of the bunch came at Zosia with a whip-sword, and would have made short work of her light armor if Choplicker hadn't repelled the weapon back on its wielder, the three lithe blades winding around his throat and digging in. An obstinate chunk of his spine kept him from being decapitated, but just barely.
"Damn," said Zosia, as they cleaned their weapons on the corpses after. "I'd almost forgotten how much fun this could be."
"Almost?" asked Singh.
"Almost." Zosia smiled.
"Blurgh," said Keun-ju, hunching over and vomiting onto the street.
"Come on," said Zosia, patting Choplicker's head with her wounded palm. "There's plenty more where these came from."
They'd dragged in tables from all over the palace, setting them up in the courtyard so there'd be enough room for everyone, from Singh's family all the way down to the formerly untouchable weirdborn who had planted the bombs under the barracks and guardhouses. It was just like the long march on Diadem, royalty and ragamuffins sharing food and drink beneath the stars. Except they were eating a hell of a lot better this time around, with hundreds of piping-hot dishes set out on the scuffed boards. Apparently the revolution was popular in the royal kitchens.
"I take back everything I said about Raniputri cooking," said Keun-ju, piling his third plate of coconut rice with nothing but pickles. "Everything, except I wish there was some fish, squid, _something_."
"Yeah, well, nobody's pickier than a beggar," said Zosia, sipping on her mahua. The flower wine reminded her of the early days with Singh, nothing to their names but the swords at their sides and a small bottle to share along the dusty road. Beside her, Singh's elder son, Masood, drained a Flintlander horn of Samothan red and clapped her on the back.
"No beggars tonight, madam, only mahārājñīs and mahārājas of a new Raniputri dynasty!"
"Uh-huh," said Zosia, eyeing his mother across the table. "And what about tomorrow?"
"We're all beggars when the sun rises," said Masood, punctuating his wisdom with a burp. "It's what we are when night falls that counts."
_Thank you_ , Singh mouthed, and, watching her old comrade mend fences with her family, Zosia was glad she'd agreed to stay and help carry the day instead of holding Singh to her word that they'd head out as soon as the fighting started. The chevaleresse threw an arm around one of her twins, Zosia had already forgotten which one. "You remind your brother of his sagacity when next his luck changes, and he goes to bed in an alley with only his fat tongue for a pillow."
"I'll remind him now that the city never would have fallen if not for my soldiers," said the girl, squirming away from her mother's embrace, but not earnestly enough to fool Zosia. "What, dear Masood, do you have to say on that matter?"
" _Dearest_ Urbar," Masood said, sloshing wine onto the table and his dhoti as he gestured roughly in her direction, "I say I would rather fight a dozen Thantifax armies by myself than get on your bad side by pointing out what a peacock you are, wearing diamonds to a war!"
They bickered on, though good-naturedly, and when a warm jug of bhang replaced Zosia's liquor, she drank deeply of the draught, and soon floated above the table. The stuff used to provide escape, but now it imprisoned her in her own heart, the droning laughter of the Raniputri and Keun-ju drowned out by the chiding in her mind. Why hadn't she and Leib taken this road, hiding in the open where friends could watch their backs, instead of fleeing to the mountains and pretending they were different people?
They had come to believe the lie as much as those they told it to, a small-town boy returning to the tranquil hamlet of his birth and bringing a foreign bride with him. Working the modest fields of their neighbors, tending their animals, harvesting roots for the pot-stills. Becoming joint mayors when the old mayoress passed away and insisted they take on her duties. Passing the years with songs and mundane sorrows and the annual pilgrimage down to the jade-tinged foothills to offer alms to the Empire, instead of actually living the lives they were born to—lives tinged not green but red, bloodshed in the ruddy dawn, and dark wine spilling everywhere by the evening...
Perhaps there was a table like this in some hell or another, where she would rejoin her husband and all the others whose lives had ended violently on her behalf. Perhaps she would someday fill Leib's cup with congealed blood, and they would eat ashes among the tombs. Perhaps many things, in the grave, to go on Choplicker's knowing glance from the shadows at her ankle. He was fatter than he'd been that morning, his coat lustrous, his teeth again white as the ivory stud in Singh's nose.
The courtyard echoed with songs and boasts and jests and even a dance or three until dawn finally intruded over the palace walls, but Zosia neither sang nor bragged, nor laughed again that night, and kept counsel only with the sated devil at her feet, silently staring back into his dark eyes until her head hit the table.
They traversed twilit deserts and beside bright rivers, through cool forests and over blazing hills where the red-tipped grass waved like a sea of burning silk. Once they spied the ruins of a tower atop a spire of white rock in the midst of a black jungle; based on Choplicker's keening insistence they investigate it, Zosia presumed it was devil haunted, but wasn't about to go close enough to confirm it. They rode on, over creaking bridges built when the Empire was young and through passes in the mountains hewed by the very gods, to believe Singh... or strong winds, to believe her children. Her daughter Udbala and her son Sriram accompanied them, with a hundred and one riders each, and their passage from the tip of the Raniputri Dominions to the Heart of the Star was as easy a ride as Zosia could remember. Stampeding through the pickets at the understaffed garrison of the Imperial border outside Azgaroth, she dared hope it could all be as easy as this: a whoop and a cry and a pell-mell race past slack-mouthed young fools, to victory!
As if life were ever so easy. Half a day later they discovered why the border station was so lightly patrolled; an Imperial regiment, recently bulked up from the garrison, sat camped in the middle of the road. Judging by the prodigious dustcloud that chased them when they cut across the foothills to ride up and over the northern Pass of Blodtørst, the regiment had a sizable cavalry to boot. No Azgarothian stallion could match the Thantifax mares, but even without risk of immediate engagement Zosia's jaw set and her eyes narrowed: the Crimson Empire was already mustering for something, and she could imagine what. Or, rather, whom. Cobalt Company _indeed_ , as if any army had a right to that name without her leadership—this Princess Ji-hyeon had some bloody nerve, if Singh's account of the girl's plan was remotely accurate.
The village of Blodtørst lay on the edges of a mirror-still pond three days' ride up the treacherous trails of the western Kutumbans. It was a pilgrimage site for both the Burnished Chain and Ugrakari worshippers, and each summer the town of several hundred swelled to the thousands. Stupas lined the western banks, inverted wooden crosses the east. The Raniputri cavalry arrived at nightfall and were given a hero's welcome, as Blodtørstians, being sensible people, welcomed all marching armies, regardless of their pennants.
"Girl, get over here," Singh said, beckoning Zosia to the shrine wall in the common room of the headwoman's hostel, once they were all settled into their shanty rooms for the night. "There's something you don't see as much down in the Dominions."
The hostel was as simple as everything else in Blodtørst, its neatly stacked stone walls unadorned by windows or even tapestries, but early winter being a full season out from any major Chainite pilgrimages, the proprietor had the curtains pulled back from her shrine. It consisted of several plain wooden shelves cluttered with idols, the Ugrakari having almost as many gods and devils as the Flintland tribes had legendary ancestors. Singh was meaningfully eyeballing one of the small statues.
The feminine figure sat on the upper shelf, beside the ferocious wargod of the Ugrakari and an ursine fellow Zosia almost remembered the name of, but not quite. Unlike her neighbors, she was decidedly human in shape, with neither extra limbs nor animal features. In fact, with that hammer and sword she looked almost like...
"No fucking way," whispered Zosia, a funny feeling spreading through her chest as she picked up the idol. It was crafted of heavy wood, briar or she was no pipe-carver, and the hair... the hair was painted robin's egg blue. "You're having me on. This is..."
"Cold Cobalt," said the headwoman, setting her tea tray down on a table and bustling over. "Please, respectfully, put her back. She is wroth to be touched."
"Oh is she ever," said Singh, putting her palms in the air and stepping back to further implicate Zosia for the crime. "Better be careful, friend, or you'll get a curse, disrespecting the Blue Queen that way."
"I don't believe it," said Zosia, looking down at the statue before remembering her manners and putting the figurine back in its place. "I mean, sorry, I meant no disrespect to your shrine."
"Doesn't bother me," said the headwoman, pushing a few errant grey hairs back under her head scarf. "The queen, though, can be testy, especially to foreigners."
"Really?" asked Zosia, relieved that Choplicker had obeyed her order to stay in their room. She never would've lived it down, if he'd been here for this. Keun-ju, too, for that matter—good that he was already sleeping off the day's ride. "You don't... I mean, you pray to her?"
"Pray?" The headwoman barked a laugh, rubbing her gnarled wrists as she stared at the statue. "She doesn't listen. But that's all the more reason to stay on her good side, eh?"
"She's..." Zosia tried not to smile. "Do you... she's not a god of your village, your people?"
"Bah," said the headwoman, probably a little freer with her tongue since they'd all drunk chaang together during the communal dinner. "Of course not! Just a woman, like all of us. Only a fool would bow to her... and only a damn fool would call her a devil, like the Imperials do. They say she's back, you know, and the Cobalt Company is big as it ever was, but I don't believe it's her. Can't be. That's the one truth of this world, the dead stay dead, praise the mercy of gods and weakness of devils."
"Well, I say she—" But whatever Singh was going to say was cut off by Zosia's glare.
"I knew her," said the old woman sadly, and Zosia felt a stab of shame at still having no bloody idea who this woman was, until she said, "Well, not to speak to, as we are. But I was with her, as a girl. The Cobalts came through, quick quick quick, but not quick enough for my mother to keep me from running away with them. Ah, what an adventure!"
_As a girl?_ Zosia chided herself for thinking this woman old—she must be a few years her junior, so what did that make Zosia? Singh was giving her a look, prodding her with her eyes to take a bow, but fuck that. Instead, Zosia said, "How many folk died on that adventure, do you think? I've heard thousands starved or got weatherbit into the grave, not counting the actual fighting."
"Thousands?" said the headwoman, sitting down on a bench at the low table and pouring herself yak butter tea. She nudged the cast-iron pot in the direction of her still-standing guests. She wasn't smiling anymore. "More like tens of thousands. Maybe as many as half our number. I don't know. People I'd known from the cribhouse dropping all around me. I was lucky to only lose a few toes. And we who weren't stout enough for war with the Imperials were charged with foraging supplies. You know what that meant? Robbing farms that wouldn't donate everything they had. Storming towns not too different from this one, hoping the locals wouldn't join up so we could steal enough to feed ourselves. We fought as hard as any soldier, I tell you true, with rocks and sticks! Not even her Villains were fierce as us, farmgirls, village boys, and plenty of others, all drunk on a dream..."
"Some adventure," said Zosia, sitting down on the opposite bench with a groan. Her ass and thighs certainly hadn't missed the saddle, even if the rest of her had.
"Ah, but it was!" said the headwoman, blowing on her tea. "I met my wife on the Long March, made friends who still pilgrimage here from year to year. Maybe Cobalt was a devil, as the Imperials say, and it was a ruthless business, no mistake. But she fought for us. Me, you, and most of all the Imperials themselves, though many were too blind to see it. She wanted to remake the world, to liberate the poor, to—"
"Bullshit," said Zosia with more venom than she thought she had in her. "She was a killer and a coward, same as every king or queen before her, and same as every one since."
"You're wrong," said the headwoman. "She was a killer, true, but she _tried_ , she did—if you'd but heard her speak to us, you would believe it was more than lust for power or wealth that spurred her. She would have brought change, too, if not for the assassins of Samoth. Things would be different."
"I noticed you didn't have a statue of Queen Indsorith on your wall." Singh smirked as she sat down beside Zosia and poured herself a cup of the rich tea.
"Do not mistake one thing for another," said the headwoman, as though they were contrary children. "I keep the Crimson Queen in my heart, and her idol above my bed. Less... _ambitious_ than Queen Zosia? Yes, yes, yes. But her soldiers are well behaved when they pass through, and it was she who designated Lake Blodtørst a holy site, not those... clerics of the Burnished Chain. Things are not so good as they would be had Zosia lived, but are not as bad as they could be."
"I think I'd better lie down," said Zosia, rising from her seat. "I feel like I'm already dreaming. Thank you for your hospitality, madam, and for sharing your tales with us."
"We're riding early, of course," said Singh. "I'll give the knock when it's time."
"May your time with the devils pass swiftly," the headwoman called after her, and Zosia walked stiffly to her room. Glancing back down the dark corridor, to where only a tea candle lit the room where Singh and the headwoman still sat, she let out a long, sad sigh. They would be gone before the sun rose, but if the Imperial cavalry still pursued them they would arrive in this village ere the moon next rose. When that happened, would they be as respectful as the headwoman supposed, or would they punish the helpless populace for aiding and abetting a crew of border-jumpers? Would they all be wiped out as an example, the way Kypck had? Had she damned another village just by setting foot in it? And how many more villages would she pass through on her ride to Diadem? How many more poor fools who bought into her myth would die with idiot grins on their faces, in war or crueler deaths, believing they martyred themselves for something other than a selfish woman's ambition, her conviction that she alone knew what the world deserved?
Choplicker nosed the door open and snuffled her hand in the dark hallway. She pushed him back into the black room and shut the door behind them.
They caught sight of the would-be Cobalt Company within a week of leaving Blodtørst, as they crested one of the Kutumban range's seemingly infinite passes. They were miles off, caravans crossing the Bridge of Grails, which spanned the Trench of Mordlust. From up here, they looked like an enormous mass of maggots swarming over the exposed ribs of the mountains. Yet this vantage also showed another force, albeit a smaller one: the same Imperial regiment they had eluded by the border. It looked to be just the infantry; even on foot, the Imperials had made much better time than Zosia's crew by taking the Black Tar Pass directly over the front range. The mass of soldiers marched between Zosia's Raniputri riders and the distant Cobalt Company, winding along the main road through the mountains. Even after Singh watched the dips and rises of the remote road for half an hour through her hawkglass, not a rider of the heavy Imperial cavalry appeared... which meant they were probably still in pursuit, coming up through Blodtørst Pass after them. Not only were Zosia and her warriors cut off from the Cobalt Company, they were being scissored between the Imperial riders and their main force.
"So close," said Keun-ju wistfully, staring out over the ocean of air to where his beloved led her army over the four bridges. "Why don't we... I mean, couldn't we..."
"Lead the Imperial riders all over the devil-kissed mountains until we find a way to go around their infantry?" said Singh, spitting a ruby that splattered on the rocks. Not a full season on campaign and she was already back on the betel. "Won't be the first time, what?"
"No," said Zosia, "though if we're lucky it will be the last."
When not taking the narrow highway carved through the Kutumbans, walking was hard enough, and riding was nearly impossible. Many a summit and decline was traversed with the Raniputri leading their nervous animals by the bridle, boots and hooves sliding on snow and dust-slick rocks. In the weeks that followed they never hit on a way to circumnavigate the Imperial infantry, and so it wasn't until the Cobalt Company came down in the Witchfinder Plains that the Raniputri dragoons were able to break north and come in for a parley. As they neared the end of their long hunt, Zosia wondered if she showed her nervousness as badly as Keun-ju. What did he have to sweat over? All he had to do was be reunited with the love of his life... Zosia was the one who might very well have to kick her ass.
# [CHAPTER
8](toc.xhtml#toc-chapter034)
That Ji-hyeon girl, man. When Sullen sat down for kaldi in her tent he'd been thirteen kinds of happy, and then fourteen kinds of disappointed when the first question she'd asked him was about his hair. Not that he wasn't proud of the high ball he'd been able to tease up with his mom's old pick—if secretly horrified that of late only white hairs came loose from the comb, instead of the black strands of his youth. No, the thing was, ever since they'd left the Savannahs, Outlanders kept wanting to talk about his hair, and a few had even been so bold as to ask if they could touch it. Some didn't even ask before reaching for his head, and a bar fight had erupted in some Kvelertakan shithole when a woman at the next table had reached over and tugged on it for no reason at all. The result of all this was Sullen would've been happier than a baby-fattened lion to talk about anything at all with this lady, _except_ his hair.
"Nah," he said, because technically she'd asked _if she could ask him_ about it, in that roundabout Immaculate way. She was meeting his gaze with both of those blood-dark eyes, and he dropped his to the delicate kaldi bowl in his hands. "I mean... what about it?"
"Has it always been that way?" asked Ji-hyeon, but before he could roll his eyes at her she said something that stopped him short. "White, I mean?"
All that ivory in his mom's pick. Without really thinking about the company he was keeping, Sullen reached up and gave a tug. The pair of curly strands he held up were as pale as everything he'd picked out of the comb. "Um... no."
"You've passed through, too, haven't you?" asked Ji-hyeon, her eagerness not at all what he'd expected from a hardened general. With that Fennec creep and the rest all booted out of the tent, she seemed... girlish, almost. "Did you keep your eyes open? I didn't. I wish I had, now. Which one did you enter? Where did you come out?"
"Um..." What the devils was she talking about? "What?"
"That _is_ what happened, isn't it? To your hair? You went through a Gate?"
"Nah!" _Through_ a Gate? There was a thought to keep you up nights. But when had his hair changed, and why hadn't Grandfather said something? When... the Faceless Mistress. Sullen remembered the look on Grandfather's face when he'd come back to camp in Emeritus, how the old man had just known something weird had gone down. He patted his hair. "It... it ain't _all_ white?"
"Oh yeah," said Ji-hyeon, holding up the polished silver kaldi press. "Same as mine, under all this dye."
Even in the blurred reflection he could see. His whole damn dome had gone snowy! He knew he should be freaked out, to say the least, but truth be told he thought it looked pretty swift. Glancing over the press at the general, he asked, "Dye?"
"Immaculate girls don't come with blue hair, Master Sullen," said Ji-hyeon, and he thought she sounded a mite sore about it. "When we came out of the Gate in Zygnema, every black strand of it was white as yours. Could be a lot worse, though, and it takes the blue better like this. I don't know how we would've colored it otherwise."
"So, um..." Part of Sullen didn't want to know, but another part of him had to. He felt the same giddy terror he experienced whenever he really thought about his encounter with the Faceless Mistress. "What's on the other side of a Gate? And how did you get out again, once you went in?"
"You've heard of the First Dark, haven't you?" said Ji-hyeon, leaning in close and lowering her voice like she was telling a ghost story. "I know the Burnished Chain says it's hell, and plenty of other cults agree, but I don't think that's what it is at all. I think it's... I think it's like a secret ocean, kind of? A living, breathing ocean, and the Gates are the shores? So when we went into it, I just felt... _weird_ , really, _really_ weird, and smelled, like, burning oil, and felt these... _things_ , lots of things..."
Sullen felt the hairs all over his body stand up watching her tell it, her eyes closed as she reached back for whatever she'd felt in that place. The Horned Wolves definitely knew all about the First Dark, but it wasn't any kind of ocean. The First Dark was what had been here before his first ancestor was born, before the Old Watchers who made her, before even the Star—it was called the First Dark because in the beginning that's all there was, blackness, and from this blackness grew all the monsters of the world...
"Anyway, it was over before I knew it," said Ji-hyeon, straightening up and shaking her hair out. "We went in the one in the Isles, and before I knew it we stepped out of the one on the Soueast Arm. It was... an experience, but not one I'll ever repeat. I don't think it's very safe, passing through them like that. Fennec said he knew how to use them, but considering what happened to _him_ , well, I'm just glad my hair was the only thing that changed. It'll be easy to dye black again."
"I think the blue looks fleet, fleet as a fox," said Sullen, regretting the compliment as soon as he said it—he'd been saving it up, to use at an opportune time, but this damn sure wasn't it. He'd gotten all keyed up, imagining Ji-hyeon jumping into a Gate, and his bowl sloshed hot kaldi in his lap from his suddenly shaking hands. To change the topic, and fast, he blurted out, "Mine must've changed this one time I met a god."
Stupid, Sullen, real stupid. He wasn't trying to show off, but how else could it come across? She'd think he was either bragging or crazy, or both.
"Which god?" asked Ji-hyeon, sipping her kaldi and tactfully pretending not to notice the mess he'd made with his.
"Faceless Mistress," said Sullen, wondering if he shouldn't be spreading that around just as he said it.
"Faceless Mistress?" Ji-hyeon furrowed eyebrows that Sullen now noticed didn't match the bangs above them. "I've heard of spirits like that, ghosts from the Sunken Kingdom. How do you know she was a god? What's she the god of? Does she have other names?"
Sullen shrugged.
"Where was she? Who worships her?"
"Forsaken Empire," said Sullen.
" _The_ Forsaken Empire?" Ji-hyeon's tone told him she wasn't convinced. "Nothing's there anymore. Nothing but ghosts and devils and bad luck."
"We were there," said Sullen. "Grandfather and me. Didn't see any ghosts, I don't think. And the only devils... the only devils showed up when she did. When she went, so did they."
"Sounds like you have quite the song to sing," said Ji-hyeon.
"Uh..." Sullen bit the inside of his cheek, watched the woman warm up her bowl from the press. He shouldn't trust her, not some fiery general who matched up in all but name to the descriptions of this Zosia woman he was supposed to thwart... but he wanted to trust her. Wanted to do a lot more than just trust. Who in all the Savannahs would've guessed he would end up halfway across the Star, with a beautiful foreign warlord asking him to sing her a song, because she sensed his song was worth a listen? If he had learned one thing from the sagas, though, it was you let your host take the first boast; that was just good manners. "After you, General."
"After me what?" asked Ji-hyeon, nodding the kaldi press in the direction of Sullen's bowl. Jittery as he was already from the fruity, acidic brew, he quickly held it out for her to fill. "And in private you can drop the 'general,' Sullen."
"Yeah?" Sullen's heart didn't skip a beat so much as vault over a solid dozen of them.
"Yes. 'Princess' will do just fine," said Ji-hyeon primly, and bizarre gods of exotic empires take pity on him, he couldn't tell if she was being serious or joking. "Now, what should I do first?"
"Oh. I just meant that since I'm a guest in your tent, you should tell the first story. Everyone thinks you're this Zosia," said Sullen, and _that_ put the seed in her beedi, no doubt, but he went on. "Me and Grandfather trekked all over the Star, looking for my uncle, and heard a hundred songs about her. Zosia, Cold Cobalt, and other names beside. You even look like what we heard about her."
"Just like Zosia, eh?"
From the look on her face, he'd made things even worse, so he quickly added, "I'm happy you're not her. I'm... delighted."
_Delighted?_ He could almost hear Grandfather snickering from halfway across the camp. But for once he'd said the right thing, maybe, because all the building irritation left Ji-hyeon in one obvious sigh.
"You're the only one," she said. "You can't know the toll it takes, seeing how disappointed they all are when I lift the visor and I'm not her, just some hooligan down from the Isles to stir up trouble."
"Hooligan?" asked Sullen, his Immaculate pretty good but maybe not what it could be.
"Yes, it means, like... a thug?"
"You don't look like a thug," said Sullen. "I can't figure anyone calling you a thug."
"Oh, they call me a lot worse things than thug or hooligan, but you probably don't want to hear those."
"No," agreed Sullen gravely. "I don't."
She laughed, as if he'd said something clever, so he laughed, too. Why not? Something doesn't have to be funny to laugh at it, so long as you're laughing with good company. Just when things didn't look like they could get any better, she slid open a drawer in her table and pulled out a small pipe packed full of red-haired skunk flowers, and even offered him first puff.
"Ah, come on," he said, taking the pipe, "after you gave me that look for asking you to chief with me the other night?"
"I'm sure I don't know what look you mean," said Ji-hyeon, giving him _the exact same look_ , all fierce with one eyebrow up near her bangs. "Now get that going, I want it to air out in here before my next meeting. Fennec is such a whiner, says it clouds my mind—unlike all the cider he puts away."
Sullen was getting it bad for this girl; he couldn't ask for things to be better.
"Well, isn't this cozy!" came a voice from the back of the tent, and a dreadful, familiar shape stepped out of the shadows. This was a nightmare, it had to be—before accepting his seat on an embroidered cushion Sullen had surreptitiously looked all around the tent to make sure they were alone, and yet here stood that awful witch from the grasslands. Hoartrap the Touch.
"You!" Sullen dropped the pipe and nearly tipped the kaldi table as he leaped to his feet. "You!"
"The one, the only," said Hoartrap, bowing low. Devils above and gods below, but the witch was even bigger than Sullen remembered, his brow nearly brushing the blue canvas canopy. "So happy to see you again, Morose."
"His name is Sullen," said Ji-hyeon, scowling at the witch but not bothering to stand. "I've cautioned you before about your sneaking and spying, sorcerer. Do you want to die?"
"I _am_ sorry," said Hoartrap, about as sincere in his contrition as a dog who's stolen dinner off its master's plate. "I assure you, my dear general, I had no intention to sneak or to spy. If I had, I would hardly announce my presence, would I? No, I have urgent business to discuss... _private_ business, Sullen my boy."
"You..." Sullen looked back and forth between Hoartrap and Ji-hyeon. It broke his heart that she knew this creature, trafficked with him.
"Yes, yes, you said that already," said Hoartrap. "Now be a good pup and go back to licking your grandfather's arse. The adults need to talk."
Had anyone else taken such a tone, Sullen would have been inclined to educate them on proper comportment. With Hoartrap, though, he was simply relieved to have an excuse to leave. He'd left his weapons back at his tent, and Grandfather said nothing but cold metal could stop a witch...
"Treat him like that again, sorcerer, and I'll—"
"Cut my lungs out yourself, yes, yes, I know," said Hoartrap. "Apologies, apologies, Master Sullen, sometimes my sense of humor doesn't translate. But we do need to talk tactics, m'dear—my little friends tell me we have a Raniputri problem to the north, on top of a possible Imperial complication, and we really should start to—"
"All right already," said Ji-hyeon, waving the hulking monster quiet and then hopping lightly to her feet. "Sullen, I am sorry to truncate our conversation. Another time, spirits willing."
"No doubt," said Sullen, trying not to color under the mirthful gaze of the witch. "Whenever. I'll be ready."
"Give my regards to your grandfather," said Hoartrap. "I'm looking forward to seeing him again, just as soon as Maroto returns to camp. That's a reunion I wouldn't miss for all the devils in hell."
The witch was trying to spook Sullen, obviously, but the memory of their last meeting kicked up something different in his mind. Glancing to the tent pole where Ji-hyeon's devil roosted among the folds of canvas, he said, "Mind your devil around him. He eats them."
Ji-hyeon froze mid–parting bow, straightening quickly. She looked... frightened? Good if she was, hanging around with a witch. "Who told you?"
"I saw him do it, out in the plains. An owlbat, just like Fellwing."
"No, no, how did you know she's a devil?"
"Oh, our Sullen's full of surprises, aren't you?" said Hoartrap, and for the first time there was real anger behind his casually nasty smile. "He's witchborn, General, or hadn't you noticed? And more than that; since last we met he's been peeking into dark corners best left lightless, or I'm no judge at all of deviltry. I'm also looking forward to hearing how you came by that creamy coif, pup."
Sullen felt deadly cold all of a sudden, and said, "Call my mom a witch again. Call me whatever, but Ma? Nah."
"A lovely woman, I'm sure," said Hoartrap. "There I go again, with my clumsy translations. I simply meant you've got, oh, how do you people put it... the blood of shamans, is that right?"
"Oh," said Sullen, too confused to stay angry. First the witch insulted his mother, now he was doling out compliments. Crazy old monster. "Yeah. Maybe. Not for me to say."
"I happen to find your eyes very handsome," Ji-hyeon told Sullen, which wasn't something he had ever expected to hear. Coming from her, it burned his cheeks right up, even with the witch looming over them. "And Choi's wildborn, too. My second. She's with your uncle, but you'll meet her as soon as she's back."
" _Uncle_ Maroto, is it?" said Hoartrap. "And that makes your grandfather... well, I suspected as much, but those two were very cagey about the whole subject when last we met! Glad to finally know how the blood flows."
"We've got plenty of other wildborn in the ranks besides Choi," said Ji-hyeon, ignoring Hoartrap, though Sullen was unnerved by how much interest the sorcerer took in his family tree. "They've got more reason than many to march against the Crimson Empire. Some of the best we have. Good people, not like others in this company, who have more questionable motivations."
"Oh, how your words sting!" said Hoartrap, clutching a burly hand to his chest. "But really, now, that kaldi's not getting any hotter, and we do have the trifling matter of waging a war to consider. So might I bend your ear, General?"
Now that he'd gotten some licks in, Hoartrap wouldn't even look at Sullen, but Ji-hyeon was all classy about it, as she seemed to be about most everything. "I was enjoying myself, Sullen, before we were interrupted. Please give my regards to your grandfather, but inform him we may be moving on sooner than expected. If we leave before your uncle returns, you may carry on with the Company until he reconvenes with us."
"Thanks," said Sullen, imitating her bow. "Really. A lot. And I'd tell you again to be careful, but you're clever enough to know that without me beating the mule. Wouldn't leave my worst enemy alone with him, I could help it."
As he left, Sullen wondered if her smile was triggered by his words or Hoartrap's obvious displeasure at them. Didn't really care much either way. It was that kind of smile.
# [CHAPTER
9](toc.xhtml#toc-chapter035)
Ask me again, Wan, and you'll have a different answer, I promise you that. Ask away. _Please_." Domingo was in better humor than he'd been since he'd dispatched that Immaculate prince back on the Azgarothian border. After the many rump-wrecking leagues of riding over the worst country the Star had to offer, headache-inducing meetings with the Ninth Regiment's interim colonel when they joined the Myuran force, a steadily worsening diet, and now the infuriating revelation regarding the nature of the weapon the Black Pope had given him, the prospect of stomping the anathema greatly appealed to Domingo. Adamant as Brother Wan was regarding the prospect, could he resist a final prod? If he did keep harping on the subject, Domingo would give his hideous dinnermate a final prod of his own—only by setting rules for oneself could order be preserved, after all, and Domingo had set a rule that he would not murder Brother Wan unless the witchborn stepped over one of the many lines the colonel had set before him. So far Wan had always drawn up short, but here, at last, in this miserable camp in the barren heights of the eastern Kutumbans, with a full-on engagement with the Cobalt Company a foregone conclusion and the monster's toe hovering over this last border, maybe he would dare to take that final step and...
"Forgive me, Colonel, I meant no disrespect," said Brother Wan, in a tone that carried plenty of what he verbally disavowed. He swirled his grappa, flicked his lizardlike tongue into the glass. "When you accepted Pope Y'Homa III's weapon, I naïvely assumed that you intended to use it. My lack of experience with actual combat has again embarrassed me."
"I took her so-called weapon, and I took on you, Brother Wan, under false pretenses," said Domingo. "I will admit I was disappointed when I peeked in that wagon and saw that this great and terrible weapon was nothing more than crocks of oil. But no matter, I thought, oil can come in handy in a battle, and maybe we can erect a means of launching them into the Cobalts. Fine. Hardly revolutionary, but fine. Setting the enemy on fire is a time-honored tradition, but this, _this_ I will not allow."
"There is something to the proposal, though, isn't there?" asked Colonel Wheatley, even more cautious than usual in his tone. Daft as the green Myuran seemed, he'd evidently come to appreciate that being co-commander of this joint operation was strictly an honorable formality, and on matters military he was not to speak out of turn. "I mean, we have the stuff, it couldn't hurt to try, could it? Might be just the thing for morale, if nothing else."
"Morale is boosted by stalwart command, not magic potions," said Domingo, drunk enough to speechify but not so far gone as to overdo it. "No Azgarothian in living memory has allowed their soldiers to poison their blades, nor slather themselves with Chain grease, and I have no intention of being the first. Long before we called ourselves the Fifteenth, we were noble enough to fight fair, even against those of less chivalrous disposition. What sort of a knight would I be, if I took to using deviltry when we already had strength of numbers and advantage of terrain? We will obliterate the Cobalt rebels absolutely, and with nothing more than cold steel and iron resolve."
"Whether or not the Fifteenth takes part, I will allow any troopers in the Ninth who desire the Chain's succor to be anointed before the battle," said Wheatley, the sudden display of backbone as surprising in this command tent as it would have been in an octopus. Apparently the bronze iron chain around the man's throat represented something more than a memento from a pious uncle or aunt. "Thank you, Brother Wan."
"Yes, yes, thank you for sowing criminal notions in the fertile soil of a greenie's empty helm," said Domingo with a sneer at both the anathema and his human sympathizer. "Since you were but recently promoted to your position, _Colonel_ Wheatley, I will pretend I did not hear your suggestion that your soldiers poison their weapons before engaging with the enemy, in clear violation of no fewer than three of the internationally recognized codes governing ethical warfare."
"In open war with an honorable opponent, yes," said Wheatley, quick enough to reply that Domingo would have bet his last biscuit that Brother Wan had coached him on the topic. "The Cobalt Company is not a legal army, though, so wouldn't there be some wiggle room—"
"There's no fucking wiggle room in my tent," said Domingo curtly. "I am amazed you could locate the errata on rebel factions in the Crimson Codices, Wheatley, when you couldn't find your own fucking command at the Siege of Myura. How fortunate for us you were off digging latrines when every other ranking officer was caught by the Cobalts, otherwise we would have had to promote some grunt with actual military experience to the post!"
"I was overseeing the sapping operation," Wheatley said, having gone the color of Wan's naked gums as the anathema gnawed at a piece of sheep cheese, watching the two colonels. "Not _digging latrines_. And the colonel and lieutenants and other captains weren't captured. They say... they say they vanished."
"Spirited away, were they, maybe by ghosts or devils?" Wheatley was making this too easy for Domingo—it felt even better to be shaving parts of this boy off with his tongue than it would have to do so with his saber! "They were caught with their greaves unbuckled, Wheatley, not once, but twice—bad enough old lady Culpepper fell for the oldest trick in the songs, sending the whole Ninth out of Myura after an obvious decoy, but then she couldn't even take back her own fucking city. While you were down in the dirt trying to... trying to..." Domingo was trying not to laugh, "... trying to blow open your own colonel's castle, the Cobalts swooped in and butchered the whole command. They vanished, all right, into an unmarked grave somewhere off the road between here and Myura. Another old Cobalt trick—if the bodies of your enemies are never found, superstitious humps will start whispering about how they weren't killed, they'll say..." Domingo lowered his voice in a passable imitation of the lad, looked back and forth between the livid Colonel Wheatley and the frowning Brother Wan. "They say... they say they _vanished_."
To say that the silence that followed was awkward would be a bit like saying gangrene was unpleasant: accurate, but nowhere close to capturing the severity of the condition. Domingo watched the trembling, wide-eyed Wheatley very carefully, in case he pounced across the table to attack him with his fork. That's what Domingo would have done, if any of his peers had talked that way to him, even in his youth. Especially in his youth.
"As I said, I mistakenly believed you intended to use Her Grace's weapon because you brought the wagonload of oil all the way here from Diadem, and me along with it," said Brother Wan snottily. Domingo had never seen the witchborn so blatantly annoyed, which, considering the innumerable times he had baited the anathema, seemed yet another feather in Domingo's already many-plumed helm. "If you had refused her gift, I never would have raised the subject, because I never would have had the pleasure of making your acquaintance, to say nothing of riding all over the Empire with you and your army."
"Good steel has a little bend in it, and so does a good colonel," said Domingo. "You are correct that I accepted the Black Pope's weapon, but I have changed my mind. I am allowed to do that. I would rather risk the lives of every soldier in this regiment by fighting the Cobalts fairly than risk their souls by using your devilish magic."
"After all of your lectures on the matter I assumed you didn't believe in an everlasting soul, Colonel," said Wan.
"See here," said Wheatley, "the Burnished Chain does not practice black magic!"
"One fellow's faith is another's heresy," said Hjortt, which didn't sound as clever as he'd thought once he said it, but no matter. He was in charge; he didn't have to be clever.
"There is no more powerful weapon than faith, Colonel—" Wheatley began.
"Codswallop! I've been hearing that line from loonies my whole life—faith is the strongest weapon, the truth is a weapon, blah blah blah. You hit me with your faith and I'll hit you with my fist and we'll see which one's a weapon!"
"Colonel Hjortt," Wan said with poorly contained frustration, "a great many of your soldiers have already asked my brethren if they will be permitted to receive the Burnished Chain's blessing before they see combat. If we could compromise, and I could anoint only those soldiers who request—"
"I don't give a quick fuck what they asked you for, Wan. A soldier will ask for enough beer to drink herself blind and enough cheese to constipate himself for a week, but that doesn't mean they should have it," said Domingo, winking at Wheatley. "Even without the Third coming over from Thao to cut the Cobalts off, between my regiment and Wheatley's we've got more than enough stiff fingers to pluck every blue pansy in the Company. The horse I sent after those Raniputri riders should rejoin us any day, and then, well! It will be a massacre, that's the only word for it—they may have devils and witches and who knows what else, but our combined forces outnumber them two to one. That's all that matters, when the horns blow, not the Black Pope's dread weapon of holy slime and fatuous prayers."
"Thank you for dinner, Colonel," said Wheatley, stiffly rising and dropping his napkin over his barely touched beans. "I think... I think I had better see if the squad I sent to check on that odd signal from the western scouts has returned."
"See that you do," said Domingo, leaning back in his chair rather than standing. Fuck _Colonel_ Wheatley. "If it turns out one of your scouts dropped his rifle and alerted the whole bloody mountain range to our presence, have the blighter hanged. That will do wonders for your _morale_ , believe you me, nobody in the Ninth will discharge their weapon without—"
But Wheatley had turned without a salute and all but dashed out of the tent. "Well, Colonel..." the witchborn said, refilling Domingo's glass. "If anointing the rank and file is out, I hope it is not too much of an imposition to ask that I bless our armies when the horns sound? Just a few quick words to—"
"It _is_ too much to ask, Wan, it damn well is. No Chain nonsense where the Fifteenth is concerned, nor the Ninth, nor any regiment within a hundred leagues of me, and that's final. I won't have you waving your rosaries around and then thieving all the credit when my intense planning and our hardworking troops bring us to victory. The queen's extra-special holy oil gets to ride right back to Diadem, along with news of our honest win over the Cobalts," said Domingo, knocking his glass back in one lusty swallow. Smacking his lips, he dealt the finishing blow: "If you really must have a prayer for them, Wan, I do give you leave to skulk about the latrines blessing the sounding of their farts... But ask for nothing more, or risk my discipline."
The anathema looked like he might squirt a tear, or even better, lose his temper... why, Domingo might have pushed Wan into saying something truly stupid, in which case that horsewhip might get some use after all. And even if it didn't, well, the warmth in Domingo's belly proved that a good tongue-beating could be even more rewarding than the traditional kind. But as he set down his glass a heart-stopping howl tripped his hand, causing the goblet to topple and roll off the table. It wasn't the first howl heard that evening, but it was a damn bit closer than the last few had been.
"Just a coyote, nothing to be alarmed about?" Brother Wan echoed Domingo's words from before, to his profound irritation. It was a low, common sort of thing indeed, mimicking a man.
"Coyote my eye, no mangy hilldog would come so close to a bustling camp," said Domingo, drumming his fingers on the table as he considered the possibilities. First Wheatley's scouts on the western ridge and their mysterious single gunshot, and now this... He rose to his feet. "If you'll excuse me, brother, I intend to go see just what in the merry hells is going on out there. I can't expect much of Wheatley, obviously, but Captain Shea should have something to report about all this caterwauling."
"Of course, sir," said Brother Wan, rising as well and offering a sharp salute. What had Domingo done to deserve this, where the anathemas were better disciplined than his own officers? "Shall I accompany you, or will you have one of the war nuns?"
"Think I'm safe walking around my own bloody camp," said Domingo, though another, closer howl took some of the scorn out of his step as he left the tent, a hand on the hilt of his saber. There was quite a bit of commotion now, as he stepped out into the chill, torchlit evening. Soldiers rushed between the rows of tents, but without betraying any definite purpose. Several gunshots came from the western edge of camp, and then a whole volley went off, the rising walls of the high valley flashing with muzzle blasts. Shouts. Screams. Howls. The pair of war nuns to the left of the tent's entrance were evidencing far less alarm than the pair of burly pureborn soldiers Domingo had stationed on the right, but all four guards looked to him for insight into what was happening, or failing that, an order. "You there, stop, stop at once, damn you!"
The bedraggled squad staggering past the command tent was a rum lot, no doubt about that, but they halted at his command. Wheatley's people, without a doubt—not the lowliest pike lass in the Fifteenth would go around in such a shoddy state. One man was being clumsily carried by three of his comrades, and the other two women supported each other, smeared with blood and dirt from top to bottom, but seeing a little action was no excuse to let your uniforms flap around half-buttoned. "Just what in the yellow hells is happening?"
None of the bedraggled morons spoke at first, trading guilty looks, and then they all started blathering at once:
"Wolves!"
"A whole pack!"
"Big as oxen!"
"Hot on our heels!"
"Enough!" shouted Domingo. "Who's got rank here?"
"Him," said all three of the soldiers carrying the big man with the bloodied leg, nodding at their human cargo. The man raised a drowsy head, saluted in Domingo's direction as best he could with two men holding him up by the shoulders, and slumped back into the arms of his fellows. Domingo recognized him at once, but couldn't place which squad of Wheatley's the man led... No matter, he wouldn't be standing at the front of the ranks when this mess was over, Domingo would see to that—this idiot was getting busted down to stable duty for dereliction of duty, failure to wear a uniform, and... and... something pawed at the back of Domingo's mind, something about this wounded squad leader...
"Begging your pardon, sir, but we need to get him to the sawbones—he's going to lose the leg as it is," said the younger of the two women leaning against one another. Domingo looked her full in the face now, then took a long, hard look at the other one, who was even stranger—her hood bulged out at the top, and beneath the cowl he made out white hair and a flash of red eyes. What the hell was Wheatley thinking, letting his witchborn wear normal cloaks instead of Chain robes? You needed to know at a glance whether someone was a normal soldier or an anathema, that was just common sense.
Another howl ripped at Domingo's nerves, from just the other side of the officers' tents, and he shooed the shirkers away without another thought. Between their maimed squad leader's ridiculous flattop and the white-haired anathema they'd be an easy enough bunch to locate for disciplinary action once things calmed down, but for now it sounded like the beasts had actually stormed his camp. He drew his saber and nodded at his four guards to accompany him on the hunt—he'd never heard of anything so absurd, a pack of wolves attacking—
He froze, having taken only two steps toward the howl, the wounded squad shuffling off in the opposite direction. It wasn't that their parting salutes had been sloppy—that would have been typical for the Ninth Regiment—but not even Wheatley would have soldiers so poorly disciplined that half of them used their right bloody hands. Ill-fitting or missing uniforms. Furtive glances. Heading east when the sawbones' pavilion was north. Domingo was slipping, to have let it go this far, but he made up for the sloppiness with a burst of insight so keen it rattled him to the tips of his boots. _That_ was where he had seen the squad leader. Unbelievable.
Pivoting on his heel, he walked leisurely after the squad. They weren't going anywhere, not laden down with their injured leader and their anathema limping along with the help of the young Ugrakari girl. Domingo's saber felt light as a baton as he closed the ground behind himself and the fleeing spies. "Oh, one more thing."
The squad lurched to a stop again, but not a one of them looked back to meet Domingo's eye. The Ugrakari called, "Yes, sir?"
"I wonder if you would be so good as to drop Captain Maroto on the ground for me, so I don't have to cut him out of your arms." Not bad, Domingo, though at his root he knew he could have done better, if he hadn't been caught so off guard by seeing one of his old nemeses here in his camp... Then, to his further amazement, the men and woman carrying the big man did as he ordered, dropping the so-called Devilskinner onto the trampled meadow grass of the camp.
The witchborn guards behind Domingo shouted in unison, and well they might, but Domingo had seen things that would make a dead man squirm, and he kept his cool even as the monstrous silhouette stepped around the far end of the command tent, cutting off the spies. They'd dropped Maroto because they had seen it first, and slowly drew weapons as the gargantuan horned wolf stalked toward them. This should be quite the show!
Still, he was close enough as it was, and he took a step back, bumping into one of his guards. When he glanced at the girl to tell her to buck up, he saw that she was gawping behind them. He followed her eyes just in time to catch a second horned wolf shooting out from a gap between the officers' tents, burying his bigger witchborn guard in a wave of furious white fur. The other witchborn darted in to help her friend, but even with the speed of devils she was no match for the horned wolf; it snapped its head around to meet her charge, the straightest of its three horns punching neatly through robes, the armor beneath, and into her stomach. It reared back on its hind legs, standing as tall as the tents as it pranced on the first witchborn it had tackled, kicking its front hooves at the impaled woman who hung limply from its horn. A solid shove of a splayed hoof and she slid off, falling through the roof of the command tent and bringing the canvas down around her as the creature dropped back onto all fours.
The horned wolf looked at its next victim, and Domingo looked into the face of death. Maroto's spies were wrong; it wasn't as big as an ox, it was bigger. His last two guards screamed for help as the behemoth took a wary step toward them, but their voices seemed remote to Domingo, as remote as the shouts of Brother Wan inside the collapsing tent, as distant as the clamoring behind him where the other horned wolf rendered Maroto's spies into offal. The only thing Domingo heard clearly was Efrain crying over the kitten his father had refused him, and then the monster charged.
What saved him was not the bravery of his guards, but their cowardice. The man and woman both tried to run but crashed into one another, limbs tangling, and, unable to resist the flurry of motion, the horned wolf careened into the pair. One of its horns speared through both the guards, but as the animal drew up short to dislodge the annoyance from its face, Domingo took a wide step around the side and stabbed it through the eye. It didn't matter if it was mortal, devil, or something in between; a distracted opponent was a dead opponent when Domingo had his saber in hand.
Except deep as his saber went, it didn't go far enough to kill it outright, apparently, for the monster reared away, wrenching his saber out of his hand and snapping his wrist in the process. Pulled to his knees by the momentum, he blinked in surprise, and before his eyes had reopened he felt a battering ram catch him in the left hip. He was in the air, pinwheels of torch and starlight all around him, and then he landed in a roll, extremities crunching and then going dead as he bounced along and finally slid to a stop. Only one eye would open, but as the world stopped reeling he saw the horned wolf that had headbutted him was crashing drunkenly through the tangled canvas of the collapsed command tent, Domingo's saber still jutting from its eye, both guards still caught on its horns. A faint slapping sound, and then another, and black blooms spread on either side of its blind eye. It died abruptly, and Domingo closed his eye and gave silent thanks to the Fifteenth, those brave children of Azgaroth who had saved their father, even when he had been unable to save his son.
"Oi!" A stick prodded at his aching chest, and he tried to sit up and assault his assailant, but barely managed to reopen his eye. He hadn't recognized the voice because he had only ever seen him across the battlefield and had never parleyed with the man during the long war, never spoken to him in peace. There could be no doubt, though, that he had remembered true: the man standing over him was Mighty Maroto, the Fifth Villain of the Cold Cobalt. Well, not standing so much as tottering on the walking stick he had poked Domingo with, the man's black-bandaged knee apparently not just a crafty disguise. "I know you, friend?"
"Yes... Colonel..." he managed through ribs that were surely broken, but then lost his air. He might never speak another word...
"Hmmm," said Maroto, biting his bottom lip as he stared down at Domingo. "Nope. Sorry, friend, I can't say I remember."
"Fifteenth Regiment, out of Azgaroth," said Domingo, clear as the lymph oozing out of him now that rage had overridden agony. After all the times they had matched wits during Cobalt Zosia's war on the Empire, this moron didn't even remember him?
"Ah!" Maroto brightened considerably, snapped his fingers. "At Ensiferum, right before Zosia snuck into Diadem and got Kaldruut with the old sneak-and-shank! You would have had us for sure, if Hoartrap hadn't—"
"Thirteenth," Domingo hissed through gritted teeth. "The Thirteenth met you at Ensiferum, not us. We fought at—"
"Got it loose!" The Ugrakari woman entered Domingo's narrow, black-speckled field of vision. She looked to be holding a huge, wet rug, blood dripping from it to patter against Domingo's cheek. Peering down at the name badge his sister-in-law had sewn on his breast pocket, she said, "Bad news, Colonel Hjortt—looks like the Cobalt Company just jacked your shit _all_ up."
"We kind of did, I guess?" Maroto lowered his voice as he leaned closer to the prone Domingo. "Make sure the queen knows I didn't mean to, you know—"
"Time to go!" one of the other spies called.
"Past time!" said another, and, offering him a blood-handed wave, the Ugrakari trotted away.
"Sorry?" Maroto offered Domingo an apologetic smile. "Sure it'll come to me, where we met. Probably right after I leave, you know?"
"Now, Maroto!"
"Right, sure. Like I said, really sorry about this—Colonel Hjortt, was it? Won't forget again, promise."
Domingo shut his throbbing eye—he'd always thought he'd be ready to look head-on at his own demise, but ignoble as it had turned out to be, he wanted no part in it. Killed by a ravenous monster in the mountains, that he could have done... but the truth was he'd been murdered by the incompetence of his own soldiers, who had let a pack of overgrown devil dogs into his camp, and a crew of obvious spies in the bargain. And now, at the very end, he was to be executed by a man who didn't even remember him. He tried to think of his murdered son, tried to think of the wife who had left them both to become an ambassador to Usba, but all he could think about was how fucking terrible it was that he should come this far, only to...
"Colonel?" Hjortt cracked his eye, and immediately regretted it. He wouldn't live out the night, bashed-in as he felt, and now the last thing he would ever see was Brother Wan's grisly visage. The anathema swam in and out of focus. "Sir, I know it must be hard to speak, but who were those soldiers who saved you? Come what may, I know you'll want commendations for them."
"They're... dead." Domingo's tongue felt heavier than his eyelid. _Stop them. Arrest them. Spies._ But no more words would leave his mouth that night, nor for several days to come. When he finally returned to consciousness and found Brother Wan at his bedside, the long-delayed intelligence came streaming out.
"Did you stop them, Wan? Are they in chains? Maroto's spies?"
"Um..." Brother Wan didn't have to give more answer than that, and Domingo let out a protracted groan, the pain of his weakness in not clinging to consciousness a few moments longer overshadowing the throbbing aches that occupied most of his body. "Is there anything I can get you, Colonel?"
"Yes," said Domingo, trying to sit up and spasming instead. "Every drop of the Black Pope's poison. And if you've got any devils or spells, those as well. Call on your heathen god, call on the Deceiver, call on every power. We're going to use your weapon, Wan, and we're going to kill every Cobalt we can find, and we're not going to be nice about it."
# [CHAPTER
10](toc.xhtml#toc-chapter036)
That Sullen boy. _Damn_. It wasn't just that Ji-hyeon could tell he was into her, if only a little. She wasn't as pathetic as _that_. Dozens of people had made passes at her, especially as her small band of mercenaries became a large one, and finally grew big enough to call themselves the Cobalt Company. Once there was a Cobalt Empire, she'd be beating them off with the blunt end of an ax, even her advisors. Especially her advisors.
She wasn't callow enough to think most of these advances arose from earnest interest in her mind, body, or soul, though suitors had called on every conceivable combination of the three. Any idiot could see she was no more than a year out from a decisive conquest of Samoth, and everyone knew if you took Samoth you took the Empire. What's more, she'd do it without any of that wandering-the-wilderness business of her spiritual predecessor. No, what it had taken Zosia half a decade to accomplish, Ji-hyeon would see completed in under two years, and without thousands of her followers starving in the process. Ji-hyeon's victory was inevitable, which surely had something to do with all these attempts on her love life—get in before she was queen, before she realized people were just after her for power. As if she were that stupid.
Sullen wasn't like that, but it was more than just his earnest attention that appealed. After all, some of the others had probably been genuine in their affection, too. In part it was his attitude, respectful but not overly so. Maybe it was just pig ignorance on the boy's part, as Fennec suggested every chance he could, but to Ji-hyeon it seemed... real, as though she'd actually impressed him without even trying. Well, maybe she'd been trying a little, because she was always on, it seemed, trying to astound everyone, trying to fill the greaves of a woman whose death had elevated her from leader to god. Yet those quiet afternoons when she had him alone in her tent, taking kaldi with the quiet barbarian, she actually felt like herself again—not like Zosia Returned, as Fennec and the rest wanted, and not like Princess Ji-hyeon Bong of Hwabun, Betrothed of Prince Byeong-gu of Othean, etcetera, as her first father had wanted, but just like... Ji-hyeon. She didn't like to think of it that way, but something in Sullen's sincere interest in her moods instead of her ambitions, in her past instead of her future, reminded her of how things could be... of what she'd had with Keun-ju.
Keun-ju. It almost didn't hurt to think of him now. Not that she was some moonstruck kid, hung up on the first boy to reach under her dress, but she had really loved him, and even now she caught herself daydreaming explanations for his duplicity, envisioning scenarios to explain his actions. It wasn't like Sullen had come along and all of a sudden Keun-ju was forgotten; anything but. She thought of Keun-ju more than ever now, and, strangest of all, Sullen encouraged her. When she had told him about their relationship, and how Keun-ju had betrayed Ji-hyeon to her first father, almost foiling her escape from Hwabun, he had nodded sympathetically and said:
"That's bad. I've been bit by beasts, and I've been bit by... by loved ones, and loved ones bite worst. Sorry, Ji-hyeon."
_Sorry, Ji-hyeon_. Simple, heartfelt, and oh so welcome. They'd been talking over kaldi, and even as the bowl went cold in her cupped hands he hadn't pressed her for more or tried to talk everything better, the way Fennec would have. She couldn't wait for him to meet Choi—when the laconic met the terse, who knew what might go unsaid?
A week later, another report came back that Keun-ju still hadn't sent word. It was the same shitty news she had received each and every month since she'd first left Hwabun with only two of her three guards. It was the not knowing where he was or what had really happened that made the pain of missing him so much worse.
"Nah," said Sullen, when she imperfectly articulated all this to him. "Pain's good. It's how you know you've been stuck, but also how you know you'll heal. Only thing that doesn't hurt is being dead."
"You sure about that?" Ji-hyeon eyed him skeptically over her ryefire.
"Devils, I hope so," said Sullen, blowing out his cheeks. "If being dead hurts, I don't want no part of it."
So he was funny, in an effortless sort of way, on top of the rest. But there was something else, too, and if it made her a shallow person, well, she had been called worse. What it was, simply, was this: Sullen was damn easy on the eyes.
Tall wasn't always her thing, and lanky but tight-muscled could go either way, but combine all that with his rich, dark skin, wide, striking features, and that halo of shocking white hair? Spirits keep her in check. Then there were those eyes... they were closer to a cat's than a man's, with inky pupils arching all the way up the cornflower blue orbs, the sparkling brightness a pleasing contrast to his perpetually serious jaw line. He had his fair share of scars, and some more besides, his nose had been broken so many times it looked off-center, and his enormous puffball of hair could do with some shaping, but still: the boy looked damn good.
She almost kissed those velvety lips, too, the night of drunken nonsense, but then Fennec had burst in with more news on the small Raniputri force that had been dogging their cat, and so she was saved the conundrum of what to do after a first kiss. For now. Gods, devils, and spirits willing, she wouldn't be spared that puzzle for too much longer. When Hoartrap informed her that the Raniputri riders would catch up to their slowly marching company within a day or two, and that his devils told him Choi, Maroto, and his noble entourage were but a few days out themselves, she decided it was time. What Sullen would do when his uncle returned had been left unsaid, as had the particulars of both her rise to power and his quest for his uncle—for all the time they'd logged since he'd crashed her camp, they had yet to revisit the aborted topic of their first conversation. It was time for that, too. Definitely.
Well, maybe.
"Did you name her?" Sullen asked, watching Fellwing squirm her way around the nearby heap of Ji-hyeon's chainmail. The owlbat loved crawling across her armor, hooking tiny talons in the links.
"My father did," said Ji-hyeon. "She was his before she was mine. They all bound their devils together, I guess—Dad, your uncle, Fennec, Hoartrap, the chevaleresse, and Zosia."
"My uncle... has _a devil_?" It took little to arouse Sullen's curiosity but quite a bit to surprise him.
"Not anymore, or else he's good enough at hiding him to fool even Hoartrap. But they all captured the creatures together, before they captured Samoth." Fellwing landed on her arm as she spoke.
"Horned Wolves don't bind devils," said Sullen glumly. "Not supposed to, anyway."
"Nor do the Immaculate, as a rule," said Ji-hyeon. "The royal family have some, but most people still think it's disrespectful."
"That's one word for it," said Sullen. "Disrespectful. The Jackal People take slaves, other clans, too, but not the Horned Wolves."
"A devil's not the same as a slave," said Ji-hyeon, stroking Fellwing and summoning a throaty croak from her beak.
"Then set her free, and see if she stays," said Sullen, which pissed Ji-hyeon right off.
"Is a horse a slave, then? What about cattle, or other livestock? I don't intend to eat Fellwing, so I'd say she's doing better than most beasts."
"Huh," said Sullen. "You're right."
"Of course I am," said Ji-hyeon, pouring them more malty liquor.
"Horned Wolves raise cattle and fowl, and trade for mules. We don't call them that, but they're slaves, just as you said. Not so different from others, much as we like to pretend. We're as bad as the rest of you."
"Well, it's nice to hear Saint Sullen admit such a mortal weakness."
"What?" Sullen blinked at her. He could be thick sometimes, the same as anyone. "Oh. Ha, no. Yes. Didn't mean to be a jerk. I'm bad, too, Ji-hyeon. Most people are, I guess. I've broken the laws of my clan. Killed one of my own people. Did everything wrong, and all because I was trying to do right. It's not easy, doing good."
It was hard to imagine the gentle, earnest man sitting across from her attacking anyone, let alone a fellow Horned Wolf. But he'd done something to come by those scars, and that white hair of his. Much as she liked him as an enigma, it was long past time she heard his tale. But that meant she had to go first.
"I've talked your ear off about Keun-ju, but you've never asked why I ran away from home, about what came before or after."
Sullen fidgeted on his cushion, knocked back his drink with a grimace. "Yeah... Sorry. I'd like to hear, I would, but didn't want to push you. I hate being pushed. Love Grandfather, but he's pushy, and much as I want to be like him some ways, that ain't one of 'em."
"Oh hells, I wasn't complaining! Quite the contrary," said Ji-hyeon, brushing Fellwing off her. The devil flitted over to Sullen, and he stuck out a finger for her to perch on. She'd never seen her owlbat land on anyone else, and like everything else in this world, that could probably be an omen. "I would call you many things, Sullen, but not pushy. You'd really like to hear?"
"Definitely," said the man, offering a sugarcube to the devil on his finger.
"So you know I'm a princess, and all that. Hwabun was a great place to grow up, though I didn't appreciate what I had until I left. Is that how the Frozen Savannahs are for you?"
"Huh. Not exactly," said Sullen, scratching his crooked nose. "See it different now that I'm gone, though. And I miss my mom. A lot."
"I miss my first father, Jun-hwan, though the last year I was there we couldn't stand each other. Yunjin, my older sister, said it was like that for them, too, when she was my age. Things get strained, especially when one of your dads is trying to marry you off. And I told you about Keun-ju, and what he meant to me. One of the conditions of the marriage my first father brokered was that Keun-ju wasn't to come with me—it would be rude, he said, for me to take my own servant into a nicer house, and my fiancé was the son of the ruler of the Immaculate Isles. Houses don't come nicer than that."
Fellwing finally got her beak around Sullen's sugarcube and carried it up to a crossbeam in the tent poles.
"So I'm supposed to leave behind my favorite guard, to marry this nebbish I've met all of zero times. The idea turned my stomach—I _loved_ Keun-ju, even though I didn't know he loved me back, not then. And so the same night I finally met my fiancé for the first time, I snuck off by myself. Well, not alone, my guards were there—Fennec, but back then I thought he was just a Chainite missionary named Mikal, and Choi, who you'll meet soon, I hope, and there was Keun-ju. And we were out in some fields looking for spirits, near the Temple of Pentacles. That's where the Immaculate Gate is, the one I ended up escaping through when I ran away a few months later—I told you about going through the Gate, right?"
"Uh-huh," said Sullen, touching his hair with a wince. "I mean, a little. The first time we took kaldi you said it was kinda like going into a sea, only the sea was the First Dark."
"Ha, I said that? Well, yeah, it kind of was... Anyway, we were real close to the one on the Isles, the Temple of Pentacles, and all of a sudden this... this spirit monster attacked us! There were smaller spirits in the field, in the pumpkins, but this one... this was like a bunch of them all mashed up together to make something huge, huge and scary and dangerous."
"I can picture that," said Sullen, nervously licking his lips. Oh, he had a song to sing when it was his turn to tell how his hair turned white, she knew it!
"So we fought it, the four of us against a monster straight out of the bedtime stories my second father would tell us about his adventures with Zosia and the rest of the Villains. And we won! It was... well, you've been in fights before, so you know what it's like. First you're too scared to move, and then something takes over, all your training wakes up, and your sword's in your hand before you know it! And you're fighting, fighting for your life! And it's just... so..."
"Terrible," said Sullen, looking into his ryefire bowl.
"Yes! No! I mean, it's scary, but it's also kind of wonderful, isn't it? Dodging out of the way at the last minute, cleaving into your enemy, fighting alongside your friends and working together like you were born to do this and nothing more! Not even thinking, just... doing, and doing it so freaking good! Hack, slash, parry, dodge, hack again! Devils above, I get tingly just thinking about it."
"Have you talked to a barber about that?" asked Sullen, and given his general demeanor, it was only by his sly smile that she knew he was joking.
"I know you've felt it, Sullen, I know it."
"Well... maybe. Yeah."
"Anyway, when it was done, and the spirit king slain, we went back to the Autumn Palace, and everything after that was just so... _dull_. And not just dull like it'd been before, but poisonously so. I was depressed for weeks after, and not just from the lecture I got from my first dad on the boat ride back to Hwabun. I think he would have been happier if it'd eaten me than he was to have me come back in to the festivities the way I did. He said I was an embarrassment, and when I asked if it was embarrassing that my other dad was one of Zosia's Villains for all those years he said yes, that was embarrassing, too. What's embarrassing about buying your life back from Death herself, with your own sword?"
"Hmmmm," said Sullen, giving it his full consideration. "Nothing, to my mind."
"Nor mine! So it was inevitable, really, that I'd decide to do what I did, even without Fennec whispering in my ear. I see now he had his own motivations for counseling me on such a course, but I'm still glad he did. Choi wouldn't even talk to me about it, as in, _at all_. When I first brought it up she said, 'I swore an oath to serve your martial needs, and will do so until I die. Do not ask me to advise on other matters, but be sure you always consider all possibilities, and do not be swayed by any heart but your own.' That doesn't sound like much, but I've never heard her say so much in one go, or so clearly, either before or since. I even wrote it down right away, because I knew I'd forget it otherwise, and forced myself to memorize it, because that's some serious, sutra-level wisdom, isn't it?"
"It is," said Sullen thoughtfully, as though he were still digesting the words.
"But yeah, I never expected Choi to come along so easily. And while Keun-ju balked at first, once I persuaded him it was the only way for us to be together he came around. I _thought_. It's not too long a sail from Hwabun to the Temple of Pentacles, and from there a few seconds to any Arm of the Star, if you know how to use the Gates, so it should have been easy to leave before anyone knew we were gone."
"So how does it work?" Sullen asked. It took a lot to freak out a wildborn, but freaked out the man definitely looked. "The first time you invited me here you told me about going through, but... but I can't even _think_ about that without feeling sick."
"Obviously it wouldn't have worked if I'd just tried to strut through on my own," said Ji-hyeon. "Who knows where I would've ended up, probably some obscure hell I've never even heard of. But long before he came to Hwabun, Fennec did some work for Hoartrap in exchange for the secret of the Gates. Now he can step into any Gate, and after a few paces come out any other, and bring along anyone he wants. As for how it works, I don't have the slightest damn notion, it was all Fennec's doing... and I don't think he's quite the expert he claimed to be, either, all things considered. What's really weird, though, is nothing happened to Choi—my hair turned white, Fennec's hands changed, but Choi's still Choi. Then again, she had white hair and horns and fangs to begin with..."
"Hmmmm," said Sullen. It was less a contemplative sound and more the noise of a dog displeased at being roused from a doze.
"Anyway, the Gate was where we were headed when Keun-ju pulled that shit I told you about," said Ji-hyeon. "I've kept telling myself it was a coincidence, that he didn't deceive us... But from inception, we all agreed that if something happened and we couldn't all go together, then whoever was left behind would send a coded message to a certain Linkensterne merchant who owes my second father a great boon. We're coming up on a year since I left, and Keun-ju's sent nothing... so maybe it's about time I made myself accept the truth about him, don't you think?"
"The truth," said Sullen, pursing his lips as Ji-hyeon rose. She used the pretext of fetching a blanket to sit down beside him when she returned. She'd thought it warm across from him, but here, with their knees brushing as she settled onto a cushion and pulled the unnecessary blanket around her shoulders, it was downright smoldering. "How do you know the truth of Keun-ju?"
This hadn't been what Ji-hyeon expected him to latch onto; surely _Don't you think I should get over my ex?_ was a more intriguing question for him to consider? Unless she had totally misread his surreptitious glances and shy smiles... "I told you, he was late meeting us at the boat, despite how many times we went over the plan, and then... then when he did come down to the dock, all smiles, every other guard on Hwabun was sneaking just behind him. If Choi hadn't spotted them we never would have launched in time; as it was, Keun-ju barely missed the boat when he jumped after us!"
"Yeah, but how do you know? I mean, what he was thinking? That he brought the guards on purpose?"
The memory stank, and Ji-hyeon stole Sullen's lukewarm bowl of ryefire to clear her nostrils with its hot scent. "You mean besides him shouting 'stop, stop!' just before he dove off the pier after us? Fennec saw him leaving my first father's chambers that very morning, and in all the years he was in our house he had never set foot there before. Later that day he bathed me before afternoon prayers, and didn't say a single word about what would have been quite the oddity, had it been unrelated. We shared everything, and the only reason he wouldn't mention my first father calling him in for an audience would be if he had something to hide. I didn't want to believe it, either, I still don't..."
"So don't," said Sullen, sounding like the words stung him but needing them out all the same. "I wouldn't, unless I had to. And right now you don't."
"What do you mean?" Ji-hyeon shivered, and, no doubt misreading it as arising from her being cold, Sullen slowly extended his arm over her back and gave her far shoulder an endearingly self-conscious squeeze. Oh, how she wanted him to keep his hand there, but he quickly retrieved the appendage and, obviously not quite sure what to do with it, flopped it in his lap.
"It's all Fennec's word," said Sullen. Mistaking her expression for confusion, he elaborated: "That Keun-ju was with your dad, your first dad, and that the merchant in wherever would deliver a message from Keun-ju, if he tried sending one. Last time we talked you said Keun-ju and Fennec didn't like each other much, and clever as Fennec is, maybe he figured a way to bite Keun-ju without making it obvious... I'm not saying nothing, just, you know, thinking. You don't seem like you trust Fennec as much as I'd expect you to trust someone who's got as much pull as he does with your people... So yeah, if you don't trust him altogether, I don't trust him at all. Especially seeing how tight he is with Hoartrap."
Sullen clamped his mouth shut, perhaps remembering that Ji-hyeon herself took the sorcerer's counsel. Perhaps he realized he'd just suggested the general's closest advisor might have played her for a chump. Or perhaps he was just embarrassed at having spoken as much in a minute as he usually said all night. Whatever the cause, he no longer seemed able to look at her, let alone meet the stare she turned at him. Not being an imbecile, she had lost many a night's sleep pondering that very question, but had always assumed it irrational, to put it kindly, and crazy fucking paranoid, to put it bluntly. That it was the first possibility an objective listener came to after hearing even a truncated version of events raised some sticky questions indeed.
Even studiously inspecting the tent poles where Fellwing nested, Sullen must have sensed that Ji-hyeon was trembling all over, because his hand crept back across her shoulder. Quite without her meaning to, her back rose to meet his fingers, pressing firmly into his cautious touch. This time he kept his arm around her after offering a squeeze, gently kneading her shoulder. His arm pulled her hair a little, but whatever.
"Are you a good judge of honesty?" asked Ji-hyeon, when she could bring herself to talk, her mind racing her thundering heart and coming out a nose ahead. "I'd like you to be here in any event, when I sit Fennec down for a talk. I want you to watch him, and if he doesn't come clean at once tell me right then and there if you think he's lying."
Sullen's hand stopped its slight prodding, his whole arm going rigid. He gulped, but still wouldn't look at her. Afire with movement all at once, he stood, his fingers swimming upstream through her hair in a rush and then falling lamely at his side. "Let's go find him, then. With a natural liar like him it won't be easy, but together we can crack him. I know it."
"Wait," said Ji-hyeon, grabbing his wrist and hoisting herself up, the blanket slipping off her shoulders. The blue-skirted, bell-shaped dress she wore around her tent suddenly felt constrictive despite its bagginess, and for a change she longed to be in her sexy, chafing armor instead of comfortable clothes. Even more confused about her feelings than she'd been when she mostly believed that Keun-ju had betrayed them, she did what she'd always done when at an impasse—charged straight ahead, hoping for the best. In this case, she blundered straight into a handsome Flintlander, still holding his limp wrist in one hand and sliding her other across his striped tunic, his muscles twitching under her touch and tightening up even more as she ran her hand over and down to his hip, until she could firmly turn him to face her. Ridiculously, he still wasn't looking at her, his chin cocked up in the air and his eyes fixed on her dozing devil. Ji-hyeon gulped, scared all over again that she'd sussed things totally wrong... Nothing to do but ask, then. "Are you going to make me climb you like a tree to steal a kiss?"
With wonderful, terrible slowness, he turned down to look her in the face. Devils below, he looked in fear of his life! "You... you don't have to steal it. But... well, what if I'm right?"
"Then we better be fast about this, just in case you are," said Ji-hyeon, and stood on her tiptoes even as Sullen leaned down. He tasted of ryefire and stale smoke, and was as bad a kisser as she'd been before Keun-ju had taught her. She fucking loved it, her hands eagerly exploring his chest, wondering what would happen now that they'd shared a first kiss and were already working on a second, a third, a fourth, forgotten gods of the Sunken Kingdom, did he feel good under her fingers...
And having the matter decided for her when a throat cleared at the entrance to her tent. She wheeled away from Sullen, barking a shin on the kaldi table, ready to bellow at Chevaleresse Sasamaso or one of the other guards for not announcing herself before barging in, when she saw Fennec himself standing there, holding the canvas flap open with a slightly shaky hand. He looked uncharacteristically nervous, his face flushed. "General, we need to speak, immediately, about—"
"Oh yes, yes, we all need to speak, and immediately at that," said Hoartrap, striding in past Fennec, whose eyes went wider at the old giant's appearance. Behind her, Ji-hyeon heard Sullen crack his fingers, his warming shadow crossing her as he stepped over the kaldi table to have a clear path to the sorcerer who said, "I wondered if you'd run for the general or the hills when you got a good look at her, Fennec old boy, and there's my answer."
"Riddles are never welcome in my tent, gentlemen," said Ji-hyeon, giving each of them her best worst scowl. "What unholy horror do I have to thank for not one but both of you bursting in here in such a rude fashion? Unless the matter is grave indeed—"
"Grave is certainly the word!" said Hoartrap, clearly overjoyed. "General Ji-hyeon Bong of the Cobalt Company, may I introduce you to the Raniputri emissaries who have been hot on our heels these many days."
Three hooded figures came striding into her tent like they'd been invited, and Ji-hyeon's fists balled at the insult. She hadn't even had time to pull on a vest over her simple dress, to say naught of actually changing into something more formal. Emissaries or emperors, Hoartrap and Fennec would have much to answer for once these foreigners were dealt with... but for now Ji-hyeon forced a pleased expression onto her face and, dipping low into a bow, greeted the emissaries in High Immaculate:
"Welcome to my camp, honored guests. I am General Ji-hyeon Bong of the Cobalt Company, and would have your names in turn so that we might—"
"Ji-hyeon!" The smallest of the hooded emissaries charged forward, crying her name, and Sullen darted between them, holding up a palm as if that were all it took to thwart an assassin. As it happened, the man _did_ stop, throwing back his hood and veil to give Sullen a familiar glare as he said, "Ji-hyeon, it's me!"
"Keun-ju?" Keun-ju! Sullen tripped over the kaldi table in his haste to get out of the way, and as Ji-hyeon embraced her old lover she heard her new one curse under his breath as he hopped on one foot. Keun-ju pressed his lips to her cheek, hard, and then she felt a tear dribble off his lips and down her chin. It was really him...
"This is just great," said one of the other emissaries, and though it pained her, Ji-hyeon quickly stepped back from Keun-ju, looking to the two older women who had accompanied him. They both had their hoods back now, and although she couldn't tell the speaker's nationality, the other woman was obviously Raniputri. "You even went for the hair. Well, why not, if you're taking everything else. By the six devils I bound, young'un, for an impostor you look perfect as a portrait."
"I am indebted to you for returning my Virtue Guard to me," said Ji-hyeon through gritted teeth. "Impostor" was not a word that got easier on the ears. "Even if your manners leave something to be desired, Auntie. Who do I have the honor of offering my thanks?"
"Ha!" The Raniputri belatedly put a mailed hand to her mouth. "Oh hells, this is too much."
"Ji-hyeon," began Keun-ju, but the silver-haired emissary's booming voice cut him off as she took a step forward:
"Who am _I_? Girl, I'm the woman your fathers hired to take you home."
Ji-hyeon's eyes flicked to Keun-ju's sheepish expression—he had betrayed her after all! Strangely, neither Hoartrap nor Fennec made a move to stop the older woman's advance, and the futility of it all sunk in. She'd been set up, and this was how it all ended. Well, not without a fight. Before she could deliver the first punch to Keun-ju's stupid face, however, the woman said something else, something that pinned Ji-hyeon in place:
"More than that, though, I'm _you_ , you devildamned brat—or don't you recognize me? I'm Cobalt Zosia, returned from the fucking grave."
From the far side of the tent where Sullen had retreated after tripping on the kaldi table, Ji-hyeon saw the man go totally still, his eyes wide as hers must be. It couldn't be her, of course it couldn't, of all the laws of mortals, gods, and even devils, there was no coming back from death... But looking into the woman's cold cobalt eyes, Ji-hyeon believed her.
# [CHAPTER
11](toc.xhtml#toc-chapter037)
Zosia didn't much think of herself as a proud person, but devils knew it felt good to shut down Kang-ho's brat. The runaway looked the part, all right, severe bangs giving way to waterfalls of longer hair, her pretty young face framed in cobalt. Her Immaculate dress was plain, as much as those garments could be, so maybe all her success hadn't gone to her head yet. Add to that her entertaining a hunky, white-haired Flintlander alone in her tent at this hour, and you had a girl after Zosia's own heart.
"It's really her," Keun-ju told the slack-mouthed girl. "I'm sure of it. She met your fathers on Hwabun, and, well, it's a long story."
"Queen Zosia," breathed Ji-hyeon, and, dropping to one knee, lowered her head. "I am honored to bow before you."
"General," said Fennec, somewhat frantically. "There's no need for all that, I'm sure. As our guest Zosia is owed hospitality, of course, but—"
"Out, Captain," said Ji-hyeon, looking up but staying on one knee. She had the ridiculous seriousness of the young and sincere etched on her fine features. "All of you, save the queen."
"Ji-hyeon..." Keun-ju said plaintively, and even knowing this girl for all of two minutes, Zosia could tell that was the wrong tack to take with her.
"Everyone out. Now."
"General, let's take a moment before deciding anything," Fennec tried again, the old fox sly as ever. He hadn't met Zosia's eyes once since he'd seen her, Keun-ju, and Singh being led to the general's tent by a dozen guards, the rest of the Raniputri waiting a few miles outside of camp. Instead, he'd swiveled on his heel and booked it back here, no doubt trying to get in a word with Ji-hyeon before they arrived. Hoartrap's crazy ass had the decency to walk them in, making his usual absurd small talk, though she could tell even he was taken aback to see her alive and well.
"Did I give an order or ask a question, Fennec?" demanded Ji-hyeon. "I'll send word when I want you back here. For now, I wish to speak with the queen. Alone."
The sinewy Flintlander nearly tripped over his feet again in his haste to be gone; he was trying just as hard as Fennec not to look at Zosia. Weird—he was certainly too young for their paths ever to have crossed before, but then again her reputation certainly seemed to precede her everywhere she went. As he passed her, she noticed a familiar tattoo on his arm, and flashed him a smile.
"Nice meeting you, too, Horned Wolf," she said in the trading tongue of the Savannahs. "No relation of Maroto's, are you?"
"Sullen nephew," he mumbled, and then was away into the night. What the hell was a sullen nephew? Maybe just some obscure Horned Wolf Tribe greeting or apology or something, though he looked enough like Maroto to be kinfolk.
"So _good_ to have you both back," purred Hoartrap, but when he moved to pet Choplicker the devil whined and avoided him, hustling to a far corner of the spacious tent with his tail tucked. There wasn't much to recommend about the crazy old wizard, but the fear he always put into Choplicker endeared Zosia to the man. Or so she tried to tell herself, anyway; if she were being real with herself, it unnerved her a bit. "We have so much to discuss, once you're all caught up with our fearless general. It's been too long, Zosia."
"Uh-huh," said Zosia, knocking fists with Hoartrap and turning to Fennec as the old behemoth left the tent, Singh accompanying him out. "Hey, Fennec! It's me! Your old friend! Happy to see you, too, fucker!"
After his initial cringing at her volume, Fennec finally faced her, smiling sheepishly. "If I'd known you were still around, Cobalt, I would have played it differently. Much differently. I'm glad you're alive."
"Hey now, don't fall apart on me," said Zosia, clapping the man in a tight hug. He'd put on some pounds, his sharply dashing features smoothed out by the years, but otherwise he'd aged a sight better than Hoartrap, Kang-ho, or even Singh. Or herself, for that matter. Slapping his back a bit harder than he probably liked, she released him. "Now beat it, me and Ji-hyeon here have lots to talk about, I don't doubt."
"Ji-hyeon, if I could stay, too, and—" Keun-ju began, but Ji-hyeon stiffly rose from her bow and laid what looked like a neck-breaking kiss on the Virtue Guard. Fennec coughed softly and, patting Zosia's shoulder, exited as well. Breaking off from her lover, Ji-hyeon pushed his chest with two fingers.
"Don't think you get to dance back in here without an explanation," she said, her voice betraying only the slightest quaver. "I'd start working on a damn good lie, if I were you. Now scat."
Keun-ju offered Zosia a weak smile as he left, the boy practically floating out of the tent. She was finally alone with the princess. Might as well start things off on the right boot.
"Looks like you've got a tidy setup here, Ji-hyeon. You can dress a pig in armor and lead him to the front, but that doesn't mean he'll be anything but bacon when the war starts."
"Auntie," said the girl, all trace of humility gone now that they were alone. "I must have misheard you. It sounded like you just called me a sow."
Zosia shrugged. "You're winning battles, it sounds like. Picking up plenty of volunteers, as well as the mercenaries you've bought from sacking all those Imperial cities. So you tell me, girl—is this, ahem, _Cobalt Company_ of yours doing so well on account of its brilliant general, or are a bunch of dusty old men whispering in a piglet's floppy ear?"
"Now that's just not very friendly," sniffed the girl, turning her back on Zosia and squatting down in front of the tent's low table. She was mucking about with a mortar and pestle, as though she were some witch preparing a philter... but then Zosia heard the kaldi beans crunch and smelled their soft bouquet, and a powerful thirst tickled her throat. It had been way too damn long since she'd had a decent cup of kaldi, the Raniputri preferring a hundred different teas. Without looking up from her preparation, Ji-hyeon said, "Grab a cushion, Auntie, I've got just the thing to sweeten that tart tongue of yours."
"Much obliged," said Zosia, but just as she was about to plant herself on the biggest, least saddlelike pillow in the tent, she saw something that stopped her short. Choplicker was sitting perfectly still on his butt, his front legs straight, his eyes fixed on the small owlbat that perched on the tip of his snout, staring back at him. "Is that... that's Fellwing, isn't it?"
"Oh yes, you know her, don't you?" said Ji-hyeon, looking up as she dumped the grounds into a silver press. There were already three dirty ones on the table. This girl put away some kaldi, to be sure. "He is... Mouthlicker?"
"Close enough," said Zosia, sitting. Watching devils commune was as creepy as camping in front of a Gate. "Your bad dad gave him to you, huh? Wasn't expecting that."
"No?" said Ji-hyeon, filling a kettle from a small cask and resting it atop the brass stove that was heating the tent. "I wonder what you were expecting, Auntie. Other than a pig in armor, of course."
"Look, let's just level here," said Zosia, all the months catching up to her now that she was sitting in a tent with Princess Ji-hyeon Bong. She'd logged over a thousand miles, and racked up quite a few more dead bodies, all to end up in a disturbingly familiar rebel camp a few hundred leagues south of Kypck. A whole year of bouncing around the Star, and she was right back where she'd started. "I don't give a shit what either of your fathers want. I don't give _half_ a shit what _you_ want. But I think that right here, right now, we can both help each other out. And to do that we have to be more honest than we'd ever be with Hoartrap, Fennec, or any of the others. Yeah?"
"Maybe," said Ji-hyeon, smiling for the first time as she settled in across from Zosia. "I guess that remains to be determined, doesn't it? You see, Blue Zosia, I know everything there is to know about you, but you don't know the first thing about me. So how can you so be so sure you have anything to offer me, or my army?"
"I know enough, Princess," said Zosia, and as much to wipe the simper off the brat's face as anything else she launched right into it. One advantage of months upon months of stormy seas and windy mountains was you had plenty of time to think. "Your daddy Kang-ho's been a part of this scheme since the beginning, not that the fucker told me so. He gave me the same sob story he gave your other dad, about your being carried off by big, bad Fennec. I don't think Jun-hwan buys it any more than I did, for what it's worth."
"Oh," said Ji-hyeon. Then, not surprisingly, given her age, she asked, "Is he all right? My first father? And sisters? Nobody's too upset, are they? They don't have any right to be, shabbily as they treated me... Hey, don't light that up in here. I don't want my tent stinking like tubāq."
"Eh?" Zosia glanced down at the pipe she'd pulled out without even thinking about it. "Really?"
"Really," said Ji-hyeon.
"You sure you're Kang-ho's kid?" asked Zosia, but she put the piece away. Ji-hyeon rose and picked a camel hair blanket up off the floor, wrapping it around her shoulders as the kettle began its keening. Once the kaldi was steeping, she settled back down, legs and arms crossed as she watched Zosia. Her air was of a difficult child demanding a proper bedtime story.
"You got anything to put in the kaldi?" asked Zosia.
"I can send for some ghee, or—"
"No, no, soju or potato wine or something?"
"Ah, sure," said Ji-hyeon, waving at a jug on the table. Ryefire, thank the devils who love us. It was almost empty, but better than nothing. "You were telling me about my family?"
"Oh yeah. They're full of shit, all of them, but you probably know that. Kang-ho helped you and Fennec run off, along with, um, what's her name, the weirdborn?"
"Choi prefers the term _wildborn_ ," said Ji-hyeon, not arguing the point about her dad.
"Right, Choi's your Martial Guard. Where is she, anyway? I heard she never left your side."
"She's with another of your Villains, Maroto. They're on a reconnaissance mission, but should be back soon. Should've been back already, in fact."
"Maroto!" Improbably, Zosia found herself delighted to hear that he was slinking around somewhere, working for Ji-hyeon. From the way Kang-ho and Singh had talked about him, she'd assumed he had stung himself to death, or was close enough to it as made no difference. Good for him, getting honest work again! "But I was saying—Keun-ju was supposed to come with you, Fennec, and Choi, all the princess's guards defecting along with their mistress. But even though Keun-ju didn't know your dad was helping facilitate the escape, your dad definitely knew you were banging the Virtue Guard."
"I say!" said Ji-hyeon, her cheeks turning as red as Samothan wine.
"Sure you do. So, Fennec helped Kang-ho pull the rug out from under Keun-ju at the last moment, stopped him from splitting with you. Then he went one further and tried to have your lover executed." Zosia watched Ji-hyeon carefully as she tried this gambit. It wouldn't hold up once Keun-ju and Ji-hyeon had a proper sit-down and he gave her his account, but right here and now Zosia needed to slide as big a wedge as possible between the princess and her second father. To cover her tail for later she shrugged, and amended herself: "Or exiled or something. The point is, your dad did him dirty—must not have approved of his little girl shacking up with a slave."
"He's not a slave," said Ji-hyeon with all the sickeningly sweet naïveté of the young and spoiled.
"Sure, sure. Anyway, your other dad must've believed that Keun-ju was innocent, or maybe just more valuable kept alive and close at hand. Since Jun-hwan obviously wears the hat on Hwabun, your boy toy stayed on in the house, twiddling his thumbs till I came along. Like I said, Kang-ho tried to play dumb with me, but Jun-hwan's more devious than his husband gives him credit. So your first father sent me off to bring you back, with Keun-ju along for the ride. Of course your second dad tried to have us bumped off along the way, but I don't bump so easy. That's me, following you, up to this magical evening."
Ji-hyeon poured the kaldi, clearly considering some new kernel of information Zosia had dropped. Good. You have to feed a chicken if you expect to take her eggs. Huffing her bowl, Zosia said, "On your word as a noble girl and a fellow warrior, there's no harpy juice in here, is there?"
"Like father like daughter? No," said Ji-hyeon, "I hate that stuff, wouldn't wish it on an enemy. My second father gave me this seaweed you can take to keep you from getting the full effect of that shit. Let's you keep your secrets, but even still it's always a rough ride."
"I've had worse," said Zosia, taking a sip of the delightful black draught. "This is nice. Earth Ripper?"
"Only the best Usban beans go into my press," Ji-hyeon said in the snobby tone you only ever hear when someone's talking about kaldi, art, or tubāq. She rolled her eyes when Zosia smirked at this, and put her bowl back on the table. "So let's see, now that you've sung your verses you'd like me to tell you my side of this, yes? Answer all your questions?"
"Oh, don't trouble yourself," said Zosia, enjoying the girl's obvious annoyance. "I put most of it together on the boat, and the rest I added up riding over here from the Dominions. You're a pretty easy case, Princess, not much to you at all."
"And this is the part in the ballad when I spill my guts, right?" asked Ji-hyeon. "You've cunningly baited me into telling you everything, Auntie Zosia, let me sing, sing, sing!"
"You think I'm bluffing?" Damn but this kaldi was good.
"Yup," said Ji-hyeon.
"Fine, Princess," said Zosia, settling in. She'd been bullshitting a little, sure, since most of the pieces hadn't actually slid into place until she'd entered this tent, but a few details notwithstanding, she had enough to impress the impostor. She hoped. "Let's start with your second dad's angle in all this. I came to Hwabun looking to get his help resolving some personal affairs of mine. Without boring you with the details, my business involves Queen Indsorith of Samoth; specifically, her ass on a platter. So when I got down to the Dominions and Singh told me good old Kang-ho wanted me dead before I could find you, it threw me. I mean, if you're trying to take on the whole Crimson Empire, and he's backing you up on that play, why not enlist me to help you out, the way he did with Fennec and the rest?"
A pleased smile from the girl told Zosia she'd fudged something here, and she thought she could imagine what.
"Or maybe Hoartrap and Maroto just showed up unannounced and have stuck around for their own reasons." From the sinking of the brat's smile, Zosia had nailed it. "Doesn't matter. Point is, your first father wants you back because he set you up with some local royalty, and your other dad helped you run away because he's got larger ambitions... but not so large as taking on the whole Crimson Empire, even if they are softened up from infighting."
There we go—General Ji-hyeon definitely pouted like a princess, but she was still trying to play it cool, sipping on her kaldi.
"Now, obviously the whole Star's abuzz about how I've returned from the dead and my Cobalt Company is bigger and badder than ever, sticking it to the Empire with both spurs. Fennec and your dad probably convinced you to go that route to lend you an instant reputation, though I appreciate you not using my name anymore—your people calling you General Ji-hyeon is more than I expected. I guess a blue-haired badass leading an army stocked up with my Villains turned out to be enough, eh?"
"If I'd known you were alive I wouldn't..." The girl seemed embarrassed. "I mean, I've always loved your songs. But I never would have done more than the hair, if not for... And I never used your name, not once, much as Fennec insisted. And the hair, helm, and armor were only because I thought it looked damn fleet, really."
"Armor?" Zosia glanced down at her dusty hauberk and kneepads. "I've worn a lot of different kits in my day, so what... Oh hells, don't tell me you wear that!"
Zosia had followed Ji-hyeon's eyes and landed on the chainmail brassiere and panties that were laid out on another table. The pieces were so small she'd overlooked them before, assuming they were scrap metal or maybe some new style of steel doilies. Looking back at the girl, she shook her head in amazement.
"I didn't think it possible, but I actually feel bad for you, half pint," she said. "Fennec talked you into _using_ that? In battle?"
"Obviously it doesn't provide as much protection as some gear," Ji-hyeon said defensively, ignoring Zosia's snort. "But the mobility it allows for—"
Zosia snorted louder. "Wearing that you'd be dead in five minutes, you didn't have your daddy's devil watching out for you."
"But I do," said Ji-hyeon. "Fellwing's better than a suit of steel plate, and not being weighed down I fight faster and fiercer than any chevaleresse."
"Devils can't be everywhere at once," said Zosia. "You think me, your dad, and every other asshole with a devil got the scars we wear before binding those fiends? As soon as you go up against someone else with a devil you're naked as a babe, or maybe that owlbat just gets distracted by a tasty morsel and you catch an arrow to the gut. You don't listen to anything else I say, save that shit for your private meetings with Keun-ju or that Flintlander kid and invest in something sensible for the field."
"Why, Auntie, do I sense some jealousy that you can't pull off that ensemble anymore?" Ji-hyeon sneered.
"Oh, I bet I could, if I felt like snagging my pubes in chainmail on a regular basis," said Zosia, pouring herself some more kaldi.
"Did you have something to say on matters other than my wardrobe, or are we done here?"
"Hmph," said Zosia. "Yes, actually. Most of your army thinks you're after the Crimson Empire, and with good reason, the way you've been carrying on. But if that were true, Kang-ho would've tried to get me on board before double-crossing me—after all, I want revenge against the Empire, so why not see if I'll help his brat take the throne? That's the smart play, and the safer one, and Kang-ho likes smart and safe more than he likes Azmir tubāq in a templewarden."
Ji-hyeon was smiling again, but Zosia couldn't tell if the girl was impressed or contemptuous.
"So it's obvious you're not really doing what everyone thinks you are. What, then, are you up to?"
"You tell me."
"Sure. Linkensterne," said Zosia, savoring the girl's petulant expression even more than the kaldi. She waited, and sure enough Ji-hyeon cracked.
"Who told you? Fennec?" It was kind of cute, watching the girl try to figure it out. "No... Dad and Fennec tried to bring Singh in on it, but she decided to put her lance with you instead, yes? She told you everything?"
"Nope. A chevaleresse's honor is such she never gave me more than a few hints, even if she knew everything. Don't know, and don't care. Figured it all out myself, as I said. See, when I came up to Hwabun I passed through Linkensterne, and my escort told me how pissed off the merchants are that it's been incorporated into the Isles. Back when the Crimson Empire held it, if you could even call it that, it was a smuggler's paradise, Lawless Linkensterne. Now, not so much, not so much at all. Even if I couldn't guess Kang-ho was running all sorts of shady business through there prior to the handover, some of your family's sailors told me exactly that in plain terms. Ever since, Kang-ho's had a bad time of it—must be a shame to wake up a househusband, when you've grown accustomed to a certain lifestyle."
"Not bad," admitted Ji-hyeon.
"Not bad!" Zosia cocked her kaldi bowl at the princess. "Brilliant is I think the term you're looking for. The only thing I can't figure out is how you used the Immaculate Gate to whisk yourselves down to the Dominions. I figured your old man set his devil free for the ability, but seeing as Fellwing's still around, that can't be it. Fennec's devil?"
"He's not had a devil as long as I've known him," said Ji-hyeon. "But you're half right. Fennec's the one who knows how to use the Gates. I couldn't do it on my own, and won't do it again at all, if I can help it."
"See, you're a smarter girl than I gave you credit for," said Zosia, the idea of walking into a Gate still giving her the shivers. "Far as your plot goes, I've got to admit: whip up the populace, put the fear into Samoth, and then offer a truce—look the other way when we take Linkensterne back from the Immaculates, and bam! A free city for the princess to rule, business is back on for your dad, and better than ever since he engineered the reclamation of Linkensterne. All his merchant buddies will be awfully indebted to the family that gave them their city back."
"Close," said Ji-hyeon. "Close enough, anyway. The plan isn't just to get the Imperials to step back, it's to enlist them. Losing Linkensterne's got to be a sore spot for the queen, and in exchange for restoring free trade to the Crimson Empire she'll be all too happy to lend us a few regiments. That wall they're building is still incomplete on the eastern coast, so we'll ride up and around and capture it from behind. Once we have the wall, we'll complete the construction ourselves, including a northern loop to shield Linkensterne from the Isles. Easy as that, we have a solid wall, and Linkensterne's insulated from both the Immaculates and the Empire."
"You call erecting leagues and leagues of substantial defenses before the full weight of the Immaculate Isles comes slamming down on your heads 'easy'? Assuming you can even take the wall, of course. Easy, she says."
"Easier than you think," said Ji-hyeon smugly. "We have people inside the Immaculate army, working the wall, and we've got way more inside Linkensterne—the merchants want this to happen even more than we do. They've been preparing all year, and when we take the wall they'll take the city. Then the citizens of Linkensterne all pitch in to help finish the wall while my coalition of Cobalts and Imperials defend the construction and hold the border from the Immaculates—the wall will be completed by this time next year. And after that, Linkensterne is its own republic, guarded by the Cobalt Company, with freedom and fortune for all."
"That's good," said Zosia, impressed. "Really good. Your first father might not be too pleased, seeing as he's got that loyalty for his Arm as you only get from an immigrant's kid, but for a dyed-in-the-wool double-crosser like your other dad, it's a huge get. Fennec and the rest earn a healthy cut of the profits, so nobody's complaining there, since they all know by now a small victory is better than a huge almost. Looking back, maybe that was my problem—I dreamt too big. Maybe instead of going after the Crimson Empire I should have contented myself with a smaller conquest, one I could have managed better."
"Except..." said Ji-hyeon, unable to stop herself from smiling as cheekily as her father. There was the family resemblance, right enough.
Zosia thought about it, came up with nothing. "Except what?"
"Except a daughter isn't some devil you can order about."
"No," said Zosia, twirling it around some more and still not getting much. "So what's your angle, then? Squeeze your old man out, take Linkensterne for yourself?"
"Ha!" Ji-hyeon shook her head, as though she were the smartest woman in the room. "Now, just what prize do you think a powerful warlord would pursue, a woman weaned on songs of the Cobalt Queen? A general with an army willing to ride after her into a Gate, if she asked them, armed with devils and black magic, at a time when a bloated empire is weak from civil war? What would _you_ do, Zosia, faced with the dilemma of familial piety or something far more glorious?"
Well, well, well. Zosia found herself grinning as wide as the girl sitting across from her. "Samoth."
"Yup," said Ji-hyeon, looking more like a general than a princess as she reached under the table and pulled out a map, followed by another jug. "And since you have your own business with the Empire, I'm more than willing to bring you on as one of my captains. You can be one of General Ji-hyeon's captains... or should I start calling you and your friends my new Villians?"
Zosia bridled at the girl's choice of words, but what came next was too tasty to spit out for the sake of pride.
"Whatever I call you, Queen Indsorith is yours, Zosia, as I imagine you have unfinished business with her from that time she executed you. Whoever else you want is yours in the bargain, so long as you come clean with me about what happened back then, and any other pertinent details you might have. Pledge yourself to my flag, Zosia, and let's remind those Crimson cowards why they fear the Cobalt twilight!"
"That's quite the offer," said Zosia, getting more excited the more she thought about it. This could work out really damn well for both of them. "Shit. So long as that chainmail lingerie of yours isn't the mandatory uniform, I'm in. Where does a long-in-the-tooth recruit sign up?"
"Pack that pipe of yours, Captain Zosia," said Ji-hyeon, clearing the table and unfurling the map. "We planned on capturing Cockspar next, but their regiment cut us off in the mountains, and so we beat a retreat down here."
"The Azgarothian regiment, you know who's leading them?" asked Zosia, her heart quickening. She couldn't believe of all the luck—
"Uh-huh, I wrote it down here," said Ji-hyeon, pointing to some chickenscratch on the corner of the map. "Heart? No, Hjortt, Colonel Hjortt—he's leading the Azgarothians, but my scouts said there were Myuran flags flying over part of the army, and I don't know who they've got in charge."
"Doesn't matter," said Zosia, licking her lips. This day just kept getting better and better—she'd be seeing her old chum the thumbless colonel a lot sooner than she'd hoped, and this time she wouldn't let her theatrical streak get in the way of what needed doing. Efrain Hjortt was a dead man. "What's your strategy?"
"Well, the Imperial regiments can't be more than a few days behind us, so Fennec wants us to pack up and get moving now, but I think the Cobalt Company might be done running. You're the expert, though, so I'd appreciate your insight."
"I think Fennec's a coward, and you're set up nicely to meet the Imperials in open combat," said Zosia, trying not to let her eagerness show. "Better put on some more beans, then, it's going to be a long night."
Zosia hunkered over the map, relieved she'd let Hjortt off the first time, so she could have the pleasure of getting him now. The only thing that tempered her excitement was the two devils in the corner, silently staring into each other's eyes.
# [CHAPTER
12](toc.xhtml#toc-chapter038)
War was indeed coming, and you didn't need to drink Immaculate devil milk to gain that insight. The signs became increasingly obvious as Sister Portolés and Heretic left the Isles and cut back across the Empire, making for the highway that would take them down to the southern provinces, where the Cobalt Company was causing so much trouble. Open towns that she had paraded through with her Imperial regiment but a year before had erected new walls; way stations that had once welcomed all travelers now viewed even a war nun of Diadem with suspicion. Everywhere she traveled with Heretic, motley militias performed drills in barren fields instead of harvesting ripe ones, and everywhere they were questioned as to their business, and scowled at when Portolés sternly rebuffed all queries.
That King Jun-hwan had claimed it wouldn't be the war they were expecting worried at the back of Portolés's mind, like the urge to sin. She had done a good thing, as far as that went, not taking Brother Wan with her. Yet in her soul she knew Queen Indsorith had been right to advise her to view even her brethren and superiors as potential saboteurs—if the Burnished Chain had sent Efrain Hjortt to Kypck as a means of provoking Zosia into attacking the Empire, they would have a vested interest in preventing Portolés from finding her and telling her the truth. This distressing possibility was given credence when she and Heretic crested a grassy butte overlooking the languid Heartvein and caught sight of four black-robed riders racing up the road after them. They weren't much more than a mile off.
"Hmmmm," she said, surveying their surroundings for a defensible position. Portolés had fought well for the Chain during the civil war, and after the reconciliation she had worked just as hard to earn the right to serve with the Fifteenth Regiment. Her time first warring against the Imperials and then working for them had honed her natural intelligence toward self-preservation. Alas, the butte was as gentle a hilltop as a lazy pony could hope for, with a lone stand of poplars set just off the road, and nothing on the far side of the rise but a leisurely ride down to a tranquil valley. "They've timed it right—probably waited all morning for us to clear the forest."
"How's that?" Heretic looked back, forth, up, down, everywhere the nun had tilted her head. "What is it?"
"My people," said Portolés. "Come on, let's picket the horses in those trees before they're on us."
"Was wondering when you'd stop for a pray," said Heretic. "You expecting them, or is this an impromptu service?"
"Heretic," said Portolés as she dismounted, "how would you like the opportunity to kill some clergy?"
"Um." Heretic glanced back over his shoulder. From here the inclined approach and its riders were obscured by the wide top of the butte. "Not sure how you want me to answer that, Sister Portolés. It might surprise you to know I'm not really a hardened killer so much as a, um, gentle knave?"
"I didn't ask if you had killed, I asked if you wanted to," said Portolés, tying her horse and the pack mule to the thickest tree. "Hop down so I can unlock you."
"This..." Heretic looked genuinely nervous for the first time since she had freed him from the Office of Answers. "I'll level with you, sister, if this is a test I'm bound to fail. So if you're looking for an excuse to do me after all our time together, I'd prefer you just looked me in the eye when you put that hammer to my skull."
"Heretic," said Portolés as she tied his horse, "if you aren't willing to fight next to me, I'll do just that, right now."
"No need to rush into these things," said Heretic, dismounting so quickly he almost fell. She'd taken to letting him ride with his legs unshackled, and in a moment his hands were free. "I don't suppose—"
"Take those two crossbows I bought in Linkensterne, string, nock, and load them, then set them on that wide stump back there," said Portolés. "The short sword in the bedroll looked to be about your size. Now."
"Sure, sister," said Heretic, rubbing his red wrists. "But, um, you are going to talk to them first, yes? It might not come to anything, right?"
"Doubtful. In a Chainhouse or the Dens we debate with our tongues, out here I expect the saints will do the talking." Portolés hefted her maul. "Saint Orakulum here died at the Encounter of the Condemned Earth, thirty-three years ago. His bones stoked the forge, and his spirit dwells ever more in its steel. He will provide a stirring counterpoint to any argument my fellows lodge."
"This right here," said Heretic as he quickly removed the weapons from the back of the pack mule, " _this_ is why people fear the Chain. If you settle your internal differences this way, what hope is there for dissent among the common folk?"
"You're smarter than you let on," said Portolés. "I'll parley with them, but you'll see soon enough the way the wind blows. Bows on the stump, sword in the ground beside them, and then lay a saddle blanket over them so they're hidden but easy to get out. And mind the safeties are—"
The bow Heretic had loaded with shaky hands went off, an arrow launching up through the rustling poplar branches. Portolés didn't look to see where it landed.
"On second thought, forget the blanket. Stand in front of the stump to obscure them with your body, until you need to start shooting."
"I thought the Chain forbade crossbows, sister?"
"Haven't you cottoned on yet?" Portolés showed him her file-blunted teeth. "I'm a bit of a heretic myself."
"Yeah?" Heretic wiped sweat from his face, almost dropped the bow as he did. This was shaping up to be a right proper martyrdom.
"If we fight, we kill, and if we kill one, we kill them all. If any escape they'll soon be back, with a local posse or two. If that happens the writs I carry mean very little to the illiterate. Be ready to fire at the ones in the rear. Less chance of your shooting me that way."
"If I... how will I know when to—"
"You'll know," said Portolés, and, hefting her hammer, she stepped out into the wide dirt track. Above her, dollops of puffy cream clouds floated across the afternoon sky. Beneath her, the browning grass in the center of the road was beaten down from countless hooves and feet that had recently traveled this way. Before her, a cowled rider crested the butte and slowed, the other three quickly appearing behind the first and reining in their horses as well.
With enough time, she could have strung a rope across the road, secured it to a rock on one end, and wrapped it around a tree on the other, so Heretic could pull it tight and trip the first horse.
With enough time, she could have dug a trench to effect the same.
With enough time, all the sinners on the Star could repent, and when the Sunken Kingdom returned from the waves there'd be no more need for hell.
When you were short on time, all you had was action, and the belief your action would work. Here, on this crisp autumn day so much like the one in Kypck, Portolés believed that Heretic wouldn't shoot her in the back in hopes of endearing himself to their pursuers—faith in a man whom she wouldn't have trusted not to murder her in her sleep when they'd first set out. How had it come to this, arming a confessed heretic and traitor to help her fight against her own people? In a few short years she'd gone from fighting alongside her brethren against Imperials during the civil war to riding alongside the Crimson soldiers, and now she was preparing to battle other war clerics in the service of the Queen of Samoth.
Well, everything happens.
And verily, it did.
As Portolés expected, there was no pretense. Why should there be, among servants of the Burnished Chain? The Chain Canticles warned that any anathema might harbor the talent for looking into the thoughts of another, and with even a sliver of a chance that Portolés could smell their deception, they wouldn't risk coming down from their horses to talk. Instead, they made to ride her down in the road.
The lead rider wore the mask of an anathema, as did two of the three behind him. Over his head buzzed the wide, smoking halo of a censer-star he swung in a deadly gyre, which explained why his fellows gave him a healthy lead. As he bore down on Portolés, a crossbow bolt flew under his steed's thundering hooves, and then a second missed horse and rider by an even wider margin. So much for Portolés's order that Heretic fire on the clerics in the back. The first rider was almost on her, the chain of his weapon still whisking the air above him.
As soon as Portolés made a step to evade in either direction he would bank his horse to pass her on the opposite side and bring the enormous iron censer down upon her.
So she waited in the center of the road, forcing him to make the choice of which side to pass her on. Twenty yards out, the horse veered into the right-hand wagon rut. At ten yards Portolés darted to that side as well, and then passed the rut, even as the horse flew down like an avenging devil. She pivoted, putting all of her might into the swing, blind for a moment to everything but the wide, empty butte before her, and then came back around with her maul. The two-handed hammer struck the charging horse, but where, she could not tell, for her maul was sent flying from the impact, and, refusing to release the handle of the weapon, she flew along with it.
The first bounce on the solid turf knocked her senseless, but the second restored her, and the third turned into a roll across the grass. She was on her feet, then, but immediately toppled back onto her arse, the world spinning as furiously as the first rider's censer-star, the chain of which had wrapped tight around both horse and rider as they fell from her hammer. She staggered upright and took in this miracle, the monk broken and bound to his steed's mighty neck by the long chain that had ensnared them both, the smoking head of the censer partially embedded in his side. Then the other three riders surrounded her, their horses stamping as they were slowed to a walk, and the time for contemplating miracles was passed.
It was as Portolés had feared—they meant to take her alive, the first rider intending to lay her out or disarm her with his long, blunt weapon rather than execute her. That hadn't worked, so now the others quickly glided off their horses. One of the anathemas broke into a sprint toward the trees where Heretic lurked, the other two clerics slowly advancing on Portolés. The masked anathema was slight but quick, his scimitar flashing in the sun, and the barefaced pureborn man had shoulders nearly as wide as Portolés's to power his mace. From the poplars, Heretic screamed. Soon two-on-one would become three against, and dizzy or not, Portolés knew her only chance was in not waiting a moment longer.
She made as though she were heaving her massive hammer at the pureborn, but as the anathema darted in to gut her with his curved blade she reversed her swing, bringing the butt of the weapon up instead of the head down. The long handle of the hammer connected with his sword, slowing it enough that when its blade slid up the shaft and into the bottom of her fist it only clipped off her pinky and ring fingers, instead of doing worse damage.
She flicked her injured hand out, and her remaining fingers hooked the anathema by his dangling rosary and jerked him into her. She brought her skull down like a comet, striking him between the eyes. The point of his scimitar jabbed into her side, rooted around as she headbutted him again. He went limp, but by then the pureborn was atop her with his mace. She had no choice but to choose between the falling anathema or her maul. With a wounded hand, the lighter weapon was preferable, so she clumsily tossed her hammer into the oncoming mace. The pureborn's weapon clattered against her maul, knocked it from the air, and concluded its trajectory, dull metal crushing the bones in the forearm she brought up to block her face.
The pain sent her reeling, despite her training, despite her intimate familiarity with the sensation of being destroyed by her church. Twisting her thumb and the two remaining fingers of her only responsive arm into the woolen cassock of the limp anathema who still dangled in her grasp, she set her heel and slung him around. The mace came down again, faster than she could track it, but this time it collided with the dazed anathema she put between herself and the pureborn. He didn't make a sound as the weapon clobbered him. Instead of falling back at this unexpected defense, the pureborn pressed his advantage, meaning to beat his colleague out of Portolés's hand.
She met his assault with one of her own, shoving the drooping body into the pureborn's path, and then following after it with the last of her wobbly momentum. Slinging her numb, broken arm out and releasing the anathema with her other, she tackled the pureborn. Big man he was, but Portolés was bigger, and with the added weight of the anathema to aid her, she took him to the ground.
Grunts, and a groan. The pureborn tried to roll free, the blood-slickened wedge of the anathema between them making him slipperier than a Tangordrim catfish... but before being taken into the church, Portolés had fed herself and her sisters on fish she pulled barehanded from under rocks in the River Tangor. The sisters the Burnished Chain had burned alive, deeming them far too corrupted for even the salvation of the ecclesiastical surgeons. Portolés could no longer recall their names.
She caught the pureborn by the belt as he squirmed free of the anathema, and, launching herself after him like one of the swifter fish pursuing a fly darting above the river's surface, she bellyflopped back down atop him. He had a dagger or something, shanked her in the chest and gut, but then she was level with his wracked face, looking at him eye to eye... and then she did for him as she'd done for the anathema.
His skull was harder than the first man's. Portolés's was harder. After the second headbutt his knife stopped poking her, and after the fourth his eyes crossed, his split nose warm against her crown as she brought it down again. And again. And again. She only stopped when a sharp boot caught her in the armpit and rolled her off him, quickly delivering a series of kicks to her stab-riddled stomach. The last anathema...
Blinking the stinging blood out of her eyes, Portolés stared up at her assassin. The anathema reached up and pulled down her mask, revealing a face scarred with pits from where they must have scoured away her fur or scales.
"Safe roads guide you to her breast," said the sister. She raised her weapon, the silver crescent winking, and Portolés tried to prepare herself for whatever awaited her on the other side of the ax. Despite everything she thought she believed, she was scared. So much for taking her alive.
The anathema yipped and stumbled back. Portolés squinted at the small arrow that had appeared in her assailant's shoulder. Fast as the anathema had faltered, she dashed forward, out of Portolés's sight—the tall, dying grass in which she lay on her back veiled everything but the reddening sky. Night was falling, and jackals would be out on the buttes soon. She thought she heard a crossbow twang, but couldn't be sure. It was quiet, save for her wheezing breaths. She willed herself to sit up, but when she tried the hot slits in her side, stomach, and chest pulsed wetly, her arm shuddered, and she collapsed back down. The battle haze was lifting, and the angels of suffering were planting their kisses all across her body. What a terrible way to die...
She felt herself drifting off, and forced herself to think of Kypck. It was how she kept herself awake when she was exhausted on watch. Guilt and shame has a way of perking one up. All those ignorant people, cut down for no reason they could ken, screaming as they were sent to their judgment. Portolés giving the order as sedately as if she were overseeing drills on a parade ground. Using her maul, a relic of the Burnished Chain and symbol of her devotion to a greater good, to bash in the skulls of the five wide-eyed, shaking Azgarothians who refused to follow her command. Not killing a single villager herself, as though that kept her clean, instead of making her just as bad as Colonel Hjortt.
Boots crunched the gritty track of the road beside her, and she focused on Hjortt, his face bubbling like the wax of a freshly lit candle in the confessionals, his ringlets flashing up like burning scrolls. She thought of Queen Indsorith, her long hair waving like a pennant in the winds that forever lash the Crown of Diadem. Maybe Portolés had done some good in the end. Maybe she'd done enough. Maybe. A living shadow fell over her, the devil of death blotting out the sky, the promise of salvation...
"Well, well, well," Heretic said, leaning over her. "You look in a bad way, sister."
"I'll bleed out if you don't tie me." Portolés found the words pouring out of her in a rush, despite how sluggish her tongue felt. "On the mule, there's a bag for this, this... a bag of bandages, a pot of ointment. Smelling salts. You've got to pack me, pack my wounds, got to..."
"I know where it is," said Heretic. He looked remarkably hale for a man who had squared off against an anathema.
"The last one, the anathema, she'll be back..."
"I see that happen and I'll convert," said Heretic, directing the crossbow in his arms down at Portolés. "Now I know why your pope outlawed these things. Gotta be evil, if it lets a common sinner like me take down the Chain's holy monsters."
"You fought... good, Heretic. Better than I believed."
"Fought? Lady, I ran for it, soon as that witchborn came after me! Led her on a hunt, and fast as I am, she soon gave up and doubled back. I figured she'd get a horse and catch me for sure, so I cut back, too, along the edge of the bluff. None too soon for your benefit, neither!"
"And now?" Portolés swallowed blood, staring up at the crossbow. "Listen to me, Heretic—I know you want to know why."
"Why?"
"Why this. Why I took you, what we've been doing, where we're going. Why this fight. Why everything."
"What makes you think I give a shit, so long as I'm free?" Heretic seemed delirious. "Free, with horses and loot and the open road in all directions! _Why_ , sister, would I care about your songs?"
"Because you're a heretic," said Portolés, shivering in the cold, wet grass. "And being curious is how good folk become heretics in the first place."
"You think you know me, huh?" Heretic pulled the trigger on the crossbow, the bolt thudding into the corpse of the pureborn beside her. "You think 'cause you read my tract you've got me pegged? Tell you what, sister—say right here and now you hate the Fallen Mother, that you love the Deceiver, and I'll listen to anything you want to tell me."
"I hate the Fallen Mother," said Portolés through gritted teeth. It wasn't the voicing of heresy that disturbed her, for without belief words are nothing; it was Heretic's utter stupidity. If he actually wanted to hear anything, he'd better stop wasting time. "I love the Deceiver. Now stanch these before I bleed out."
"Sure." Heretic suddenly seemed chastened. "Of course, right. Hold on, hold on."
He returned with the chains she had bound him with instead of bandages. He kept apologizing, his hands shaking as he secured the bonds. She didn't struggle, and he didn't look her in the eye. Only when her broken wrist was manacled to her bloody one did he fetch the barber's bag. After that he followed her instructions adequately. When he was done he propped her up on the body of the pureborn monk and returned to the horses. He came back atop her bay, wearing the soiled robes of one of the anathemas.
"All right then, sister," he said, his voice quavering. He had probably never killed anyone before, to be so shaken up about it. He made the sign of the Chain, offering her a loony smile as he did. "I'd say we're even now. Don't wait up for me."
Then he was gone, leaving Portolés with a pureborn for a pillow and the bloody heavens for a blanket. She deserved this, she knew, but the Empire didn't deserve to have Zosia wage war upon it for the crimes of an overly obedient war nun and her rogue colonel. She prayed then not for herself, but for the Star, that she might recover just long enough to complete her quest. The color bled from the sky, her words slurred, and her prayers trailed off. She might have died, or maybe it was just sleep, she could hardly tell the difference as she closed her eyes and fell under, into the First Dark.
# [CHAPTER
13](toc.xhtml#toc-chapter039)
Purna looked right smart in her horned wolf hood, Maroto had to fess. Choi had helped her rig it up proper from the smallest hide, so the four horns jutted out from the girl's head in imitation of the weirdborn, and the horned wolf's limp snout hung down between Purna's eyes. Diggelby and Hassan had split the other hides into matching mantles, and Din made a crude tiara from the teeth. Neither Maroto nor Choi had taken trophies from their encounter with the horned wolves, other than a clutch of new scars. The wounds they'd picked up from the confused Imperial recon squad on their way down from the pass were scratches in comparison, and would like as not leave little lasting reminder of their barmy dash to the enemy encampment. Thinking back on all his wild days with Zosia and her Villains, here at last was a deed to match those adventures of old, and surpass a good many of them. Whatever Imperials had made it through the night would have songs to last down through the ages, ballads to commemorate the time a gaggle of rebels led a pack of horned wolves crashing down onto their regiment...
For his part, the only ditty Maroto was singing was "Give Me a Cot, a Bottle, and Four Whores." As they ought to be given a hero's welcome back at the camp of General Ji-hyeon, it seemed one of his songs was going to come true, for a change. There was nothing like returning to camp with all of the people you left with, and good information to boot.
For as many miles of hard ground Maroto and his scouts had covered over the preceding weeks, the Cobalt Company hadn't progressed much—after Myura they'd gone up into the Kutumban mountains to throw the Imperials off their trail and spent a few weeks resting their army in the Secret City of the Snow Leopard. When they left the kind nuns of that mountain sanctuary the Cobalts had meant to come crashing down on Azgaroth, but then the regiment from that self-important province unexpectedly appeared on the horizon to intercept them. The Cobalts had been obliged to cross the Bridge of Grails and double back east rather than risk tangling with a larger force that held the high ground. If only the general had known her valiant scouts were wrecking the shit out of that very Azgarothian regiment, she could have had the Cobalts come up from behind and hit 'em while they were still pulling wolf teeth out of their arses, but that was war for you—the best tactics oft revealed themselves in a moment of desperation, rather than coming in early enough to let you get your ducks in a row.
The Cobalts had marched down into the Witchfinder Plains, not a terribly long way north of where they'd started, and still many leagues from Diadem. Maroto was surprised to see that the Cobalt Company had made a proper camp in the high foothills a mere five leagues north of the road that had taken them down from the Kutumbans, rather than making all haste to put more distance between themselves and the Azgarothians. But then the general seemed dead set against following the example Zosia had laid down two decades prior of cutting and running from the Imperials for years on end, whittling away at the Crimson hordes and slowly swelling her rebel ranks as she led them on a wild chase from one end of the Star to the other, and back again. No, after less than a year of rabble-rousing and small victories, General Ji-hyeon was taking the fight straight to the Imperials—no other reason for digging in at this spot unless she meant to greet the pursuing regiments that had harried her through the mountains.
Couldn't rightly blame her for picking a defensible spot to make a stand, though, since Maroto had finally remembered where he knew Hjortt's face—and the Fifteenth—from; those were the mad bastards who had kept the original Cobalt Company on the run for well over a year straight, shaving pieces off their rebel army every time they stopped to catch their breath. Hjortt must push his crew like a devil pushing at a mortal's temptation, sacrificing any goodwill he might have fostered with his soldiers to get them marching early and keep them marching late when the chase was on, all day every day. You simply couldn't expect a bunch of volunteers and sellswords to put in hours like that, which made the Azgarothians the fastest regiment on the Star.
So yeah, even taking time to recover from their wolf bites, the Azgarothians could probably catch the Cobalts before they reached the Haunted Forest or any other populated region where they could replenish their supplies. That was the problem with being so successful so fast—before you knew it you had more mouths than you could feed, and no teat to stick 'em on. General Ji-hyeon probably hoped to take down a few owlbats with one bow, by leading the Azgarothians into a serious engagement—check another Imperial regiment off her list, and steal their stores when the day was won.
If the day was won. Assuming they hadn't lost or gained many heads in the Kutumbans, the Cobalt Company had eight thousand pikers, stickers, hackers, and other broke-arse, poorly armored foot; a thousand archers, crossbowers, and gunners; five hundreds chevaleresses, knights, and other folk who could ride worth a damn and had a horse to do it on; another hundred or so weirdborn of various abilities; and three out of the Five Villains. Even if you took into account that Hoartrap was as dread a fucker as he'd ever been, those weren't great numbers, especially since by all accounts the Church of the Burnished Chain had a few of their own sorcerers, though they called them cardinals instead of witches. Whether or not one of those creeps was with Colonel Hjortt's company, the two scary robed fuckers who'd gotten the worst of the horned wolf attack in the Imperial camp were definitely weirdborn, so apparently the church had reversed its decision to burn all so-called anathemas since the last time Maroto had encountered the Burnished Chain. Under King Kaldruut those arseholes had wanted to burn everyone, it seemed, the whole bloody Star, presumably as part of some hideous ritual to summon that mother of devils they worshipped or some equal insanity, but maybe they'd figured out it was better to let the Star burn itself, and weirdborn wield torches as well as anyone.
During their reconnaissance, Maroto, Choi, and the nobles—Maroto's Moochers, as Fennec had dubbed them when they'd set out, despite Maroto's insistence that they should be called the Dandy Dogs—had counted enough Imperial heads to know the odds were long indeed even without Chain-indentured weirdborn taking part. They had seen the still-sizable remnants of the regiment they had spanked at Myura taking a southern pass through the Kutumbans, and while the Cobalts rested up and planned strategy in the City of the Snow Leopard those Myurans must have looped up to merge with the marching Azgarothians. On their own a few thousand Myuran soldiers wouldn't have posed much threat, but when Maroto's Moochers had led the ornery horned wolves through the Imperial camp they'd had an unprecedented peek at the true power of the joint regiments:
Twice as many grunts as the Cobalt Company.
Twice as many gunners and bowfolk.
A cavalry to match the Cobalts, and then some.
Add to that the two cavalries of no less than two hundred riders each the scouts had glimpsed at various points on the distant slopes, no doubt coming in to beef up the Azgarothians, and it was shaping up to be a real shitshow in the plains.
Not that Maroto gave a devil's damn; he'd let Purna have her fun, putting in real time as a bought killer, and now that the stupid part of every war was fast approaching it was time to cut out. He'd been thinking, ever since their run-in with the horned wolves, that adventuring was a lot more fun than he remembered. Sure, he was nine kinds of injured—even before one had been sliced open on a rock, his knees had started complaining about all the fucking hiking—but so long as they laid up somewhere for a while before setting out in earnest he'd be off this stupid crutch. And it might have been his imagination, but he was sure his paunch had shrunk a bit since the Panteran Wastes, so that was as clear a sign as any poison oracle's prophecy that he was on the right track. Hells, he'd even put it to Choi, see if she might be willing to buy out whatever contract she had with the general—she was as eerie as waking up to seeing your devil sitting on your chest, watching you sleep, the way Crumbsnatcher used to do, but eerie could be good... eerie could be damn appealing, in fact. He'd put in his time with countless lovers of most any and every sort, but he'd never had a weirdborn so far as he'd known...
_Wildborn_ , he reminded himself, not weirdborn. Coming up in the Isles she'd prefer that, no doubt. He wondered if she liked having her horns touched... once the left one healed up, of course. She was almost as bad off as he was, after that tumble down the mountainside, but had sprung back a sight spryer than he'd managed. Impressive as any miracle, the way she'd danced over those mountains, facing monsters without a flinch. Maroto could get behind a woman as good in a pinch as she was. So to speak.
"What are you leering about?" asked Purna as they saluted their way past the innermost ring of sentries, and Maroto checked himself. Some weird—wildborn, wildborn, some _wildborn_ —could peek in a fellow's mind, they said, and so no more thoughts like that. Not as long as Choi was walking with them, anyway, instead of a mile off on point.
"Wild game," said Maroto, licking his lips as he watched Choi's heavy brigandine skirt sway back and forth across the back of her knees as she crested the foothill they climbed. Could hardly tell she had a limp from that horned wolf. "Hungry, is all."
"I know, right?" said Purna, following his gaze. "A freebooter can't live on beans alone. What I'd give to roast that rump..."
"Shut it!" hissed Maroto. "She'll hear you."
"Worse things than letting a lass know your intentions," said Purna. "If you don't make a move on that, I will."
"Careful, barbarian," said Diggelby, coming up between them, Prince cradled in his arms. He had barely put the dog down for so much as a shit ever since they caught up to the cur on the edge of the Imperial camp. "Our Purna's not the sort to share her supper, even with a starving man."
"Oh grow up, you two," said Maroto, his eyes back on _that arse_... but then Choi glanced back over her shoulder, and Maroto blushed as Purna cackled.
"I'll report to Ji-hyeon," said Choi, eyeing them with little amusement. "You can come, or not."
"Not!" said Din and Hassan in unison from where they took up the rear, and Din added, "Party tonight in our tent, Choi, come by after you're done."
"We all have some _serious_ drinking and drugging to catch up on," said Hassan as they all stopped atop the last hill and could take in the tent city of the Cobalt Company spread halfway up the first serious slope of the Kutumbans, what few grasses that weren't trampled flat swaying in the balmy lowland breeze. "You most of all, oh tireless leader."
After a contemplative silence, Choi nodded once, looking almost amused for a change. "Yes. I'll come."
"Huzzah!" cried the nobles and Maroto as one, and Purna threw her arm around the broader woman's shoulders and gave her a squeeze meant to pass for comradely. Maroto knew that move well, had used it a hundred times himself, but smiled to think himself above such things now. This wildborn would surely appreciate a mature, respectful lover far more than some fumbling teenager.
"You should all see barbers first," said Choi, inelegantly withdrawing from Purna's embrace. "The white tents."
"You more than us," said Maroto, not about to be outmaneuvered by a pup like Purna. "I can give Ji-hyeon the basics while you get patched up. I'd feel better if you'd see yourself tended to before bothering with a simple report, Choi."
Purna rolled her eyes and Choi looked rightly cautious. "I am... fine. We can give the report together, if you like."
"I would like that," said Maroto, nodding seriously as Purna mugged from the other side of Choi. "We'll go together."
"Have fun!" chirped Diggelby. "I've got ten taels that says I'm through a parcel of Agonist cheroots before you're free of the command tent."
"I'll take that," said Hassan. "I can't wait to see you puke up your guts after a month off the stuff."
"Double up with me?" asked Din, and Diggelby frowned when Hassan readily accepted. "You're about to be down twenty, Count; Diggelby's been lining his panties with tubāq leaves every morning since we left."
"Spying on a gentleperson during their toilet?" said Diggelby, abashed. "You have no shame, Duchess!"
"Not really, no," said Din, spitting a brown clod onto her friend's boot. "I've just been chewing mine, since Choi said smoking was off-limits."
"It's got to itch, absorbing it through your treasure," said Hassan thoughtfully. "But I expect Diggelby's long accustomed to that sensation in his knickers."
Choi resumed walking, Purna keeping pace with her, and Maroto hobbled quickly after, saying, "Surely you don't have any interest in a stuffy tactical meeting, Tapai Purna?"
"Quite the contrary," said Purna, pulling her hood back a bit. It was still far too raw for her to be wearing it, and the stink must be singeing her nose hairs. "You've got to start somewhere, eh, Maroto? You wait and see, I'll be one of Ji-hyeon's Villains before this campaign is won!"
"Huh," said Maroto, waving at a gaggle of rough-looking camp followers who crouched around a breakfast fire at the outskirts of the tents. "I actually had some things I wanted to talk about, before any plans for the future get hammered hard. It concerns the both of you."
Choi looked as intrigued as Purna, for a welcome change. Purna asked, "And what might those _things_ be? I've told you every day since we set out, Maroto, you're a fine ally, but I'll not be a rich man's plaything. And as much as you say you'd like to have Choi right there on her knees beside me, sharing the load, I doubt she—"
"Deceiver's wounds, I never said that!" cried Maroto. "I'm being serious here, Purna!"
Choi's expression was unreadable, but she was definitely giving Maroto her full attention now. Purna winked at Choi and said, "Not that I don't find you most comely, Captain Choi, because I verily do, but anything involving Maroto's womb-hammer—"
"Purna," said Maroto, closing his eyes. A brilliant if wicked play on her part. "Please."
" _Fine_ ," said Purna. "What's the story?"
"War's no good," said Maroto, having to wing it because his carefully prepared speech was completely forgotten, now that Purna had flustered him. "I've been in enough of them to know that, and know it well. And besides that, I took an oath to Queen Indsorith long ago that I'd not take up arms against her. I've been playing that promise way too loose until now, by pledging to defend you, Purna, but once the battles really begin I won't be able to pretend I'm not breaking my vow. Not so long as I'm with this army."
"This oath," said Choi, her expression all too readable now. "You never spoke of it to Ji-hyeon."
"No," said Maroto. "But not because I'm working for that Crimson arsehole, nor will I ever. Fuck Queen Indsorith, and double-fuck her Empire. Not the good kind of fucks, neither. But I swore an oath on my devil, and that's the end of the matter—truth be told I don't know what'll happen if I take one more step over the line, so I don't mean to find out."
"Why?" asked Choi, then seemed genuinely taken aback for the first time since he'd met her. "I apologize. It is your past."
"No, no," said Maroto, having picked up enough of Choi's odd way of speech to know _past_ meant _private business_ to the wildborn. "I don't owe either of you the tale, sure, but I'll freely tell it, since we're friends. And since I expect you to trust me."
"Damn," said Purna, punching Choi's arm to the woman's confusion. "I've been trying to pry this verse of the song out of him since the Panteran Wastes. He must really want to get into your—"
"Purna!"
"Sorry, sorry, go on!"
"I'll make it short, give you the full version some night around a fire," said Maroto, since they were already getting into the camp and he wanted to make his play before they reached Ji-hyeon's tent. "My... Zosia, Cobalt Zosia, you all know about her, that we were..."
"Your general, yes?" asked Choi.
"That," said Maroto, the despair of her passing hitting him all over again, in this blue-bedecked camp that should have been hers. "And... I loved her. Truly. Like no other, before or after. And she loved me, too, I know it. Old Watchers keep me, I love her still."
"From the songs, I figured..." said Purna after they walked a ways in silence, both women slowing their paces to Maroto's relief. Even with Choi's ministrations it felt like his knee was going to rip open again from all this limping about on it. "I'm so sorry, Maroto."
"Dusty as it is, the wound still feels fresh," said Maroto, and snorted. "It's the stuff of songs, all right, and that'll teach you to aspire to such glories. The good ones all end in tears for everyone but the bard. If she and I had but a wee bit more time... shit. Anyway, she died. Queen Indsorith cut her down in a duel and threw her corpse off the top of Castle Diadem, earned her crown the same way Zosia won hers. You all know that, it's ancient history."
By Old Black's teeth, this was harder than Maroto expected. He cleared his throat, cleared it again. "I was away from Diadem when it went down, but you'd best believe I returned as soon as I heard. Meant to tear down the whole fucking place, meant to make the castle itself bleed out and drown the city in blood, till it reached the very throne room... But Indsorith was ready for me. Offered me the same as Zosia had offered her. A duel to decide the matter. Fair terms. She didn't even want to toss me down onto the city after, if I couldn't lay her low, just my oath I'd be done making trouble for her... and... and I fucking _lost_."
Devils, was that his voice breaking? They stopped walking, and Purna put a hand on his shoulder. Cracking his neck, he pulled himself together. "So that's it. The short version. Why I can't in good faith keep on with General Ji-hyeon. Really, though, even if I could, I wouldn't."
"Yellow as a canary's marrow," said Purna, trying to help him wash down the lump in his throat with a swig of her sass. Daring to glance at Choi, he saw neither suspicion nor scorn in her ruby pupils, but maybe... sorrow? It cut him, that look, like strange as he'd thought her up until recently, the wildborn was no different from him, that she knew nothing could be worse than failing those you've sworn to save. Then Purna slapped him on the back again, said, "So what you're telling us is you've got an excuse, but even if you didn't, you'd still be too fear-footed to throw down."
"There's being scared, then there's being smart, and while I'll fess the two are often confederates, this ain't about being scared of a scrap." Maroto waved his hand at a crowd of youths running sword drills in one of the camp's clearings. "Once the Imperials come down on us, all of them are dead."
He pointed past the practicing soldiers to one of the kitchen tents beyond. "All them. And everyone there, and there, and there, too. To Ji-hyeon's credit, it won't be as bad as when Zosia led us. Things were real dark then, on account of the Imperials burning any village they didn't trust, and they didn't trust many by the end, so it wasn't just fighters in our camps, it was all their families, too, young and old. So it won't be that bad... but it'll be bad enough."
As they passed the drilling boys and girls, an Usban knight leading them, Purna said, "Really, it can't be as hopeless as all that! Everyone dies? I don't think so."
"Maybe not everyone," said Maroto. "But it'll be worse for the survivors, believe me. And even if we pay so high a price that Ji-hyeon wins her war, what then? You think the Imperial provinces will just hand over their titles and castles to another conquerer? You think she'll be able to rule, without killing a hundred thousand more, be they soldiers or serfs? Even after all Zosia did, or tried to do, once she had the throne it was like she wasn't even there. Orders she gave got mistranslated or mysteriously lost; her move to fix the crooked system by sending the rich folks to work the fields was a fucking disaster of epic proportions. More died in her reforms than died in the war, I reckon. Not that it was all her fault: the whole ruddy Empire worked against her. You want to bring a land together, give them a common enemy, and for the merchants, nobles, and politicians, that's exactly what she was. Why would it be any different this time around? I won't say there aren't folk who benefit from a well-fought war, but you rarely find them within a hundred leagues of the front."
Devils, but Maroto was parched after that sermon. They'd come up on the busy cooks, and he dug around in his purse for a suitable bribe. Choi and Purna waited until he'd talked a furry-faced wench into selling him a wineskin of retsina before they continued on their way, Choi surprising him again by cutting straight to his bone. So to speak.
"You would have us disgraced with you, before we even give the Imperials a chance to repay us for the wolves?" She didn't sound mean about it, so much as... perplexed.
"Nothing disgraceful about avoiding a pointless war," said Maroto, offering her the skin after he'd drained half of the pinewine in one tug. "Not suggesting we go off and join a Khymsari monastery, neither—there's more battles than you could ever hope to wage, just waiting out there for you. For us. We work well together, don't say we don't. The three of us, and Diggelby, Din, and Hassan, if they're game, could be the Six Chums or what the fuck ever, seeking out adventure on every arm of the Star. Monsters and maniacs, devils and darker things yet are lurking in forgotten ruins and dungeons, and we could—"
"No," said Choi, though she'd taken a slug of his wine willingly enough before passing it to Purna. Then, thoughtfully, she added, "Thank you, Maroto."
"Yeah, I dunno, either," said Purna apologetically. "This is... I mean, the Star will always be there, right, but a war like this doesn't come along often! It's easy for you to say they're no fun, since you've already had your sport. I'd prefer to fight one myself, a'thank you very much."
"That's not why," said Choi, though whether she was speaking for her own reasons or Maroto's he never knew, because just then Chevaleresse Sasamaso emerged from a tent, and after doing a double take, hurried over to them.
"Here's a sight to please the gods of war and wine! What news from our flanks, friends?"
"News that first goes to General Ji-hyeon," said Choi, and it was only the resurgence of her frostiness that reminded Maroto it had thawed for a few clement days. "We have only now returned."
"Really?" Chevaleresse Sasamaso gave Maroto a sly grin. Fucking Crowned Eagle People, always with that _knowing look_ shit. "Well, let's not waste any time, then! I'll show you to the general's tent; since we settled in here I've been moving her nightly, as you ordered, Captain Choi."
Chevaleresse Sasamaso led them at a sweaty canter through the camp, ill-respecting the fact that Maroto and his people had just spent a month doing little but hustle around on aching legs. Neither Choi nor Purna responded to his frequent glances. Well, so much for happily ever after, anywhere but here. Making matters worse, when they got to Ji-hyeon's tent they were informed by the guards that she was still carrying on a private meeting with a Raniputri emissary who had arrived the night before, and not even Choi was permitted to enter. Awkward.
Chevaleresse Sasamaso insisted they follow her to meet some other visiting dignitaries, but Maroto was only half listening. As was always the case when a pass or a business proposal failed spectacularly, all he could think about was getting away from Choi for a while... but really, looking at the whole tapestry here, what the fuck was he supposed to do? Wander off on his own again, swinging his mace by his own bad self as though he were some punk kid waving his treasure around? That was a loser's play, right there, and Maroto was no—
"Craven!"
Maroto tripped over his walking stick at the outburst, looked frantically around at the tents hemming them in. Felt like an idiot as he did; this exact scene had played out a couple of times over the years, when he'd be drinking in some tavern or squirming in some stinghouse and a random punter from the Noreast Arm would insult one of his companions with the term, but Maroto would jump up, thinking somebody had recognized him from—
"God of devils," he whispered as his eyes landed on his father. His _dead_ father, mind, his long, long-dead father. Considering the old bastard was supposed to be twenty years with his ancestors yet towered over half a dozen feet in the air, strapped to some mule-faced kid's back, Maroto figured he could be excused for not noticing him immediately.
"Oh, how you'll be wishing it was she instead of your daddy," said Da, his smile wicked as those of the horned wolves who had harried them down the mountains. The old man's mount stepped fully out of the shade of a tent now, and Maroto nodded in appreciation of the young pup's vigor. He didn't look like much, but the casual way he moved, as though he didn't have a mean old fucker tied to his shoulders, implied a certain ferocity. That, and silver where due, his big snow-white helmet of hair looked fleet as fuck. "Craven, Craven, Craven, you've let yourself go, m'boy! Look at that gut! Are you with child? Has one of those women put a baby in your belly?"
"You..." Maroto wiped his face with the back of his hand, blinked at the stony kid supporting his dad. Could it be? Could it not? Who else but... "Nephew?"
"Sullen," supplied Da, and right enough, the kid's mug tightened even more as he stared down Maroto. He'd earned that name, to be sure. Recognizing that other folk accompanied Maroto and they had stopped as well, Da switched over to Immaculate, probably trying to make his shaming all the more public. "He did what my own son was too _craven_ to try. He stayed with me, saved me, carried me home, tended my back when even your sister refused to help. Took on the wrath of every Horned Wolf to see me through. He's the son I never had."
"Damn," said Maroto, not put out in the slightest by his father's vitriol; how could he be, when it was proof that this was really his old man? That both of his kin had somehow survived that terrible day, in spite of his cowardice? The three of them had songs for one another, no doubt, but for now he raised a fist to knock against his nephew's knuckles for having the strength to do what he had not. "You're either crazy or stupid, kid—both times I broke clan law I took off with the quickness, and still barely made it out alive. Can't imagine trying to live a week around those arseholes once you got on their bad side, say fuck-all of coming up in the village, staying to earn a name and a few thaws after, to look at you."
Sullen didn't say a damn word, and didn't meet Maroto's fist, either. Left him hanging like a fucking punk. That would be enough for a fight, right there, between two proper Horned Wolves, family or no... but they weren't Horned Wolves anymore, not really. Maroto dropped his fist. Give the pup a bone and all...
"It's an honor to meet you both," said Purna, stepping up next to Maroto. "I am Tapai Purna, a—"
"Ruddy heretic!" gasped Da, pointing at the telltale horns jutting from the hood Purna had pulled back on her shoulders. "We're all exiles now, Craven, but to dress your grungy lover in the hide of your people? Where is your decency, man? Where is your _shame_?"
"I'm not his lover, and if you call me _grungy_ again I'll wear your skin instead," said Purna, as easy as she'd offered the introduction. Her hands rested casually on the hilt of her kakuri and the butt of her pistol. "Maybe bridle up that big boy of yours when I'm done—looks like you could talk a whole cart's worth of shit from up there, out of reach of repercussions."
Sullen's beefy fingers rolled up into fists, but Da just smirked and patted his grandson's shoulder. "Well, that's about as respectful a tone as I'd expect from one of Craven's confederates. I think I heard that a tapai is a prince of the Farthest Mountains, aye? Tell me Prince Purna, how much did your royal jester here trade you for that pelt?"
"She—" Maroto began, but Purna spoke for herself.
"Took it myself, not a week past. I'll fess your son helped, and our comrade Choi here, too, but it was me who delivered the beast back to the First Dark, so it's me who wears his crown. If you know my people, you know we don't wear what we don't kill... So are you an old fool who's forgotten what little he once knew, or are you just an asshole looking to get his face broken in?"
Da had his smile on now, the hungry one he wore just before taking a bite of you, but Sullen of all people intervened.
"Tapai Purna," he grumbled. "Grandfather's had his say, you've had yours, and all with ears ken the victor. Let it be enough."
"First my feckless son leaves me for dead, and now my grandson would light the pyre," clucked Da. "Very well, very well, peace to you, Prince Purna—after all, can't say Sullen here's had the opportunity to claim such a prize as you wear like a silk scarf wrapped 'round the fat neck of a trader's spoiled husband. Where we come from that means you deserve more respect than I showed ya. Peace to you, Tapai, from Ruthless of the Horned Wolves—we'll wrestle properly in Old Black's Meadhall someday, when I have my legs again."
Purna was clearly elated, but praise whoever listens that she held her tongue and bowed to the old windbag. It was queer as a devil's smile, seeing the kin he'd given up for dead so long ago, but queerest of all was that rather than feeling relief or joy he was just pissed off that Da was already being such a fucker, and his nephew was clearly harboring some hard thoughts toward him. All he could do was be righteous and hope for the best.
"Da, Sullen, I figure you already know the Crowned Eagle, since she led us here," he said. "And the rest of my crew's getting stitched up, but yeah, this here is Choi. She's wildborn, same as you, Sullen."
Sullen tensed up, maybe on account of his being able to pass better than the prong-horned Immaculate and riled that Maroto would out him so casually. The boy had grown into his huge, bestial eyes, so unless you were looking you might not even notice he wasn't strictly human. Choi came forward and offered a sharp, curt bow.
"Choi Bo-yung, Martial Guard to General Ji-hyeon," she said, her sharp little teeth clicking in that way Maroto was getting seriously into.
"Ain't wild," said Sullen defensively, though he had the sense to curtsy back. "No offense, yeah, but I'm shaman blood, not wild-what-have-you. Ji-hyeon, she speaks proud of you, ma'am. Honored to bow to you."
"You've spoken with the general?" said Maroto, wondering just what these two savages had told Ji-hyeon... and just what they were doing here in the first place, far as obvious questions went.
"Oh, they're right cozy," said Da. "Though the hours he's out, don't reckon there's a lot of talk involved, am I right, laddie? If that general was as serious about leading this army as she is about wooing him, then—"
And just like that, easy as skipping a stone, Choi's sword appeared in her hand. Sullen's jaw fell loose, the boy paralyzed with mortification. Chevaleresse Sasamaso stepped right up, too, the head of her glaive swishing down to point at Da's sneering face. The Crowned Eagle knight said, "I told you the last time, old wolf, what would happen if you disrespected our future queen."
"Last time?" said Choi, and that tore it, right there—you didn't say Ji-hyeon's chamberpot smelled of anything but fresh-baked cakes around Choi, not if you valued your vitals. Before Da could open his evil mouth again, though, another voice spoke, one that filled Maroto with relief. He was dreaming, was all, and since none of this was real there was nothing to be concerned with. Should've known, soon as the ghosts of his father and nephew appeared. Might as well enjoy it before he woke up, and he turned to her as she casually insulted him.
"A Maroto family reunion? I'd heard there were destinies worse than death, and now I know there's truth in the old sayings."
Usually when he dreamt Zosia, she was as he'd last seen her, young and hale, if haggard around the eyes by the long campaign to take Diadem, and then the harder campaign to rule the Empire after she'd won the Crimson Throne. In dreams her hair shone like its namesake, as dark a blue as the waters of the Bitter Sea crashing into the Noreast fjords, and she usually appeared in a similar garment to the chainmail kit her successor actually wore... if not significantly less. Choplicker rarely made an appearance in his dreams, thankfully.
Now, though, he dreamt Zosia as she'd probably be if none of the badness had ever happened—older and sharper, her hair molten silver instead of cobalt, those delicate lines around her eyes now spread down to the corners of her mouth. A simple hauberk, much like those she'd favored in the early days, hung from her broad shoulders, baggy woolen trousers in the Raniputri style bunched over her thick legs. And looking not a day older than the last time they'd met, Choplicker stood at her knee, offering a good-natured bark and then rushing him.
"Zosia." He breathed her name as a prayer to stay asleep a little longer, and dimly realized that Purna, Choi, and Sasamaso were all taking a knee at the invocation of her name, only Sullen too stupid to bow before her. It felt so good, he said it again. "Zosia."
She shrugged, her barely contained grin now sloshing out at either side of her mouth. Reflexively, his hands went down to push the snuffling devil away from his crotch, as though Choplicker were a real dog, and that was when it sunk in—the devil's nose was cold as the grave against his palm, the slobber that greased his fingers warm as a beating heart. He felt it, he felt everything. No dream, not even one bought from a centipede dealer, could be this real.
"You going to play with that fiend all day or are you going to give me a hug?" Zosia asked, that perfect smile that had become so rare in the last few years of her life now splitting her mouth wide. She stomped over to him in her heavy boots, instead of gliding above the hard-packed earth. Not a dream. Not a ghost. _Zosia_. She raised her arms, palms up in a _What are ya gonna do?_ expression, and Maroto took a breath, something he hadn't done since hearing her voice for the first time in twenty years. "You look like shit, old man, if I didn't—"
Maroto seized her in his arms, dipped her low, and kissed her full upon the mouth, the way he'd always meant to. She tasted of whatever curried lunch she'd had, of stale kaldi and stale tubāq. She tasted alive, and he kissed her harder, hands squeezing her as firmly as he dared, savoring this delicious moment of surprise before her tongue unlocked itself and kissed him back, kissed him the way she'd always wanted to...
Instead, she bit his tongue, jerked her head away, and kneed him viciously in the crotch.
# [CHAPTER
14](toc.xhtml#toc-chapter040)
Devildamn Maroto to the worst hell, and devildamn Zosia for thinking fondly of him, even once! She laid the lecherous bastard out on the ground, returning his saliva to him in a glob that spattered into a freshly scarred ear. He stared up at her, wide-eyed and stupid as ever at her response to his most unwelcome advances. She would have kicked his teeth in if a short girl with an awfully big flintlock pistol hadn't scrambled to her feet and pointed her weapon at her.
"You ever touch me again and I'll kill you, Maroto," growled Zosia, ignoring the gun-toting tot. "By the six devils I bound, I mean it."
Was he... was he _crying_? Maroto turned his eyes to the ground before she could be sure. On closer inspection he did look in a bad way, worse by far than any of the other Villains in general, and freshly torn up around the leg, arm, and face. Maybe she'd really hurt him...
Whatever, that was a long time coming.
"You didn't need to lay him out!" said the girl with the gun. "He's just happy to see you!"
"That excuse might work for Choplicker humping your leg, but I expect a sight more from anyone who walks on two legs," said Zosia, and let out a big breath as Choplicker growled at her suggestion. She couldn't remember the last time she'd stayed up all night planning out tactics; back in the Dominions they'd done their plotting by daylight, as chevaleresses deemed it dishonorable to do so at any other time. Glaring down at her old Villain, she saw he was still inspecting the dirt at her boots instead of apologizing. "Same old fucking Maroto, eh? Devils keep us."
"Captain," said one of the guards Ji-hyeon had assigned Zosia, "if I might show you to your tent now, I believe Maroto and Captain Choi need to report in with the general."
"Sure," said Zosia, sizing up Maroto's people. That stern Noreast kid from Ji-hyeon's tent was there, wearing a mean-faced old man like a backpack. There was another Flintlander, this one a chevaleresse in banded plate, and a po-faced broad with hair paler than Zosia's, and small black horns to boot. This last was giving Zosia the devil eye, an easy enough trick when you've got red eyes by birth. None of them said shit, though. Returning the wildborn's stare, she said, "You're Choi, then? On behalf of my fellow Villains I apologize for any harassment you had to endure from this creep whilst patrolling."
"Unnecessary," the woman said, her pointed teeth looking as sharp as her tone.
Well, all you can do is try to be nice. Zosia turned her back on them, Choplicker falling in with her and the guards. A cool cot in a dark tent was sounding even nicer than it had before.
" _Captain_ Zosia?" she overheard the Ugrakari girl mutter as she helped Maroto up. "Devils keep _us_."
Zosia knew better than to nap for more than a few hours. Between the position of the sun and the pounding in her skull when Choplicker roused her with a sticky lick to the cheek, she supposed he was actually honoring her requests for a change. Well, he might be in a good mood; the monster had eaten more over the last year than he had in the previous twenty, and with war imminent, he'd be feasting plenty more in the days to come. She'd barely finished getting up and packing a bowl before the guard outside called:
"A visitor for you, Captain."
"Care to place a bet on which one?" Zosia asked Choplicker. "You're not acting the piddly puppy, so it can't be Hoartrap. Maroto will need to have a proper drunk on before he shows his face again, so that leaves Singh looking to see why I was in the general's tent all night, or Fennec eager to learn the same. Hmmm. Coming!"
Yet, parting the flap, she saw it was none of the Villains, but that Ugrakari pal of Maroto's. The guard handled the introduction, since the fiery-eyed sprat didn't seem inclined. "Tapai Purna to see you, Captain."
"Royalty, to see a lowly captain?" Zosia winked at the girl. "Let's see a salute, Your Highness, and you can come on in."
Tapai Purna stiffly raised a fist beside her freshly washed face, and Zosia held open the tent for her. As rich kids went she looked ground pretty sharp, a poorly tanned horned wolf hide wrapped around her shoulders, the rest of her kit a motley, well-worn assortment of ringmail and spider lace, bronze caps and leather straps that probably passed for fashionable in this brave new world. She looked less like a tapai playing soldier and more like a soldier playing tapai. Nice legs, too, emerging from the bottom of her pelt—Maroto had an eye for quality, give the old dog his due. "To what do I owe the pleasure, friend?"
"I hope it will be a pleasure," said the girl, making straight for Zosia's table and plunking down a flask she'd had up her sleeve. "I've brought Immaculate peatfire and Madros sticks, if you'd care to break cork and wrapper with me."
"Quickest way to my good graces," said Zosia. "I can guess why Maroto sent you, so—"
"Maroto doesn't know I'm here," said the tapai, offering Zosia a cigar and flicking the end off her own with the blade of an enormous kakuri. Zosia was almost impressed—this generation of adventurers seemed harder than hers had ever been. Then again, they had stellar examples to follow. "He'll be even more ashamed than he already is, if he knows I came on his behalf. So unless you're an even bigger, sloppier asshole than everybody already thinks, you'll keep this between us."
"You're a real charmer, Tapai," said Zosia, putting her full pipe down on the table and accepting the cigar.
"Purna," said the girl. "Tapai's my mother, or my brothers. I'm just Purna to you, Captain. I didn't buy my way into this army, I earned it. Same as you."
"Same as me?"
"Those Raniputri who just arrived are yours, right? We've been watching you off and on for weeks, coming through the mountains. Assumed you were a mercenary vanguard of the Imperials you were ahead of, but I guess they were just chasing you?"
"That's the shape of it, but I wouldn't call the Raniputri mine. If anything goes cockeyed, they'll side with Singh over me."
"I wondered if that old knight was her." Purna opened the door in the hanging lantern and lit her cigar. As Zosia followed suit, Purna said, "So that means the only missing Villain is Kang-ho. Quite the reunion."
"I'd say his daughter fills in just fine," said Zosia, doing her best to downplay how fucking rapturous it felt to have a genuine Madros cigar back between her teeth. The strong, earthy black wrapper tasted like coming home. "She makes a better general than he ever would, that's for damn sure. Don't tell me you grew up on the songs of Cold Cobalt, too."
"Can sing them in three different dialects," said Purna, and there at the perimeter of the girl's hard-ass act was a quick flash of excitement, eagerness. "It's warm in here, mind if I shed my skin?"
"Sure," said Zosia, taking the girl's hood and slinging in onto her cot. Purna was boyish enough to give Zosia a nice little tingle, but nice little tingles quickly turned into queasy guilt as she thought of Leib. Tried to remember the sensation of his hands, really _feel_ them... and found that like so much else about him, she was losing that, too. He'd never begrudge her a fling, of course, not now that he couldn't help relieve her tension himself. He would want her to have some fun, forget her burdens for an hour or two, but knowing that only made her miss him more. Besides, the last person to give her a nice little tingle had stolen her pipe, the only thing of Leib's she'd had left, and now she was stuck with Maroto's discarded briar, and a cigar from Maroto's little friend. "What do you want, Purna? I'm a busy woman."
Purna laughed. It sounded almost real. "Anything I want, I take. You probably think I'm sniffing around for gossip. How's the Cobalt Queen still alive? Why are all the Villains back together? Are we on the cusp of another golden age?"
"And you're not a little curious?" Zosia opened the girl's flask, and when a glance at Choplicker provoked no warning bark, she took a deep swig. Like he'd told her the last time she'd been poisoned. Ah, smoky cigars and smokier peatfire for breakfast. Just like old times, right enough.
"Woman, I couldn't give a bad vindaloo shit," said Purna. "It's all _very_ exciting, of course, but I didn't come here to listen to you gloat about past glories, or promise me new ones. I came here to talk about Maroto."
"Look, girl, I don't know what he's whispered in your ear—"
"He hasn't whispered anything in my ear," snapped Purna, taking a puff to calm herself and then blowing a perfect smoke ring right at Zosia. "We talk. As friends. Comrades. And I can't say why you crawled out of whatever hole you've been hiding in, and I can't guess why so many of the Villains have assembled, but I know exactly why Maroto's here: because of you."
"Is _that_ what he told you?" Zosia passed the flask over and idled back over to her cot, sitting down with a grunt at the twinges in her knees and back. "It's bullshit, Purna. Nobody in this camp knew I was alive until I rode in last night."
"Exactly," said Purna, taking a pull and swishing it around her mouth before continuing. "We were way the fuck out in no-one's-land, past the Panteran Wastes, when he heard some bartalk that you were back from the dead and raising hell in the Empire. He fell for the same line most everyone has, thinking General Ji-hyeon was the dread Zosia returned. So Maroto led me and my friends on a tour of the whole fucking Star trying to find you, only to end up more miserable than ever when we finally caught up to the Cobalt Company a month or so back. Broke his heart all over again, and he only stuck around because he didn't have anywhere else to go, and I wanted to see what the mercenary life was all about."
"So?" Zosia looked up at the naïve girl. "Am I supposed to be touched?"
"So he's probably the only one in this camp who's actually happy to see you," said Purna, which put a run in Zosia's cigar, all right. "The others might be overjoyed to have a living legend roll into camp, because its good for morale and all that shit, but do you think anyone else cares about you? He's loved you since before I was out of short trousers, and when he finally sees you again he gets carried away, and you punk him in front of everyone!"
"Damn right, and I'd do it again without thinking twice," said Zosia, wondering how in all the Usban names for hell this runt had actually made her feel a stab of guilt for what was clearly a justified reaction. "Maybe he's changed in every other way a person can, but from where I sit he's an even bigger asshole than ever. I offered him a _hug_ , as I'm sure you noticed."
"Hugging's nice," said Purna, coming over and sitting down beside Zosia on the cot. Close enough to make a hard-up widow wonder, then looking sidelong at Zosia in a way that took a lot of the wonder out of the equation. "You've never got carried away, wanted something so much you didn't care who might be watching?"
Zosia glanced at Choplicker, who had the courtesy to totter off to a corner and sit down facing the wall of the tent. Damn, but Purna wasn't wasting any time—that was a welcome change of pace. If they were still talking about Maroto then Zosia was a devil's auntie. And if she was reading this wrong, better to get it cleared up now, lest she be strung along the way she had with Bang. Tossing her cigar on the dirt floor of her tent, she patted the girl on a convenient break in her armor between kneepad and mail skirt. Her flesh felt warm as the peatfire.
"Zosia," Purna said, her bangs falling in front of her eyes as she slowly leaned forward, tossing her own cigar onto the floor. "I didn't come here to..."
"We can have it any way you want, Purna," said Zosia, feeling her heart start to gallop as she caught a whiff of the girl's fresh sweat mixed with the smoky fragrances of Madros and the Isles. "I can talk for hours about what a bastard Maroto was, always with a smart word about my body, constantly trying to talk me into a pity-fuck, or you and me could pass the time some other way, maybe."
"You..." Something she'd said had snagged Purna just off the edge, and the girl took a swig off the flask instead of Zosia. Wiping her mouth, she sat up a little straighter. Away from Zosia. What the devils had she said wrong? "I mean, obviously, you and Maroto... you had something, once. Right? Even if you don't want to anymore?"
"So you would rather talk about him," said Zosia, wondering, hoping, praying, and doubting that by clearing the air where that pervert was concerned they could get back to whatever had almost happened. "Sure, we had something once—we were friends. Then he decided he wanted to fuck me more than he cared about most anything else, as far as I could tell. Hells, maybe we were never even really friends."
Zoisa took the flask back and emptied it before continuing. "You know he would never spar with me? Ever. Said he was worried he'd mess up my pretty face. So then I told him I only slept with those who had bested me in combat, and the next fucking day he had the dull irons out, pushing me to duel him. After that I had to fight him not to fight him, if you follow, but he never got lucky enough to beat me, praise the gods of steel. So that's what we had—a very, very sick relationship, contrary to whatever lies he told."
"He never _said_ anything happened," said Purna. She seemed as heartbroken as old Maroto, lying in the dust. Nothing less sexy than sadness. "I just thought he was being discreet. Romantic."
"Oh, girl," said Zosia ruefully. "Maroto's been called a lot of things in his day, by me and others, but I don't think he's ever been accused of either discretion or romance."
"Shit," said Purna, slumping a little. "Shit and damn. I really wanted to... Never mind."
"Really wanted to what, patch things up between us? You can't patch something that doesn't exist to be rent in the first place. And if you thought enticing me into some devil's three-way with you and him was ever going to—"
"Ew, no!" said Purna. "I do _not_ want that!"
"So if we're done talking about him, then..." said Zosia, giving it one last go and sliding her hand back onto Purna's leg. Even a low fire can be banked up after all.
"Shit shit shit," said Purna, scrambling to her feet. Her cheeks were as red as Maroto's had been when she'd rebuked his kiss. "Shit! Don't get me wrong, I'd love to, you're even hotter than I imagined. But... shit!"
"Purna," said Zosia, "take a deep breath, now. This doesn't have anything to do with anything; we're just two women talking in a tent."
"If you and he had... even once, that would be one thing!" said Purna, grabbing her hood from beside Zosia. "But I can't, not now. Of course he can be a creep, and a jerk, and a hundred other things, but he's also my best friend. I can't do this, much as I'd like to. It would kill him. Shit!"
"You don't owe him anything," said Zosia, but she could tell the girl was long gone, even as she stood there kneading her cloak in her hands. "Neither of us do."
"No," said Purna, all her boldness gone. "Please don't tell him we even... Bye!"
And just like that, Zosia was alone in her tent again. This was getting really fucking old—she'd never had so much trouble getting laid in her life. It was coming up on a year... from the first time on, had she ever gone a year? A month? Not a week, if she could help it.
On the bright side, according to Ji-hyeon the Imperial regiment pursuing the Cobalt Company was none other than the Fifteenth out of Azgaroth, led by Colonel Hjortt himself, so as far as the vengeance game went, Zosia couldn't have prayed for a better hand. She was keenly looking forward to seeing the thumbless murderer again, and breaking the shit out of her oath to kill him last—him, and his entire cavalry, and his big war nun bodyguard. It was almost too perfect an offering, a regular Kypck reunion.
Had Indsorith sent her pawns here as a sacrifice to appease Zosia, as though she were some ravenous devil that could be sated? Doubtful. It was far more likely the Fifteenth Regiment was set out as bait to draw her into a trap, but that was just fine with her—the Crimson Queen of Samoth wasn't the only one who could sacrifice an army for the sake of a personal vendetta, and if the Cobalt Company had a rough time of it when the battle raged, that was a small price to pay for vengeance against those who had killed her husband, her people. Then, long after the smoke had cleared and no sign was found of Cold Cobalt, the queen might be alone one night in her throne room, when an unexpected guest joined her...
Choplicker whined, and Zosia reached for Purna's smoldering cigar butt to throw at him when she saw the real cause of his outburst: Hoartrap had appeared in the opposite corner of her tent, smiling like a freshly freed devil.
"Just when you think it can't get any worse," said Zosia. "Don't tell me you've learned how to materialize out of thin air."
"Would that it were so," said Hoartrap, wiping dust off the front of his robes. "I unpin tent posts and squirm under just like everyone else, I'm afraid. The key is doing so when the occupants are too busy to notice."
"There's mercy in hell, then," said Zosia. "I don't suppose you can conjure some booze?"
"Ah, now there is a trick within my talents," said Hoartrap, removing a small bottle from the cavernous pockets of his saffron robes. "Care for a puff as well as a tipple?"
"Since it worked out so well the last time, why not?" said Zosia. With a sigh, she looked at Choplicker. "Fine. You're off until he is, but if I catch one word that you've been into any mischief at all—"
But the devil didn't wait to hear the rest of her oath, shooting out of the tent and away from the wizard as fast as his legs could carry him.
"I don't think he missed me," said Hoartrap. "A pity, I've thought of him often since you both disappeared."
"All right, Hoartrap." Zosia hopped up from her cot in a quick, pantherlike motion that she'd be feeling in her hips for hours to come. She strutted toward him with a bravado that felt as patently false as Purna's, hoping it wouldn't come down to her and Hoartrap. Hoping for once Choplicker hadn't strayed far. "I need you to be totally straight with me for the first time in your miserable life. Did you put those Imperials onto me at Kypck, or was it the queen? Lie to me and it'll be a lot worse for you."
"I never even suspected you were alive," said Hoartrap, patting a hand to his breast. "I swear it on all the devils I've eaten. Don't think I didn't check, either! Choplicker kept you well hidden—did you manage to bind him a second time, or did he do that out of love?"
"He tricked me," said Zosia, relieved to feel all the fight slough out of her. "Kept me hidden, all right, just as long as it suited his needs. Wondered why he stuck around for nigh on twenty years after I offered him an out, and now I know—he turned it down. You ever hear of a devil saying no to an easy wish?"
"No," said Hoartrap, scratching at a boil on his bullish neck. "Which makes one wonder if the wording of your wish was such that he honored it without your notice, and is indeed a free devil. There are songs of ancients in Emeritus who befriended devils, rather than binding them."
"If that were true Choplicker could do whatever he wanted, whenever he wanted," said Zosia. " _There's_ a cheery thought."
In a great swirl of robes, dust, and mighty-thewed legs, Hoartrap sat down on his ass in the middle of the tent. From an inner pocket he removed the pipe Zosia had carved him thirty years past from a black gnarl of nigh-petrified oak he had brought her, claiming to have dredged it from a swamp. It took ages for that oak to dry, and the peaty bouquet of the bog never quite left the wood, but Hoartrap seemed delighted in the result. The downward curve of its yellow horn stem was inlaid with leopard palm where it joined the black oak shank, the wood carrying downward another inch before swooping back up and out into a bowl shaped like a half-bloomed tulip. The rough stratifications of the unique wood made it look less like a pipe and more like a grotesque snail shell or ebon stinkhorn. As he packed the piece from a ratty leather purse, he said, "We have so, so much to discuss, old friend."
"Mmmm," said Zosia, retrieving from the table the bowl she'd packed earlier. She remembered how touched Maroto had been when she'd given it to him at that kaldi house back in Linkensterne, just a year or two before he helped her become Queen of Samoth, Keeper of the Crimson Empire. "Another time, old Touch, I'm about talked out at present. You amenable to a more meditative meeting?"
"Oh sure," said Hoartrap jovially. "You know I love nothing more than sitting and staring silently at you for hours, occasionally murmuring portentously."
"So long as you don't talk," said Zosia, canting her pipe to accept the floating flame Hoartrap offered her. Light. Puff. Tamp. Light. Puff.
That order.
As far as plans went, this one succeeded wildly, and Zosia settled back on her bed with a groan. What a fucking day. The best part was that even after staying up all night with Ji-hyeon planning strategy, even with the better terrain, she was still unconvinced any of their tactics could overcome a much larger force with military experience—the Imperials had the numbers, like they always did, and even with that green kid Colonel Hjortt leading them, the new Cobalts were still in for one tearjerker of a song. She had helped talk Ji-hyeon into throwing down here and now because if the Cobalts carried the day, she could have her vengeance on both the cavalry that had slaughtered Kypck and the colonel she had foolishly let slip through her fingers, but if the Cobalts couldn't pull this off, it might be one of her last days on earth.
And how was she spending it? Sexually frustrated, smoking a pipe that she had thought peerless when she'd carved it but now saw it for the crude work that it was, a pipe that was burning far too hot due to the Oriorentine blend having dried out in her purse. Her only companion was the evilest man she'd ever met, and adding insult to injury, his bottle contained crème de violette and his pipe smelled more flowery still, packed with a mixture of astringent, powerful tambo and some soapy brown flakes that made the whole tent reek like a geriatric's perfumed undergarments. Cold Zosia, former Queen of Samoth, this is what a year of hard work and heartache gets you: exactly what you deserve.
Just like old times, sure enough.
After a substantial interval of pungent contemplation, Hoartrap broke his promised silence. "Want to go to a party later?"
# [CHAPTER
15](toc.xhtml#toc-chapter041)
There had been times when Domingo hated his son. Not the sort of thing any father cares to admit, but there it was. No matter which way you sliced it, when you got to the bone of the boy you found marrow of the purest yellow. Efrain Hjortt wasn't just a coward, either, he was also a weakling. And a sniveler. Hard as Domingo had tried to help the lad become worthy of his mother's house, firm as the Azgarothian Academy had been with the boy, nothing seemed to help—he had the spine of a jellied eel, and the vicious selfishness of a living member of that species. Away on campaign for months at a stretch, if not longer, Domingo saw the boy grow in great bounds, but never to discernible benefit. Each time he returned and saw Efrain the boy's sneering smile was broader, as was his belly, but while he eventually became somewhat adequate with a sword, there was no doubt this indolent teenager would never be fit for commanding anything more important than a dinner party. He wanted to blame his sister-in-law Lupitera for retarding Efrain's maturity, he wanted to blame Concilia for casting off her family and moving to Trve, but at his heart Domingo knew that his son's weakness stemmed from neither the influence of his aunt nor the absence of his mother.
Yet still he had told himself his son would come into his own, that all he needed was that push into the saddle. And Domingo Hjortt, decorated Colonel of the Crimson Empire, Baron of Cockspar, a shrewd ruler in peace and war alike, was totally, utterly wrong. For most of the boy's life, Domingo had vacillated between lying to himself about Efrain's quality and despising the child for possessing none. What a waste.
Now, as Domingo lay broken and battered in the back of a wagon, bouncing down a seemingly eternal mountain road, he was done with delusions about Efrain, and all that remained was hatred. Efrain was the reason he was here, and thus Efrain was the reason his left hip had shattered under a horned wolf's headbutt. Efrain was the reason he'd lost all feeling in his right arm. Efrain was the reason half his head was so swollen from slamming face-first into the ground that he still couldn't see out of one eye, a full week after the attack. Efrain was a chump who never should have been in charge of a modest kitchen, let alone a regiment, but that was no excuse for getting himself wrapped up in ridiculous plots and then murdered for his trouble.
Really, how did any ranking officer get himself killed, in this day and age? Once again Efrain had scraped new lows, bringing his aged father down with him, and the only way for Domingo to restore his honor was to avenge his son. He was as bound by familial duty to catch Efrain's killer as Efrain had been to lead the Fifteenth, come to think it, both men destroying themselves in the name of the other, and there was another nasty bump in the road to aid him in shedding a few tears over the tragedy of it all. If only Lupitera had been here to witness it all, she'd have given him a standing ovation—the shows down at the Iglesia Mendoza didn't have a red herring on the drama of the Hjortts.
Unlike most of those tragedies, this bit of overwrought theater would have a happy ending: drenched in blood, the old hero unmasks his enemies, and executes most of the cast. His maneuver with the Immaculate prince turned out to be unneeded, but then a little comedy to break things up always made the serious bits hit harder. To think he had actually been worried that the pope was wrong, that all the rumors were false and Zosia was as dead as she deserved to be. That this new Cobalt Company was just a band of phonies, led by the runaway Immaculate girl that Prince Byeong-gu had been chasing. Funnier still, even in his current condition Domingo was relieved to know that the Stricken Queen had indeed cheated death, that she was the one who had murdered his son, that she was the one who had ordered the horned wolf attack on his camp. Even without catching her old Villain Maroto sneaking past his tent, Domingo would have recognized that insane tactic as bearing the stamp of Zosia—no one else in all the songs of today, tomorrow, or yesterday would have dared such a deranged, suicidal maneuver.
Much as it hurt to admit it, he could learn a trick or two from his blue-haired archenemy—her gambit had paid off. Even if she had sacrificed a few soldiers in the course of luring the monsters down from the mountain, the Fifteenth had lost over a hundred foot soldiers, fifty-some archers and gunners, and their two best witchborn guards... and that wasn't even getting into the Ninth's losses, or the horses the retreating wolves had carried off when their blood thirst was sated, or the panic that the attack had caused. Another fifty soldiers had deserted that very night, and running them down and hanging them had wasted a full day they should have been on the march. How do you wage war against such madness? Countering with some deranged, devilish maneuvers of his own was just the thing to bring Zosia down for good, and make it take this time... Not like he had much to lose, unable to ride a horse of his own and needing an anathema to help him so much as take a piss. As the Burnished Chain became increasingly popular in the Azgarothian court as it did everywhere else, Domingo's insistent hewing to the godless ways of his ancestors was viewed as increasingly eccentric, so it would probably come as quite the relief to everyone back home when they heard he had destroyed the Cobalt Company with the help of the church.
"Sir?" Splayed in his deep nest of padding and pillow in the wagon bed and unable to move his neck without extreme distress, Domingo kept his gaze on the crimson twilight leaching into the high peak looming over them but knew who had ridden up beside him without needing to see her.
"What is it, Shea? I'm a very busy man."
"The witchborn scouts? They've returned with news."
Domingo closed his eye, speaking with more patience than he thought he possessed. "And what is the news, Shea?"
"The Cobalt Company, sir? We've found them. They appear to be fortifying a camp?"
"Where?" Domingo's heart soared into the darkening sky; he had anticipated another agonizing pursuit all over the Star, but maybe twenty-odd years on, Zosia was as tired of running as he was of chasing her.
"Where the road comes down into the plains? They cut north as soon as the ground evened out enough for their wagons. Their camp is where the foothills back into some famous mountain... It's called the Lark's Tongue?"
"I've ridden past it," said Domingo, remembering, remembering... "Good position. Not great, but good. Steep ridges come out on either side of where they'll camp at the base, so we won't be able to flank them, but that also means they'll have nowhere to run—the mountain's too sheer to safely climb away." Thinking, thinking... "Smarter than I thought. The Cobalt Company's burning their boats so the volunteers can't flee if the battle takes a turn. She's transforming her little blue mice into cornered rats. Just when I think I've got you figured out..."
"Sir?"
"Just pondering, Shea. A colonel mustn't be afraid of a good ponder from time to time." It wasn't right, her digging in for a last stand already. Zosia was changing up on him, so he would have to do the same to stay ahead. "How far are we from their camp? At earliest?"
"If we go the usual extra hour tonight? We're overlooking the plains now, so we should be down by late afternoon tomorrow, and from the foothills another solid day will take us within engaging distance. But we're still waiting on the all clear from Diadem, and the last owlbat we received from Colonel Waits said that the Third are still most of a week out from—"
"If I wanted to know where the Thaoan regiment was I'd have asked, Captain, and as far as the queen's written permission to engage the enemy goes, I daresay it's a bit late to get hung up on every formality," said Domingo, his mind swooping through the haze of time and memory and toward the silhouette of the Lark's Tongue overlooking the Witchfinder Plains. Cold Zosia wasn't the only one who could pull a trick to surprise the devils, and while he certainly hoped the Black Pope's weapon proved as devastating as advertised, a little insurance never hurt. "Inform the men we'll be stopping in half an hour for dinner."
"Very good, sir, an early night will still put us—"
"Three hours' rest, cold rations, and then we're marching through the night—just like the old days," said Domingo, wishing he could crane his neck to catch Shea's frown but wanting to save his strength for rarer game. "We won't catch the Cobalt Company with snoring troopers, Captain. Now find Colonel Wheatley and have him join me on the command wagon. There's a certain suicidally risky tactic I need to consult with him about."
"Sir?"
"Slip of the Lark's Tongue, Captain," said Domingo, groaning as the wagon bounced and his entire body warred to see which bit could cause him the most discomfort. "Be a good officer and keep it to yourself, lest I find myself in need of volunteers. By the time Waits limps in from Thao we're going to have every Cobalt head on a pike, save Zosia's—that one's going back to Azgaroth in a box. I'm going to mount it over my son's tomb."
"Zosia, sir?" Shea sounded as incredulous as she always did when he mentioned the Stricken Queen, like her old colonel was going soft in the helm. "You don't think the rumors—"
"You don't think at all, if you know what's good for you," said Domingo. "You're a soldier, damn it, not a bloody philosopher. Now fetch Wheatley, and bring along Wan, too—when you're bringing hell down on a pack of sinners, you can't have too many devils to help deliver the goods."
# [CHAPTER
16](toc.xhtml#toc-chapter042)
The villagers Heretic impressed from the nearest hamlet brought a wagon with them. Portolés and the corpses of the other clerics all went into the bed, and then they were brought back downstream and taken over a rattley bridge. They passed through the hovels clustered on the riverside and then left the road, bouncing over a marshy field until they reached a great heap of wood the local children had gathered. The corpses went onto the pyre, and then oil went onto the corpes, and then the morning sky was obscured behind a wall of black smoke. Half-conscious in the back of the wagon, Portolés imagined she could see the Sunken Kingdom rising out of the mists of the Haunted Sea, but when a gust parted the smoke she saw it was just the thatched roof of a nearby hut on the far side of the pyre.
As her brethren burned, Heretic led the villagers in a bizarre dance around the blaze, the billowy cassock hanging off his lanky body making him resemble a living scarecrow. Portolés assumed it must be some pagan rite, but found out later that Heretic had successfully passed himself off as a brother of the Burnished Chain and told the ignorant villagers they were helping him in a funerary ritual for fallen clerics. He thought this a lot more amusing than she did. He explained all this in a hut set back on the willowed banks of the Heartvein, after the local mudhusband had tended to Portolés with a liberal mix of medicine, miracles, and mummery.
Heretic kept up his deception for the length of Portolés's recovery, and lest she give the game away, he only removed her gag at mealtimes. He told the mudhusband she was the ringleader of a renegade band of heretics, and must be healed in order to stand trial in Diadem. Portolés's former prisoner had quite the time of it, dining and gossiping with their elderly host and the man's daughter, dozing his days away by the river with a bottle of their best plum brandy, explaining that he couldn't offer any prayer services in the village as he was a war monk, better suited to acts of worship unfit for a friendly town. Portolés lay locked in the root cellar, alone with her prayers.
"Don't think they believed me, mind," said Heretic as they walked their horses around a frozen bog on the misty morning when they finally left. "Sure they saw right through me, but were happy enough to help the revolution, so long as they could honestly deny it after the fact."
Even without the gag Portolés wouldn't have spoken. Partly to deny Heretic the satisfaction, since he seemed of a mood to keep her as oblivious to his intentions as she had kept him to hers. Partly because riding a horse was agony, a perpetual stitch in her side and a tender throbbing in her guts and mangled hand. The stab wounds to her chest hurt like the worst kind of penance but had failed to puncture a lung, praise the Fallen Mother, and cinched as it was against a wooden brace, her broken arm only hurt when she moved. All told, she felt worse now than she had lying on the twilight butte, unsure if Heretic planned on returning.
"You know what he said, old Dafhaven back there? He said you were lucky he was also an animal mender, or he wouldn't have known what to do with you. Said under the skin you were more beast than woman, and that's what saved you—said a real person got worked over the way you did, their vitals would be too bad off to tend. Praise the Black Pope you were born a monster, yeah?"
The gag was so tight it hurt to smile, the straps cutting into the corners of Portolés's lips. For a time the only sound was of hooves cracking through hoarfrost and ice-capped puddles, frozen reeds snapping off against their flanks. On the far side of the fen they rejoined the road, but only long enough to cross it before plunging back into the cold, damp woodland on the far side. Heretic knew enough to keep them off the highways, after what had happened on the butte, and lest they encounter more agents of the Chain, he had them both change out of their robes and into plain linen and wool garments. Portolés had never felt so naked and vulnerable as she did in the heavy peasant's frock Heretic gave her, but it also brought the familiar tickle of the profane to her breast. She had no idea what gear remained on the pack mule, if her writs were safe, but she noticed he had salvaged her maul. A fine omen of his intent, that. Maybe.
"You know, when we first set out I wondered if you were one of us," he said when they'd made camp for the night on a soggy knoll jutting up from another expanse of miserable marshland. "There's a bigger concentration of support in the Dens than anywhere else in Diadem, you know that? Might seem odd to a pious maid like yourself, but a lot of your kind aren't happy with being called anathemas, treated worse than devils, by the same church that expects them to die in the name of the Savior. To sacrifice your whole life, serving an institution built to oppress you... Hey, are you asleep?"
Sitting with her back against the stump he'd chained her to, Portolés opened her eyes and gestured at the gag with her manacled hands. When he frowned across the small fire but did not rise to remove it she closed her eyes again. He could talk, but he couldn't make her listen—something he'd taught her, early in their acquaintance. Then she heard him squelching toward her, and held in a word of thanks as his grimy fingers pried the gag out of her mouth.
"I'm right curious, as you said back on the hill," said Heretic, holding a waterskin to her lips. She took it, and didn't spit it out when she tasted the sweet and flat barleywine of the Heartvein provinces. No sin there, so long as she didn't ask for it. "Denied it at first, so's not to give you the satisfaction. Wasn't planning on coming back for you, neither, not at first, but when I hit that river town a couple leagues out I couldn't help myself. Wasn't just that you saved me from the Office of Answers, or just that you'd fight your own kind without so much as squeezing out a fart by way of parley... But both together, well, that'd raise the interest of anyone. I can't read the hightalk on those documents you flash around whenever someone gives you lip, but I recognize the Royal Crimson Seal from the warrants they waved when they arrested me. So what is it you're after, Sister Portolés? What's your mission, up in the Isles, and now taking us all over the Empire? Why'd you bust me out, and keep me with you this whole time, instead of bringing along Imperial loyals, or Chain folk? You really one of us?"
"Cut this gag off for good and I'll tell you," said Portolés. Heretic considered this, then shrugged and sawed it off with the same knife that had punctured Portolés's bosom. He tossed the hated thing on the fire, her saliva popping and hissing as the gag twisted in the flames like a serpent. "All right, Heretic. You have many questions, but I'll do my best to answer some of them."
"My name's Boris, damn your tongue," said Heretic. " _Boris_. After all we've been through you could do me that courtesy, calling me by the name my mother gave me."
"I took you with me because the Fallen Mother put you in my path," said Portolés. "I fought my brethren alongside you because the Deceiver turned them against me. What I am after, my mission, as you say, is to do the will of the Savior, be it in the Isles, the Empire, or in hell itself. And as for whether I am, as you say, _one of you_ , well, only the Fallen Mother or the Deceiver can say for sure—we are all mortal wretches born to die, _Heretic_ , so in that respect, yes: I am one of you."
Heretic shook his head, frustrated as she'd yet seen him. "You... you've either got a better sense of humor than I expected, or you're even crazier than the rest of your kind."
" _My kind_ meaning anathemas? I told you, Heretic, I am one of _you_."
"Your kind meaning Chainite crazies. It'll go better for you if you're up-front with me, Portolés, here and now, before anyone else gets involved."
"That sounds awfully familiar," said Portolés, enjoying herself for the first time since the Battle of the Butte. For all his high and mighty posturing, as soon as he had the chance he'd treated her even worse than she'd treated him. "I wonder where I've heard that sort of talk before. Oh yes, it was in the Office of Answers—the Askers said something similar to your friends. How many of them confessed, I wonder. And how much of a difference do you think it made in the end?"
"Try to be nice..." Heretic shook his head. "Just to show you I'm not the same as Imperials, or war nuns, for that matter, I'll keep my word where the gag's concerned. But when I turn you over you'll wish you'd leveled with me."
"I don't doubt you, Asker Boris," said Portolés, denying him the satisfaction of her asking whom he intended to turn her over to, and in the process giving herself a faint and fleeting thrill. "And I thank you for your mercy. Now, shall I take first watch, or did you have more questions for the accused?"
Heretic didn't have much else to say, either that night or the ones that followed, and as they broke away from the river and moved west Portolés contemplated the best way to escape. Outside the city of Black Moth she almost managed it, when he left her chained around the trunk of a cypress in the surrounding woodland before riding into town. By the time he got back, laden with supplies, she had sawn partway through the tree with her chain, her wrist dripping black in the light of his lantern. He sighed theatrically and moved her to a bigger tree before settling in for the night. She'd assumed he'd be meeting with other traitors, tracking down underworld sorts who would have a standing bounty on Imperial or Chain officers, but he'd come back far too quick... meaning he'd just been restocking on food and beer, as he'd said.
"You're a naughty nun, no mistake," said Heretic. "You know they call this place the Haunted Forest? I hurried back on account I was worried for your safety, leaving you tied up in such a place."
"My savior," said Portolés.
"Only one you'll find in these woods. Here, thought you'd find this interesting." He passed over a torn flyer, and by the light of their fire she saw two familiar words blackening its surface. Even now they made her throb with something approaching awe. She looked Heretic in the eye. "You believe, do you?"
"I believe in what she stands for," said Heretic, setting their camp cauldron on its tripod. "Got you some bean mush and weeds, since I know how much you hate the saltpork we've been living off, pious girl like you."
"And what does Zosia stand for, then?" Portolés thought she had a fair understanding already, but it never hurt to ask for more details. "Freedom from the yoke of the oppressor? For your comrades, anyway?"
"Freedom for all," said Heretic. "No gods, devils, nor other scapegoats. No queens, popes, nor other vampires. Just people, helping each other."
"And if you have to kill a few hundred thousand people who disagree with you, well, that's not a bad cost, is it?" Portolés rather enjoyed playing his part, could see the sport he'd found in baiting her. "Open your eyes, Heretic; she was just another despot, peddling the same old story under a new name. Nothing more."
"Nothing less, either," said Heretic, looking up to where the paltry light of their fire faded into a darkness that was all the deeper for their having kindled a flame. As if he saw the answer there, in the night, he said, "Thing is, sister, I'm beginning to wonder if some of the crackpots in our party weren't on to something. The ones who say she's still alive. People really believe it out here in the Empire, too, you can tell they do—maybe she's rotting in some Diadem dungeon. Maybe death was too good for her, by Indsorith's thinking. When the overlords start reading your tracts instead of just burning them, you have to wonder..."
Portolés did wonder, as she had most every day since setting out, how Heretic would react if she told him the simple truth: Zosia lived. This knowledge she so easily carried within her sullied, bestial body was a weapon so powerful it might change the fate of the Empire, the fate of the Star. She had stumbled on a secret, _the_ secret, and through the trust of her queen, an anonymous anathema had become transformed into a force of unspeakable influence. Like all weapons, she could be destroyed or cast aside, but if she could reach Zosia in time and convince her that the queen hadn't ordered Hjortt to attack Kypyk, she could win a war before it was even fought. Not bad for a chained-up witchborn who still had nightmares of screaming peasants dying under her orders.
"You've got that look again, Portolés," said Heretic, watching her closely. "That look like maybe you know something of what I speak? Like maybe that's why you wanted a rebel to ride with you, and not just because you could rely on me to fight any Imperials or Chainites that came after you. You wanted an expert on all things Cobalt."
"Now what would make you say such a thing, Heretic?"
"You're the worst damned bluffer I've ever seen. Here's a confession for you, sister, and it's been a long time coming..." Portolés perked up, couldn't help herself. "That book you've been reading down to the fibers, the one you took from the Office..."
"The one you wrote, Heretic?" Portolés hungered for his revelation the way she still hungered for Brother Wan. "That book?"
"That's the one," said Heretic, and like many who offer a confession, he looked half gleeful, half disgusted. "I didn't write it. Haven't even read it. Was an old bird in our party, Eluveitie, was working on it. She was in the Asking Chamber, too, though I didn't see where."
"Confession sets us free to see the Fallen Mother," said Portolés soberly, liking Heretic more than ever. "Did you take the credit to spare her especial attention from the Askers, or to gamble on finding yourself a way out?"
"I..." Heretic spit, which gave her answer enough. He didn't know himself. "Doesn't matter. We'll both hear some answers right quick, sister. Some lasses I met in town said they'd been hunting along the front of the Kutumbans, but beat it across the plains because the Cobalt Company's pitched a camp right in front of some mountain they call Bird Tongue."
Portolés felt the darkness at the edge of their firelight contract, as though the night itself had held its breath. She'd prayed, of course, prayed hard and long that Heretic would take this road. He was curious enough that it seemed possible, but she hadn't let herself believe, not until she heard the words from his own lips, but now that he'd said it she knew there had never been a question. What Queen Indsorith had planted inside Portolés could only be released when she met Zosia, and recognized her for the old mayoress. Then and only then would Portolés ascend from too-faithful servant and admittedly lousy messenger to savior of incalculable lives. Or destroyer, it was all a matter of perspective—once Zosia heard that the Black Pope had probably sent Hjortt to murder her husband and raze her town, would she seek an alliance with Queen Indsorith to go after the true perpetrator? Would the information Portolés delivered prevent the coming war between the Cobalt Company and the Crimson Empire but bring about a final, fatal civil war between the Empire and the Burnished Chain, with Zosia's army marching alongside Imperial regiments? Would she prevent an imminent massacre, only to cause a greater one? The seed cannot predict if it will become wheat or snakeroot, or what use its crop will be put to...
"You all right, sister?" Heretic looked concerned, but not concerned enough to leave his steaming stew pot.
"Never better," said Portolés, wiping tears from her cheeks. "You mentioned... the Cobalt Company?"
"Aye, I'm sure you've heard enough to know the stories behind them. A flesh-and-blood army led by a blue-haired ghost. If you believe the legends, which I'm not so sure I do. Whoever truly leads them, though, they'll be happy to have a war nun delivered to their door, especially one on a secret mission for Diadem. Seems like my people back in the capital have the same enemy and the same strategy, so why not throw in with these Cobalts?" Heretic watched her intently. "Nothing to say to that?"
Portolés fought to keep the relief off her face. She should have just freed Heretic from the onset and followed him after her quarry, trusting that higher powers had set him in her path as a human bloodhound. The uncertainty of what would happen when she finally caught Zosia filled her with unspeakable raptures, uncertainty about whether she brought miraculous peace or delivered infernal war, and she shuddered against her bonds. "I say you were dead right from the first, Asker Boris: we'll both have some answers before much longer. Now what do you say you loosen these chains enough so we can play some cards?"
# [CHAPTER
17](toc.xhtml#toc-chapter043)
Maroto's wounds hadn't festered and none of his bones were broken, but other than the barber's welcome report he didn't have much to feel good about. Of all the hells he'd waded through, of all the nightmares he'd lived, he'd never imagined one as dread as this. Zosia, beautiful, brilliant Zosia, alive... and she hated him.
Well, to get real about it, that wasn't quite right. But bloody well close enough. If she'd hated him she would have thought of him from time to time. This was so much worse—she'd been off somewhere for twenty years, doing devils knew what, with devils knew whom, and she'd never once dropped him a clue that she was still alive, because he didn't even warrant her notice. If he'd died back when she was Cobalt Queen—or if he'd seemed to, anyway—she wouldn't have carried a candle for him, wouldn't have missed him every day, the way he had for her. She didn't give an easy shit about him. Never had, like as not.
"Come on, old man, I thought it was your kin over there they called Sullen, not you!" Diggelby swayed in front of the bonfire, dancing shapes limned against the night behind him. He held out a bottle, and Maroto took it, though he'd already drained enough to fell a dozen lesser drunks. Scowling across the fire at him was Sullen, though the pup hadn't brought Da to the party. Maroto waggled the bottle at his kin, who spit into the fire and looked away. Right, it was time to get something more than a shit-eyed stare out of that punk, find out what his beef was, and how bloody a cut it was...
"Whoa, steady on, man!" said Diggelby, catching Maroto as he took a wobbly step and nearly pitched into the fire. "Here, you lazy lumps, clear a seat! Dance for your captain's pleasure, or pay the price!"
Din and Hassan dutifully rose from a nearby divan, clapping Maroto on the back and saying the sort of overly cheerful crap you always fed to people you felt sorry for. Maroto wondered if there was a single cart horse or guard dog that hadn't heard about his encounter with Zosia that morning. Collapsing onto the couch, Diggelby pressed something into his hand. Something wriggling.
"A graveworm. Magica, the best!" whispered Diggelby. "It's good for what ails you, Captain. Just make sure not to chew it!"
"Know what to do with it," grumbled Maroto, the old hunger upon him as soon as he felt its carapace in his palm. It'd been right around a year since he'd been stung, so a graveworm would be just the creepy-crawly to ease him back into the habit... Though at his prime he'd gulped a dozen at a time, when he couldn't find bees or centipedes, and barely felt a thing.
"Good chap," said Diggelby, doing a clumsy Mustakrakish two-step away from the recumbent Maroto. "Don't forget who gave him to you, once the cryptcrawler's in your legs and you're ready for a first dance!"
"Uh-huh," said Maroto, opening his hand and watching the graveworm squirm in his fist. Purna bumped into Diggelby, danced off him with far better moves, and after a few twists and turns, she practically fell on top of Maroto.
"What've you got there, Moochroto?" she asked, sitting on the arm of the seat and rubbing his shoulder. "Whoa, hey, Diggelby give you that? No call for that shit, man, you told me you were off the bugs for good."
"Told you lots of stuff," said Maroto, admiring the way its papery shell shimmered in the firelight.
"Yeah, you did," said Purna. "Look, I know... I know it sucks, right, but banging bugs over a girl? That's not your style, Maroto. You're better than that."
"Better than what?" sneered Maroto, and popped the graveworm into his mouth. It tickled his tongue, and he dry-swallowed it, savoring the way it fought against the inevitable even as it went down. Just like people, bugs were, once you got acquainted with them. He regretted it even before Purna bolted up, slapped the back of his head.
"I love you, man, but you need to grow the fuck up already," she snapped.
"That's rich, coming from a brat who wants to play war because she thinks murdering people's a laugh." He regretted that, too, but she didn't hit him again. If anything, she softened a little.
"Look. You decide to stop feeling sorry for yourself tomorrow, let me know and we'll split this waste before lunch. Go to any Arm you want. But I won't ride out with a stinghound. Think about it, Maroto—adventure with me and the gang, or kill yourself with bugs because you can't let go of a dream. It's up to you, buddy."
"Yeah?" Getting the fuck away from here definitely sounded like a plan.
"Yeah. You take tonight to throw yourself the biggest pity-party you ever had, and in the morning we go. Promise." She looked like he must, heartbroken for no good reason, and, giving his hand a squeeze, she set her shoulders and got down to some serious dancing.
Maroto felt better already, the graveworm hitting him harder, faster, meaner than he expected. Good old Diggelby probably had a crate of cemetery dirt loaded with the things, and once they were free and clear of the Cobalt Company, who knew what sort of sport they could find? Ride over the mountains and knock off some Dominion stinghouses, set up a mobile operation... invest in a rolling aquarium like they'd had in the Wastes, but stocked with centipede warrens. Ooh, or maybe combine the design with an ice cart to keep the icebees cool, have a whole bloody apiary on wheels. Nice.
And there she fucking was again, appearing by the fire with Hoartrap. Girl knew how to suck the air from a party, bringing that monster. She caught sight of him, and he bobbed his bottle at her, fully expecting her to turn away, give him the low visor all night. That was how she'd always played it in the old days, after a kind word or gesture on his part got taken the wrong way. Instead, she made a beeline for him, and he hauled himself upright to meet her charge. Get ready, you fuckers, the night's entertainment has arrived, another stupid fight for no reason at all...
"Hey," said Zosia, standing in front of the divan. "Got enough room for a big-boned broad on that couch?"
"Sure," he said, wondering if the graveworm was giving him the walking dreams. Eat enough of those things and you'll see all kinds of shit. "Yeah, definitely."
She sat down next to him, stiff as a lance. She was stiff, like, not him... Devils, but this worm had turned since last he'd gulped one; he could barely keep his thoughts out of his mouth, or his mouth out of... Devils. He took a pull from the bottle to sober himself up, tasted every grain and hop that had gone into the pale Raniputri ale, handed it to her. She took a swig, then another. Smiled at him.
"Sorry about earlier," she said. "I'm... shit, man."
"Yeah, definitely," said Maroto again, nodding. "I mean, me, too. I was... I was excited to see you, was all. Didn't mean anything by it."
Her look told him this wasn't quite doing it, so he dug deeper, tried harder, hooked some of the stuff Purna had laid on him earlier that afternoon in his tent.
"Nobody likes getting grabbed like that. I wouldn't, Diggelby kissed me like that. Me being happy to see you's no excuse."
There was the smile again, and she huffed in that cute way that let him know they were in the mend-things-up stage, and in record time. Maybe she _had_ missed him! "Which one's Diggelby?"
"That crustfop, dancing with Purna."
"Wow. Yeah, he looks terrible."
"Diggelby's all right. They all are. Solid."
"So it's true, then?" Zosia took out a pipe and pouch from her hip-bag, blind-packed it while overlooking the crowd of revelers. "Mighty Maroto took a pack of princelings under his wing?"
"Kids saved my life, no joke," he said, nervous she would ask him what had happened to the briar she'd carved him.
"I heard you lot saddled up a pack of horned wolves and rode them into an Imperial camp last week. Any truth in that?"
Maroto laughed, almost couldn't stop, then calmed his happy arse down. "Not much. A good song, though."
"Definitely," said Zosia. "Be right back, I'm going to get this going. You have one you want me to light?"
Shit shit shit. Anxiously scratching the side of his flattop, he inadvertently dislodged a cigarillo he'd bummed off Din earlier in the evening and tucked behind his ear. Salvation! "Sure, fire this dog for me."
"And I thought you only sucked sticks for coin," said Zosia with a wink, and headed over to the fire. She still had those legs, and her arse had filled out nicely, still tight with muscle but widened with age. Dark thoughts, Maroto, dark indeed—she looked a sight better than he did these days. When she returned, he took the cigarillo and puffed contentedly on it.
"What's with your kid? He got it in for me to make a name for himself, or what?"
"Kid?" Maroto followed her gaze and saw that Sullen was still glaring at them. Hard to believe it possible, but the kid looked even meaner, now that Maroto had some company. "Nephew. And I'm the one he's coming hard at."
"Yeah? The way Choplicker's been nodding at him, I thought for sure it was me he was sore on, for some reason I've long forgot or never knew. That ball-licking devil's always liked you, though, so maybe that's all it is, Choplicker looking out for his old litter mate." Zosia waved at Sullen, beckoned him over, but he pretended not to see her. "Aw, he's playing hard to get. Think you're going to live another night, Maroto."
"Scary fucking savage is giving me the death eyes and she says it's nothing to worry about." Maroto shook his head happily. He had half a mind to go give Sullen a hug. "Where is Slopchops, anyway? Didn't used to let him out of your sight."
"You know how they get when Hoartrap comes around, decided to go easy on him," she said, the unasked question of Crumbsnatcher dangling between them. Let it fucking dangle all the way down to the lowest hell. "Anyway, what's the nephew's story? That your dad I saw riding him before?"
"Yeah, that's Da," said Maroto, trying to blow a smoke ring and fucking it all up. "Still haven't figured out what their song is. That was the first I knew they were alive, when you decided to haunt my arse. Hadn't said ten words to 'em, and haven't said one since."
"No shit?"
"Not even a toot," said Maroto, delighted to see her shake her head and grin at his wit. "They were the whole reason I cut out on my clan the second time 'round, you know? Thought about it lots, sure, but never would have left if..."
"Second time 'round? You went back?" She poked him in the ribs. "Come on, dish."
"Shit, where to start?" Where to start indeed—maybe with Zosia playing him so hard he'd wrecked his life trying to avenge her, when she hadn't even had the decency to really die? He had half a mind to make her sing first, but this was his couch, sort of, and that made him host, and hosts take the first round. Some rules can't be bent. "Um... okay, yeah, so a ways back, I... I got burned out on, well, everything, so I decided to head back to the Savannahs. Go home, you know? Start over."
"You always said they'd kill you if they ever saw that ugly mug again." Zosia blew a perfect smoke ring with those perfect lips.
"Oh, they wanted to, and they would have, definitely," said Maroto, feeling the glares of the Horned Wolf council burning at him from across time and space. "But I figured the one thing that would settle me with the old bastards who run the clan was a big show of contrition. Of the physical sort, yeah? So I brought along what was left of my nest egg and laid it at their feet, told 'em that ever since I ran away as a pup I'd been working up enough dosh to come back and atone. Wonder of wonders, they let me back in."
"Some things are the same the Star over."
"True. I had to duel the meanest Wolf in the clan, too, but I think Da went easy on me, so it weren't no thing." Weren't no thing but a mark on his belly where his father had nearly gutted him in the honor pit, but what family didn't leave its scars? "Um, and since I'd left before I'd earned my name, I had to take the one they decided on for me."
"Which was..." From the gleam in Zosia's eye he wondered if she already knew.
"Not important. Anyway, after all that, I was a Horned Wolf again. Was _weird_ , you know? Going from who I was when I rode with you, sleeping in palaces, to sharing the old floor cot with Da and my sister and her babe... That'd be Sullen, there, when he was but an ankle-biter. Sweetest kid I ever saw, too, wonder what soured him so."
Except Maroto knew, of course, knew without a doubt: it was him. Who else? The closer he got to folk the deeper their frowns, and you don't get closer than blood.
"I gather your retirement didn't go much better than mine," said Zosia, teasing him like she always did with the promise of a good song.
"Definitely not. At first things were better than I expected—I wasn't just trying to fit in, I was trying to be the best Horned Wolf in the clan. Followed every little rule." Which was true to the letter; the clan never imagined a Horned Wolf would intentionally stick his arm in the hives on a daily basis, and so there was no law forbidding it—why get yourself stung when the snowmead they produced was a far milder and nicer buzz? Da had told Maroto only the shamans of old ever let the icebees kiss their flesh, bringing them portents in peace or vigor in war, so the first time had just been an experiment, see if the bugs of his people were anything like the stinging insects he'd used a time or two during the Cobalt War, when one of the Villains needed field surgery but didn't need to feel it... Turned out icebees agreed with Maroto like few things ever had, rendering the sharp memories of his murdered beloved and his failure to avenge her into a dull dream, transforming a washed-up loser who did nothing but ponder the mistakes of the past into a proper Horned Wolf who pondered nothing at all, doing only what was expected of him—he'd floated through his days and nights in the Savannahs like a man resigned to drowning, drifting through the numbing depths of the freezing sea...
"You still with me, Maroto?" said Zosia, nudging him with the bottle.
"Sure, sure," said Maroto, accepting the warm beer and draining the witchpiss in the bottom. Damn graveworm hadn't ridden him this hard since he didn't know when—the kids must get better bugs in the old capital than he'd ever been able to afford. "Just getting my thoughts sorted. See, I did some dumb stuff after you... after I thought you died. Felt pretty low, and wanted to prove to myself I could still be of worth, somewhere, to someone, even if it was just the craziest fucking clan on the Noreast Arm. And I fell right back into it, which was even stranger because some of my people had converted since the time I'd left."
"Converted to what?"
"The Chain, man, the Burnished Chain—you believe that shit? While I ran off to raise devils in every other Arm but home, some missionaries had worn down the council, struck some deals to get a church built right back behind the meadhall. Craziness."
"Something tells me the Noreast denomination is a little different from what they practice in Diadem," said Zosia.
"Not as much as you'd think! But yeah, they hadn't gone all the way over, still kept a lot of the old ways... which was just confusing 'cause Da _hated_ all that shit, so he'd be lecturing me on how I was a disgrace to the clan at the same time he'd be running the clan down for allowing the conversions. And I..." Was high as balls constantly. "... wasn't quite myself, 'cause I was trying to play it straight as a Horned Wolf when there was some debate over what that even meant anymore, so when shit went down and I had to make a choice, I fucked it all up. Bad. Like, the worst."
"The Mighty Maroto made a mistake?" Zosia dug around under the divan and retrieved another of Diggelby's bottles. "I don't believe it."
"This was epic even as far as my fuckups go. We were warring with another clan, some devil-worshipping nutters called the Jackal People who guard the Noreast Gate. Scary bastards, pale as snow and twice as cold. They'd been stealing some of our people, throwing them through."
"Damn! They tried that shit on the Horned Wolves?"
"Not more than the once." Maroto grinned. "We brought it down on them, hard. Sullen there was his dad's knife-bearer. Couldn't have been more than six or seven. It got bloody, as war does, and we won, as we usually did. But Sullen's dad got killed, and Da took one square across the back, the kind that kills slow—the Jackal People grease their swords with this pepper oil, so it's even worse than it sounds. Just wrecked his arse."
"Damn. Takes a special kind of asshole to poison up before a battle."
"Yeah. I wanted to carry Da back, see if we could mend him, but Horned Wolves... It ain't done. So we left him, and when my nephew wouldn't leave his granddad's side, we left him, too. Left them to the ghost bears and snow lions and any of the Jackals who fled that might come back and find them."
"Cold. That doesn't sound like your people," said Zosia. "Doesn't sound like you, anyway."
"Horned Wolves are fucking savages," said Maroto bitterly. "Crowned Eagle People, Walrus Folk, Snow Lion Tribe, Orcas, and a hundred other clans are all decent, and I don't have to tell you that the free cities of the Noreast Arm are the most civilized on the Star. I mean, West Mastodon's as stunning a metropolis as any in the Isles, and the poet-philosophers of Reh give the Raniputri a run for their hemlock... But the Horned Wolves are just as barbaric as the Troll Lions or Jackal People, only difference is they gave up on human sacrifice. Last week, sure, but they did away with it."
"Wait, your old man and the kid were _sacrifices_?"
"They wouldn't call it that, but yeah, that's about the shape of it. No such thing as a crippled Horned Wolf, or an old one—you can't run with the pack, you get left behind it. It's fucking stupid. And I was wigging out, big-time, Da screaming his jaw off from the pepper in his spine, Sullen just staring up at me with his witchy cat eyes, and I didn't know what to do. I didn't have any fucking idea. But then my sister said good-bye to her son and our father, going back with the rest of our people, and I told myself if she could walk away from her own child and the dad who praised her every day of her life, I ought to do the same to a nephew I barely knew and the old man who'd never wasted a breath whistling he could use on running me down. I left them, Zosia, left them to die."
Even without the graveworm making him all emotional he would've needed a minute then, watching Sullen watch him from across the party with murder in his leonine eyes. Zosia puffed her pipe, let him come to it in his own time, instead of pushing him like the other Villains would have. Devils, how he'd missed her.
"I went back for them, Zosia, I did." Maroto closed his eyes, gritted his teeth. "Three days later. Took me that many nights of lying awake all night, hearing Da screaming in my ears while my sister slept like a babe, that many days of folk finally treating me with respect around the village, to figure out what you've known since I first started talking, what I'd known when I'd quit them the first time—the Horned Wolves are fucking crazy. And crazy as I was right then, I wasn't crazy enough to ever be right with that kind of bullshit. So I left. Again. For good. But I ran all the way back to the Jackal People's lands before I did."
The cigarillo had gone out in his fingers and Maroto flicked it away.
"I figured I'd give them... an apology, if they were dead, or take them with me, if they'd managed to live. I prayed, Zosia, for the only time in my whole fucking life, I actually prayed they'd lived out those nights, prayed to my ancestor Old Black, prayed to the Fallen Mother, prayed to darker things best left unnamed—anyone who would listen. Even told Crumbsnatcher I'd let him go if I got back and they were waiting for me, offered him his freedom if I trotted onto the battlefield and even just my nephew was sitting there, alive and hale and able to come with me. Should've known when the rat didn't take the cheese that it was hopeless, but I prayed on...
"The lions and vultures had been all over that field. Da and Sullen weren't the only ones whose bodies were gone. And I knew if I'd worked up the courage to do what I knew was right a few days earlier, they'd be alive. I could have kept them safe. So I said a few empty words, shed a few guilty tears, and said good-bye to the Savannahs. Some Horned Wolves came after me near the border, trying to cut me down so I couldn't shame them twice by leaving again, but they couldn't catch me. I hit the Body of the Star and never looked back."
Maroto took the bottle Zosia offered him and drained the whole thing, not noticing it was one of Hassan's nasty sour ales until the contents were in his belly.
"Who saved them, then?" Zosia asked. "You know that much?"
"They saved themselves, I guess." Maroto smiled across at Sullen, a real warm smile, but the kid just stood and walked off into the night. "Sounds like Sullen dragged Da all the way back to the village as I was getting up the moxie to leave, and then they got back right after I left to look for them. Wide as the Savannahs are, we missed each other, two riders in a fog going different ways. When they returned, the clan couldn't very well deny them their place at the fires, seeing as they'd pulled themselves back on their own, but I imagine it wasn't the welcomest way for Sullen to come up. Horned Wolves don't appreciate being proven wrong. And now they're here. That's all I've got."
"That's enough," she said, and when he felt behind his ear for the cigarillo he'd already smoked she passed him her briar. Zosia was always good that way, too good to an arsehole like Maroto. Another storm of wizard fire exploded in his chest as he realized her pipe was the same tankard shape as the one she'd made him, the one he'd lost or sold or broken while he'd been so strung out he hadn't known his arse from a hole in his heart—Zosia had carved two identical pipes, then, one for herself and one for him, something she'd never done for any of the other Villains, something he had never even noticed, too busy eyeing her haunches or tips to look at her personal briar. She had cared about him, even if it wasn't in the way he'd hoped. Still did, to see the emotion on her face as he put his lips to the black stem, shivered to taste her saliva and the tang of tar on the end of the pipe. The graveworm did its dance in his belly, from one pole to the other, happy then sad then happy again.
"You need to talk to them, Maroto. You tell it to them like you did to me, not a word out of place, and you'll need to come up with another name for that kid, because Sullen won't suit him anymore."
"Yeah, I will. Tomorrow, when I'm clearheaded." Of course, being off the bugs so long he'd be all kinds of hungover, but another worm from Diggelby would help get him up and able—only cure for a graveworm before bed was another one for breakfast. After that, though, he'd be done with 'em for good. He'd promised Purna, and a man has to keep his promises. "What about you, Zee? Never heard how you came up."
"Hmmmm," she said, not looking any more amenable to the topic now than she had the dozen times he'd tried to pry it out of her over the years.
"Hey, no need for that face." The last thing he wanted was to spoil things, now that they were looking up. He gave her back her pipe with a final twinge. He'd smoked plenty of tubāq since losing her gift, but never from a pipe—penance for his folly, and smoking a pipe was a lot easier to give up than the bugs that had caused him to lose the dearly loved briar in the first place. "How 'bout the song of your resurrection, then? What the devils happened, Zosia? Did they lock you up in Diadem instead of icing you? Or have you been in on this new Cobalt Company scheme from the get-go, biding your time, waiting to spring from the shadows like the Allmother returned? Both?"
Shit, that hadn't been a wise move at all—she looked even unhappier now, but with a big sigh, laid it on him: "I chickened out, Maroto, after that first year on the throne. I _fled_. Made it look like I died so no one could come after me. Set myself up with a new life. Our victories and our failures, _my_ failures, I tried to put it all behind me. Should've known it wouldn't work."
She was quiet, and as much as Maroto knew she'd prefer to come to it in her own time, his mouth did its thing, as it always did, when he had the worm in him. It was the graveworm's fault, not his. "So what, you caught wind of Fennec's play and couldn't resist coming out of retirement? Setting the record straight? Having one more adventure? Trust me, I can relate, even after I found out it wasn't you leading the new army, I stuck around for my buddy Purna's sake, and now that we've been up to our old exploits my taste for the stuff is coming back in a big—"
"They killed my husband, Maroto. Our whole village. Children. Animals. Everyone."
Shit. Shit shit shit. No damned wonder she didn't welcome his kiss, she was in mourning, she—
"I thought it might have been one of you," she said quietly. "Not you, obviously—you were the only Villain I was sure about, Maroto. And now I'm sure it wasn't any of the others, either. I was right from the start: Queen Indsorith went back on her word. Gave me enough time to hope it had worked, gave me enough time to relax, really invest myself in a place, in people, let me believe I had won... and then she did me just like I did her. She must have led a happy life before I became queen, before my efforts to fix the system wiped out her family, and nearly killed her, too. So when it was her turn to be queen she gave me a happy life, and a family, and... and then gave me exactly what I deserved. Just over a year ago, now."
"Wait, what—the queen? She did that? I don't get it..." Maroto struggled for something, anything to say. "... but I don't need to. I know you didn't deserve that, though, nobody deserves that."
"No, they don't," said Zosia softly, looking a lot older right then. "A lesson I learned too late."
"She double-crossed you," said Maroto, the graveworm making him smarter, sharper. "You gave her the Crown to leave you alone, and she double-crossed you. That's what happened."
"Yeah," said Zosia. "That's it. Pretty damned simple."
"And now you're going to get her, right? Now you're going to teach her what fucking wages Cold Cobalt pays a double-crosser, yeah?"
"That's the idea," said Zosia, scratching her silver hair. "Cold Cobalt returns, and all of Samoth trembles."
"All of the fucking Star!" said Maroto, standing up. "We'll make the world remember us! Make the devils shrink back into their holes! Kick the Crimson Empire's teeth in! Yeah?"
"Yeah," said Zosia, getting up, too, and handing him her pipe. "But in the morning. I'm dead on my feet. You want to finish this?"
"Sure, yeah," said Maroto, taking it greedily, when a dire thought reasserted itself. "Except... shit."
"Shit?"
"Shit shit shit!" Maroto wheeled around and stomped the divan, meaning to splinter it in his rage. His heel bounced off the springy seat and he fell flat on his back, his busted knee throbbing. Brays of laughter from a dozen arseholes looking to get their heads split, but score one for Maroto: he'd made Zosia smile again as she helped him up.
"You doing okay, oh conqueror of ales?"
"Yeah. No. Look, Zosia, after I heard you died, I did something stupid. Really stupid."
"I heard you fought the queen," said Zosia, not even trying to hide her smile. "Despite the express orders I left that my Villains were to serve her in my stead."
"Orders don't mean shit," said Maroto. "I mean coming from you, of course they do, but how'd I know they weren't fakes? Anyway, I played it all wrong—left Crumbsnatcher out of it, got her to take me on in a square duel. I won, I won. And she won, I'd pledge not to hassle her ever again. And... and..."
"And the girl can fight, can't she?" Zosia stood on her tiptoes and kissed Maroto on the cheek. It was the first time her lips had ever voluntarily touched him, and it felt better than anything he'd ever won or stolen. "We'll figure something out, Maroto, we always do."
"Yeah," he said, relieved he hadn't wrecked the divan as he collapsed back onto it. "We always do."
"Oh, and try not to lose that again," Zosia said, winking at him, and it took Maroto a moment to realize she was talking about the pipe in his hand. What? No, it couldn't be... But turning the pipe over for the first time since she'd let him hit it, he saw that the bottom of the bowl still bore the two marks she had carefully etched into the wood all those years ago: a Z, for the carver, and an M, for the intended owner. His hands started shaking so badly he nearly dropped it, and he looked up at his old friend with tear-filled eyes, wondering how in all the devils she'd found it, but not wanting to risk breaking the spell by asking.
"I've been a fool," was all he could manage, but it seemed to be enough.
"Every day since I've known you, but then you've had ample company."
"Maybe..." Maroto rocked his head back and forth, but nothing shook loose. "Maybe I'll have a better comeback in the morning."
"It's really, really good to see you, Maroto," said Zosia, turning away, but at her words the graveworm turned to ice in his belly, spreading its chill to every part of his body. He felt sick. "Sleep well, brother."
He couldn't respond, couldn't do anything but cling to the pipe he didn't deserve and sink into the divan, shaking all over. He watched her go, watched Cobalt Zosia, the woman he loved, sway over to the fire and exchange a few words with Singh and Fennec, and then disappear back into the camp. But she had been here, beside him, no vision nor ghost, but Zosia. And maybe it was the graveworm and maybe it was some sick game of the devils, now that the bargain was fulfilled, but he knew beyond any doubt at all that this was what Crumbsnatcher had given him in exchange for his freedom. Maroto was on the divan in the center of the Cobalt Company and he was simultaneously in a Pendleton stinghouse, strung out on bad bugs, pressing his lips to his devil's velvety ear, whispering the words that had doomed them all:
"Bring her back to me. Just let me see her again and I'll let you go. Please, please, just bring her back to me."
And Crumbsnatcher had granted his wish, just like devils were supposed to. The rat couldn't resurrect someone who had died—that was the one wish not even a devil could grant—but reuniting two old friends would be short work for a creature that could see into the future the way mortals look into the past. Zosia thought Queen Indsorith had ordered her soldiers to go after her as part of a long-simmering revenge plot, but Maroto was sure Indsorith had only sent her assassins because Crumbsnatcher had made the queen think it was a brilliant idea. The queen, or someone else, it scarcely mattered—whoever had decided to target Zosia and her people, they had only done so because Maroto's devil had made them. Everybody had heard songs about devils planting evil thoughts in the minds of mortals, and even if a devil couldn't make you do something that wasn't in your nature, the Star was brimming with bloody-handed reavers who wouldn't take much more than a nudge to go after a vulnerable village, the Queen of Samoth included.
Maroto was coming up on a year clean of the bugs—well, he would be, if not for tonight's one-off—but point being, it was last autumn that he had sobered up one morning and discovered Crumbsnatcher missing. Zosia had said her husband and all their people were murdered around that time. It was the only explanation; Crumbsnatcher had burrowed into someone's brain and made them decide to kill Zosia's people... Hells, the executioners might not have even known it was Cobalt Zosia they were targeting.
Zosia was ready to tear the Empire apart for vengeance against Queen Indsorith, and she had just kissed Maroto on the cheek. Maroto had as good as slit the throat of Zosia's husband when he'd loosed his devil, as good as chopped down anyone else who had died along the way. He had destroyed the world of the woman he loved more than his own life, and all because he was so fucked up on bugs he'd made a wish that no sane mortal would ask of a devil: to bring back the dead.
"Bring her back to me. Just let me see her again and I'll let you go. Please, please, just bring her back to me."
# [CHAPTER
18](toc.xhtml#toc-chapter044)
Grandfather said the Old Watchers only took notice of humans when they were bored and in need of sport, and this was the same reason mortals first turned to the devils. Grandfather said it was up to shamans to interpret the words of the divine as they came down through the rustling of leadwood leaves in autumn and new grasses in spring, to unravel the whispers of the infernal from the crackling of a wildfire some hot summer's night, or read the lacing of ice on a chamberpot some cold winter's morn. Grandfather said when a devil spoke a mortal listened, but only a shaman could reply. Grandfather said when a god spoke only a shaman could hear, and a wise one wouldn't talk back.
But Grandfather also said the tastiest treat under heaven was creamed honey badger, and Sullen knew for a fact that shit was _nasty_. And Grandfather also said the Horned Wolf way was best, that all other peoples of all other lands were wicked or corrupted or dastardly or just plain arseholes... But if that was true, and the Horned Wolves were the chosen people, why had they been so down on Sullen and Grandfather? What did it say about _them_ , that the Horned Wolves had hated them so much they'd tried to kill them rather than just letting them go?
And sure, getting really real here, but what did it say about Sullen, that he kept deferring to Grandfather even though the old man seemed increasingly full of shit? When they'd finally found Uncle Craven and Grandfather had somehow used the opportunity to talk shit about Ji-hyeon even as he was exalting Sullen, had Sullen ripped the old baggage off his back? Other than their first night in camp he hadn't once given Grandfather a talking-to about respecting the woman he already intended to pledge his service to, come what may with his uncle. It had always seemed easiest to just ignore his crotchety ancestor, but maybe by doing so he was just feeding the fire of Grandfather's hubris. In any event, he wasn't doing himself any favors, letting Grandfather poison everything with that tongue of his.
It was time to talk to the old man, Sullen decided as he walked back to their tent. Grandfather had ordered him to follow Uncle Craven that night, to see what sort of a man this "Maroto" really was. From Sullen's reconnaissance, he seemed to be about the same as any other, still glum from his earlier shaming at the hands of Zosia, and hoping to hasten the healing process by slathering himself in drink, smoke, and companionship. Yet when Zosia had joined Maroto on his couch by the bonfire, Sullen decided he had enough to worry about for one night.
At least occupying himself with stalking his shady uncle and the woman a god had ordered him to kill took his mind off Ji-hyeon, and the return of her handsome lover.
Good for her. Good for both of them. He wanted her to be happy, after all. It's not like it would have ever worked out, a savage wooing a princess... Except for a minute there it had seemed like the princess was intent on wooing the savage.
Sullen realized he was approaching her tent instead of his own and abruptly changed course, much as he wanted to stroll past and see if lamps were lit inside. Would it be better if they were, if the sounds of talk and laughter came to him, or if all were dark and quiet?
Anyway, he had more important things to think about. Like thwarting Zosia. That was how the Faceless Mistress had put it: thwart her. That could mean damn well anything. Didn't have to mean murder. Then again, it might...
The rub was, he didn't feel much compulsion to do anything, now that he'd seen the woman in the flesh. He'd expected to feel some deep urge, some need to throw her down and do the god's will without a moment's hesitation... But he was having a real devil of a time getting too worked up about it. He didn't want a bunch of kids to die, of course, for a whole city to be consumed by liquid fire, but being real with himself, the whole situation made him melancholy rather than righteous or wroth. He mostly wished Zosia had never shown up at all... and not just because she had brought Ji-hyeon's lover back to her. He was happy for Ji-hyeon. _Delighted_ for her.
He bumped into a pack of drunken, reeling soldiers and muttered an apology he didn't really mean. What a bullshit night. Here he was, halfway across the Star from the Savannahs, having traveled as far as any hero in the epics, and he felt just as small and stupid as he had back home. He could recite a hundred ballads, could tell you how Old Black had outwitted the sea devil of Zozobra, of Rakehell's lusty adventures in the Lair of the Minotaur and how he'd escaped that monster's bed, but when it came to his own song it was like he'd forgotten the words and bungled the meaning, clueless as to what canto ought to come next. They always seemed to know what to do, his ancestors, ready with a quip or a stab in just the right ear, learning from their mistakes and outfoxing their enemies... Yet Sullen could barely figure out where to take a shit without upsetting someone in this bustling camp of exotic foreigners, and if you don't know where to attend such basic business, what hope is there for navigating the real challenges set before you?
Maybe that was the problem—maybe Sullen was just in the wrong sort of song. Maybe instead of a great warrior or trickster his lot was always to play the dullard, bumbling into trouble to the amusement of any listeners. The Song of Sullen Half-wit, the Horned Wolf without a brain in his skull or a fang in his jaws. There was a song he could hum by heart, even if the words escaped him...
Stalking back to his tent, he saw Grandfather still set up in front of the small fire he had built for the old man before going after his uncle. Great.
"What's the word, laddie?" Grandfather asked as Sullen steadied himself and stepped out of the shadows.
"Nothing, Fa." Giving him a talking-to could wait until morning, or longer—why ruin a perfectly bad night by stirring up Grandfather? Sullen dipped into the tent, and closed his eyes in impotent frustration as the old man called after him:
"Come on out, laddie, we need to talk. Got a beedi rolled and ripe for the ripping."
Sullen fished around in the dark tent until he found his bandolier of sun-knives, then a water jug, and then a strip of cured horse to snack on, and only when he couldn't stall any longer he came back out and sat down heavily across the fire.
"My, but you're in a mood tonight," Grandfather said when Sullen took out a whetstone and set to sharpening the multiple blades on each of his branching knives.
"What?" Sullen said around a mouthful of meat, not looking up from his work.
"I don't expect nor welcome all the gory details of your courtship with that prissy girl, but if you want to tell me what's irked—"
Sullen stood, letting the bandolier fall into the dirt save for the knife he gripped in his fist. "Last time, Fa. Blood or no, last time. She's got a name. And she deserves better from scrawny old dogs she gave a place by her fire."
Grandfather sneered up at Sullen, but for once he didn't say anything smart, just gave a curt nod. That would have to do. Sullen sat back down as Grandfather set a braid of pinestraw aflame and lit his beedi.
"Shall we talk about your uncle, then?" said Grandfather, holding in his smoke and offering the smoldering cone. "Or that Zosia woman?"
Sullen turned down the sweet-smelling saam, much as he wanted it. He couldn't stand to be any closer to Grandfather at present. "Whatever you want. They got right, looked like. Drank 'round a fire. Like you do."
"Well, touching as that is, I'm mostly curious as to why you mean to murder them both," said Grandfather, taking another long pull, his fingers as dark and wrinkled as the leaf between them.
Sullen went all chilly, didn't know what to say. "Huh?"
"Huh," said Grandfather. " _Huh_. You might be black as the god of the Jackals to these pasty-arse fools, but you're clear as branch water to me, pup. You've been killing them with those lion eyes of yours ever since you first peeped 'em, same as you've been doing something else with your eyes to that... to General Ji-hyeon Bong, Second Daughter of Jun-hwan and Kang-ho, Future Queen of Samoth, and however the rest of it goes."
"You think if I give 'em a look it means something?" said Sullen, embarrassed that Grandfather had seen through him so fast and so sure. Embarrassed, and maybe a little relieved. It was the scariest thing out there, keeping your own counsel when affairs got complex. "You think if it _looks_ like I give 'em a look, it means shit?"
"Heed me, Sullen," said Grandfather, but for a change his tone seemed conciliatory instead of chiding. "Whatever else they are, neither my son nor that friend of his are stupid. I seen what you were thinking, and you weren't even thinking it at me. I'd tell you to be wary, except I respect you too much to treat you as a child. You know what you're about. But I've been sitting here all night pondering your surly mug, boy, and for the life of me and the life of your mother, I can't reckon why you mean either of them trouble."
"For serious?" Sullen stopped sharpening his knife. "After hearing you yuck-mouth him every day since I can remember, you don't know why I aim to kick Uncle Craven's arse? You and Ma been telling me how bad he needs it since before he even left us! Probably whispered it to her belly before I even busted out, before he even came back."
"Ahhhhh," said Grandfather, puffing on his beedi. "That's it, then. You're _still_ sore on him for leaving, eh?"
"Him leaving don't mean shit," said Sullen, wishing there was a way to make the words sound proud instead of petulant. "Good riddance. I mean, _we left_ , didn't we? And we left on account of you thinking he did right, cutting out on the Horned Wolves that second time."
"I know what I think about my son, Sullen. I'm asking what you think, though I can guess."
"That's fleet," said Sullen, shaking his head. "What do I think, then, since you already know all?"
"I think it's the particulars of how he did it," said Grandfather, and there was some comfort there to soften the sting. Horrible a bastard as Grandfather could be, he was good, loving, and understood Sullen in ways he didn't always understand himself. "He cut out on us, left us to die on that battlefield, and all because he chose to stand with the Horned Wolves instead of his nephew. Instead of his own dad. We needed him most, needed him as much as anyone could ever need his kin, and he sided with the clan over us. That'll happen. My daughter did the same, which I don't reckon you need reminding of?"
"Nah, it was different for her," Sullen said quietly, still hoping after all these years that this time it would ring true to his ear. "Whole different thing."
"Sure it was," said Grandfather in a way that told Sullen the old man wanted to believe every bit as much as his grandson. "I don't reckon either of us can blame your mom for leaving us there, walking off with her brother and the rest. Shit, she's more Horned Wolf than anyone on that damned council, so her doing it the old way, that's fair. And what makes it so different, what this whole oryx chase comes down to, is that when you drug me back home after the battle, she was still there, part of the clan as always, but your uncle was long gone. And all these years later you're still raw-hearted he didn't stay with us—he was cutting out anyway, why not do it a day or three earlier, rather than leaving his kin to die on account of a principle he never lived up to nohow? That about the shape of it?"
Sullen eyed his shimmering reflection in the blade he held, nodded. "About."
"Yeah, I've wondered that, too," said Grandfather, and it felt like cold creek water washing the dust off your face to hear the old man admit that he didn't know everything. "Every day since it happened, and every minute since I looked him in the eye this morn. _Why_. Thing is, laddie, I don't think he knows himself."
"That makes it all right?"
"Hells no! But you always know why you do something, Sullen? I sure ruddy don't, and I've had a good deal more thaws than you to get the measure of myself. What matters is that you, me, him, we all got the same idea, sooner or later, that those we came up with, those we'd given our lives to, they weren't worthy of our love, and so we all cut out on what the Horned Wolves had become. And now that we've finally run him to earth I think we owe our blood enough to put the question to him, and see if he can do better now than he did then. What happened when we were Horned Wolves means as much as yesterday's morning shit; what matters is what we do goin' forward. We're family, Sullen, and if that doesn't mean something, then we're no better than the rest of our clan."
It was quiet for a spell after Grandfather's wee speech, and Sullen put his knife down and went around the fire to sit beside the old man. Taking the dead beedi from him, he relit the half-burned saam and took a deep toke. Kept it in, absorbing the smoke along with the old man's words. Grandfather, man, that guy knew some stuff. Exhaled, and let out some of the bad air he'd been holding for most of his life. "You want to go have a verse with him now? I can take us."
"We weren't the only ones he'd given up for dead," said Grandfather. "If even one of those songs we heard about the two of them on the road here has even one honest refrain, they'll be talking till dawn. Him and that Cold Zosia are tendin' to their business, we'll let them tend. You're just hard on her 'cause of how she did your uncle this morn? You might hate him, but don't like seeing your blood whooped in front of half the camp?"
"Her? That? Nah." Sullen took another hit, held it till his eyes watered. "She... You don't wanna know."
"Thank the false gods and true ancestors I got a grandson so wise he knows me better than I know myself," said Grandfather, taking the beedi back. "I shiver to think what I'd do, I had to have a thought of my own."
"Nah, Fa... She... Look, you told me you didn't want to hear none of what that Faceless Mistress I met in that big-arse spooky temple had to say. The Soueast Arm, remember?"
"You think I'm so dotty I can't recollect where we was when you met a god?" Grandfather looked down at the beedi and then passed it back without taking a hit. "I wondered, after. Ever since, whenever we heard the name Zosia you got a hungry look on you. Hells, even the Horned Wolves knew about the Cobalt Queen, but you never seemed to take an interest in those songs... until that Emeritus temple. Yeah, I wondered."
"So you want me to spit or not?"
"Not, not," said Grandfather quickly, raising his palms. "These ears have done well by not having the words of the gods pass through them. But..."
"But?"
"But there's a lot of gods, Sullen, many more than just the Old Watchers who made our ancestors. The Star's got more gods down here than there are birds in the heavens, even with the Chain spreading their One True Faith shit all over. It ain't wise to rile any of them, sure, but that don't mean you have to take a knee before them all, or you'll never be able to stand on your own."
"But you always said a shaman had to listen, and I'm not saying that's what I am, but... shit, Fa, I don't know."
"Listening is always good," said Grandfather, staring off past the fire, into the dark between the tents. "But that ain't the same as always doing what you're told. You done that, you would have left me on the field and gone home with your uncle and the rest, and neither of us would be here right now."
Sullen nodded. He nodded a lot when Grandfather spoke. How the devils had Old Black or Rakehell gotten along so well without an ancestor to help them? "So... so as far as Zosia goes, what the Faceless Mistress said about her..."
"I told you, boy, I don't know, I don't want to know, and I don't envy you the burden you were born to. But where the gods are concerned, be very, very careful. You think Horned Wolves are petty, vengeful fuckers, well, our people don't have a patch on the gods... And this Zosia? She walks with one, or I'm no judge of devils."
"What?" Sullen swallowed, fearing where this was going. "Her coyote devil, you think it..."
"I know better than to think on such matters," said Grandfather gravely. "But that thing's as like to a mere devil as that Zosia is to an ape in the Bal Amon jungles. A devil king's just what we call the god of our enemies. So whatever other voices you heed, Sullen, listen to your grandfather here—stay wary."
The wind whipped down through the camp, the fire crackling. Sullen threw his arm around his grandfather and said, "Pretty sure I heard you say you weren't going to lecture me about being careful, on account I wasn't some kid climbing dagger trees."
"Old folk are allowed to break their word, laddie, and blame it on senility," said Grandfather, squirming away from Sullen's embrace. "One of the sole benefits of being too old to remember ever being young!"
Their laughter was short-lived, cut off by a canine whine from the side of their tent. A shadow detached itself from the darkness and tottered into their firelight on sleep-wobbly legs. Something shaped like a dog but weren't no dog at all. Zosia's devil. Its chalky tongue lapped noisily at its jowls as it appraised them, its black eyes swallowing the firelight instead of reflecting it. It barked once, what Sullen prayed was a friendly bark, and then strutted past their tent, disappearing into the slumbering camp of the Cobalt Company.
"That's us to bed, then," said Grandfather with a shiver. "If he's out prowling, who knows what else walks this night."
They went in, but for all the wisdom he'd found in Grandfather's words, Sullen found sleep to be as evasive a quarry as any he'd hunted across the Frozen Savannahs.
# [CHAPTER
19](toc.xhtml#toc-chapter045)
Ji-hyeon slept alone. Well, slept was more of an aspiration than an accurate description. She pitched about in her sheets, occasionally punching a pillow.
Keun-ju had asked to stay with her, and she had wanted him to, but after her all-night plotting session with Zosia, who seemed as talented a tactician as her reputation implied, a morning nap had barely prepared Ji-hyeon for endless meetings with Choi, Fennec, and her other new captain, Chevaleresse Singh. So when she finally had time for Keun-ju in the late afternoon she was already yawning, and the three presses of kaldi they had put away during their long, draining conversation imparted twitchiness to her already rattled nerves, rather than bringing alertness and clarity. She felt better, after listening to his side of events. That Fennec and her second father had thwarted Keun-ju from accompanying her out of typical old-man objections to her being in love with her Virtue Guard wasn't all that surprising, but trying to convince her that Keun-ju had betrayed them to her first father was a dick move too far. If Zosia hadn't shown up when she did, Keun-ju would still be stuck on Hwabun, and Ji-hyeon might have given up on him altogether.
Yet even after hearing that what Sullen had suggested, what she had hoped, seemed to be the truth, her mood was somehow tart instead of sweet. So she had sent Keun-ju off, his pouting lip protruding through his sheer veil, to give herself time to digest everything. A good night's sleep would set her right... if she could ever manage one.
Keun-ju. How many times had she imagined their reunion? In her mind it had always involved a frantic stripping of clothing, jamming her tongue in his mouth to stop the flood of achingly earnest poetry, and then a furious fuck. This would be followed by a second, leisurely, completely relaxed undertaking, such as they had never been afforded under her parents' roof. As general of the Cobalt Company, she could bed whomever she wished, they could doze off in each other's arms, and no one could stop them... But their romance in Hwabun now seemed a lifetime ago. The Princess and the Virtue Guard was a song she knew by heart, but seeing him here, the same old Keun-ju he'd always been, while she had become a totally different woman...
As if that were true. Rolling onto her back, she stared at the dark dome of her tent where Fellwing clung. Loath as she was to admit it to anyone, herself most of all, she hadn't really changed all that much. She was still getting all gooshy over forbidden boys, wasn't she? Being real, as Sullen would put it, wasn't the truth that she felt weird about Keun-ju returning because she had finally gotten over him, finally felt the warm appeal of somebody else's regard? She loved Keun-ju, she did... But if that were true, why wasn't he next to her in bed? Why was she wondering how Sullen felt? Why did she miss the boy, when it had only been a day since she had last seen him? He had all but run from her tent as soon as he realized who Keun-ju was, and had made no attempt to call on her... Not that it had been very long, but still.
Also, hey, what about the war she was waging? What about all the lives that depended on her? What about all the lives she intended to claim in her quest? What about _that_ shit? Rolling back over, she buried a furious shout into her pillow. She immediately felt better, but then a concerned voice called from just outside her tent:
"General?"
"I'm fine!" she replied, scolding herself for being so childish. She was lucky the guards hadn't stormed her tent, overhearing a muffled scream in the dead of night!
"Can we come in, or you come out?" called the guard, and Ji-hyeon sat up in bed, trying to keep her annoyance focused on herself rather than the people sworn to guard her life.
"I'm coming, I'm coming," she said and, fumbling around in the dim tent, found the bulky coat Sullen had forgotten in his haste the night before. Sliding her arms into its cavernous sleeves, she stumbled into some sandals and emerged into the night.
"Sorry, General," said the guard, quickly rehooding her lantern after blinding Ji-hyeon with it. "I thought I heard something. Very sorry."
"Yeah yeah," grumbled Ji-hyeon, hoping it was close enough to dawn that she could just stay up. "What watch is it?"
"Second, General," said the other guard. "Just after midnight."
"Hrmph. Look, I'm going for a walk, but I don't want you two crawling up my ass."
"Of course, General," said the first guard. "Let me grab somebody from the back of your tent to replace us."
Ji-hyeon stomped in place to warm up, the icy stars overhead casting a wan light over the camp. There was still a bit of revelry taking place, distant songs and laughter reaching her as they had back in the west wing of Hwabun, when her parents had sent her to bed before a party ended... But in this quadrant of the camp all was quiet. When the guard returned with two others, Ji-hyeon took off at a brisk pace toward a small but steep hill that stuck up from the tents like a single tusk jutting from a fang-filled maw. Fellwing reeled back and forth above her, a deeper swatch in the quilt of moonless night.
The tents fell away as Ji-hyeon climbed up to the overlook. Loose stones and damp grass made her slip a time or two, but she soon conquered the hill. The guards hung back enough to give her the illusion of solitude, but their constant presence was as exasperating as it had been back on Hwabun. The more things change, eh, General?
A pentacle of small stones garnished the crown of the hill, but Ji-hyeon didn't know if it was an ancient site of worship or something recently erected by devote soldiers. The Lark's Tongue rose ominously above her, even the first low ridge of the mountain seeming to dwarf her and her humble hill. Her scouts had assured her that the other sides of the mountain and all of its immediate neighbors were even more treacherous than the face, but while that meant they couldn't be ambushed, it also meant they had no escape route. Zosia had insisted that making themselves so obviously vulnerable was the only thing that would provoke the Fifteenth Regiment into attacking immediately instead of waiting for reinforcements, but gazing up at the Lark's Tongue Ji-hyeon felt the uneasy dread that comes in the space between when a decision is made and its consequences revealed.
Sticking her hands in the pockets of Sullen's coat, she was happy to discover a stale beedi. He had seemed pleasantly surprised to find she had a taste for the same flowers he did, albeit of a lesser potency—maybe the varietals were different, or maybe the leaves he rolled them in added something; but whatever the cause, she found his smokes a little intense. Having forgotten her pipe back at the tent, however, she would take an intense burn over none at all. Besides, contemplating an imminent battle with a massive Imperial army probably warranted a little intensity. Doubling back to her guards, she lit the beedi on one of their hooded lanterns and then returned to the hilltop, savoring the taste of fragrant saam and bitter leaf, the mental weight of Sullen warming her all the way down to where her naked knees emerged from his coat...
She wandered into the center of the circle of stones and slowly twirled around, the camp laid out on all sides of the hill and creeping up the flanks of the mountains, dozens of bonfires and hundreds upon hundreds of smaller lights blazing even at this late hour. Thousands of soldiers, all ready to die at her command... or more accurately, thousands of mercenaries willing to kill to get her a crown, and all for a tael or two of silver. A few were volunteers who'd actually swallowed her song, true believers of the Cobalt Cause... a few, but probably not many. And the only thing her advisors could agree on was that the Imperials would be on top of them anytime now, and no matter how brilliantly they planned or fought, hundreds if not thousands of their people would die. Her heart began to canter beyond her reins, and she leaned down and stubbed out the beedi in the heart of the stone symbol, wishing she had something to focus on other than the enormity of her responsibility.
She looked east, beyond the lights of her army, where the hills rolled as black and vast as the night sea north of Hwabun, but without the flash of distant lightning where the Sunken Kingdom slept. Would she ever see that view again, leaning on the railing between her two fathers, her elder sister reciting poetry, her younger running around on the deck, working off the tiny cups of kaldi Kang-ho had talked Jun-hwan into allowing her?
The answer was obvious. She might see the Immaculate Isles again, but only from a distance. She'd tossed her family aside, and by the time this was over even her second father would be furious with her. Not that he deserved any better; the future he'd offered her was every bit as self-serving as the one her first father had. Actually, when you got right down to it, Kang-ho's invitation was far more selfish than Jun-hwan's—if she had done as her first father had asked and married Prince Byeong-gu, she would have still had her family, been able to visit Hwabun whenever she wanted. With Kang-ho's plan, though, there was no fucking way she would ever set foot in the Immaculate Isles again, and it was likely her first father would never speak to her again, either. Seizing control of the wall and then working with the Imperials to expand the fortification to protect her freshly conquered city-state of Linkensterne wasn't just an act of war against the Isles, it was an act of treason against her people, against her very family. Her second father had never phrased it like that, of course, he'd spun it as a grand adventure for his little girl, and wasn't he living proof that you could shame the shit out of your family and still make everyone happy in the end? It would serve him right to be disappointed by what she had planned, the conniving—
"Captain Fennec to see you, General," called one of the guards, her voice jarring up here above everything.
"Just the man I wanted to see," she said, and straightened to watch him huff and puff up the last dozen feet of the rise.
"You're up late, General," said Fennec. A few strands of dyed-black hair had escaped his ponytail, and he wiped them off his sweaty face, tucked them behind an ear. "Considering your counsel with Zosia kept you up so late last night, I would think you'd be abed."
"Were you watching my tent, Captain?" Ji-hyeon crossed her arms. "Or did you also happen to decide tonight was ideal for stargazing?"
"Hoartrap roused me," said Fennec, plopping down on a wide stone set in the pentacle's border. Now that her eyes had adjusted to the starlight, she could see the worry plain on his face. Had she ever thought this old devil looked young and handsome? "He wants a word with you but, since you're sometimes resistant to his uninvited appearances, suggested we come together. I told him to hang back down the hill until I'd said my piece and softened you up, then he could see if you felt like granting another audience."
"Tell me, Fennec, were you as relieved as I to see that Keun-ju safely found his way back to us?" Even in the dimness she could see he'd given up on playing her, making no effort to conceal a grimace.
"Ji-hyeon, you need to understand that it was for your own good that—"
"Oh, _fuck you, Brother Mikal_. It was for your own good, which is to say, my second father's—you never gave a shit about what was best for me! You still don't!"
"I do," said Fennec with that maddening sincerity he used to lubricate every lie. "Always have. I greatly prefer your company to that of your father. Either of them, as it happens. But we never would have gotten out of the Isles without Kang-ho's blessing. I wasn't the one to inform him of your dalliance, either—if you two had been more careful or, gods forbid, patient enough to wait until we were free to consummate your affair..."
"Enough," she said, glad the starlight was not so brilliant as to illuminate a blush. "You lied to me, Fennec."
"It's what I do best," he said with a shrug. "It never would have worked your way. To get you off Hwabun I had to convince Kang-ho I was on his side, not yours, and so that's what I did."
"And all this time I thought we were on the same side."
"I knew if Keun-ju truly loved you he would find a way back to us," said Fennec, peeling off one glove and then the other to let his clawed hands cool off in the night air—they must heat up something awful in the kidskin gloves. Watching him flex the grey-furred digits, Ji-hyeon gave silent thanks that only her hair had changed from their passage through the First Dark. From the panicked whimpers he'd issued when they'd emerged from the Raniputri Gate in Zygnema and he'd seen what his hands had become, their guide had not expected such a drastic transformation to his person. Yet nothing had changed about Choi—weird, but then Choi and weird went together. The beedi was catching up on Ji-hyeon now, and she found herself unable to stop staring at his altered hands, wondering what would have happened to her if she'd dared to open her eyes as they floated between Gates... But then he caught her staring and put his gloves back on sometimes. Between the snide comments he'd made about Choi's ancestry and the pride he took in his appearance, the man clearly didn't appreciate that a casual observer might now mistake him for wildborn. "It's all a moot point, though, isn't it? Keun-ju's here now, so I say there's no harm done."
"Moot point? No harm done? I spent the last year thinking he betrayed us, and he spent the last year trying to find a way back to me!"
"I swear on the devil I loosed, I wasn't convinced he wasn't secretly working for your first father. I'm still not, to be perfectly frank. It was safest to let you believe what you believed, rather than being distracted."
"I'm sure." Ji-hyeon crossed her arms, hating that a part of her still wanted to believe him. "How charitable of you."
"It was a selfish ploy, I'm not arguing that." Fennec sighed and hoisted himself back to his feet. "But be honest, if I had come clean as soon as we stepped out of the Raniputri Gate, would you have carried on with the plan, a plan that's going to drastically improve the lives of countless people... Or would you have turned straight back around and gone after Keun-ju?"
"I didn't think honesty was a word you were familiar with," said Ji-hyeon, refusing to admit he had a point. Vocally, anyway.
"The Burnished Chain says that everything happens," said Fennec, waving an arm over the camp beneath them. "I never put much stock in their teachings, and even less after I stole the habit of a missionary, but they might be on to something there. Everything happens. Whatever led us here, Ji-hyeon, we're all together now, you, Keun-ju, me, and Choi. Just like we planned. Life got in the way, as it always does, but in the end, here we are. Don't let the details trouble an already burdened brow, one responsible for the fates of thousands."
Ji-hyeon clapped slowly and softly, sufficiently buzzed to be amused rather than annoyed. "A beautiful speech, Captain Fennec. How foolish of me to focus on the details, when all they amount to is your betrayal."
"Don't be melodramatic," said Fennec.
"What do you want, Fennec?" she asked, really needing to know all of a sudden. And thirsty, so damn thirsty. "I mean it. I know what the others do, more or less, but what about you? What is it you _really_ want? What would you take, if there weren't any... details to get in your way?"
Fennec's jagged smile broadened, but he didn't speak.
"What happened to your devil?" It was the most personal question you could ask, but after all the ways he'd made her squirm over the years she figured he owed her a little fidget of his own. "Father's wish was that Fellwing serve me instead of him, which was a clever way of going about it, but what about you? What did you want so badly that you gave up the most valuable treasure a mortal can possess?"
Fennec's grin had become a grimace, and he muttered something in his native Usban.
"What's that, Captain?"
"Doesn't matter," said Fennec, sounding as weary as she'd ever heard him. "Hold on to yours, Ji-hyeon. Whatever you'd trade Fellwing for, you'll find it was a poor bargain."
"So you don't think I should see if she could get me a glass of wheat ale? My mouth feels dustier than your scruples."
"I would advise against it," said Fennec, smiling at her just like he used to when they were goofing off back at Hwabun, and she felt an urge to hug him. Smothered that urge with a pillow.
"Not even if it was a really cold one, with a slice of orange?"
"Not even for that. Now, it is very late and I am not as young as my beautiful and talented commander, so maybe I could trouble you with a concern or two that I harbor?"
"Maybe, maybe not," said Ji-hyeon. "Depends on the concerns."
"Zosia," said Fennec immediately. "I don't know what you two talked about, and I don't need to, but—"
"Ah, I'm afraid that's a 'maybe not,' Fennec, but rest easy; your name didn't come up more than once or twice."
"This isn't about me, it's about you, and it's about her—if you only heed one thing I tell you, it's—"
"Don't trust her?" said Ji-hyeon.
"If you would let me finish..." said Fennec, a wonder the words escaped between his clenched teeth. "You can trust Zosia, but only so far as her best interests lie. As soon as someone gets in her path, watch out—it doesn't matter if it's you, or me, or all her old Villains combined; if Zosia doesn't get her way, it's trouble for whoever disagrees with her."
"A happy thing that she and I are in agreement, then," said Ji-hyeon, remembering how radically the older woman's demeanor had shifted when she realized her impostor was eager for her help in a shared goal.
"For now, yes. But tomorrow, who can say? You've always been able to say no to me, Ji-hyeon, to Hoartrap or Choi or Chevaleresse Sasamaso... And even when we disagreed with your orders we carried them out. Zosia is not a woman you can rebuff and expect her to listen." Even in the darkness Ji-hyeon must have displayed her irritation fairly well, for Fennec raised his palms in peace, and said, "I'll say no more unless you ask me to. I could tell you stories..."
"I've heard the stories. She doesn't frighten me."
"No? She should!" Fennec glanced over his shoulder, as though Cold Cobalt were a devil to be summoned by repeating her name. "She frightens me, the other captains, even Hoartrap—a woman willing to lay low for twenty years before emerging like a cicada devil to enact her plans is capable of anything. She doesn't rush into things. She came here, came to _you_ , because you have become part of her scheme, and I know from experience that Zosia will sacrifice anything or anyone to get what she wants."
"Unlike you," said Ji-hyeon. "Or my second father. Or Hoartrap. Or me."
"She—"
"She's off in her bed sleeping, where you should be, too, Captain Fennec—you've already snapped your trap quite a bit for one night, if you want it to be sharp for the morrow."
"May I share my other concerns with you first? They are urgent."
"If they were so urgent, why didn't you start with them?" Ji-hyeon groused. "Whatever, fine. Just be quick about it."
"I did start with them, days ago, and have repeated them twice daily since we made camp." Fennec was in his obnoxious listen-to-reason mode—she could practically predict the words even before they left his mouth. "We shouldn't _be here_ , Ji-hyeon—that was the Fifteenth who met us in the mountains, and they'll be on top of us in two days, if not sooner. The whole point of our plan to lure them out of Cockspar and then have my allies in the city open the gates for us was to _avoid_ fighting them. If we don't have their city, we don't have anything to barter with—why would the Imperials call off fighting and help us take back Linkensterne when they have us trapped and vulnerable?"
"They hate the Immaculates more than us, and are galled about the wall being built?"
"I'm not so sure about their hating anyone more than us right now. And you heard Choi's report—there were pennants for both the Fifteenth _and_ the Ninth when she and Maroto brought a pack of monsters down on that Imperial camp. The Ninth are Myura's regiment, Ji-hyeon, meaning whoever survived the slaughter at their castle has combined forces with Azgaroth's regiment..." When Ji-hyeon apparently didn't show enough awe at having this intelligence repeated to her for the umpteenth time, Fennec's tone became almost frantic.
"We are about to meet the single most effective regiment in the Empire, on the bloody _Star_ , and they're bringing with them revenge-minded Myurans. Add to that Maroto's cunning plan of being chased by wolves straight into the Imperial camp, where your subtle scouts apparently made no secret they were Cobalt agents, and you have one very angry army coming to bear on us, and you'll do what, exactly, to preserve our precarious position? Ride out and explain everything? Tell them we never really meant to kill all those Imperial soldiers and citizens, we just needed to get some practice before heading back to Linkensterne? Offer them a cut of the action if they start taking orders from you instead of the Crimson Queen?"
"Seemed like a good idea at the time," said Ji-hyeon, trying not to smile.
" _If_ we had snatched the capital of Azgaroth out from under them, _if_ we had strength of numbers, _if_ we hadn't antagonized the Imperials quite so much up until this point, then _maybe_ we could have parleyed them into helping us take Linkensterne. It was never a sure thing, but now, here, boxed in by hill and mountain, the only sure thing is that we die like devils in a trap. We should never have hammered down stakes, not here, but there's still time to pull them out. I can rouse the officers, give the order now, and we'll be safely away by dawn. If we're still here when the Azgarothians arrive, it will be _catastrophic_."
"We need supplies, Fennec, we'll never keep our strength marching to Linkensterne if we don't get more rations, rations that the Fifteenth has in abundance—it's as simple as that."
"It's as simple as liberating every town and farm between here and the Immaculate wall! It's as simple as losing a few hundred, maybe even a thousand to starvation and exhaustion, but the rest of us live long enough to resupply somewhere else. We send our terms of peace to Diadem and the Fifteenth, who will be hounding us every step of the way, and who knows, maybe it still works, maybe the queen is bitter enough over losing Linkensterne that she decides to back our play. Maybe not, but either way we're alive to regroup and think of something else!"
Seeing the spittle fly from his lips, it finally dawned on Ji-hyeon what was going on here. Fennec didn't know her intentions, of course, but even if he had, he wouldn't have been put at ease, because for all his experience and bluster, Fennec was scared. Terrified. He sounded like a condemned man pleading reason with his executioner.
"We're not abandoning camp, Captain—we're staying here until the Fifteenth arrive."
"Then we are utterly _fucked_. If only from bullshit chivalry and respect for their Myuran comrades, the Fifteenth won't listen to our terms, they won't, and so we will have to fight them. And if we fight them at our current strength, we _will_ lose, and then the game is over, and nobody gets to go home."
"I am home, Captain," said Ji-hyeon sharply. "Any more concerns, or can I let my captain go get some beauty sleep, now that he's assuaged his conscience?"
"Nothing more," said Fennec, now playing the disappointed uncle as he turned toward her guards. "Pray sleep on it, Princess, and remember that everyone in this camp trusts you with their lives."
"It's General, not _Princess_ ," Ji-hyeon called after him, and, unable to resist, added, "But give it time, you might be calling me queen."
He stopped walking, looked back at her. "It's true, then. I don't know how Hoartrap does it. Well, let me say it again, in case you misheard me before—I'm with you, not your father. And assuming we live out the week, I'll be more help to you if I know your intentions, instead of only his. _General_."
Then he was just a silhouette tramping down the hillside, and Ji-hyeon looked up to where Fellwing wheeled above them. She felt the winter air, then, breathing its corpse breath down the mountains they had zigzagged up and down, and she pulled Sullen's coat tighter around her. It smelled of sweat and saam and the kaldi they'd shared, and she breathed it in, exhaling smoke of her own, and even as Fennec stopped for a word with the guards she heard a foot crunch the grass at her back. She turned, pleased with herself that she registered no surprise at seeing Hoartrap standing where she'd been minutes before, at the heart of the pentacle.
"Do you have a few moments to spare an old Villain, General?"
"For you, sorcerer?" Ji-hyeon tried to smile. "Anything."
"Oooooh, careful, careful," he said, rocking one of the stones with his foot. "One must always be mindful of how she words things, and never more so than when addressing my kind."
"Devils, you mean?"
"Well, we're both honest to a fault, but that's about as far as the resemblance goes. Come to watch the Imperials arrive, have we?"
"Hardly," said Ji-hyeon, but when she glanced back over the plains a shiver coursed down her spine. Far, far out in the frozen black sea of the night-draped hills, an orange glow outlined the southern horizon. She rubbed her eyes to make sure she wasn't just glimpsing a scout's campfire, but no—it was too remote, and that she could make it out at all from this distance meant it came from something far grander than a few scavenged logs. "That can't be... Why would they build their fires this late?"
"It's possible they've been marching late, and have just made camp," said Hoartrap, stepping beside Ji-hyeon and squinting into the south. "Or they're still at it, advancing by torchlight. In the old days, the Fifteenth had a real monster of a colonel—he'd trained his troops to live off a few hours of sleep a day, and march clear through blackest night. It was something to see, riding out with the original Cobalts. This great fiery wyrm, relentlessly pursuing you across the moonlit world... Brings back the memories, I tell you, seeing that right there. I'd wager cold coin that's the Fifteenth down from the mountains, and they're on the move."
It might have been her imagination, but the light did seem to waver as she watched. Now the dark hills really did look like the Haunted Sea beyond Hwabun, the fox fire in the distance completing the picture. Ji-hyeon's throat tightened as she stared out onto the Witchfinder Plains. This was it, then—the Imperials had come to kill her and every single one of the people who had trusted her to keep them safe... the people she had ordered to make camp and build pickets, digging in for a battle that never had to happen. They could have packed up and moved anytime, she could have ignored Zosia's counsel and delayed this confrontation, like Fennec and all the rest had urged, but now it was too late. Even if she gave the order to move out tonight, to move out right fucking now, it would be well after dawn by the time they were packed up and moving, and how close would the Imperial regiment be then? Too close, was the answer.
"Eh, they're still leagues away," said Hoartrap, as though he was already bored with the subject. "I'd be surprised if they attack before tomorrow."
"Tomorrow!" Ji-hyeon felt sick. While they'd been bivouacking in the Kutumbans after leaving Myura, the days and nights had inched by, slow as arthritic snails, but now everything was moving far too fast.
"Don't fret, General, I'm sure you'll have scouts and advisors stalking your tent by the time you get back down, eager to deliver the intelligence you've already seen with your own eyes. But for now why don't we—"
"Cut to the chase, Hoartrap," said Ji-hyeon, ripping her eyes away from the hypnotic glow on the horizon. Turning from the beacon of an enemy army to the milky, misshapen face of a dangerous and unpredictable devil-eater wasn't much of an improvement.
"It's to be war, yes?" Hoartrap's smile was as warm and welcoming as the farthest frozen star. "You and Zosia were alone far too long in the command tent for it to be anything but."
"Hasn't that always been the goal, Captain?" Ji-hyeon watched the sinister bastard carefully, wondered if she could detect it even if he gave anything up. "I mean, you and Maroto stumbled on us quite by accident back in Myura, didn't you? So why would you expect the aim would be anything less than the conquest of Samoth? Of the whole Empire, in time? That's what we've been moving toward all along, isn't it?"
"Nothing could make me happier than learning you are sincere in your intentions toward our beleaguered opponents," said Hoartrap, nodding his head toward the light to the south. "Yet for all your talk of Samoth this and Crimson Empire that, where in your little war does the Burnished Chain fall?"
"They fall hardest," Ji-hyeon said with more passion than she meant to betray. Getting mad felt good; it made her decision to stay and fight seem justified. Besides, if you couldn't be honest with your devil-trafficking warlock, who could you be honest with? "The Crimson Empire is nothing but the carrier, the Chain is the sickness. The things they do to wildborn, to their own people, and all in the name of the _higher truth_... And their higher truth is spreading. I know that firsthand, growing up in the Isles, and coming in from Zygnema we saw whole Dominions that've converted. Hells, Sullen says even the Flintland tribes are taking a knee. The Chain's the real enemy, and always have been."
"A fine speech," said Hoartrap with exaggerated solemnity. "I'm just relieved you're not actually working for them."
" _Working_ for them?" It was hard to tell when Hoartrap was being serious, and she didn't want to waste her indignation if this was just another joke.
"Oh, you know, a silent partner in your campaign against the Crimson Empire—the Chain's last rebellion failed, so perhaps they colluded with you to overthrow Queen Indsorith. You get Samoth, they get the Empire, standard stuff. Don't tell me you haven't even considered it?"
_"No."_
"Good for you! Ethical standards are commendable in the young, though they can become terminal if left untreated. Of course, if the Chain's not secretly supporting you, then we're all in for some very, very bad times. The Fifteenth are going to come down on us like devils on fresh sin."
"That's been the plan ever since we made camp," said Ji-hyeon, barely able to keep her eyes on Hoartrap instead of the lights of the Fifteenth. "Have any other uncanny portents for the future, oh wondrous seer?"
"Ha! Well, maybe one or two. Would you heed advice, if I offered it?"
"First I'd have to hear it."
"Hearing can be harder than it sounds," Hoartrap said, and, following his gaze upward, Ji-hyeon wondered if he was eyeing her devil or the indifferent heavens beyond. "What do you think they want, I wonder?"
"Who, the Imperials or the Chain? Or the devils?"
"The devils, of course. I've been studying them my whole life, and the question is always what can we squeeze out of them? How do we bind them, everyone asks. And once we do, what will we accept in exchange for setting them free again? But there's so much more to it than that—why did they build the Gates in ages past? As a means of egress from their world into ours, surely, but to what end? To prey on mortals, but then turn around and grant our every wish once we shackle them? What sort of creature wields such power, yet is so easily captured by bumbling mortals? It's the question of our epoch, isn't it, lurking behind every faith and every fairy story, tugging at our curiosity... What do they want from us?"
"The Immaculates say they want to be left alone," said Ji-hyeon. "Nothing more."
"Oh, the Immaculate sages say quite a bit more than that on the matter!" Hoartrap clucked his tongue, and with a muttered word, the stars began to wink in and out of view. What at first caught Ji-hyeon's heart as witchcraft revealed itself to be something altogether more wonderful, and terrifying: dozens of other devils now shared the night sky with Fellwing, dancing with her owlbat. She didn't know if she should fear for her devil... or for herself. "The mysteries of the Forsaken Empire and the Sunken Kingdom are not so mysterious, when you've read as broadly on the subject as I; back when they were just plain old Emeritus and Jex Toth, those legendary combatants fought for the same stakes we do today. Do you know that until they destroyed one another the Frozen Savannahs had never seen snow? And the Panteran Wastes were more like a paradise than a hellscape?"
"What happened?" asked Ji-hyeon, scarcely able to believe even Hoartrap knew how the Age of Wonders had ended.
"What have we been talking about? War, a war that sought to harness that which cannot be predicted nor controlled. There are things far, far greater than the devils you've seen, lurking out there in the First Dark, beyond the Gates. Entities that could never squeeze through such a narrow doorway. But there are other ways to pass over, given enough time and assistance... And there are ways to keep them at bay, despite the machinations of their servants."
Ji-hyeon shuddered, though she no longer felt the chill of the night. "It's late, sorcerer, and I have a war to wage in the morning. If you wish to swap ghost stories with an eager member of the Bong family, I suggest you visit my first father."
"Oh, we go way back, Jun-hwan and I," said Hoartrap, arresting Ji-hyeon's retreat before she'd even taken two steps. This monster knew _both_ of her fathers? "But it's you I'm talking to, isn't it, _General_? You know how the historians always talk about the great wars, like the one that claimed Emeritus and the Sunken Kingdom? They always come back to a very particular euphemism for all that bloodshed, all that killing. Can you guess?"
A tragedy. A waste. That was how her father had always referred to the war he waged with Cold Zosia, but Ji-hyeon didn't think these were the words Hoartrap spoke of, and so she simply shook her head.
"No?" Hoartrap smiled wide enough to swallow her, the Cobalt Company, the distant fires of the Imperials, and every star in the sky. " _Sacrifice_ , General, a term with which you must acquaint yourself, if you wish to take the Carnelian Crown. No victory without sacrifice, ask any veteran officer. And if the sacrifice is great enough, well, that's how wars are won. That's how you buy back what was otherwise lost forever. That's how you demonstrate to your opponent that you cannot be defeated. With a mighty enough sacrifice, any obstacle can be overcome, no matter the odds. Anything is possible."
Whatever he spoke of, Ji-hyeon was sure it wasn't simply the imminent Battle of the Lark's Tongue. Feeling as vulnerable as she had as a child in a nightmare, she extended her hand and called for her devil. "Here, Fellwing. We're going to bed."
Looking up, it was hard to pick her devil out from the flock, and it only became clear which one was Fellwing when the others began to harass her. The small owlbat tried to dip away but the others gave chase, jostling her about, forcing her to climb instead of fall to Ji-hyeon's shaking hand. She looked to Hoartrap, desperate, and with another smile and a murmur the other devils were gone, and Fellwing quickly landed on Ji-hyeon. The devil squirmed anxiously into the wide cuff of Sullen's coat, shivering against her wrist. Without another word, Ji-hyeon wheeled away and hurried back toward her guards, the far-off blush of the Imperials definitely brighter now than before. As she fled, Hoartrap called after her:
"Don't fret, General, we're on the same side here. And when the time comes, I stand ready to make _any_ necessary sacrifice."
# [CHAPTER
20](toc.xhtml#toc-chapter046)
The Fifteenth marched all night, and as they raised their camp alongside the sun, Domingo used his hawkglass to survey all from a hilltop. He would have liked to stand in the bed of the wagon instead of sprawling there like an invalid, but propped up on his pillows he could still get a good enough view to know he had once again gotten the job done. Red canvas tents spread out across the surrounding foothills, and just beyond them the Lark's Tongue beckoned. The Cobalt Company was still hidden from sight behind those last few rolling hillocks, but the scouts assured him that only a league west the last foothill descended into a long valley, and on the far side of this vale his enemies waited. They had not retreated at the last moment, as he'd feared they might, and that meant as soon as he gave the order the decisive victory Cold Zosia had always denied him would finally be his.
Well, whenever his soldiers had gotten some sleep he could give the order; they had earned a little rest before the battle, yes they had. Domingo knew he had a reputation as a taskmaster among the other Imperial colonels, but what none of those gossips realized was that he didn't push his troops because he didn't value them, or considered them beasts of burden. He pushed his troops because he knew Azgarothians were made of sterner stuff, that they could take it, and when they'd once again risen to the challenge and proven their mettle, his heart swelled with pride. He loved his regiment, because they had earned his love, damn it, even that fellow there picking his nose as he sat on a hogshead. Go on, lad, mine all the silver ye may; you've earned it!
Domingo lowered the hawkglass from his eye, the instrument too heavy to hold up one-handed for long stretches. He turned it over, admiring the glint of the sunlight on its engraved surface, and let out a long, unhappy sigh. This was all that was left of Efrain; that blackened, thumbless thing they had put into the family crypt wasn't his son, it was just burned meat. If that anathema Portolés hadn't returned the hawkglass along with his remains, Domingo would have had nothing to remember his boy by, out here at the end of the hunt, with vengeance at long last within reach. He had never thanked her for bringing it back to him...
Nor should he have, not when she was at least partially responsible for Efrain's murder in the first place. That then was something for him to set his sights on, once the Cobalts were all killed—finding that witchborn war nun and bringing her the same justice he was about to mete out to Zosia and her army. Back in Diadem the Black Pope had made some noises about Brother Wan perhaps being able to help Domingo find Sister Portolés along the way, seeing as they were likely pursuing the same quarry, but that had been another exercise in frustration. Not that he had expected such a miracle from the hideous little monk; the Empire was a big place, and the only people you ever bumped into were the ones you would prefer to avoid.
A speck of movement caught Domingo's attention to the north, but when he raised the glass again nothing was there but a grassy hillock. Ah, no, one of his mounted scouts appeared in the eyepiece and then was gone again, riding damned fast, and here came another. Domingo dropped the glass to get a wider view, squinting north. The hills between him and the riders obscured most of the action, but a pack of his people seemed to be hounding a pair of dark riders, chasing them toward the western mountains. Cobalt scouts, obviously, rumbled as they sought a peek of the Fifteenth's camp—well, Domingo's riders would soon give them an eyeful!
He raised the glass again, but it was hard to track the fast-moving riders from this distance with his off hand. As they arced southwest, he caught another glimpse of the fleeing scouts, and he nearly fumbled the hawkglass. For a moment, the rear rider had almost looked like... but no, that was just an old man's mind playing tricks on him. From this distance what he had thought was a familiar face was just a pale blob that his imagination played with. The rider wasn't even wearing Chainite robes. Still, he looked again with the glass, hoping to calm his racing heart, but the riders were gone again behind some higher hills, and from here they would either make the Cobalt camp or be caught by their Azgarothian pursuers outside of Domingo's sight.
Not that it made much difference, really—either way they would be dead by this time tomorrow, along with every other member of their rebel army.
It was a scene straight out of the Chain Canticles, a lone believer and her doubting companion riding at breakneck pace toward their goal, the full might of a corrupt army rising behind them like a tidal wave of iniquity. If anything, it might be a little over the top, even by Canticle standards, especially as arrows fletched with cardinal feathers started whizzing past them when they refused to heed the final shouted warnings of their pursuers. Sister Portolés couldn't have asked for a more portentous entrance.
They reached the crest of another of the steadily steeping hills, horse froth running down their legs as they pushed their steeds beyond hope of repair, and then looked out over the final valley before the Kutumbans stabbed up from the plains. There at last they saw what both the war nun and her captor had taken on faith would be there, a camp nearly as impressive as the one at their hind, save here flew Cobalt pennants instead of Crimson.
If Heretic had not believed the gossip he heard in the last town that the Cobalts had come down from the mountains and made camp here, they never would have found them in time. If they had been spotted sooner by the sentries as they circumnavigated the Imperial camp, they would have been caught an hour ago, and all the prayers of Samoth's queen would go unanswered. If Heretic had not unchained her legs that morning so she didn't have to ride sidesaddle, or if the Imperials who pursued them were better shots—
"Fallen fucking Mother!" Portolés cried as an arrow embedded in the back of her calf, causing her to kick her exhausted horse all the harder. The fire burned its way up to her knee and down to her ankle, but all she could do was pray her horse had a little life in him... And then Heretic whooped in triumph, and glancing back she saw that the Crimson riders had stopped at the top of the hill, giving up the chase. Looking back into the valley, she saw a dozen of the Imperials' blue-blazoned cousins riding up to meet her, these outriders not looking much friendlier than the crimson ones they'd left behind...
Heretic seemed almost repentant as they were stopped in front of the command tent, the size of his eyes telling Sister Portolés he had never expected the Cobalt Company to be so enormous. From the point where they had been stopped by the mounted sentries in the vale, it had taken them well over an hour to reach the heart of the camp—the stop at a white pavilion to have the arrow pushed through her leg and a poultice tied on the wound barely took ten minutes, the rest of the time spent climbing steadily higher through the labyrinth of tents. Above them, Lark's Tongue Peak cast an imposing defense for the army's rear.
"Wait," said the burly chevaleresse who had intercepted them at the outskirts of the tents, sending the outriders back to their duties and escorting the prisoners into camp herself. She entered this final wide, nondescript tent without announcing herself, and from within came the sound of low voices. Heretic whistled nervously, rubbing his hands together against the morning chill now that the sweat had dried and the panic faded. The knight reemerged, flanked by more guards. "All right, these lads'll take any weapons you have, then you can come in and tell the command what you told us."
"Can..." Heretic looked guiltily at Portolés. "Here, hold up, let me take her chains off her wrists."
"You wish to unshackle your prisoner before taking her into the command tent?" The chevaleresse looked amused. "I don't think so."
"It was only to keep her in line until we got here," said Heretic. "She's not a danger."
"That true?" The chevaleresse's flinty eyes looked up into Portolés's. "Big woman like you isn't any danger? That hammer we took off your packhorse, suppose it belongs to your ferret here?"
"You heard the ferret," said Portolés. "I'm no danger at all. The maul's for shoeing our horses."
"Look—" said Heretic, but the knight shut him down.
"No, _you_ look, son—I'm all kinds of curious to hear how an underfed thug like you put the manacles on a hoss like her. And I think you'll sing that song just as well with her in chains as not. Now get in the tent."
And just like that, Portolés ducked under a pole and found herself in the command tent of the Cobalt Company. Their maps and other papers had been flipped upside down, the whole rebel crew standing from their stools at her arrival, as though she were a foreign dignitary they hoped to woo and not a suspected spy, or worse. Heretic bumped into her as he came in, and the chevaleresse entered last. She and the other guards all had their steel drawn. Two empty stools were brought over to the other side of the table, and the young Immaculate woman who was clearly in charge waved them to their seats. In the lantern light, the girl's shock of darkly dyed hair could be cobalt, even, and Portolés let out a miserable sigh. Whoever led this army, it wasn't the mayoress from Kypck. Which meant her mission had failed, the weapon her queen had given her was useless, and she was about to be screwed in a big, bad way.
"Well, Boris of Diadem, the ditty you sang for my sentries intrigued me enough to grant you an audience," the Immaculate girl said, her cupbearer filling a bowl with hot kaldi and offering it to Heretic. "I am General Ji-hyeon Bong, commander of the Cobalt Company, and for the moment you have my full attention."
Bong? Sitting forward on her stool, Portolés peered at the girl, trying to see a family resemblance... Was Bong a common Immaculate surname? If not, if this general was the daughter of Kang-ho and Jun-hwan...
"Um, yeah," said Heretic nervously, "so she, Sister Portolés, I mean, I was a prisoner, in Diadem, but then she took me prisoner, but when I got free I took her prisoner. Shit. Let me start over."
Portolés sat back on her stool and took in the general's cabinet as Heretic blathered: an older Raniputri chevaleresse with an impressive mustache, a grotesque hulk of a man with a sickly smile on his wasted features, and a good-looking Usban fellow of middle age. Nondescript as this last member of the command was when seated beside the rest, his breastplate identified him, the prancing foxes embossed on its polished surface a dead giveaway. Here then were three of the Five Villains, straight from the forbidden songs of the Stricken Queen, all of them taking orders from a girl who was likely the daughter of the fourth. Interesting...
"Do you have a staring problem, Chainite?" said the general. "Or would you prefer to wait outside while your handler gives us a very compelling reason to believe you're not both Imperial assassins?"
"Whoa, hey!" said Heretic, standing so quickly he almost caught a sword to the spine before the guard standing behind him realized he was being foolish rather than dangerous. "That's not me, not at all. We nearly got nabbed by the Crimsons, trying to get to you—ask your scouts or whatever, your people who saw us being chased in here by them. They wouldn't be trying to kill us if we were with them, would they?"
"They evidently didn't do a good job of it," said the bewhiskered knight who had to be Chevaleresse Singh. "That bandage on the weirdborn's leg looks fresh, but it's obvious the rest of her injuries are weeks old."
"I'm on your side, I swear it!" said Heretic, prompting Portolés to wonder just what heretics swore on. "I was her prisoner, but then we were bushwhacked by some other Chainites, and she got tore up bad enough in the exchange I got the drop on her. Took her to you because you seem to be fighting the good fight, and I couldn't well risk trying to sneak back into Diadem with her, could I?"
"Yes, yes," said the man Portolés presumed was Fennec. "You told the sentries, one rode ahead and told us. What strikes the general as odd is your presumption that we are, as you say, on the same side. That, and the timing of your appearance, prisoner in tow, just ahead of an advancing Imperial regiment. And claiming to have invaluable information for us! How wonderfully convenient it all is."
"No, no, no, it's not like that!" said Heretic. "We came west from the Haunted Forest, and when I was buying food in Black Moth I heard it from some hunters that the Cobalt Company was laying down a camp here, in front of that big mountain. They said they'd seen you coming and cleared out just in time. This was a few days back, and those ignorant assholes said the Imperials from Thao were still a little ways off—last thing I expected was to come across the plains and see that nest of 'em between you and us. We went wide north to go around 'em, but their scouts—"
"Thao?" said the general, exchanging glances with her cohort. "You're saying Thao's regiment is already marching this direction?"
"That could be your disinformation," murmured the giant, loud enough for all to hear. "They've come to stir you up, push you into flinching first."
"I know what I heard, but I won't vouch for it being true," said Heretic, and it was quite something, to see the lad who had taunted his oppressors in the Office of Answers tremble under the gaze of his idols. "All I know is if you're fighting the Empire, then I'm on your side, it's easy as that. I mean, if I was a spy wouldn't I come with a better story? Maybe I'd have some claim to know what the Imperials are up to out there? I don't know shit, beyond what I told your people already, and that's the True Queen's truth!"
"You say this war nun rescued you from torture in Diadem, and fought her own people along the road, yes?" asked the chevaleresse, waving the cupbearer over to refill her kaldi bowl.
"I don't just say it, it's true," said Heretic, realizing he was the only one at the table still standing, and retaking his seat.
"And you also told my sentries you had information that would be valuable to any enemy of the Empire, but that you would only share it with those in charge," said the general, rocking back on her seat. "So... what is it?"
"Right, yes," said Heretic. "So Sister Portolés here—"
"That's your name, Portolés?" asked Hoartrap the Touch. Portolés was more certain of his identity than any of the others. He was, by all accounts, a devil-eater and known witch.
Portolés offered the faintest suggestion of a nod. Things were about to get very warm in here, and she wondered how best to play this.
"So yeah, I don't know what she wants, or what, but she's working for the queen, not the pope, I'm sure of that," said Heretic. "Pretty sure, anyway. I searched her kit after she got all beat up by the other clerics and found some papers with the Royal Crimson Seal on it, and a roster, I'd guess. Names of soldiers, rank, that sort of thing."
"Ah, and here's that invaluable military intelligence our guest knows nothing about," said Fennec with a yawn. "Can't say we're in for much trouble from the Imperial command, if this is what they think passes for believable disinformation."
"Look here, all of you... you lippy churls!" said Heretic, jabbing a finger at each of the seated officers in turn. At the moment these four were the most dangerous people on the Star, and Heretic was barking at them like they were part of his petty resistance back in Diadem. Portolés would miss the lad, once they were both burned alive as enemy agents. "I'm not a spy! And whatever the sister is, I don't think she's a spy, neither. It was never her plan to come here and find you, far as I know—we started off and went straight up to the Isles, and then were coming down for the Dominions, I think, when—"
"The Immaculate Isles," interrupted the general. "She took you there? Which cities, which islands?"
"Well, we come up through Linkensterne, and then went to, whatsit... Hwabun, Hwabun Island, and then turned right around and—"
"What were you doing there?" the general demanded, not looking at Heretic anymore. Well, that certainly answered the question of the girl's lineage! Portolés doubted they'd need more than this girl's stare to get the kindling going underneath them. "I expect your full cooperation, woman, from this moment on. We both know that whatever royal errand you were on, it's definitely come to an end now."
"Has it?" Portolés couldn't help herself; perhaps it had been an early way of insulating herself from further harm or despondency, but whatever the source, there was no cushion nor chair she preferred to the hot seat. "With all due respect, General, I believe I'm the only one in this room who can speak with authority on that matter."
"Ah, so you do speak!" said the general. "And eloquently as any ambassador, I must say. Are you an ambassador, Sister Portolez?"
" _Portolés_ , Sister Portolés, and I think you could say I am something of an envoy." It was so hard not to smile, but one look at how much pleasure the ancient Hoartrap was also taking in this exchange helped check her mirth. "The issue, General, is that I was not sent to treat with you."
"That so?" Ji-hyeon looked like she might throw her kaldi bowl at Portolés. "But you were sent to talk with my fathers, were you?"
Oh, but this was getting good! "It is an unfortunate clause of my assignment, General, but I am forbidden from discussing my business, which is to say Queen Indsorith's business, with any but the object of my inquiry. Your father King Jun-hwan seemed to be doing quite well, by the by—I found him most cooperative."
That did it, though Ji-hyeon clearly thought better of it at the last moment and hurled her bowl against the wall of the tent instead of at Portolés. Temper, temper, General.
Chevaleresse Singh cleared her throat. "I would remind the general that according to the Articles of Aghartha, all laws regarding the treatment of prisoners of war apply only to combatants, abettors, and commanders. When it comes to suspected spies, well, there really isn't as much errata as you'd think. An _unfortunate_ oversight on the part of the authors. Whatever you deem necessary to secure the safety of your troops is permitted so long as—"
"Torture, is what the chevaleresse means," said Portolés. "And here my ferocious warden had led me to believe that the Cobalt Company was above such immoral tactics."
"Immoral, sister?" Fennec looked sad. "I'm sure you heard that word quite a bit, growing up as an anathema in some miserable Chainhouse. Did you find redemption after your first round of penance, or your fiftieth?"
That hurt a bit—how did they always know? Portolés didn't have wings or a tail, Savior knew she never even lisped anymore, hadn't for years after all her whispering to herself in her cell, getting every word right... Yet somehow, they always always knew, as though her impurity gave off the stench of rotten eggs.
"Nothing to say, race traitor?" Fennec pushed.
"No call to bring that into it," said Heretic angrily. "We're all meant to be equal, ain't we? That's the Cobalt Code, ain't it? Or is everything I heard about this new Cobalt Company being the same as the old just as false as its general?"
That was definitely the wrong thing to say. General Ji-hyeon was flushing red as an absolution candle, and Chevaleresse Singh stood with a flourish of her cape, drawing a mighty sword. Fennec was amused but mostly hiding it; Hoartrap was delighted and making no effort at all to conceal it. Good show, Heretic, good show—it always was the believers carrying the standard, volunteering for the front, while the cynics and the realists hung back in a command tent.
Come to think it, what did that make Sister Portolés?
"Right, sorry I'm late," came a familiar voice from the tent's entryway. "Tried to rouse Maroto but he's sick as a dog. Came straight back here, but met some frazzled scouts on the way, and brought 'em with me—you need to have them come in and report right fucking now, they say the regiment from Thao is creeping less than three days out from... _Hell_."
Turning to the door, Sister Portolés felt a seesawing mix of relief and fear to see the old woman from Kypck... who looked pretty seasick herself, upon recognizing Portolés. She'd hardened up since last they met, and she hadn't been soft then, either. The dog was at her side, though he now appeared closer to an adolescent than a greysnout, his tail wagging enthusiastically as he trotted over to Portolés to say hello.
The war nun stood and bowed, the dog licking her face. She smelled the wrongness on his breath, tasted it in her suddenly aching tongue—the two sides of the scarred tissue seemed to be trying to rip themselves apart again. She straightened up quickly to get away from the creature. A devil, no doubt about it, and, looking closely at the approaching woman, Portolés saw the jagged scar on her jaw that Queen Indsorith had mentioned.
It was as Indsorith had feared. This wasn't some random hillbilly mayoress with a chip on her shoulder; this was Zosia, the Stricken Queen. The long year since her people had been put to the sword didn't seem to have softened her ire much. And Fallen Mother bless them both, Portolés had found her in time.
"Lady Zosia," breathed Portolés, closing her eyes to better savor the sensation of salvation. "Lady Zosia, I have been sent by Queen Indsorith to—"
The first punch caught her in the throat, and the second nailed her tightening stomach. A month ago the nun might have shaken off the blows, or at least hidden the distress they caused her. A month ago she didn't have multiple puncture wounds to the chest, sternum, and belly. She went down, and would have gone down harder if Heretic hadn't been there to catch her. Fennec and the chevaleresse had scrambled over the table and pulled Zosia away, but only after she'd rabbit-punched Portolés's side four or five more times. The anathema felt the stitches tear with each blow, but did not cry out or resist. This was why she had come here after all.
"Get the fuck off me!" Zosia, spitting like a wildcat, threw Fennec across the table. Hoartrap snatched his kaldi bowl out of harm's way at the last moment, but did not rise to assist. Chevaleresse Singh got behind the furious woman and contorted a leg and an arm around her, then tightened her limbs, immobilizing her. It was something to see, what had seemed such a gently lined, welcoming face back in Kypck now transformed into a mask of the Deceiver himself, Zosia's teeth bared and her nostrils flaring. Splayed out in Heretic's arms beneath the wrathful woman, Portolés fancied she could feel heat emanating from her.
"Enough!" barked Ji-hyeon. "Enough! Do you want to die, Zosia? Outside until you calm down, and if you can't act like a grown woman, don't come back!"
Hearing the general address the woman by name sent more waves of bliss shuddering through Portolés. She had not failed. Not this time. And now her wretched, cursed body could finally do something miraculous, could finally be used as her queen intended. Perhaps she had been destined for this, or perhaps it was all an accident, but everything happens, and the Crimson Queen of Samoth had bid her take any measures to ensure that it did.
"Whatever this fucking asshole says, don't trust her," said Zosia, trying to kick at Portolés and nearly carrying Singh to the floor with her. "Let me go, damn it, I'm all right now, I am. We got a history, is all. Bad, bad fucking history!"
"And a future," said Portolés, Heretic helping her back up. Even without the chains on her wrists the sickening aches in her stomach and side would have made it an arduous task. There was dampness under her habit there, but she couldn't worry about that now, not with the end of her quest at hand. She just had to live long enough to deliver her queen's will, and then there would be no battle between the Imperials camped out in the plains and these mercenaries, no war at all between the Cobalt and the Crimson. Everyone in the tent was staring at the battered war nun. "A short one, if you want, but we must talk. She sent me after you. Queen Indsorith."
"Think I don't know that, witch?" Zosia tensed again, but so did Singh. "Think I'm too fucking dense to see the starshine on the altar?"
"No," said Portolés, then repeated it, to her own mutinous body, "No, no, no..."
That heat spreading through her, numbing the pain, had begun creeping up her throat, and she tried to stay still, so as not to succumb to vertigo. Closed her eyes, but that only made it worse. She was so close, she could feel the warmth of salvation... but it was cooling now, drifting away, leaving her to steam in the frozen black center of the earth, where only devils dwell...
"Sister!" Heretic was shouting from above. "Sister!"
"Gods below, she's bleeding!" came another voice, from yet higher still. "What did you do..."
"Didn't hit her that hard." Zosia's voice was muted by the warm water as Portolés sank down and down, toward the Sunken Kingdom. The last thing she heard was the woman mutter, "Not so hard as she deserved."
# [CHAPTER
21](toc.xhtml#toc-chapter047)
Zosia stormed out of the tent, ignoring the girl shouting after her, but didn't get ten feet before Ji-hyeon snatched her arm and whirled her around. The little princess almost got a fist to the chin, but then Zosia caught herself and let the arm drop. Good thing, too, for only as she let herself breathe and really take in her surroundings did she notice that Chevaleresse Sasamaso had the drop on her, glaive ready, and Zosia doubted the woman would take kindly to her beating on the general.
"Captain Zosia, I will have order in my tent, if nowhere else," Ji-hyeon said, meeting the older woman's hard eyes with some steel of her own. "Whoever that woman is to you, she is _my_ prisoner. She knows something, maybe lots of things, but we can only make her tell us if she's alive. Do you understand?"
Being lectured by this blue-dyed child enraged Zosia almost as much as seeing Sister Portolés had. "That fucking witchborn and me have a history—"
"I didn't ask why," said Ji-hyeon, her fingers digging into Zosia's arm when she tried to pull free. "I respect you enough not to, just as I didn't ask why you looked so... _interested_ when you heard the name of the Azgarothian colonel leading the Fifteenth Regiment. Tell me or don't, in your own time, but for now all I need is for you to tell me you understand."
"Oh, I understand," said Zosia, wrenching her arm free at last and making the Flintlander knight have to sidestep around the general to get a clean thrust at Zosia, if it came to that. Zosia looked past the two women, to where Choplicker came strutting up to her. If she disarmed the chevaleresse and used her own weapon against her, and then the general, her life would get a whole lot simpler—who in the Cobalt Company wouldn't prefer the real deal to an impostor?
"Good," said Ji-hyeon, letting out a big breath. "Good. I know you wouldn't act without reason, but please appreciate my position. That woman claimed to have valuable information, but now she's unconscious. This is a problem."
"Yeah, it is," said Zosia, letting out a big breath of her own, along with a shudder at the dark thought that had seemed so reasonable but a moment before. She'd gotten worked up at seeing that piece-of-shit nun Portolés, lost account of herself, but now she'd calmed down enough not to think that murdering her new friends would help her situation. From the way Choplicker was looking back and forth between General Ji-hyeon and Chevaleresse Singh, she supposed that ingenious notion might've had a little help slipping through her admittedly leaky sense of morality. "That woman's an agent of the queen, directly responsible for murdering hundreds of innocent people."
"She freely admitted to coming here on the queen's orders, to talk to _you_ , Zosia, and you alone." Ji-hyeon rubbed her temples, and it occurred to Zosia that this brat was trying not to lose _her_ patience—how was that for a change of pace? "I would very much appreciate it if you could get any pertinent information out of her when she recovers. If she recovers."
"Oh, I'll get it out of her, all right," said Zosia. "But I can tell you plenty about her now. She's the guard dog of Colonel Hjortt—you know, the asshole leading the Imperial army we're about to throw down on?"
" _They_ are about to throw down on _us_ , you mean—wasn't that the plan?" said Ji-hyeon, and Zosia felt another pang of guilt at encouraging the girl to go ahead with meeting the Fifteenth Regiment in open combat... but then it passed like an unwelcome burp. As soon as she'd heard which regiment was bearing down on the Lark's Tongue, and that Colonel Hjortt indeed led them, the temptation was too great for her to dismiss—she'd been overconfident to let the boy off with only a dethumbing at Kypck, and couldn't pass up a second chance to settle the debt he and his cavalry owed her. Besides, with her help, the Cobalt Company could probably take the Azgarothians. Probably.
"If there's nothing else, then?" said Ji-hyeon, and Zosia realized she'd been daydreaming of all the things she'd do to Efrain Hjortt once she met him on the battlefield.
"Not yet," she said. "I'll interrogate Portolés as soon as she's up."
"Delightful. Now, though, I need to send terms to the Imperial camp that's sprung up overnight—if you would excuse me?"
"Sure, don't let me keep you," said Zosia, not feeling abashed so much as... thirsty. Both the prospect of a vicious fight to the death and the niggling sensation of regret parched her something awful, always had. A drink and a smoke to wind down what might be her last day on the Star, a talk with the asshole who had helped assassinate her people, and then a good night's sleep before taking the fight directly to her old pal Colonel Hjortt, who'd evidently learned how to hold his reins without thumbs. That order.
"They've sent an owlbat, sir?" said Captain Shea, as though common practice was the most outlandish thing she had ever heard.
" _And?_ " said Domingo, even the ordinarily pleasant thought of leaping off of his padded cart to assault her too painful to contemplate. Just sitting upright made him queasy and faint, but at least his subordinates hadn't tried to force him out of it into another tent. Sleeping under the stars to the lullaby of marching boots was an experience Domingo counted among the few unexpected pleasures of his return to command. "Surely the extent of the message is not _This is our owlbat, we await your reply_?"
"And they wish to have your agreement that at noon tomorrow we meet them in the valley for... um... _a combat both fair and honorable_?"
"Those riders who evaded our sentries must have delivered news of the Thaoan regiment's approach," said Brother Wan from his seat on the riding board of the small wagon. "Small wonder they want us to rush in before reinforcements arrive. They must think you very simple indeed, to—"
"Wheatley's people will be on the backside of the mountain by now," said Domingo, talking to himself more than the war monk or captain. Scowling at the map he had spread over his lap and legs like a blanket, he looked west to where the Lark's Tongue brooded over his camp and the countryside beyond. Not more than a single league to his reunion with Cold Zosia, and despite being wheeled up on a hillock overlooking the whole of the Fifteenth Regiment, a shiver went up his good leg, and a bolt of misery drizzled down the other. "Assuming Wheatley follows my one simple command and sends us no messages, there's no way the Cobalts will predict an ambush at their rear. Not one of such magnitude."
"It does look a good deal steeper on the face than it did from the mountains," agreed Brother Wan. "Presuming the Myurans don't have overmuch difficulty navigating those ridges on either side, they'll start down when they see us cresting the last hill into the valley?"
"Then, or when the Cobalt horns blow. Simple and elegant, like all the best stratagems," said Domingo. "This one is called the wolf trap—we snap them between our steel jaws and catch them fast. No escape, once we pour up from the valley and Wheatley's people come down the mountain."
"Wolf trap..." Shea seemed to have a thought stuck in her head like a stringy piece of meat catches in the teeth. He could see her worrying at it, brows knitted, then she said, "Isn't that the maneuver the Stricken Queen's rebel army used against the Fifteenth in the Shadow Deserts, at Wild Throne?"
"That was the place," said Domingo, remembering the battle like it was... like it was twenty-some-odd years ago, but he remembered the broad strokes. Said strokes were not pretty, not pretty at all. _Unrefined_ , was the word he would use. Yet effective. "Our best tutor is often our enemy."
"Lord Bleak is the best, isn't he?" said Shea, and for the first time Domingo found himself intrigued instead of exasperated by his first captain. "There's poetry in _Ironfist_ that I've not heard in any ballad. Ah. Sir?"
"Well put, Shea, well put," Domingo allowed. She was a student of war, then, if nothing approaching a scholar, but we all start somewhere. Efrain had never remembered a word of Bleak, despite Domingo's frequent quizzes. Alas, neither verbal lashings nor the more traditional sort improved the boy's memory or whetted his interest, to such an exasperating degree that Domingo had to ask if Efrain was making a mess of his lessons on purpose. Though why ever his son would do such a thing—
"Just a moment more of your attention, sir?" said Wan, leaning down from his perch over Domingo like a great raven prodding at a dying dog. His beady eyes were on the map. "If we are to agree to this luncheon with the Cobalts, which seems perspicacious, I should think we must do so without further delay."
"Excuse me? You think accepting their terms seems _perspicacious_ , Brother Wan?" said Shea, perhaps coaxed into offering an actual opinion from the crumb of approval Domingo had tossed her.
"You don't, Shea?" asked Domingo, and when she began to balk he hurried her on with the stick since he never carried a surfeit of carrots. "I know you have a notion, so spit it out, damn you, unless you think a Chainite anathema knows tactics better than a captain of the Fifteenth?"
"Sir! Even with the rests we took along the way, the regiment's had over a full night and a day of marching, and with making camp here at the end of it all, most didn't get to sleep until the late hours of this morning." Shea's eyes were so bloodshot, Domingo wondered if she'd rested at all. "Pushing them onto the field less than a full turn of the sun from now seems... rushed? Especially with our holding every advantage save terrain, and the Thaoan regiment only two days out... sir?"
And he'd lost her again to indecision, but just for a moment there she'd shown some shred of competence. That shred had been thin from neglect and flapped about more as a handkerchief signaling surrender than a pennant flying proudly above an advancing army, but it gave Domingo an unexpected flash of optimism for Azgaroth's future after he had gone into that horrible endless night where nothing stirs, not even the regrets of a disappointed father...
"Sir?"
"Hmmm, yes, quite so, quite so. Excellent reasoning, Captain," said Domingo, imagining Shea wore much the same expression Efrain would have that fateful birthday, had he received a kitty cat instead of stern steel and a harder lecture. "A pity I cannot put it into practice. Accept their terms, Shea, noon tomorrow it is."
Ah, and there was the actual look Efrain had displayed, all resentment and confusion. It looked no better on Domingo's first captain than it had on his son, and he waved his one responsive hand in front of his face as though he could dispel her like an ill smell. She didn't question him, however, which was more than he'd been able to say for Efrain when the boy was in one of his moods.
"We attack at noon, then," she said. "I will inform the officers to prepare for—"
"We attack at first light, Captain," said Domingo irritably. "For the love of the living, don't go around giving orders I haven't made. We tell the Cobalts we will meet them at noon, but tell the officers to have everyone moving an hour before dawn."
"A fine and auspicious hour," said Brother Wan, as though Domingo's motivation stemmed from Chainite mumbo-jumbo and not pragmatism.
"An early hour, was my thinking," said Domingo, and, not wanting Shea to go away thinking the war monk steered anything but his command wagon, he added, "It seems underhanded, I know, but the Crimson Codices are quite clear—we're not officially at war with the Cobalts, which makes them insurrectionists, not combatants worthy of our usual chivalric standards. If I know Cold Zosia, and I do, she'll have the same notion—yes, come to think it, Captain, have our people ready to go _two_ hours before dawn. Then we _might_ get the drop on her."
"And so with your permission, Colonel," said Wan, "shall I anoint the regiment _three_ hours before dawn, to make sure my people have ample time to complete the ceremony before we march? Everyone must have the holy oil upon their brow before we carry out the ritual, otherwise the effect could be... catastrophic."
"Catastrophic?" That was not a word Domingo liked to hear as regarded the safety of his regiment. "Explain yourself plainly so even an old blasphemer like me can understand, Wan. If you can't guarantee the safety of my people there's no fucking way we're using this oil of yours."
"The oil, Colonel, is not the weapon," said Wan patiently. "The oil is what protects our people, when the ritual is completed. The wrath of the Fallen Mother will fall upon the field, and anyone out in that valley who does not bear Her Grace's mark is at risk of being conflated with the Cobalt Company."
"Hmmm," said Domingo, all his doubts about this plan returning... but the scouts reported the Cobalt Company was even bigger than anticipated, and with Wheatley off on the other end of the Lark's Tongue, it would be far too dangerous to go forward with the attack and not use the Chain's weapon. Without it, and with the Cobalts dug in on the high ground across the vale, the battle could go either way, especially if Wheatley's attack on the rear was somehow delayed.
"I assure you they will be perfectly safe so long as they receive our blessing and anointment," said Wan. "All of my brethren will be down on the field with them—I would not ask your soldiers to undergo anything my people would not."
"If we waited for Colonel Waits to arrive?" Shea said, a pleading note in her voice, and that irritating doubt was what pushed him into it.
"Everyone gets the oil, then," Domingo decided. "We rest today, and three hours before dawn, anoint the troops and carry out your ceremony. We're using the Chain's weapon."
"Sir, I really think—"
"Dismissed, Captain Shea," said Domingo, looking out at the Lark's Tongue so he wouldn't have to see Wan's smug expression. "Get that owlbat headed back to the Cobalts quick as you can. Mustn't keep my old friends waiting."
A pox on every graveworm, and a royal one on Diggelby. Maroto had felt worse—the gods of chance demanded such, given the life he'd led, the beatings he'd endured, the substances he'd abused. Still, he couldn't rightly remember such an occasion, whatever the gods of chance had to say on the subject. He didn't think of himself as one given to hyperbole, but he would rather, in all seriousness, be chopped to death by hatchets than feel this way a moment longer. Really dull ones, wielded by blind toddlers. He finally mustered the strength to produce a moan.
"Somebody drink too much?" Purna poked her head into the tent, delivering a blast of raw, corrosive energy directly into Maroto's brain, exploding his eyeballs in the process. He pulled the sweaty blanket over his head to block out the sunshine.
"Something I ate," he said. "I can handle my drink, woman."
"Sure," said Purna, and through the thin blanket he could tell she'd let the flap fall shut, banishing the hated sun. He poked his face out again as she brought a sloshing jug over to the nest he had made on the floor. "Brought you some millet beer—old Ugrakari cure, hoof of the yak that kicked you."
"Uhhhhh." Maroto shuddered, refusing to believe she could be that vicious.
"Snowmelt. Just the thing to get you up and ready to face the morning. Or afternoon, as the case may be. Hey, what's this? Thought you didn't smoke a pipe anymore—don't tell me you brought someone home in your state!"
Pipe? Oh yes, the pipe!
"That's the only briar I ever loved, the one I lost," said Maroto as Purna put the piece back down on his mound of shed clothes. "She made it for me, made one for all of us, and somehow... somehow she brought it back to me."
"No way, that's one of Zosia's pipes?" Purna whistled. "That'd make smoking one almost worth the trouble. Can you teach me? Can I smoke musk flowers out of it?"
"No," said Maroto, something even worse than the evilest hangover of his life welling up at the thought of Zosia, a shadow in his aching skull. "Need something solid in me, Purna, or I'll fucking die."
The words brought another spasm; food was the last thing he wanted, but he knew from voluminous experience that it was a necessary devil.
"Maybe a nice slice of crow, since I warned you against eating that worm?" Maroto must have looked sufficiently pathetic for her to soften a little. "Choi and Zosia are scaring you up a plate of something hot."
"Zosia." It came out as a moan, the foreboding cloud at the edge of his awareness dispelled by the howling wind of reality. Maroto remembered everything. He dragged himself up into a sitting position, took the offered jug of deliciously cold water. After slurping some down, he tried to focus on Purna. "She's here?"
"Just missed her, champion—too busy blowing your guts out on yonder tent wall." Purna nodded toward the source of the stench Maroto only now realized was not rising from his own clammy body. Hey, he hadn't thrown up on himself—things were looking up! "Guess you two worked things out, yeah?" she asked.
"For now." Maroto shivered. Holy fucking devils, was this really all his doing? Had his sting-addled wish set in motion every bad deed that had led to Zosia coming here? Undoubtedly—this had Crumbsnatcher's tracks all over it. That rat loved nothing more than whispering in a sleeping ear, making it so you woke up thinking you'd had the greatest notion, or remembering something that had never happened... like receiving an order to execute a certain venerable citizen in a remote mountain town... Devils have mercy, Zosia had said her whole village had been murdered, a husband... That tore it, he was going to be sick again. This time he didn't make it to the side of the tent.
"I'm just going to see what's keeping Choi and that breakfast," said Purna, talking in the stilted tone of one being very careful not to breathe through her nose. "There anything else I can bring you?"
"Yeah," Maroto gasped between retches. "Diggelby's fucking head."
Thrice Sullen had carried Grandfather to Maroto's tent so that the three generations of Horned Wolves could finally sing for one another, and three times the girl wearing the pelt of their people had rebuffed them at the flaps. Purna, something Purna they called her, and she hadn't been rude about it, more annoyed at her captain for being so hungover he'd spent the whole day getting out of bed just long enough to puke before collapsing again. But the last time she hadn't even looked up from the card game she was playing with her comrades, all of whom also wore horned wolf trophies. Instead, she had just waved them off and said:
"Soon as he's sensible I'll fetch you. He ain't been up for more than five minutes at a stretch, though, so don't expect poetry from the poot."
"The poetry of Maroto; now _that_ I would like to hear!" said the duchess with the horned wolf tooth tiara perched atop her high wig.
"Yeah, thanks," Sullen muttered, carrying Grandfather back toward their tent. "With our luck he'll puke himself to death before we even get to hear his side of the song."
"We should be so lucky," said Grandfather. "He drops dead, we'll take his bones and grind 'em down to make you a weapon like the ones my mother used to wield. Iron forged with the ashes of your ancestors is the most powerful metal there is."
"Yeah?" Sullen hadn't heard this tale before. "Great-Gran had something like that?"
"One knife made from each of her mothers," said Grandfather, leaning in close to whisper in his grandson's ear, as though the camp was full of spies just looking to steal an old man's stories. "They never missed, Sullen, _never_."
"Huh."
" 'Huh' is all you ever say. _Huh_. Oi, laddie, see that hill there?"
Sullen saw it, all right: the camp backed into and partially up the base of a foreboding mountain, and right before the climb got really bad and the tents fell away was a tall spit of brown grass. Highest point around, short of climbing the mountain or one of the two ridges that came down like walls on either side of the camp, and without need for further clarification he tramped toward it as the Lark's Tongue speared the setting sun.
"There we are," said Grandfather when Sullen finally topped the hill, a crude symbol of stones at his feet and the whole world spread out beyond them. "That's something to see. Your Immaculate girl is in for it now!"
That she was. From down in the camp they could only see the ridgeline of the grassy rise across the low valley, but up here the foothills looked nearly as flat as the plains they melted into, and damned if the whole countryside didn't look like it had broken out in an angry rash. The Imperial camp wasn't twice as big as that of the Cobalts, but it was close. And from those Crimson tents to the valley floor it couldn't have been much more than an hour's march; from the valley floor to the first Cobalt tent was less than half that.
"Don't look good, does it?" said Sullen sadly. Their time was nearly out; as soon as tomorrow the battle could start, and what the hells would they do then? More specifically, what would Sullen do with Grandfather? He couldn't expect the old man to understand his need to fight in a war that they were no part of, nor could he leave Grandfather behind and go fight on his own—if he fell, what would happen to a Horned Wolf who hadn't walked on his own in over a decade? After all they'd been through, it looked like they might have squandered their only chance to talk to Maroto the day before, and now the battle might come before they could try again. Which meant they had to set out into the mountains that very night if they wanted to avoid a war between Outlanders, but it also meant leaving behind his uncle without giving him a chance to set things right... and leaving behind Ji-hyeon, which almost seemed worse. "Don't look good at all."
"Good?" Grandfather snorted. "Looks ruddy _great_ , laddie. If I'd known they remembered how to fight a real war out here, I would've followed Maroto the first time he left the Savannahs."
"Yeah?" Sullen didn't think he'd ever heard Grandfather call his son by that name.
"Yeah," said Grandfather, "I'd near given up on the notion, but looks like there's still hope for me makin' it into Old Black's Meadhall. If that many Imperial curs can't send me to the ancestors, then I reckon I might have to reconsider my whole mortality."
"You mean you want us to pledge our arms to the Cobalt Company?" said Sullen, half relieved to have the matter sorted in the best way possible, but only half, mind. He still hadn't seen Ji-hyeon since Zosia had brought the girl's lover back to her—as if Sullen needed more reason to be sore about the one called Cold Cobalt—and the notion that he now had an excuse to visit the general made him almost as happy as it did skittish.
"If that's what it takes to coax a smile out of you," said Grandfather, rapping his knuckles into Sullen's hair. "If the two sides are the Imperial dogs who dragged their Chain clear up to the Savannahs or anyone ruddy else, I'll raise my spear beside anyone ruddy else. Besides, that white witch wants us to leave, which is all the more reason to stay."
"Hoartrap?" Sullen gulped. If Grandfather found out—
"You did a lively dance keeping that from me, Sullen, though why you felt the urge I'll never guess. You think I'd be so ired over his bein' part of the crew that I'd wriggle after him on my belly, snapping at his ankles?" Grandfather's fingers burrowed through the hair that had caught his hand and scratched affectionately at Sullen's scalp. "Well, I suppose I might have, once upon a time. But he came by one of those evenings you were at your ease with that blue-haired... young lady. We had a talk, he and me, and we had a couple more since."
"Damn, Fa," said Sullen, impressed as ever with his grandfather's coolness. "You've known this whole time? I thought I was slick about it."
"Slick as pinesap."
"Huh. So what'd you talk about?"
"Never you mind," grumbled Grandfather. "You've kept enough of your secrets; I'm entitled to a few of my own. The relevant point is he wants us both gone, wants it in a bad way, which is why I've decided to stick around. I scare, the same as any mortal, but I don't scare by the likes of him. Now shake a paw, it's getting on in the day, and if we might die tomorrow I aim to get a good night's sleep first."
Even with the hardest battle of her life within spitting distance, Ji-hyeon couldn't help grinning as the four of them sat around the table in her tent. It was the first time in nearly a year that they had all sat together, sipping kaldi and passing a waterpipe, and for as much as the world had changed, they had not. Sure, she picked up more on minor frictions, like the glares Keun-ju would launch through his veil at Fennec or the saucy winks Fennec would fire back, or Choi's skepticism about both of her other guards, but those things had always been there, just swimming too deep for her to catch.
"Are you sure you wouldn't have the rest of your council in here for this?" said Fennec, nodding down at the map. "Just to make sure all qualified heads have a chance to take it in?"
"If she were worried about qualified heads, Brother Mikal, she wouldn't very well have you in here, would she?" said Keun-ju, sipping his kaldi.
"I've given a lot more people in this camp a lot more cause to wish me ill, Keun-ju, so I wouldn't make such a production about it," said Fennec. "Ji-hyeon seems to have gotten over it, so—"
"Enough barking," said Choi, which was enough of a burn coming from her to quiet them down. "Our general offers us paramount honor. Who else but her bodyguard need know her every movement?"
"I've done this enough times to know it's not as simple as we three keeping an eye on her," said Fennec, but he'd thankfully dropped some of the snide. "In a battle this big, if the general insists on leading from the field—which I still advise against, protective devil or no—the other captains need to know where to find her. An effective army is a coherent army, and plans we've spent a hundred hours perfecting may well fall apart in the first hundred heartbeats of the fight. If that happens we will need the command to regroup, and to do that the general _cannot_ penetrate too deep into the front, and the other officers must have some idea of where to find her. _Does that make sense?_ "
"If you bleating peacocks had let me speak, I would have told you that the rest of the officers have already gone over the plan. Several times, in fact." Ji-hyeon yawned, the gurgling pipe having counteracted the kaldi. "The Crimson agreed to meet us at noon, so I want everyone ready by dawn. No, make it an hour before light, just to be on the safe side. For now I think we'd all better assume this is our last night on the Star, and do some things we'll regret if we live out the morrow."
Fennec rolled his eyes, Keun-ju coughed and turned his face away, and Choi just looked befuddled. The more things change... However tomorrow's battle shook out, Ji-hyeon was glad these three were here to fight beside her, just as they had that fateful night of the Autumn Festival when she had found her calling.
"General," one of her tent guards called in. "Masters Ruthless and Sullen request an audience."
"Send them in!" Ji-hyeon realized she'd practically chirped it, and rubbed at her eyes in exaggerated fatigue to cover a blush of her own.
"Isn't the hour rather late to be meeting common mercenaries?" asked Keun-ju, and she'd been away from him so long Ji-hyeon couldn't tell if he was teasing her or actually jealous.
"Oh, I don't know," said Fennec, smirking at Keun-ju. "A general should always be accommodating for her troops."
"You _guys_ ," said Ji-hyeon, secretly loving the weird sensation of having her Hwabun crew here, providing a chorus to her new life just as they always had to her old. "They're probably just telling me they're leaving. They never actually pledged to..."
Ji-hyeon trailed off as the familiar shape of Sullen stepped into the command tent, the source of his delay now obvious: he'd had to unsling his grandfather from his back before entering the low-ceilinged tent, and now held the old man in his arms like the Star's nastiest baby. In all the excitement of the last few days, she hadn't been able to carve out enough time to see him, and now that he had come to her, was it really just to say good-bye? Their business was with Maroto, and if they had resolved it she might never see him again...
The old man said, "Sorry to interrupt, General Ji-hyeon Bong, General of the Cobalt Company, Second Daughter of some Immaculates I don't know nor ever will, but my grandson and I need a quick ear."
"Uh. General." Neither the presence of his grandfather nor Ji-hyeon's still-seated retinue seemed to be putting Sullen at ease, but then Choi clapped her hands together and rose to her feet.
"We will respect your secrets," said the wildborn, waving Fennec and Keun-ju to accompany her out. Ji-hyeon appreciated the gesture, but Choi's unique vocabulary proved especially mortifying—what was so bad about the word "privacy"? "Secrets" sounded... pretty damn appetizing, where Sullen was concerned, but that was beside the point. Choi was addressing Sullen now, of all people. "Has your uncle overcome his weakness?"
"Doubt he ever will!" said the old man, evidently appreciating Choi's turn of phrase more than Ji-hyeon. "If fear was a muscle, my son's would be bigger than his biceps."
"Choosing not to fight is not the same as fearing it," said Choi, taking the same chiding tone with this scarred-up geriatric as she always used to with Ji-hyeon. "I have seen how adeptly he avoids combat, how his eyes move when his body does not, how swiftly he strikes, when left with no alternative. When he chooses to spill blood, I believe he will prove himself undeserving of your scorn. When I asked of his weakness, I misspoke—I intended to ask of his injuries."
_Misspoke?_ In all their years together, of all Choi's strange turns of phrase, that was one term Ji-hyeon had never heard the wildborn use—she would clarify or translate, sure, but was as careful and precise with her language as she was with her sword. From the look Fennec and Keun-ju exchanged, they were similarly intrigued by this development.
The old man was less impressed. "The boy's certainly _adept_ at avoiding fights, I'll grant you that. I guess all your tongue-wagging means the _Mighty Maroto_ hasn't signed on for the big one, has he?"
"No, he has not," said Choi, and was that a trace of melancholy in her voice? "But it is honor that hamstrings him, not fear. You called him Craven, but that is incorrect. He is crude but strong. He is hurt but hopeful. He is loyal but conflicted. He is rash. Too rash. He has a devil inside him, but I think he can win against it. He will fare better with the tusks of his friends to face it."
Both the old man and Sullen looked taken aback at this, and they didn't even realize how rare a speech it was; usually prying that many words out of Choi required making an enormous error that demanded complicated correction. Then Choi gave them a nod and hustled out, but Keun-ju and Fennec seemed to have forgotten to leave.
"All right then, you two, if you'll excuse us—" Ji-hyeon began, but for the first time that she could remember, Sullen interrupted her.
"Nah, they can stay. General," he added quickly, eyes everywhere but on her. "We won't take but a minute, and I don't mind your captains or guards hearing what I've got to say."
"So say it," said the nearly toothless Ruthless. "Or I will."
"I knew you came to the Cobalt Company on your own business," said Ji-hyeon, feeling Keun-ju's gaze as she bowed to the two barbarians. "I have appreciated our time together, but unless you wish to be caught up in a war that you have no stake in, this is the time to go. I am... _delighted_ you came to say good-bye."
"Nope," said Sullen, and he took a knee with his grandfather still cradled in his arms. "I do have a stake in this, General Ji-hyeon Bong, Second Princess of Hwabun, Daughter of Jun-hwan and Kang-ho Bong: you. I pledge myself in your name, because you're the first person I've met outside the Savannahs who deserves all my respect, and more than I can give besides. If you say this war is worth fighting, I believe you." Sullen was looking up into her eyes now, and without glancing at Keun-ju or a mirror, Ji-hyeon couldn't tell if she, Sullen, or her Virtue Guard looked the most embarrassed by his proclamation. It might have been a three-way tie. "If you'll accept my oath, I'm yours until you release me from the Cobalt Company."
Ji-hyeon nodded, doing everything in her power to keep the smile inside her mouth, but Sullen must have caught the edge of it like he always did, for his eyes lit up as he slowly rose. Grandfather gave her something that might have passed for a salute, and said:
"I go where he does, so that means you've got my word, too." He winked a rheumy eye at her. "I wouldn't have laid it on so thick, mind, but I approve the arrangement, if you follow. If we could discuss restitution—"
"Another time," said Sullen quickly. "We'll leave you to your planning, then, General. Just wanted to make sure it was all sorted, since there's noise around camp about tomorrow being the big day. General. Um, Captain Fennec. Captain Keun-ju."
"I'm a Virtue Guard, not a captain," said Keun-ju, meeting Sullen's guileless, friendly glance with a flip of his veil. "It was so nice to finally meet you, after hearing all of Ji-hyeon's tales—I hope when the day is won and we can all return to being civilized the three of us can sit down for kaldi. I'm sure we have so much in common."
"One thing, at least," said Sullen, bolder by half than Ji-hyeon had seen him since that first night he showed up in camp. But quick as the confidence came it fled, no doubt impeded by his grandfather's snickering and Fennec's loud snort. "See you both around out there, I guess."
"I guess we will," said Keun-ju, and then Sullen was out of there as fast as his tightly muscled legs could carry him. Keun-ju whistled softly as Sullen ducked out of the tent. "Oh. So that's what you see in him."
"Are you sure you don't want to ask him to be part of your bodyguard?" asked Fennec. "You can't buy the kind of protection he'd offer you; it has to come from the heart."
"Or somewhere lower," said Keun-ju. "What?"
"Both of you, go," said Ji-hyeon, shooing them out into the twilight. "After all that scintillating conversation I'm quite exhausted, and think I may actually get a good night's sleep for a change. Don't come back until an hour before dawn."
Fennec made tracks, as he usually did, but Keun-ju hung back, his veil rustling in the breeze as he leaned in and whispered, "What about that whole we-may-die-tomorrow business? Making lusciously regrettable decisions? I've missed you so much..."
"I've missed you, too," said Ji-hyeon, pecking him on the lace-hidden cheek. "Now, as soon as you fetch Sullen and get him to agree to a three-way split, we can get on with treating tonight like our last."
Keun-ju pursed his lips and blew, kicking up the edge of his veil. " _Really?_ "
"Maybe for my next birthday," Ji-hyeon murmured, not really able to stop herself now that she'd gotten this close to him. She'd kept Keun-ju at arm's length when he'd first returned to her and they'd had their talk, because she still couldn't shake the doubt that his story was almost too plausible, that maybe he hadn't told her the whole truth... But then again, even if his allegiances were in question elsewhere, she knew she could trust him in bed. Oh, how she'd longed for him, every day since she had left Hwabun... Well, okay, most of them. "Tell you what, Keun-ju—let's go back inside and you can show me how much you missed me."
He'd missed her just as much as she'd missed him, apparently.
Zosia spent all afternoon with Singh and her kids and then ate dinner with Fennec, bullshitting her old friends nearly as much as they bullshitted her. Everyone had their doubts about the coming combat, but Zosia did her best to assuage them—she wanted all hands on blades when the day broke, and if people started losing their nerve now, an already dicey ploy would become unwinnable. In the end all it took was Zosia agreeing to pay the Raniputri mercenaries double what Ji-hyeon had already promised them, and telling Fennec that if he tried to change teams now she'd add him to her shit list. It felt good to know that threat still carried weight with people who knew her from the old days.
As the night wore on she went to check on Maroto again, but to hear his chums laugh about it the old bastard still hadn't recovered from his overindulgence of the night before. Diggelby had just given him something to help him sleep through the night, so after bandying a few words with Purna, Zosia ambled on. Not having much else to do, she took her time getting back to her cot, content to idly follow Choplicker as he snuffled along. In the morning thousands of people would die terrible deaths because a few narcissists were convinced they knew what was best for the Star, and one revenge-minded woman was willing to exploit them. Tomorrow old friends and new might die. Tomorrow the Star might be a very different place than it was this evening.
But tonight Zosia was going to sleep like a contented stinghound tucked in by his favorite centipede. Why shouldn't she? Melodrama aside, odds were the imminent battle wouldn't be the end of the matter; enough of one side or the other would retreat, gather their strength by preying on helpless villages who aided them from either fear or fervor, and then they would all go at it again. That order. Repeat as needed.
She could practically feel the tents humming with nervous anticipation. This was what they'd all signed up for, war... but to hear the other Villains tell it, and to read between the lines of Ji-hyeon's boasts, they'd yet to face a real engagement like this one. Whichever side was victorious, the devils would have more than they could eat on the morrow.
Choplicker seemed to be leading her somewhere through camp, looking over his shoulder to make sure she was with him before turning this way or that. She wanted him on good behavior during the battle, so she went along with him instead of reeling him in. It felt like a dream... no, not quite, it felt like she was wandering through a memory. This night, long as it already felt, might as well last forever—she'd paced camps like this before, the eve of a big tussle, twenty years ago, twenty-five years ago, thirty years ago... and for all the battles she'd won or lost, here she was again.
Ah, so that was what he wanted. The dog had backed his butt up so a friendly guard could properly scratch his rump. The tent the boy watched was the one they'd put the war nun in to convalesce, though the sawbones hadn't thought much of the weirdborn's prospects. Had Zosia known the sister was riddled with half-healed wounds before laying into her that morning, it wouldn't have changed her course—it was as overdue as it was richly deserved. Be that as it may, the war nun's continued unconsciousness was getting irritating, with her master Hjortt's army scheduled to attack anon and nary a confession yet extracted. Zosia had already stopped by twice that day to see if Portolés was alert, but whatever the barber had stung her with to ease the pain had put her down but good.
"She up?" Zosia asked the guard, who looked up from Choplicker and quickly snapped a salute.
"She came 'round and took some water when I got on," he said. "She's asleep again, I think, but I can wake her for you, Captain. My pleasure."
"Not just yet," Zosia decided, as much to spite Choplicker as to give the witch more time to recover before interviewing her. Depending on what she had to say, it was probably best if she was able to take another punch or two when the time came. "I'll be back for her soon enough. Thanks."
Choplicker made to go in anyway, but at a sharp whistle he slunk back, baring his teeth at her but not making a sound. Zosia offered the guard a stiff salute, and from the grin on his face she supposed she'd made the kid's night. Heading straight back to her tent, she gave Choplicker a reproachful shake of her head as he whined again. Whatever terms the queen offered now that she knew her assassination attempt at Kypck had failed, nothing could turn Zosia away from her due.
Slithering out of smoky, sweaty clothes in the chill of her tent, she supposed that was the real tragedy of it all. For all her musings that night, the truth was that she was here because she set out to bring down the queen... but even if she had died in Kypck alongside Leib and their people, this war would still be happening. General Ji-hyeon's plot against the Crimson Empire was exactly what Zosia had vowed and wished for, right down to the color of the flag on the rebel standards, but here on the cusp of successful retaliation, she was just another participant in a cast of many thousands. She had traveled to the far corners of the Star, only to find that the means to her end was doing just fine without her. She had become redundant in her own vengeance.
Crawling under her furs, she let out a long, wistful sigh. She had abandoned the Crown of Samoth precisely because she had concluded that it was beyond her power to change the world. Well, that and a guilty conscience over the realization that she had hurt just as many people as any tyrant before her, whatever her intentions. Now, twenty-some years older, she was all set to stir up the same crock of shit she'd thrown out the last time around, and for the same obvious reason—she thought the sovereign of the Crimson Empire was an asshole.
Except this time around she had only herself to blame for putting the crown on the queen's brow. Maybe she wouldn't sleep tonight after all.
# [CHAPTER
22](toc.xhtml#toc-chapter048)
Portolés was dreaming of Brother Wan when her eyes began to burn. She stumbled out of her visions, into the glaring lantern light, and tried to rub the itchy crust from her eyes, but both her hands were shackled to the makeshift frame of the cot. She felt languid from more than sleepiness and injury, and remembered the biting centipede the sawbones had offered her when last she woke. Had she accepted? Probably, from the heaviness of her limbs and the lightness of her head, though she had no personal experience with such medicine—the Holy Barbers of the Church declared it a sin to distract an anathema from the material experience of its redemption, and so when they had corrected her tongue, teeth, and other failings she had felt every prick of stitch and rasp of file.
"You look well," said Cold Zosia, the Stricken Queen dragging a stool over next to the bed. The old woman shimmered, and Portolés closed her stinging eyes, offered a prayer to the Fallen Mother for strength. When she opened her eyes they had adjusted to the brightness of the room, and there could be no doubting the woman before was of flesh and blood, not dream and smoke. "Probably could have given you a few more taps and you'd be no worse for wear, big strong monster like you."
"Zosia." The name sent a shiver down Portolés's spine even now. "This is an honor. It's not often a lowly nun is granted audience with a god."
"Oh, it's not so rare as your people make it out to be," said Zosia, crossing her legs. "But I don't think Indsorith sent you all the way here just to talk theology."
"Not much time, now." Portolés licked her lips, amazed that even with the drug, simply talking was so painful. The sawbones who had tended her had told her to make peace with her Savior, but she hadn't reckoned on it coming so quick. She wondered if she'd been dying ever since Heretic had rescued her from the butte, if need alone had kept her alive this long, and now that her confessor had finally arrived she could be set free. "I provoked your general before. That was unwise. If the Immaculate girl truly commands here, if only in your name, you would do well to bring her here as well."
"Oh, the kid's in charge, all right," said Zosia. "But what makes you think she wants to hear anything out of a Chainwitch?"
"Queen Indsorith wishes to prevent war. I have the authority to broker a peace on her behalf, something the Imperial regiments harrying you lack. If I can convince your Immaculate general, if _we_ can convince her, there will be no battle. There will be no _war_."
"Before Ji-hyeon hears word one of anything you have to say, _I_ need to be convinced," said Zosia, not sounding as though that possibility were very likely. "So somehow dear Queen Indsorith got the idea that I was going to lead a rebellion against her? I wonder who put that notion in her head?"
"It wasn't her order," said Portolés, keeping her voice low. Given Zosia's demeanor, it was imperative she not provoke the woman's wrath, lest it overrule her reason. But how could you keep someone calm when discussing the crimes you had committed against her? "She never ordered Colonel Hjortt to Kypck, never ordered him to make an example out of _any_ village. She never ordered him to execute anyone, not your lover, your townsfolk. None of this was her doing."
"Oh, well all right then!" Zosia threw her hands up. "I'll admit, I was a little worried on that account, but you've put my mind to rest. I will quibble with your choice of words, though—he was my _husband_ , they were my _friends_ , and you _butchered_ them."
"You have no reason to believe me, I know, but—"
"But what?" There was that temper Portolés had been warned of, a temper that might ignite an empire. "She had her move, but she fucked it up. Or rather, her assassins did—that's really the only thing an assassin needs to do, assassinate the target. And now that she sees the plan got botched, she sends you here as a peace offering? I'm supposed to think that it was coincidence that her troops went rogue, coincidence that they happened on Kypck instead of any other of the Empire's thousand other backwaters? Does she think I'm a _complete_ idiot?"
"No," Portolés said patiently. "She does not. She knows better than that, doesn't she? Something terrible happened to you, to your people, and now you are doing what anyone would expect you to do. And given your history, it is obvious that you would suspect the queen, even if it hadn't been Imperial soldiers who came for you."
" _Our history?_ " Zosia raised an eyebrow. "I've told no one of what happened between us, even after everything at Kypck. Am I to understand she broke _all_ of the oaths we made to one another?"
Devils take centipedes and all their soporific kind, Portolés was making a real mess of this. She had tried to talk the queen out of sending her for exactly this reason; that devilish tongue of hers always found a way to betray her. She bit the wicked flesh before trying again. "Given the graveness of the crime against you, and the importance of my mission, she thought it necessary that I know everything. So that if I found you in time you would know beyond any doubt that she sent me, and that I speak with the authority I claim. If I were acting on behalf of any other party I could not know what I do. I am her vouchsafe against further deception."
Zosia was listening now, really listening for the first time. "Prove it, then."
"Prove what?" Portolés wasn't stalling, she really didn't know what else to say that could convince this woman.
"Tell me the whole story, then, or rather, the version she told you. Then we can hear what I'm sure is a most convincing argument as to why she isn't the one I should blame."
"If you insist, Mistress Zosia." That foul curiosity that forever plagued Portolés's heart thrummed in delight at the prospect of having Zosia provide corroboration to the queen's most secret of songs. "Queen Indsorith was a lesser daughter of a minor noble in the Juniusian Court when you killed King Kaldruut and captured the Carnelian Crown. When your first mandate as Cobalt Queen was to disperse the Empire's wealth amongst the people, Junius was first to resist. And like all provinces who refused you, they suffered swift repercussions from your soldiers. What members of Indsorith's family survived your assault did not last long in the Ketzerel labor camps you exiled them to. Only when her last relations perished in bondage did the queen escape, coming to Diadem with a poorly conceived plan to assassinate you."
"She described it as 'poorly planned'?" Zosia smiled for the first time. "Well, I suppose it was."
"She was caught before reaching the second floor of the castle, but instead of a public execution you ordered that she be brought in chains to your throne room. Thereupon you had your private audience." Portolés waited, assuming this would be enough, but Zosia waved her on as she pulled out a curved black pipe and set to lighting it. "She said you looked... tired. You asked her what she intended, armed only with a sword and a grudge, and she told you what had happened to her people. Not to beg for mercy, but to be heard, but once, before her death. Everyone, even an Imperial noble, recognized that your reforms grew from a desire to help the people, but in doing so, countless innocents were paying the price. Instead of being ill-starred to be born a turnip farmer, they were ill-starred to be born noble, or landed, or devout."
"Your church, sister, was as corrupt then as it is now." Zosia blew smoke at Portolés. "I only wish I'd ignored my advisors and put every last one of your clergy to the sword. They said the Chain would help ease the transition to an egalitarian Empire, but those black-robed vultures conspired with the merchants and nobles to thwart me at every turn. That's my chief regret, that I didn't raze every Chainhouse before departing. But please, continue, this is all quite good."
"Yes, well..." Small wonder the church outlawed the mere mention of this woman's name. "After she had spoken her piece, you lectured her on the difficulty of ruling any land, let alone one in such desperate need of change. She responded with an insult, something about how Samoth would be hard pressed to find a worse ruler than you. That, she said, is when everything about your attitude changed, and you challenged her to the duel. And the rest is the rest, but you must believe that she would never, ever repay your—"
"The duel," snapped Zosia. "What did she tell you of it? I told you to tell me everything."
"My apologies," said Portolés, the sickeningly strong fumes of the woman's pipe filling the tent. "You told her... you told her you would grant her wish, as any devil would, and released her from her chains. You ordered her to resume her quest against you, then and there, but cautioned her that your duel could only result in death or exile. Then you fought, there in the throne room, on the edge of the precipice."
"Yes, then?" Zosia leaned forward. This woman was even prouder than Portolés, eager to relive her victory through the war nun's words.
"You defeated her—forgive me, I have not the tongue for describing whatever brilliant feint you felled her with. But after, as she lay disarmed on the floor, expecting you to deliver your hammer to her heart or perhaps kick her over the edge, to fall upon Diadem as an example, you dropped your weapon beside her. Lifted her up. Planted your crown upon her brow, and explained your meaning: she had accepted your terms, even if she did not rightly understand them, and as you were the victor she was bound to obey them."
Surely this was enough... but apparently not, Zosia waiting, a hungry smile behind the marrow-yellow stem of her pipe. Portolés concluded the tale in as colorful and flattering a fashion as she could manage.
"She was to learn firsthand whether ruling an empire and safeguarding the happiness and security of its subjects was as easy as she supposed. You drafted documents meant to guarantee the loyalty of your Villains as well as the rest of the governing bodies you had installed, and then you vanished from the Star. You even cunningly secured a fresh corpse from the pauper's field, and after the two of you dyed the dead woman's hair to match your own, she was hurled over the edge of the throne room to prove the story of your defeat—from that height, little remained of her features in the street below, save long cobalt hair and your dress. Queen Indsorith had won much more than she had set out to gain, and in exchange you were permitted to fade into the night, never to be seen again."
"Yessssss," Zosia said, savoring the telling of the tale far more than Portolés would have thought possible. After an uncomfortably long silence, and then, as if only just remembering more recent events, she snapped straight up on her stool and pointed her pipe at Portolés. "And Indsorith bided her time, patient as any devil, and only when I had long stopped fearing any retribution she sent you after me, to avenge her family. To take everything from me, just as I had taken it from her. The only difference is I never intended to hurt her, never intended to hurt anyone. I was healing the Empire, not harming it."
So says every tyrant, thought Portolés, but for once her tongue did not betray her. "So you believe."
"So I believe." Zosia nodded, standing. "Thank you, sister."
"Hear me out," said Portolés, realizing the arrogant woman meant to leave. "I... I beg you, Zosia, now that I have proven myself the messenger, listen to the message. Believe what you will when I am done, but pray, hear me out, in the name of your murdered people."
"I think I've heard enough," said Zosia. "Except, perhaps, why Indsorith should send you, of all people, to deliver this message. And why a war nun of the Burnished Chain would do the bidding of the Crimson Queen instead of her Black Pope—it is true that you fought your own kind on the road, is it not? Much as I'd like to claim the credit, the wounds you will die from came not from my hands, but those of your beloved church. Don't tell me you simply grew tired of being treated as a beast by those who hitched the plough to your back?"
"It wasn't Indsorith," said Portolés, praying her sincerity overcame a devilish tongue and the false tranquility of the insect sting. "Anyone who wished to hurt the queen would set you against her. What better means of harming her, of harming you both, than giving you cause to war against her? If she'd wanted you dead, don't you think she would have tried a little harder? Please, Zosia, you are too smart to be led by the nose like this, you know better than any that war will never—"
"That's not what I asked," said Zosia. "Now tell me, why are you the messenger of this tale?"
"Because I was the only one who knew exactly what you looked like now." Portolés closed her throbbing eyes. "And to convince you of her sincerity. I have not come alone."
"No?"
"No." Portolés looked up at the tear-blurred woman. "In my valise are writs that give me absolute authority to act on the queen's behalf, as I said, but there is something more. A manifest of the names of all the soldiers under Colonel Hjortt's command who were present at Kypck. A sacrifice. As soon as I reported what happened, how queer it all was, and what you looked like, and your dog, the queen realized what treachery was afoot."
"A sacrifice, eh?"
"Yes, Mistress Zosia, one to prevent a needless war. We are her gift to you, a token of her sorrow at your loss. I swear on the Fallen Mother, I was with Colonel Hjortt from the day he was given command of the Fifteenth, and not until we captured and killed your husband did he make any mention of such a plan. Queen Indsorith believes it was the Burnished Chain, and that must be why they sent agents after me, to stop me from alerting you to the truth."
"Hmmm," said Zosia, and to Portolés's elation she actually seemed to be considering it. "The Chain sent an Imperial colonel, knowing I would blame the queen. Interesting. That's why your Black Pope sent assassins after you, and why you fought them?"
"I... I can't say for certain why she sent them, but I fought them because they would have stopped me," said Portolés. "I don't even know for certain how the Chain found out my mission. I... A brother of mine, in the Chainhouse, he may have spied on my thoughts, after I met with the queen."
"So you have no actual proof that the Chain ordered Hjortt to target me and my people?"
"None," said Portolés, knowing that here at the end of her mission she mustn't deviate one step from what the queen had told her, mustn't stray from the truth even to better convince Zosia. Besides, Boris was right, she was a terrible bluffer. "The queen has no evidence to point toward the Chain or any other suspect; the single thing she is sure of is that she played no part in it. Allmother have mercy, knowing Hjortt as I did from serving in his bodyguard, it might have been as simple as that idiot hoping to seize an extra parcel of land for himself before the smoke cleared from the civil war. However he settled on his wicked course, it was not sanctioned by the queen. She is not your enemy. And unless you order your Immaculate general to stop, or talk reason to her if she in more than name commands this army, there will be another war, the worst war yet. She said that across all the Star, only you and she know just how pointless another war will be—even if you but agree to look over my writs and display them to whoever leads the Imperial army that threatens you, it will be enough to stop the killing before it is too late. She entrusted me with the most powerful weapon on the Star, and bid me deliver it to you, by any means: the truth."
Portolés shuddered, so much talk winding her as much as a jog up every flight of stairs in Diadem.
"That's only half my question, though, sister—I can tell you believe, I can smell it all over you... So why go against officers of your church, especially when you discovered that your queen gained her crown by treachery and deceit? She made a deal with a devil, Portolés, and yet you buck at your chains to serve her."
There was that hungriness again as Zosia pocketed her still-smoldering pipe and leaned down over the bed, no doubt hoping to catch a crack in Portolés's façade. There was no façade, so there would be no crack. For the first time, Portolés put into words the worm that had nested in her heart ever since Kypck. For all the orders and armies and schemes of mortals, it was true that nothing could destroy so absolutely as the truth.
"I came because I am guilty. It was I who carried out Hjortt's order. I was punished when I led the Fifteenth's cavalry back to the regiment, but not for the true offense. My superiors in the Chain told me that what I did in Kypck, to you and your people, was no sin, no sin at all. That I did no wrong there, for I am a vessel of the Fallen Mother, and that by killing them I had saved the souls of pagan peasants. But Queen Indsorith... alone, in her throne room, she told me that it was evil. That it was a crime, no matter what justifications I might present. And she is right." Portolés wept silently, her eyes becoming gummy as she shook with shame at what she had done, remembering how steady her maul had stayed as she brained the five Azgarothians who refused her order, one after another. Her faith had shielded her from this pain for so long, it was liberating to finally feel the full force of it. The magnitude of it was nothing short of heavenly... She had discharged her duty, and as she let the grief shake her she heard Zosia above her, crying as well.
No. She wasn't crying at all. She was _laughing_.
Unable to wipe away the thick film coating her eyes, Portolés blinked up at Zosia. The woman seemed to get ahold of herself, knelt down by Portolés's head, and murmured:
"You have acted with commendable bravery in the service of your Empire, Sister Portolés, and I cannot blame you for what happened at Kypck. I forgive you everything."
Of all the possible ends Portolés had contemplated, she had never dared hope for Zosia's absolution. An unexpected sob slipped out of her before she could stop it.
"There, there," said Zosia, stroking away Portolés's tears. "Was there anything else you wanted to confess, while you have such a sympathetic ear?"
There was. Portolés wanted to tell Zosia how good it had felt watching Efrain Hjortt burn alive, how the first step on her long road to the Lark's Tongue had come when she had decided to leave the little colonel to his fiery judgment... But here at last, her obligations met, she found herself finally free of the pride that had always governed her tongue. It was enough that she had done the right thing, she didn't need to crow about it, especially not to the woman who had set the fire in the first place; all Portolés had done was do nothing, despite the screams of a burning sinner.
"I... I thought I knew more than anyone in the Chain, even the Black Pope," she said, feeling the burden of this last sin rise from her breast as she finally articulated what had so long gone unsaid in the back of her warm heart. "I rebelled in every way I could think of, sinned for the sake of sinning. I did everything they expected an anathema to do, because I... because I wanted to prove they were wrong. That the Fallen Mother loved me no matter what they said. That if I pushed myself far enough, she would reveal herself to me. I just wanted to see her, to see the truth behind the Chain, before I went to whatever reward awaits me beyond this earth."
"Oh yes, plenty of rewards to go around, sister, and plenty of earth, too." Zosia laughed again, a malicious bark. "But since you're so keen to see some truths, maybe I can assist..."
The blur that was Zosia leaned down and ripped out Sister Portolés's left eye. An enormous, heavy hand fell over her mouth, and try as she did to keep her right eye shut, thick fingers dug under it. Another searing rip brought a gasp up her throat, only to be choked off by the palm sealing her lips, a thumb and ring finger pinching her nose shut.
"Everything all right in there, sir?" a voice called from just outside the buttoned flaps of the tent, and a masculine voice replied:
"Better fetch the barber, lad, the nun seems to have had a fit."
Portolés thrashed in her chains, but they had bound her well to the bed. The tent came back into blurry focus, and even being smothered she still shuddered with relief to realize her eyes hadn't actually been plucked out. They still burned, and, blinking the slime out of them, she saw not Zosia looming over her, but Hoartrap the Touch. He held her tight, suffocating her, and with his free hand waggled two shiny black leeches he held between thumb and fingers. Those must be what he had ripped off of her eyes. Tilting his head back, he dropped them into his mouth.
"Here's a little secret for you, sister, since you've been so free with yours," he whispered, his mouth full of blood as he chewed and talked. "Devils come in all shapes and sizes, and if you know what to do with them, any miracle is possible. The only difference between the Chain and my sort is that we sorcerers are honest enough to own up to our deceptions, once the parlor trick is over and the applause dies down. Would that all my audiences were chained down and drug-addled when I came calling with a pair of leech goggles!"
Portolés tried to bite him, but her teeth had been filed too close to the gums. The pain in her old wounds was nothing compared to the heat spreading from her chest, up her throat, pounding behind her eyes. She went limp, praying he would release her, if only to gloat a little longer. His hand tightened instead.
"At the time I didn't want to interrupt your little sob story, but I do think that having carried out your orders so diligently you're entitled to a little peace of mind where your church is concerned. I would hazard that you and Indsorith are absolutely correct about the Chain having sent Hjortt after Zosia to set this charade into motion. That's also why your own people tried to kill you before you could reach her, obviously, obviously. And the simple reason for all that plotting and scheming is that the Burnished Chain wants this war just as bad as me. That last little civil war of yours didn't claim nearly enough lives to summon the powers we're both after. This next one, though, promises to be a real corker—who knows what might happen, if the sacrifice is great enough!"
Black stars bloomed in Portolés's vision, the man rising rising rising away from sight, his voice still hissing in her ear.
"But do you know the biggest secret of all, my devil-blooded, witchborn friend? It's that none of you are devil-blooded at all, nor born of a witch, nor any of the other lies they spread around campfire and Chainhouse. You and your breed, my dear, are _divine_. There's a reason that more and more of you are born every year, despite there being fewer and fewer devils making their way into our world. It's because they're not where we've been, but where we're going. You're not some degenerate legacy of a corrupted ancestor—you, my child, are the future. Our future. There will come a day when your kind rules the Star, and whisper songs of savage mortals, the great fiends of antiquity..."
Portolés convulsed, felt something give in her chest, but even as she went to meet whatever gods or devils would have her, his fingers dug deeper into her flesh, his lips brushing her gnarled ear.
"But thank the Fallen Mother, that day is still a long way off."
# [CHAPTER
23](toc.xhtml#toc-chapter049)
Since sleeping without cares was apparently out of the question, Zosia would have settled for sleeping at all, but it wasn't to be. She did have few waking dreams of Leib lying beside her on the cot, humming the old marching songs she'd taught him during their annual summer treks up to that icy lake on the far side of the divide, the only place on the whole Star where she'd been able to pretend, if only for a few days of camping, that she and her husband had truly escaped the whole Star, had found themselves a sanctuary. If they could have stayed there forever, swimming in mountain-cold water and then warming up in the grass, instead of always having to return to Kypck, pink from the high mountain sun and reinvigorated for their duties to the village...
Yeah, that didn't really count as sleep. Grumble, stub her toe in the dark, get her armor on backward the first time around, stumble out of her tent an hour or two before dawn, and make the barber wake up the weirdborn nun even if it took every bug in his bag. That order. Aside from the last, she executed her plan flawlessly.
They had already moved her corpse out of the tent, knowing the white pavilions would be overfull within a few hours, if the battle went off as expected. The man who had brought her in had apparently been tasked with her carrying her out of camp so that she wouldn't start stinking up the place prematurely. The guards Ji-hyeon had assigned to keep him in custody had scared him up a spade and accompanied him up the rise to the edge of camp, lest this be some bizarre part of their plot. Thanking the sawbones who had given her the disheartening information, she was glad for once to have Choplicker along, the devil leading her uphill without needing to be asked.
They found the man ankle-deep in his work, his two handlers sitting on their asses until one of them recognized the approaching woman and they both scrambled to attention. She didn't even bother returning the salute or acknowledging the grave digger, her full attention on the lump of sackcloth. Squatting over the corpse, Zosia couldn't unearth her satisfaction, deep as she dug—she should have taken more time doing it, she told herself, but no, that wasn't quite it. Nor was it the soon-to-be-resolved business with the cavalry of the Fifteenth and their Colonel Hjortt, business Zosia had told herself and her adversary would be a far longer time coming... Vengeance is something best enjoyed when it's piping hot on the plate in front of you, rather than hoping it'll still be there when it cools down a bit, so she had no intention of letting Efrain Hjortt off the hook a second time, assuming she'd land him a third. What it was, she decided, was that this was all coming just a little too easily, the war nun, the colonel, and the cavalry who had carried out the crime at Kypck dropping square in her lap, just as she joined up with an army big enough to help her seal the deal. Zosia didn't believe in destiny, but she certainly put stock in deviltry, and focused her full attention on Choplicker, who was staring up into the dark morning, toward the night-swallowed Lark's Tongue. Could it be...
"You're really her, aren't you?" said the prisoner, leaning on his shovel.
"Get back to work," barked one of the guards, but Zosia said, "It's fine, I want to talk to him. Both of you, piss off back to camp."
"The spy—" began the other guard.
"I'm not a fucking spy!" the man spat, but then that was what any spy would say, wasn't it?
"He's in my custody now," said Zosia. "Dismissed. If I hear another word about it, I'll have Ji-hyeon whip the both of you, but only when my wrist wears out from taking the first round. Now get."
Watching the guards shuffle back down the steep decline, the prisoner seemed even less happy than he had with them riding his ass. His rationale made sense, when he voiced it. "I'm going in here with her, aren't I?"
"Depends," said Zosia, a thought striking her, and she pulled back the sheet to see if... But no, it was indeed Sister Portolés under the cloth, eyes staring at her maker or maybe at nothing, who among the living could say for sure? "Barber said she had a fit?"
"Oh, I don't doubt it," said the man dejectedly. "Getting your fresh wounds beat back open by a madwoman will give you the fits something bad. Betting fellow would say I might be about to have a fit myself, soon as I dig a deep enough hole."
"Like I said, depends," said Zosia, about to rise back to her feet when the faint smell of stale smoke crept up her nostrils. Leaning close, she took a sniff of the woman's shroud. Especially noxious toilet water and strong tubāq, a blend she would have recognized even if the barber hadn't mentioned that Hoartrap had been the one to pay a call just before the run shuffled off the Star for good. His presence at her deathbed was damning enough, but that he'd evidently taken enough time to stink up the place with his pipe raised even more questions...
"What was she supposed to tell me?"
"Like I said in the tent, to the _general_ , I don't know. Found some papers on her after she got beat on enough for me to slap the chains on her, but couldn't make much out of 'em: writs with the queen's seal and a roster of soldiers. That's the extent of it, so if you're going to put your devil on me to get the truth, do it quick and see for yourself I'm no liar."
"Devil?" Zosia rose to her full height, but Choplicker kept his attention on the unseen mountain, sniffing the dark as he took a few more tentative steps up the slope. "She told you that?"
"Lady, she never told me shit, other than a bunch of blather that sounded less like Chainite double-talk and more like the half-baked tracts I helped pass out back in the Jewel." The man was evidently the sort who liked sassing his betters, even when they held his life in their hands. Maybe especially then. "I know because I read those pamphlets, listened to the songs. Cold Cobalt has a devil to do her bidding, don't she? Or was that just another misprint, somewhere along the way someone scribbled down 'devil' when they should've wrote 'dog'?"
"We know which regiment is out there, so why wouldn't you come up with a better story, one where you rode in with the Fifteenth?" Zosia was talking to the dead war nun, but the man spoke for her.
"Hey, Cold Zosia, True Queen of Samoth?" She looked up at him, an already gaunt, dirty face made all the more hellish by the faint light of the lantern the guards had left. "Fuck you, lady."
"Fuck _me_?"
"Yeah." He nodded, as if warming to the idea. "Definitely. I believed in you, in what they said about your ways being better than those of the Chain or the Crown. I risked my life to keep your dream alive—maybe it wasn't much of a life to risk, but it's the only one I got, and maybe it wasn't my dream, just something I heard about secondhand, but it _meant_ something to me. The only thing I hate more than the Crown is the Chain, so yeah, the Song of Cold Cobalt was something I believed in. And you know? I _kept_ believing, right until I saw you lay into her. It took me lying and scheming and getting luckier than any devil to bring her here, to where I thought it might do some good, and what does the wise Zosia do? You killed her before she could even make a case for herself!"
"For a son of Diadem committed to the Code of Cobalt and dead set against Chain and Empire, you seem awfully broken up about a dead weirdborn."
"Her name's Portolés. Sister Portolés," said the man, staring at the war nun's winding sheet. "I never would have taken her here, I'd known you'd be just as bad to her as her kind would be to you, given the chance. So much for a fair shake. So much for a better world. You're no better than the Chain or the Crown, you just wear a different color and shit on different folks. Now, are you going to fuck off and let me bury her, or are you going to kill me? Because after the hours I put in serving the false memory of a dead woman who ain't even that, I'd appreciate the courtesy of not digging my own grave. Let the birds and beasts have me, maybe they'll find more use for a willing soldier than any of you lot ever did."
The lack of sleep must have caught up to Zosia, pried back her shell a little, because she felt his words like a snail feels salt. It wasn't just the speech itself, the final fist shake of a desperate, tired man who saw his own death not five paces away. It was that he obviously believed it, believed it as much as she believed the sun set in the west.
All across the Star, Zosia and her agenda had been championed by people she had never met, never even heard of, people who put everything on the line in her name... And all across the Star, she disappointed them, because at the break of day she was just as petty and stupid as they were. She felt an urge to tell the man to flee into the darkness and start over somewhere else, his mind scrubbed free from the oily film of idealism, while she finished digging a grave for the woman who had helped burn her world to ashes. She also felt an urge to snatch the shovel from his hands and beat him with it, a harsh lesson, but well needed, to never waste a breath praising a woman you know only from songs to her memory.
A horn blew from down in the valley, where the sentries had intercepted the man and the war nun the day before, sparing Zosia from having to choose between her urges. The man looked at Zosia, Zosia looked at the man, and then they both looked down at the dead servant of the Chain who had traveled so far to find her. Choplicker kept his gaze on the Lark's Tongue that only he could see, and then started barking fit to raise the dead, trotting up into the darkness. Yet the dead did not rise, and the man went back to digging as Zosia went after her devil.
Ji-hyeon was half dressed and less than half awake when she heard the first horn, and Choi and Fennec rushed into the dim command tent before the second sounded. Fennec helped himself to a bowl of kaldi while Keun-ju assisted Ji-hyeon into the rest of her armor—the plain but sturdy breastplate, greaves, and hauberk Zosia had helped her put together. Pulling the helm modeled after Cold Cobalt's over her head and feeding her long blue hair through the back, she took up the thick iron scabbard that housed her twin swords.
"How ready are we?" Ji-hyeon asked, her knees weak from more than the busy night she'd spent with Keun-ju. Maybe the day would be won and they would have plenty more time together, but they hadn't taken any chances. "How close are they?"
"They'll be most of the way across the vale before Singh and her riders are in position to support the rest of the cavalry, but that's all right." Fennec sounded like he was trying to convince himself as well as her. Not an auspicious start to the morning. "What good's the high ground if we leave it to meet them, anyway?"
"What good's fighting at all, before there's enough light to see the enemy?" said Keun-ju sleepily.
"They're trying to smother us before we're able to make the most of our defense," said Ji-hyeon. "A good thing we're early risers. If the other captains don't show up in five minutes we ride without refreshing, and hope they remember their roles."
"Tapai Purna's squad will reinforce your guard, General," said Choi, offering a curl of bone the Ugrakari girl had taken from a horned wolf. "She offers this horn as a token of esteem for the honor."
"Maroto's people?" asked Fennec. "What good are scouts at the front?"
"They are much better at fighting than scouting," said Choi. "Too loud. Too wild. They volunteered to scout for a reason, but without Maroto they'll have no cause to avoid honor-making."
"So Maroto never took the oath?" Ji-hyeon tried not to be too disappointed. It would have been something to have all the Villains with her, but if only two were sitting out the fight, her absent father and the grizzled barbarian would be missed the least. "I'd hoped he'd come around, especially after Sullen and Grandfather—"
" _Grandfather?_ " Keun-ju tugged the last strap of his banded armor tight. "I didn't realize I'd missed the wedding!"
"Maroto swears too many oaths, rather than not enough," said Choi, whatever the devils that meant.
"General, I do think we need to reconsider your whole leading-from-the-front strategy," Fennec said. "Even with your devil protecting you, it's just too dangerous—"
"This isn't my first dance," said Ji-hyeon. "I know better than to wade in too deep. I'll just bust a hole in their front line, then fall back. Repeatedly if needed. But I have to be close enough to the action to see where I'm most needed, not hiding out in the rear."
"In that case you may wish to sound the horn, General," said Choi.
"What? Oh! Come on," said Ji-hyeon, rushing outside with her guards following her. Chevaleresse Sasamaso had their horses ready, five reins wrapped in her gauntlet. There was something surreal about the camp being this bustling and loud by torchlight, with not a star in the black predawn sky. More horns sounded from all over the camp, from all over the valley, and, lifting her visor, Ji-hyeon slid Purna's gift between the steel canine jaws to wrap lips around the horn and blow a high, mournful trill.
Now that it had begun in earnest, nothing could stop the Second Cobalt War.
"Nothing's going to stop me from finding her," said Maroto, although, swaying on his gelatinous legs in the blinding lamplight of his tent, he had to agree that Purna had a point. He couldn't risk breaking his oath to not raise arms against Queen Indsorith more than he already had, but he also couldn't hope to find Zosia in the middle of a battlefield without doing just that. Still, he couldn't let something happen to Zosia before he could come clean about his wish to Crumbsnatcher—she was about to go out and kill a whole lot of Imperials, all because she blamed them for something that Maroto had accidentally set into motion. It might not change her plans for the day, since Zosia had never turned her nose up at fighting Crimson soldiers, but she had a right to know. Not just for her future, but for theirs—he'd fucked up enough for ten lifetimes, and couldn't live another day knowing Zosia thought him a friend instead of the source of all her hurt...
"Still with us, big guy?" said Purna, and Maroto realized he'd almost fainted. Again. What had become of the insatiable stinghound, that a single graveworm could lay him flat out for a day solid, and keep harassing him into the following morning? Only one thing for it, really.
"Diggelby, I need to see Diggelby. Right now."
"Don't blame him for your appetites, Maroto," said Purna, flicking him in the chin and nearly sending him sprawling. "You must be comfortable in that bed, since you were in such a hurry to make it. Now crawl back in it so I can get to work—we're riding out with the general, I just wanted to say good-bye in case... Well, I wish you were coming. It's going to be _epic_."
"I am," Maroto decided, everything making sense now. Giving Purna his best serious face, he said, "I swore an oath to protect you, Tapai Purna, and I don't break oaths."
"Except to the Queen of Samoth?" Purna looked skeptical.
"Not even to her. Now, help me to Diggelby's tent—he's been collecting shields from every encounter we've had, since clear back at that ambush in the Wastes. Says he's going to mount them in his den once he gets back home. I think he could spare a few in tribute to King Maroto."
"Whatever, man," said Purna, though she wasn't much of an actor—girl was over the moon her old hero had decided to get out of bed. "But if you can't walk out of his tent on your own, there's no way I'm letting you get in the fight."
"Don't worry about me," said Maroto as she helped him into the breastplate he'd mostly been using as a platter at the mess tents. "The Mighty Maroto's got a trick or two yet to impress the devils."
Sullen crawled out of nightmares and his tent, on his hands and knees beside the cold remains of their campfire while horns bleated and packs of bleary-eyed soldiers rushed all around, torches waving in the darkness. He focused on the dirt between his hands, terrified to look up at the black sky lest he see the Faceless Mistress looming over him, returning to claim him for failing to carry out her will. Yet when he refused himself another moment's fear and looked up, he saw only the darkest purple that preludes dawn. A dream, nothing more. Wiping his mouth and seeing the greasy black smear his lips left on the back of his hand, he allowed maybe it was a little early to call it.
A soldier rounded his tent at a full run and nearly careened into him before pivoting past. It was the other woman his uncle ran with, the duchess, dressed in what looked something like a scalemail catsuit. She had one of the weakbows Grandfather hated so much, though it was the largest specimen he had ever seen, all polished wood and inlaid metal gleaming in the light of the lantern her companion carried. Hassan was the bloke with the light, and in his other hand was the meanest-looking sword Sullen had ever seen, all serrated edges and hook tip. It provided a dull, earthy contrast to his frilly armor—Sullen hadn't even known you could dye leather pink, but it admittedly suited the man.
"Sullen!" said the duchess. "Just the moon-head we were looking for!"
"Moon-head?" Sullen touched his globe of white hair, too self-conscious to be mad.
"Your uncle Maroto extends his most sincere wish that you and your grandfather join us on the front," said Hassan with a bow, "where we may fight side by side, back to back."
"Huh," said Sullen, remembering what had happened the last time he trusted his uncle on the battlefield and not so sure he wanted to give him a second chance just yet. What if he was the one to end up crippled on the ground, begging for Maroto's aid?
"We shall be acting as the personal guard of General Ji-hyeon," said the duchess. "It is the most honorable of—"
"We'll be there in five minutes," said Sullen, hopping to his feet and ducking back into the tent without wasting another breath. Dark as the tent was, his eyes seemed to be getting keener by the night, and, giving Grandfather a firm nudge, he started fitting his gear in place. Only when he was all set and the old man had yet to respond to his patient muttering for him to get up did he take a closer look at his grandfather. His heart stopped, and his "Get up, Fa," never left his lips.
Only Grandfather's face emerged from the blankets, but that was enough to tell. The old man's eyes were wide, his face frozen in a contorted rictus, his tongue drying out in his slack mouth. Sometime in the night, he had...
"Sulllllllen." The voice drifted from Grandfather's slack mouth.
"Fa! Are you... What's wrong?"
"I... Cannnnn't..."
Even now his voice was fading, and Sullen put his ear to the old man's lips as tears began to well. "What, Fa? Tell me."
Grandfather cleared his throat, a gummy, smacking sound, and whispered, "I can't feel my legs."
Sullen slowly sat back, staring at his grandfather. The old man lost it, laughing until he coughed, and then laughing some more.
"Not going to be able to feel your arms, in a minute," grumbled Sullen, but he was smiling, too. It was time to see if they could find Grandfather a worthier end than dying in his sleep, a million miles from home. As if in answer, another horn sounded from the front.
"What the bloody shits are they doing?" Domingo demanded of nobody at all, but Brother Wan glanced back at his passenger and answered the rhetorical question anyway.
"I believe they are announcing our attack, Colonel Hjortt," said the anathema, his ghoulish face so pale it could be seen even on this Gate-black morning.
"That was one of our horns, not one of theirs," said Domingo. "Think I don't know the difference? Some dunce in the ranks is giving away our position!"
Another Imperial horn sounded, this time from the left flank instead of the right, and before Domingo could mount a proper splutter the damned cavalry issued a toot of their own from the vanguard. What was the point in sneaking up under cover of darkness if you blew your fucking horns the whole way? Was this the kind of cocksure madness Efrain had cultivated among the ranks? If so, good riddance to bad command.
"Perhaps the officers mean to alert the Myurans to the attack?" said Brother Wan.
"What attack? There is no attack, not until we can see something—oof!" A bump in the murky morning punctuated Domingo's point with bone tremors and a heaving stomach. "Stop the cart, Wan, this is more than close enough—I said take us down a bit, do you know what a bit means? At this rate dawn will find us in the bloody valley, bumping up against the rear, and I need to be able to survey the full field."
"I wouldn't have you miss that," said Brother Wan, tugging the mare to a stop with malicious abruptness. "No, I want us both to be able to see everything."
If only Domingo's body could be mended by willpower alone, he would have leaped from his bower in the wagon bed and punched Wan in his lipless mouth, and not stopped until his knuckles were full of splinters from the anathema's wooden teeth. If only, if only... Domingo was even more on edge than he usually was at the start of an encounter. He already regretted his decision to employ the Black Pope's weapon, though so far all he had seen was a disappointingly mundane prayer performed over his regiment while the witchborn clerics walked down the lines, dabbing oil on their foreheads. After it was all done and they started moving out he'd asked Shea if she'd felt anything during the ritual, and she said she'd felt bored, so apparently you got the same result from taking the oil as not. Wan had tried to talk Domingo into accepting the mark as well, but he had countered by pointing out that Wan himself had said only those on the battlefield would be at risk, and as Domingo didn't intend to set a single wagon wheel in the valley there was no need for him to find religion this late in life.
"It was wise to press on instead of waiting for the Thaoans," said Brother Wan, tying the reins on the wagon's unlit lantern post and stretching his thin arms. "What a pity it would have been, if Colonel Waits had lived up to her name and insisted we postpone the attack until the queen sent her permission."
"Waits is a damn good woman, damn good," said Domingo, not much liking having his thoughts, however sensible, repeated back to him by this witchborn. "I appreciate her enough not to put her in a prickly position. And what did I tell you about sticking your nose into my nut, Brother Wan?"
"Do you wish to know a secret?" said Wan conspiratorially, twisting around and slinging his legs over the back of the riding board, so his dusty sandals brushed the edge of Domingo's padded command nest. "It's something I've never told anyone, not even Her Grace."
"Hmmm," said Domingo, not appreciating how chummy Wan had become ever since he'd come out of the horned wolf attack with a few bruises from a tent collapsing on top of him while Domingo was dashed near to pieces. Wan evidently took his grumbling for assent, as he usually did these days.
"You know why Her Grace entrusted this mission to me, and me alone, don't you?" The eagerness in the witchborn's voice was disquieting, but around them the black was finally giving way to grey, allowing Domingo to see his guards... Except even after suffering through the needles of pain in his neck to peer around, there was no sign of the six stout pureborn soldiers he had ordered to replace the two who had fallen during the wolf attack. He was alone with Wan on the dew-dusted hillside as light finally returned to the Star. "Besides my commitment to the Burnished Chain, and my ability to carry out this morning's ritual, there was another reason she blessed me with this sacred mission. Can you guess why?"
"Haven't the foggiest," said Domingo, cheering himself by focusing on the lack of mist this morning.
"It's because I share a... special relationship with Sister Portolés." At the mention of the queen's assassin Domingo spat over the side of the wagon. "Her Grace interviewed me after being apprised of my abilities by Cardinal Diamond, and of course my history with Portolés. It was then I was deemed essential for the job—the thought being that if we caught Portolés upon the road, I could plumb all her secrets, no matter how dearly she wished to keep them."
"This is not news," said Domingo, wondering just where this nonsense was going. He could see a bit farther down the hill now, and the silhouette of the Lark's Tongue was coming into view above the distant fires of the Cobalts, but he still couldn't make out the valley floor. He could hear distant shouts and the clang of metal, though, and it sent a warm thrum through him, just as that concerto does through every good colonel. "On further evaluation, take us closer, Wan, we're still higher up than I thought."
"I will take us down soon enough, Colonel," said Wan, and the casual refusal to follow an express order filled Domingo with a loathing quite unlike anything a civilian, or even a son, could ever inspire. "As I was saying, I entered into our pope's confidence in part because she assumed I might be able to dig into her mind anyway, and in part because she was sure I could look into Portolés's. Have you guessed my secret yet?"
"You're a bloody dull storyteller?" said Domingo, though they both knew that wasn't true, and the real reason was beginning to materialize; like the lightening landscape around them, even with large swaths missing a definite shape was taking form.
"The truth, Colonel Hjortt, is this..." Wan narrowed his eyes at Domingo, muttered something unintelligible, then grinned. "You blame yourself for Efrain's death. You regret not doing more to prepare him for the role he took on. You think that by punishing everyone else who played a part, however small, you can absolve yourself of the greater sin."
Domingo stared in horror at the anathema, then lurched forward to seize him by the cassock. He doubled over in pain without even getting upright, the jarring motion making him feel like a saw was slowly grinding across the back of his neck. Through gritted teeth, he managed, "I told you what I'd do if you looked."
Brother Wan clicked his horrible, inhuman mouth. "And that's my secret, Colonel Hjortt—I didn't. I couldn't, even if I wanted to. No witchborn can, as far as I know. My secret is the secret of all anathemas, that we concoct excuses for the pureborn to treat us with respect or, failing that, caution. Like others in the Dens, I possess excellent intuition, something you and I share, but also empathy, in which most pureborn are deficient. No witchborn would ever disavow someone of the belief that we could peer into their innermost thoughts, for to do so would be to sacrifice one of our few advantages. But in truth, anathemas of my presumed powers are simply good listeners, good guessers, and good at altering our personalities to endear us to those we seek to convince—if you had seen me interact with Portolés, you wouldn't have recognized me, I don't think. Why do you think they say our abilities work best with those we know intimately?"
"But I felt you, I felt you rooting around in my skull—"
"What you felt was nothing more than your own paranoia, Colonel."
"Why are you telling me this, then?" said Domingo, wrenching himself back up into a seated position against the back of the wagon bed.
"You try it," said Wan. "Put yourself in my position, factor in everything you know about me, my desires. And _guess_."
Domingo had made the barber use the scabbard of his saber for the splint on his leg, but in this position there was no hope of drawing it. Meeting the anathema's too-friendly gaze, he said, "You don't think I'm going to survive long enough to tell anyone about it."
Brother Wan's bulbous eyes widened in mock amazement, and he raised his arms to the dawn. "Behold, an anathema in our midst! This witchborn mind-reader has passed itself off as Baron of Cockspar, but now reveals itself!"
"If you think you can take me, monster, I'm ready for you," said Domingo.
"Tut-tut," said Brother Wan, squirming back around on the riding board and untying the reins. "Maybe you don't have the sight after all. Or maybe your mind is enfeebled with age. Don't you remember that I wanted you to bear witness to the battle?"
The wagon jerked forward, and Domingo shuddered as another paroxysm passed through his spine. "Whatever mad schemes you've hatched, Wan, my regiment may surprise you yet, and their colonel most of all."
"I think you're the one in for a surprise," said Wan as he drove the wagon down the long hillside, the first light of day shining on the glittering masses of the Fifteenth, and the Cobalts who manned their pickets on the far end of the valley. "Before it's too late, are you sure you don't want to be anointed? It's not too late to receive the Chain's blessing."
"Think I'll manage without," said Domingo, offering a silent apology to his murdered son. For all his experience, for all his vigilance, he had fallen into the same trap as Efrain. Why had he ever allowed an agent of the Chain into his command tent? He had learned long ago to salvage wisdom from his failed efforts, but of all his unsuccessful plans, this was far and away the worst, and one he might never be able to learn from.
"This is the worst plan you've ever had, no mean feat," said Purna as Diggelby laid one jar after another on his tea table with all the pride of a new parent showing off his progeny.
"The best ones usually are," said Maroto, thumping the pot in his hand and provoking the finger-long centipede into striking the glass. "I'm telling you, Purna, I won't be any use like this—only cure is a bellyful of the worm that gnawed me. It'll make me better than new."
"Until you come off it again," said Purna. "How bad will it be next time, if you keep eating them?"
"Baaaaaad," said Diggelby. "I know from experience."
"Me, too," said Maroto. "I swear on my honor, Purna. This is the last time."
She gave him a look he knew all too well, and it would have broken his heart if it wasn't busy racing at the prospect of another worm. She wanted to believe him enough that for the moment she did. Or maybe he wanted her to believe enough that she was going along with it; the end result was all that mattered. "I'm going to see what's taking them. Hurry the hells up. We should've already rendezvoused at the command tent."
"Ack," said Diggelby, pulling a face as he chomped his worm and passed the box to Maroto. The bug-headed noble didn't even take his own advice; he'd told Maroto just the other night not to chew the things. Extracting one of the grubs that extruded from the piece of bamboo laid in the box, Maroto gulped it in one go, then had another for good measure. And a third; these were a lot smaller than the one Diggelby had given him before, so he had to make sure he took enough to overpower his hangover.
"You really should keep them in cemetery dirt," he said, passing the small box back over. "I didn't even know they could live anywhere else."
"Ah," said Diggelby, nodding with the air of a master imparting wisdom to a novice. "Graveworms require such soil, but these little fellows are only found in this rubbery bamboo that grows down in the Dominions, on the border between—"
"Diggelby," said Maroto, more focused than he had felt in memory, and not from ingesting the bugs. "Diggelby, what did you just feed me? A graveworm, right? Just some exotic breed?"
"Hmmm?" Diggelby's eyes were all pupil, and Maroto began to panic. The pasha was off his fucking gourd on grubs. "Oh no. Nothing like a graveworm. Bamboo worms are..." He grinned, showing teeth dripping with white goo. "Unique."
"Unique _how_?" asked Maroto, having no idea if his pounding heart and sweaty brow stemmed from the insects in his belly or his anxiety at what they might do. He could have just slit his own throat.
"Dreamy," said Diggelby, waving his hand back and forth and giggling at the tracers they left hanging in the air. Wait, what? Ancestors watch over him, Maroto was already starting to hallucinate. "Something to help you sleep, and see such sights as—"
"Diggelby, you dumb moron, I said graveworms, _graveworms_!"
"No," said Diggelby, sounding completely sober as he leaned forward and pointed at Maroto. "You said you needed another of the worms I fed you last night. Last night I gave you one of these, because you'd spent all day puking and I knew you'd never sleep through the night without it. The graveworm was _two_ nights ago, so don't blame me if you can't communicate with language like most upright persons."
"Why would I want to take something to sleep right before a battle!"
"Because when you take a hit off of this guy, you'll be more awake than you've ever been in your life, and still get to see all the dream stuff from the bamboo worms." Diggelby held up an empty wine bottle with an enormous scorpion clicking angrily in the base. "I put him in when he was tiny, and he's grown too big to get out. I don't know what I'll do when his stinger won't fit through the neck." Diggelby inserted his pinky into the opening, and before he'd wiggled it twice the monstrous arachnid jumped clear up the side of the bottle, burying its stinger in the fingertip. Diggelby yanked it out with a yelp, his pale pinky turning as blue as the bands on the scorpion's back. "You have to be quick about it, or your finger will swell and you'll never get it out."
There was a time when Maroto would have tried to stick his tongue down the neck of the bottle to get the most out of the experience, but those days were mercifully gone. Well, not so gone, then, considering he was starting to feel a torpor in his limbs from the whatsit worms, and sleeping this one out was starting to sound pretty capital, as Diggelby would say... The dreams of last night were returning to him now, stranger dreams than any he'd ever lived, and going back to that place would be so nice...
No. He had oaths to keep, and grabbed the bottle from Diggelby. Tried to, anyway, but his numb arm just knocked it out of his friend's hand, and it shattered open on a steel spike protruding from the shield at Maroto's feet. There was a desperate moment where nobody moved, and then everyone moved at once. The scorpion scuttled out from the shards of glass, and Maroto managed to get a sandaled foot in its path just as Diggelby lunged forward to grab at it, inadvertently headbutting Maroto in the stomach. Bless the gods of the undergrowth, for the scorpion planted its stinger deep in Maroto's ankle before scurrying across the tent and into the heap of Diggelby's bedding.
"I'll find _you_ later," Diggelby called after it in a come-hither voice. "He got you, didn't he?"
"Uh," said Maroto, vibrating all over. It felt like he had injected magma into his ankle, the hit unlike any scorpion he'd ever sampled. He definitely wasn't drowsy anymore, his thoughts coming faster than he could voice them: "WhatkindoffuckingscorpionisthatDiggelby?"
"I don't know the Classical Immaculate name for the species," said Diggelby thoughtfully. "I just call it _that brute I found in my slipper back in the Panteran Wastes_."
Maroto stared at Diggelby, who seemed to be swelling like a puffer fish, ripples extending down his fleshy neck and across his padded caftan. He had just dosed Maroto with two separate exotic bugs, neither of which even an inveterate connoisseur of his experience had tried before, and one of which was presumably unknown outside of the wilds. They were both still giggling when Purna shoved her melting face into the tent and told them to move their arses. Snatching up the two heaviest shields in Diggelby's collection, Maroto glided after her. He had promises to keep, even though breaking them always came so much easier.
# [CHAPTER
24](toc.xhtml#toc-chapter050)
So much for her esteemed personal guard. With first light showing but not a one of Tapai Purna's crew, Ji-hyeon mounted her charger and gave a final blow of her horn. With Keun-ju, Fennec, Choi, and Chevaleresse Sasamaso leading the dozen mounted knights that made up her bodyguard, she cantered through the camp, waving her flag-spear and picking up a wake of foot soldiers as she rode down the base of the Lark's Tongue, toward the bloody battle at its foot. Dark as it remained with the sun still hidden beyond the foothills, Ji-hyeon was pleased her army had been ready to meet their attackers, and begrudgingly impressed by the initiative of the Fifteenth Regiment.
The Crimson cavalry had attempted to crash through the pickets and pikers stationed just where the incline steepened, but before they'd reached the massed infantry more horns had sounded and the Cobalts responded in kind. Faaris Kimaera was an old sellsword Fennec had scared up in Nux Vomica, and the master horseman had led the motley Cobalt cavalry down from the southern ridge to intercept the Crimson riders. When the Imperials veered across the edge of the valley to meet them, Chevaleresse Singh's dragoons had swept down from the northern ridge, striking the Crimson cavalry across the rear flank. Beset on two sides by riders and with the Cobalt pikers jabbing at them from the slope above them, the Crimson cavalry nevertheless held their own. They defended their sides, repelling the Cobalts from penetrating their troop, and pushed hard up the hill, meeting rebel polearms with heavy lances and crushing the tightly packed defenders under hoof as they broke through the front lines. Behind them, the Crimson foot were charging fast, a wave of blood crossing the valley to wash up the base of the Lark's Tongue.
Avoiding the press of her main infantry, where she'd do more harm than good trying to break through and the soldiers jogging after her would be wasted, Ji-hyeon led her retinue and the several hundred infantry who had followed them from camp around to the north, where their fellows were thinner on the ground. Mostly deaf from the cacophony of the battle before she even joined it, she reached Kimaera's cavalry and skirted their edge, meaning to bolster their defenses from the charging red infantry while the Cobalt riders drove inward to meet Singh's contingent, squeezing the Crimson cavalry between them. Hoisting her spear aloft and giving the flag a final wave, Ji-hyeon set the weapon and spurred her charger into the oncoming horde, Choi on her left with an enormous crescent-bladed moon-spear and Keun-ju on the right with a long, tasseled trident. Fennec seemed to have fallen behind with Kimaera's cavalry, but her mounted knights and the crowd of panting foot soldiers still trotted behind them. Fellwing circled low over Ji-hyeon, and she tried not to be reminded of a vulture as her speeding horse delivered her to the fiercest battle of her life.
Arrows sped back and forth on either side of her, and then Ji-hyeon's charger crashed into the raging red sea. Her flag-spear punched through the breastplate of a bellowing woman in the front, and Ji-hyeon dropped the weapon just in time to avoid having her arm wrenched out of joint as the horse carried her deeper into the enemy infantry. She jerked the reins to wheel back out of the horde, but the Imperials were packed too tight all around her, with more pushing in all the time. Worse still, the Cobalt soldiers she had intended to lead into the fray had fallen behind, and now the front line was behind her. She had used this maneuver half a dozen times, but never driven so deep into the enemy. Shit.
Pikes jabbed at her, swords scraped across her horse's chainmail, bounced off her greaves. She fumbled her twin long swords from their scabbard, nearly dropping one as an arrow ricocheted off the side of her helm. Adept at riding as she'd become since leaving Hwabun, wielding a sword in each hand while surrounded by a furious armed and armored mob didn't allow for elegance, or much control of her charger. The warhorse was a better steed than Ji-hyeon was a rider, fortunately, his controlled bucking and kicking preventing her from being dragged down by the Imperials.
For now, anyway, the Crimson soldiers were throwing themselves at her, eyes wide under their pot helms and mouths flecked with froth as they careened at her, heedless of her horse's hooves or her steel blades. They were clearly mad with rage, behaving less like trained soldiers and more like fire ants swarming their prey. In the past her legendary appearance had instilled palpable fear in her foes, but here the soldiers betrayed no trace of anything resembling recognition or even understandable wariness, only a fury that was all the more disturbing for its presence on virtually every face. A man with skin as red as his tabard kept spitting and foaming after her sword jabbed through his throat, as though hate alone might keep him alive.
Two more men seized her leg on the other side, and as she swung around to beat them back, her faceplate was misted with blood as Choi's moon-spear hacked one of their heads off and embedded in the neck of the other. Still he clung to her greaves, trying to pull her down, and with a slash of a sword she completed the job Choi had started. Arms already sore, she spurred her horse's left flank, and the well-trained animal angled them back around as best he could in the tumult. Yet as he turned and Ji-hyeon saw Choi's spear blade fanning through the air to beat the red soldiers back, she realized in the press she had no idea which way they had come. This was exactly what Fennec had tried to warn her about; she'd done a very, very stupid thing, and was on the verge of panic when a chirp from Fellwing caused her to look up, beyond the chaos, and see the Lark's Tongue off to her left.
"Fall back!" she cried, but even as she gave the order she realized she couldn't hear her own voice over the raging battle, couldn't see Keun-ju or Chevaleresse Sasamaso or any of her other knights, only the turbulent waves of red curling with flashing steel and, impossibly distant, the ragged blue line of her infantry. A pike jabbed up, glancing off the snout of her helm, a sword pierced her charger's armor, causing him to rear up violently and nearly dislodge her, and Ji-hyeon cursed herself for the biggest fool to ever jump headfirst into hell.
By the time Zosia slid back down into camp, corralled the hundred confused foot soldiers Ji-hyeon had given her to command, and had them tap a like number of archers from the formation firing down into the valley, the Cobalts holding the front already looked to be in some serious shit. They'd be in a far riper mess if she didn't get things in hand on their rear, however, which she had to repeat three times to the lieutenant commanding the archers before the woman would let her take off with a hundred sorely needed shooters. Then it was a race back up the hill, through camp, keeping her eye on the exposed hump that marked where a small plateau jutted out of the Lark's Tongue five hundred feet farther up the mountainside. Any moment she expected to see the first Crimson soldiers crest it and come charging down the steep slope into camp, but nothing stirred among the rocks and cacti. The Lark's Tongue was bare to the hump and nearly bald from there to the summit, with only a few low bands of the pine that swathed the surrounding mountains, but she never would have scrambled high enough to spot the flashes of metal coming around the mountain's shoulder as the sun finally rose if Choplicker hadn't made such a stink about it.
There was nothing beyond the front of the range here but a lot of rough country, and ever since the Fifteenth had left the road fifteen miles south to follow the Cobalts' trail they'd been monitored by scouts, who'd reported no contingents splitting off to flank them. That meant the ambush had been set into motion before they even came down from the mountains, which bespoke a degree of tactical sophistication Zosia never would have credited to Efrain Hjortt—the boy must be taking things a lot more seriously since she'd cut his thumbs off. He couldn't have spared a large force for such a risky course through the trackless wilds, but it might have been enough to cripple the Cobalts, if Zosia wasn't there to help. She knew a classic wolf trap maneuver when she saw one, though she'd always led the Imperials into them instead of building the gambit around an existing camp; a lot could go wrong if you didn't already have both units in position to crush the enemy between them, as she hoped to demonstrate by taking that defensible plateau first and firing on the Imperials as they came scrambling down from the pass above.
As they reached the upper edge of camp, the runner she'd sent to alert Ji-hyeon of the ambush came huffing around a tent and waved her down. He didn't look like he had good news.
"Let me guess," Zosia called, "our fearless general's decided to lead from the front?"
"Uh-huh," panted the runner. "But I found these two, looking confused, in front of the command tent, so I brought 'em, 'cause you said bring any able hands."
The tallest figure Zosia had ever seen caught up to the runner, looking a sight less winded. Zosia grinned up at them, and called out in the Flintland tongue, "Well, you don't get more able than four hands on two legs, do you?"
"Uh," said Sullen, not meeting Zosia's gaze. "It's you."
"Manners, laddie," said old man Ruthless, resting his hands on his grandson's bulb of hair like it was a pulpit for his oration. "Anyone to lay out my son the way she did is worth a nod, if not a drink. What shall we call you, madam, since we've not been formally introduced? On the road we heard a lot of titles, so let's see, is it Cold Cobalt Zosia, Forsook Queen, Captain of Cobalts and Banshee of Blades, First Among—"
"Zosia is fine," she said, seeing where Maroto had inherited his love for the sound of his own voice. "I'll just call you Ruthless and Sullen, since I hear those are your names. Fair?"
"More than," said Ruthless.
"What..." Sullen was staring at Choplicker, who'd come over and rubbed his head against the man's leg. "What's your devil's name?"
"A devil's true name is a powerful thing, Sullen." A few concerned murmurs came from behind Zosia, but she didn't really mind his outing the fiend—if she didn't get to enjoy anonymity anymore, neither should her devil. "I just call him Choplicker."
"Huh," said Sullen, scratching behind the monster's ear to an appreciative yowl.
"I'm more concerned with mortal affairs than my grandson," said Ruthless. "Your errand boy said swords were needed to meet a pack of Crimson cowards stealing down the hill, that the shape of it?"
"Fa," said Sullen quietly, looking up from Choplicker but still keeping his eyes off Zosia. "We're supposed to fight with Uncle, help out Ji... General Ji-hyeon."
"And they weren't where they said they'd be," said Ruthless, "and the lady wants further proof against cowardice. What're you moaning about?"
"It's a big battle, Sullen," said Zosia. "You'll do more good for your uncle and friends by thwarting an attack on their rear than you will by wandering out into the field, hoping to find two fighters amidst twenty thousand."
"That many?" said Ruthless gleefully. "Oh, this ought to be a fine sendoff!"
"Yeah, all right." Sullen looked bashful as a virgin asked to dance by the most notorious rake in the room, and it gave Zosia a petty pleasure to see him squirm. Whatever Maroto thought about his motivations, it was plain to Zosia the boy either wanted her dead or in bed, or maybe he didn't even know which he wanted.
"I'm trusting you to watch my back, Sullen," she said, unable to resist, and that finally did it—he looked her in the eyes, and she saw the last thing she'd expect from a hard-looking Horned Wolf: he was scared of her.
"Yeah. All right."
" _Yeah, all right_ ," his grandfather mimicked, and, reaching behind the boy's head, he pulled out one of the crazy-looking knives certain Flintland tribes used to throw at one another. "We've snapped and snarled enough, now let's put our teeth to some use!"
"Up we go, then," said Zosia. Raising her voice to address the archers and foot assembled behind her, she shouted, "I'll whittle a pipe for the first one of you to draw Crimson blood!"
A handful of huzzahs, and whole lot of confused stares. What was the Star coming to?
"Or a bottle of the best booze in camp, your choice!" That got a proper showing out of the ignorant blackguards, and Zosia set off up the escarpment, trying not to be too annoyed that the one skill she took actual pride in commanded such little regard. Oh well, a bottle was a lot easier to procure than briar and a lot less work once she had it; her hands would be busy enough in the days to come.
First Sullen and Da were a no-show at Diggelby's tent, and when Purna got tired of waiting and dragged the Moochers to the command tent they found Ji-hyeon had left without them. Suggestions that they stop off for another round were shot down by Purna, who had her meanest face on. Maroto didn't see what the rush was, considering that the swirling patterns of blue and red that flowed across the valley floor didn't show any signs of fading. Around that time, though, Maroto stopped being able to hear anything Purna or the others said, his one good ear filled with the grinding of insects beneath the earth, graveworms stirring from here to the far valley, rising to the surface to feed...
Purna led them down, but Maroto couldn't look at her anymore, couldn't look at Diggelby or Hassan or Din, because when he did he saw right through the garish makeup and the skin beneath it, saw all the way to their yammering skulls. He put all his attention on Prince, because Diggelby's lapdog kept looking up at him with this weird little smile as he trotted along beside the crew, and while he didn't look much like a dog anymore, at least he didn't look like a walking corpse with its face all chewed away by scavengers, and by Old Black's loose tooth, Maroto had never had a sting trip him out this bad. He was bugging _balls_.
"Will you stop!" Purna said. Maroto looked up from Prince, relieved to find the grinding riot in his ear had quieted, replaced by the good old-fashioned ruckus of countless people murdering each other. "Thank you."
"Eh?" But the sound returned as soon as he said it, and Purna's skull snapped at him again, a blackened skeletal finger pointing to her jawbone. "Oh."
Maroto stopped grinding his teeth, and the sound stopped, too. Funny how that worked. He closed his eyes, told himself when he opened them again the world would be back to normal. He gave it a go, and saw they'd come down the hill and were less than a hundred paces from the back of the press, bodies fucking everywhere, people wandering around them holding their limbs and where their limbs used to be and weeping and dying and sometimes both, blood welling out of the very earth, and Purna popped him in the cheek, like that ever worked except in the songs.
"Maroto!" The skull under the horned wolf hood sounded just like Purna.
"That'sdefinitelyme," he said, hoping he sounded convincing.
"Some people saw her ride in around there, but it's going to be a mess just getting through our people to the front—you wait right here until we come back with Ji-hyeon, all right? _Don't. Move_."
Purna was gesturing off into the cloud of whizzing weapons and splattering gore that floated in front of them. As he squinted, it was like his confused brain thought he was already in the mix, because things started getting all precise the way they did when he was in real trouble, the incoherent blur of the battle coalescing into a hundred thousand crystal clear images: An ax cleaving an arm off. A woman bringing a shield up too slow to intercept the spear that was going to puncture her heart. A horse brained with a mace. The rider swinging his sword into another man before his horse even knew it was dead.
"Right, good. _Stay_. If you have to move, go back to the tent," said Purna, turning away, but before she'd taken a step an arrow launched from two hundred yards deep in the melee came hurtling down to skewer her face. Well, hurtling was selling the song a little hard; it just kind of drifted down, like it didn't have a care in the world, leaving a shimmering trail in the dawn sky, and so Maroto wasn't in a hurry, either; he just bumped past Hassan, apologized for the slight, and then long-stepped up beside Purna, raising one of his shields to neatly catch the arrow before it killed her. The point shivered on his side of the shield, having penetrated both steel and wood just above his sweaty grip. Could've planned that better; an inch lower and it would've gone right through his hand! He'd have to be more careful.
The human eyes in Purna's skull face wobbled at him, Hassan gasped in belated shock, and Din said, "Fallen Mother's mercy, I've never seen a mortal move like that."
"I'maVillainyeahdidn'tgetmyreputationleadingnoguidedtoursofthePanteranfuckingWastes," said Maroto, and Diggelby laughed and laughed, swooping Prince up in one arm and waving his crystalline cutlass around in the other like this one actor Maroto had run with who had this great mad pirate character he'd play, and Purna patted Maroto on the shoulder and sounded a little freaked out when she thanked him but didn't try to make him stay behind anymore, and they all started running to some quarter of the world-encompassing battle that was supposedly better than the rest of it. Leave it to the nobles to know where the best party is happening.
"Question," Maroto hissed back at Diggelby as they wove through the throng, not wanting to alarm the others. "We'rethebluesandthey'retheredsyeah?"
Diggelby was still laughing when another arrow arced down from the clear morning sky, too fast for even Maroto to stop, an evil black tracer wavering in the air behind it, and it was a queer thing, to be looking at a laughing friend and know they were dead even before they were, to see them acting alive and hale but know they were a ghost and just didn't realize it yet. Yet instead of spitting the fop's lace-ruffled neck, the arrow was nudged over at the last moment by a breeze, the missile hitting some poor bastard behind them, snuffing out some stranger's friend instead of his. Maroto started laughing right along with Diggelby, because when you got right down to it, there wasn't anything more hilariously random than war.
Sullen had fought against the tide of the camp, a flood of eager, frightened, and resigned faces flashing past him as he made for his uncle's tent. It was empty, and when nobody returned after a few minutes he hustled Grandfather over to Ji-hyeon's tent, but he'd just missed them, too. It seemed smartest to wait there until someone came to tell him what to do, even with Grandfather harassing him to just run down the hill with the rest of the Cobalts and see what they could find at the bottom. The truth was, Sullen couldn't bear the thought of his leaving the command tent only for Ji-hyeon or maybe Uncle Maroto to wander over just after they'd left, so he made Grandfather promise to wait ten minutes, since the clashing armies in the valley wouldn't be going anywhere.
And once again, he should have listened to his grandfather, because the sweaty guy who had run up, poked his head in the tent, and then told Sullen to follow him back to some fight that was happening ended up delivering him right to Zosia. And now he'd gone and told her he'd watch her back, so there was another fool thing he'd blundered into—after giving his word, he wouldn't feel right carrying out the will of the Faceless Mistress. Not today, anyway. So that was maybe a good thing, gave him one less thing to worry about... Unless she'd somehow figured out he'd been sent to do her mischief, and meant to use the confusion of battle to move on him before he could move on her. Unless that.
"You watching that back?" whispered Grandfather as Sullen scrambled up the steep, grit-slippery slope. Above them, the ridgeline they'd called a "hump" poked out like the mountain's potbelly, but they still had a climb ahead of them to reach it. Zosia was a few lengths ahead of them, and yeah, being real with himself, he had been watching her back a bit; hard not to, from this angle, leather britches taut against her posterior.
"Shut it, Fa," said Sullen, but that must have answered the old man's question well enough, because he brayed with laughter.
Glancing back, Sullen promptly stubbed his toe and went down on one knee, gashing it open on a shelf of rock. He barely noticed, gawping out at the valley beyond the camp. Big a host as the Cobalt Company had seemed, the Imperials were bigger by half, at least—he'd only seen glimpses of the Crimson army after he and Grandfather had met Ji-hyeon in the mountains, when the Cobalts would get a vantage point to look back on their pursuers, and those peeks had barely hinted at their true mass. The two armies had collided right at the base of the mountain, stirring up dust, and while no ground seemed to have been given yet, the mass of red-dressed soldiers stretched back and back from the front, blanketing the valley clear to the next hill.
Impressive a sight as it all was, what had put the slack in his chin was the shadow following fast behind the Imperials, a shadow that persisted even when the slowly rising sun was obscured by plumes of dust. Devils. The incorporeal ones that Ji-hyeon called "spirits," but still, a dire host of them, and Sullen prayed to Old Black and Boldstrut that they were merely scavengers looking for an easy meal. The only time he had seen so many swarm at once was when the Faceless Mistress had used them as her doorway into the world of mortals, and a dreadful thought slapped his heart into a gallop: what if she had come for retribution, to punish Sullen for siding with Zosia instead of carrying out her desire? They didn't appear to be congealing together, though, so perhaps it wasn't as bad as that...
A tumult from just below reminded him of his immediate concerns, and he saw that the foot soldiers and archers were clumping up around and beneath him on the rock- and cactus-spined slope, shiny faces staring anxiously up at him... no, past him, to the lip of the escarpment that now obscured the rest of the mountain. Zosia had also paused her climb, flat on her stomach just below the summit, her devil slinking sideways along the crest of the scarp with a decidedly uncanine grace. Setting his boots in the slippery rock dust, Sullen hauled himself up beside her as she turned back to the trailing troops and put a finger to her lips before waving them up.
"They're here," she whispered to Sullen and Grandfather, eyes shining like her hair in the cold autumn sunlight. "Be on top of us any moment. Their archers catch us here, we're all dead. You ready?"
"Um," said Sullen, trying to think something nice, since it might be the last thing he thought. He tried to picture's Ji-hyeon's sly smile, but she melted into the Faceless Mistress. "Yeah. Okay."
Below them, one of their soldiers slipped, dislodged a stone, and it bounced down to camp, clattering all the way. Nothing stirred above them, most of their soldiers still a hard minute's climb from the top, minimum.
"You ready to see your ancestors, Fa?" Sullen whispered over his shoulder as Zosia nocked an arrow in her bow, her hammer strapped to her back.
"Hells no!" muttered Grandfather. "So make sure you keep that worthless melon of yours between me and the arrows—you're the only protection I got."
"Horned Wolves don't wear armor, Fa," said Sullen, and, glimpsing their shadow on the slope above, he saw that the old man had a sun-knife in each hand.
"Horned Wolves? In case you ain't noticed, boy, you and me been Possum People for well on twelve thaws—now move that pouch, boy, and let's show these red dogs how it's done!"
When charging any hill there's a dreadful uncertainty of where and when the curve of the earth will reveal you to those at a higher vantage. The operative word being "vantage"; the high ground was contested for good reason. As she rose slowly from her crouch, bow ready, what had seemed like such a sharp edge above her now became a gentle curve, the tops of a few pines coming into sight as she rose. Sullen stayed lower, taking those last few uncertain steps up to where the ground leveled off, his grandfather craning his neck for a peek from his own personal high ground.
There, across the grass and rocks of the plateau, was a shaded stand of pine, and Zosia let out her breath, relaxed her bowstring. Despite Choplicker's wariness, there were no Imperials. Yet.
She waved her troops up, and at her signal a shout came from the trees, followed by a half dozen arrows—Sullen had already broken into a zigzagging charge and they whipped past him; the one that would have struck Zosia's leg kicked up dirt at her feet thanks to Choplicker. Zosia steadied herself, drew, and fired on one of the silhouettes that had stepped out from the cover of the trees. It was easy to play hard with a devil minding your interest, but Sullen and his grandfather didn't seem to miss the advantage, both men howling as they quickly crossed the narrow plateau.
"Up and fire, up and fire!" cried Zosia, Choplicker whining as he ambled in front of her to take any more arrows that might come her way. A few more of them did as Zosia's troops stormed the hump, but went wide with a bark from Choplicker. One struck a young boy from Rawonam who had told Zosia he'd brought his own hunting bow when enlisting with the Cobalts. He died screaming on the ground as his comrades spread out on the ridge and drew beads on the pack of Imperials hiding in the dozen stunted pines that curtained the back of the plateau.
Their task was made infinitely harder by Sullen, who ran ahead, crashed into the pines, and fell among the Imperial archers like a panther that had been caged too long, only to be released into a paddock of red deer. A panther with a furious, armed monkey riding its back. The boy's spear was a wet, ruddy blur between the trees, and from his back the old man hurled a giant, multibladed knife at the startled archers. The two men resembled one of the Ugrakari gods Zosia had seen on the old headwoman's shrine in Blodtørst, a hulking, four-armed scourge of the iniquitous.
Blades alone rarely prevailed in a bowfight, though, and even as Zosia's arrow struck the crotch of one Imperial, another dozen arrows flew from her Cobalts, making a choice fucking mess of what would otherwise be a rather scenic grove. The situation managed, she hustled across the plateau, motioning her soldiers after her.
Sullen and his grandfather looked bewildered to be alive and unharmed as the last archer writhed screaming on the ground, a sun-knife in her stomach, and Sullen finished her with his spear before retrieving the old man's throwing weapon and passing it up to him. The wind rustled through the pines as she stepped into the copse, and all of a sudden Zosia remembered the musty smell of Leib's hair when that awful Azgarothian colonel had plunked his head down on the table where they had eaten nigh every meal for twenty years, and she stumbled, steadied herself against a tree. She gagged, and swatted Choplicker away as he pranced around her feet, merry as one of Maroto's fop friends.
Fast and hard as it had come, the dizzying sense of déjà vu passed. Glancing up to see one of her archers slit the throat of the wailing kid whose groin she'd shot, she straightened up from the tree, shook out her limbs, spit. It wasn't nice, it wasn't clean, but it had to be done. The bright-eyed young Imperials who had helped that asshole Hjortt murder her husband and village probably hadn't shed any tears, and neither would she. If someone was worth hanging her head over, it was Pao Cowherd, the boy Choplicker had dragged all the way up the mountains over Kypck just to die by her fire, not these well-armed scum.
"Thanks!" said Sullen, seeming relieved. Well, why shouldn't he be? He was alive. "That's one we owe you."
"My pleasure," said Zosia, trying to mean it.
"I know you didn't come all the way up here to stick a handful of dastards," said the bloodied old man. He looked like a vampire out of the songs, clinging to his victim. "So where's the hunt?"
"Huh." Zosia straightened up, trying to get it together. There were people here who were depending on her to keep them safe. If that wasn't the biggest joke of all... "See the crest on that one's tabard? A one-handed man with a greatsword is the seal of Myura. Your uncle's scouting party saw over two thousand of them in the mountains, and then saw their banners again when they brought the horned wolves down on the Imperial camp."
"I haven't heard that song!" said Ruthless. "Maroto did _what_ with horned wolves?"
"Let him tell it," said Zosia. "Later. This is just a few of 'em, is the point, scouts sent ahead to secure the hump. Which means—"
"Yoo-hoo!" a high voice came down the mountain, and everyone ate dirt save Zosia, who recognized the greeting, and Sullen, who stepped behind a tree. Following the voice, Zosia saw that beyond the trees the Lark's Tongue resumed its steep grade up to another, higher hump, and beyond that, the peak. There was a cluster of red shapes on the upper ridge, but as she watched they began marching down the faint hunting trail that linked the two plateaus.
"It's all right," Zosia called to her troops, then to her whining, nervous devil added, "I think."
As the Cobalts watched them with ready bows, the Myuran regiment came down in single file from the upper hump, and even when they slipped and fell on the steep descent not a one removed hands from head. Zosia counted just shy of three hundred surrendered Imperials, and as the first shivering Myuran prisoner reached the pines, a lumbering figure took up the rear of the train.
"Line 'em up on the edge of the scarp back there," Zosia told her perplexed soldiers. "If they run down to camp, shoot 'em. Anyone without a bow waits here and escorts prisoners over to the archers."
"Is that..." Sullen didn't look so relieved anymore.
"Oi, that's him," said his grandfather, spitting over Sullen's shoulder. "If it's no harm to you, Zosia, we'll be headed back down to the real fight now."
"Sure. I don't like him much, either," said Zosia. "Good thing the Imperials weren't the only ones to cozy onto the notion of an ambush from the rear, or we'd have been in real trouble. I've learned every devil has its uses."
Ruthless nodded his agreement at that as his grandson carried him off, but the look Sullen gave her over his shoulder left a lot open to interpretation. Sometime soon she'd have to pry him open, one way or another, and see if the boy held a pearl for her, or something less pleasant.
"The wolves didn't wait for me?" said Hoartrap as he brought his last prisoner in, the Myurans looking ecstatic to be handed off to hard-bitten enemy soldiers. "Well, I'll catch up with them another time."
"A few thousand Myurans against one old greasebag?" said Zosia, ambling back across the saddle with her miserable devil, the misery-inducing sorcerer, and the final haunted-looking Imperial, a young man with iron on his chest but none in his step. "What happened to the rest?"
"I'm innocent, I swear!" said Hoartrap, the stumbling prisoner shuddering at this but not turning to refute the claim. "They lost most of their party getting this far; treacherous river crossings, sheer passes, and something involving an avalanche, is that right, Wheatley?"
The captured officer nodded curtly.
"I may have had a hand in the last, I admit it," Hoartrap stage-whispered loud enough for Wheatley to hear. Zosia rolled her eyes—if he was claiming responsibility, then he probably hadn't been involved. "We _did_ lose a few coming around that last pass, to the saddle above, but I'm sure Cold Zosia will be fair in her dealings with the surrendered Myuran regiment."
This finally got Wheatley to look back at them. She hadn't thought it possible for him to look more frightened, but there it was. "You... you're her?"
"Hjortt tell you about me?" Zosia asked.
He nodded once, eyes growing even bigger.
"Good," said Zosia, the last traces of her temporary weakness flushed out in one heaving sigh of relief that Ji-hyeon's intelligence had been correct and Colonel Hjortt still led the Fifteenth. She quickened her step, eager to get down to the main event now. Hoartrap picked up the pace, too, forcing Wheatley to step lively indeed as they came up to the edge of the plateau where the rest of the prisoners sat, still cupping their heads in their hands.
"If I could ask one thing—" began Wheatley, but Zosia cut him off, looking out over the Cobalt camp and the battlefield beyond.
"You cannot. I'm a busy woman, and I'm sure Hjortt cautioned you against getting on my bad side."
"That's... interesting," said Hoartrap, and, glancing over at him, Zosia was unhappy to see that he was as confounded by the sight as she was, sausagey fingers drumming on his lips.
"Interesting?" Zosia looked back to the battlefield. The ragged front line still held, if only by a few sturdy threads, but beyond it, in the massed Crimson infantry, the soldiers were aflutter with activity. Weird activity. It almost looked like they were... "That's really not your doing?"
"I'd be a lot happier if it were. We'd better get down there and pull our people back," said Hoartrap, a rare tremble of anxiety in his voice as he started down the mountain. "Or things will get a lot _more_ interesting very soon. And not the good kind of interesting, like you want."
In another rare turn, Choplicker's mood improved immediately, despite the presence of the hated sorcerer. Of the two portents, Zosia wasn't sure which was more disquieting, and, ordering her people to bring the prisoners back to camp, she hurried down to see just what in all the fucking hells was happening out there.
# [CHAPTER
25](toc.xhtml#toc-chapter051)
Such language!" Wan tsk-tsked in Domingo's ear. After delivering them to a small grassy hump partway down the last foothill before the Lark's Tongue, Wan had unhitched the horse to graze and crawled back into the wagon bed beside Domingo, so they lay shoulder to shoulder against the back of the cart, overlooking the valley. There was supposed to be a battle taking place, but instead... instead there was all _this_.
Domingo lowered the heavy hawkglass, hand shaking, mouth dry, lame arm and shattered leg forgotten. His thumb traced the etching of his son's name on the silver band set in the brass instrument, and most of the fight left him then. Until he'd seen the battlefield he'd held out hope of Shea or some other officer riding back to report, of managing to draw his saber despite his awkward position sprawled out in the back of the wagon, of anything... But the anathema had outfoxed and outfenced him at every juncture, and not a one of the Azgarothians he had brought to this place was going to come rescue him, because they were all too busy losing their minds and dying in droves.
"I'll tell you one last secret, Colonel," Wan said, throwing his spindly arm around Hjortt and giving him a comradely squeeze. "I had my doubts anything would happen. Or it would go halfway, and then... poof, nothing. That smoke, though, you can see that even without your glass, that means the ritual is proceeding just like Her Grace said it would."
"This... _this_ is the pope's weapon?" Domingo tried to remember the particulars of the ceremony he had done his devil's best to ignore while it was taking place. "All that chanting about sacrifice, the Fallen Mother's kingdom ascendant... You fucking poisoned my people."
"Poisoned them? We _saved_ them, Domingo—I may have told a fib or two to convince you to go ahead with the ritual, but I spoke true when I said it was the highest honor to be marked by the Fallen Mother. They will be the martyrs who end this war."
"I... I did this to them. I let you..." Domingo could say no more, his tongue as heavy as his heart. His soldiers had trusted him, and he had doomed them all.
"You did the right thing," said Wan, in the same patronizing _good-for-you_ tone Domingo's wife had used when Efrain so much as pissed in the right pot. "Even after you agreed to take me and the oil along, there was initially some concern that you would raise... _secular objections_ to the anointment of your soldiers, which was why I proposed using it as a poison for their blades instead. It seemed much more in line with your pragmatically disciplined bloodlust. I didn't know how to proceed when you declined both a blessing and a poison, but then those rebels brought their monsters down onto your smug shoulders, and a wolf's tongue convinced you of what my own could not."
"You smeared the same shit on my regiment's foreheads as you did on their weapons?" Domingo was still shaking, but no longer from fear and revulsion at what was happening to his people, at what they were doing to each other, or to see the earth smoking beneath the feet of his soldiers. He trembled because he had never wanted to kill anyone or anything as much as he wanted to kill the anathema that reclined beside him.
"Actually, most of it ended up on their brows, not their swords. We couldn't bring nearly enough of it for both, and if you can only consecrate one weapon, well... It's taken years to store up enough oil from the Chain's hives to make another go of it. The last time there wasn't enough, or something went wrong. I don't know. It was before my time, back when Shanatu was still pope, and a young one at that."
"Windhand," breathed Domingo, clenching the hawkglass in his fist.
"Oh, you were there?" Wan took his arm back from around Domingo's shoulder and sat up, all ears. "What was it like? Did it happen like this? What was different?"
"I wasn't there—it was the Fourth, out of Boleskine. But I heard stories," said Domingo, not afraid of dying, not afraid of much, but revolted to find the world was an even worse hell than he'd always thought. Soldiers he'd marched with for years were down there in that vale, and plenty of new blood that had flowed in during Efrain's short command, and now they were...
" _What_ stories?" said Wan, desperate for it. Domingo sneered at his enemy, here at last some small victory he could claim. But then the anathema climbed on top of his legs like a child demanding a bedtime song from his parent, and the weight of even the slight monk on his broken leg caught Domingo's breath in his chest. "Quick about it, old man, I want to be able to watch when it happens. For all their gossip at the table before they sent me off, not even the pontiff and cardinals know for sure how it will transpire here, or what exactly happened at Windhand. We lost everyone there."
"Soldiers turning on one another," Domingo gasped through the pain in his leg. "Killing each other. Worse. Eating each other alive. Worse. Like... like they're doing out there."
"Oh," said Wan, disappointed. "Well, this time it's going to work—we have lit the beacons and prepared the offerings, and back in Diadem the Holy See will have worked stronger rites yet. She _will_ bestow us with her bounty. The Day of Becoming is upon us, oh wretched doubter, and I'll even allow you to bear witness. She cares about you that much, Domingo—even after all your childish blasphemies, even though you refused her mark, you still get to be a martyr for the Burnished Chain. Saint or sinner, pureborn or anathema, the Fallen Mother loves us all!"
Despite her training, despite her youth, despite her skill, despite even her devil, Ji-hyeon was a dead woman, dead as her horse, dead as her bodyguards—the only time she found one of them in the churning flood of clashing metal was when she tripped over a familiar corpse. She could barely raise the one sword she'd managed to hold on to, and though Fellwing could eat well in such a place, the devil was exhausted, too, reeling drunkenly just above the melee. If not for whatever trick Hoartrap must have pulled to drive the Crimson soldiers mad she would have already fallen, but even with the wild-eyed infantry murdering one another as readily as they attacked her, there were too many of them.
The mob had thinned out substantially, but she was still surrounded by the enemy on all sides, and as she cut down one woman, a second looked up from where she squatted over a fallen comrade. Blood ran down this woman's chin, and from the gory chunk she clutched in her hand—Ji-hyeon staggered backward, realizing what the woman was doing but unable to accept it.
A hand knotted in the hair that flowed down from the back of her helm, yanking her off balance. She tried turning, stabbing behind her, but the hand held her too tight, and then something heavy slammed into the small of her back, popping links in her hauberk, a clump of her hair coming out by the roots as she fell facedown in the trodden turf. All her friends were gone, and if Fellwing could no longer protect her, that could only mean she had lost her devil, too... and it was entirely her fault.
She wanted to roll away and spring to her feet, to put her sword between her and her foes, but her body seemed done with the whole affair, scalp burning, ears ringing, head swimming, the world reduced to a tiny window between the steel jaws of her helm. Two men locked in an embrace tripped over her back and went down beside her, mouths snapping at one another's faces. From the black, bloodied soil between her and the wrestling soldiers, steam began to rise... no, black smoke, curling into phantasmal shapes as it rose, the earth warming the metal of her armor, and Ji-hyeon watched the fumes thicken, knowing she had to get up but wanting to stay down just a little longer.
This was why Fennec and all her other advisors save Zosia had tried to talk her out of leading a charge. What in all the Isles had she been thinking, ignoring everyone but a notorious madwoman? The front wasn't where you went to give orders, or intimidate your enemies, or rally your army. The front was where you went to die. A screaming wildborn war nun fell to the smoking earth just in front of her, and then the woman's bestial face exploded as a mace muted her forever. Ji-hyeon closed her eyes, just needing to rest, just needing to muster her moxie, and then, and then she would go back to the war...
She felt herself begin to melt into the black earth, and it made her skin prickle and her mouth water just like when she'd gone through the Gate, her body coming alive in a way it never had before nor since.
Then someone pulled her glove off her left hand, the chill air feeling so refreshing on her skin after being baked in her armor that Ji-hyeon moaned. She tried to look and see who was helping her out of her gear, but the helm was so heavy she couldn't lift her neck. Then a mouth closed lovingly around her middle and index fingers, sucking on the sweaty digits. It felt nice, letting her know the dream she was embarking on was shaping up to be a good one. Then the teeth closed, hard, crushing the bones as they chewed her fingers. Ji-hyeon screamed, rolling over and surprising the Imperial cannibal into scrambling to her feet. She took both of Ji-hyeon's fingers with her. That fucking settled it; Ji-hyeon tightened her grip on her sword and jabbed it up through the woman's groin, into her belly. The cannibal fell and Ji-hyeon rose, her heavy boots now feeling light as silk slippers as she kicked in the woman's horrible, thieving face.
"Take my fingers?" She shook the throbbing wet wreckage of her hand at the cannibal as she stomped her. "Take _my_ fucking fingers! I'll give you my fucking toes, too!"
A man burst from the miasma at her side like an eagle diving at a trout, and Ji-hyeon pivoted out of his path, her backhanded swipe opening his throat as he passed.
"Fucking _eating_ people?" Ji-hyeon demanded of the crowd. "Fucking eating _me_? Do you want to _die_?"
A woman glanced up from feeding to catch Ji-hyeon's blade across the temple, her skull splitting like a dropped pumpkin.
"Come on, then! Come take a bite!"
Two screaming soldiers covered in so much blood Ji-hyeon couldn't tell which side they fought for ran past her, flailing their weapons around but failing to cut more than the haze around her head. She sheared through one's ankle as they fled back into the chaos, then poked him through the back as he fell. Poked him again, harder, black ooze welling out of the holes she'd punched in his thin leather jack as she looked up for the next challenger, the world at last beginning to make sense again through the jagged mouth of her wolfish helm.
_"I'll! Kill! You! All!"_
Forms shimmied all around her in the cloud of smoke, the incense-rich fumes condensing, and then a dark silhouette came low at her. She brought her blade down, a wild cry on her lips—
Then twisted her sword away at the last moment when she recognized Keun-ju. In the dimness she had almost hacked his head off when he stumbled out of the haze. He was drenched in blood, a spear broken off in his left shoulder, but he still held the four-tiger sword she had given him: Keun-ju was alive, and he was here... And then Choi appeared through the smoke after him, the wildborn looking even worse off than Keun-ju, bleeding from every limb. In the crook of her arm she carried Fellwing, the owlbat shivering.
Ji-hyeon tried to greet them, but only a horrible laugh emerged from the canine mask of her helm.
"We have to go!" Keun-ju shouted in her face, as though Ji-hyeon were deaf, but then that was a sentiment that deserved an emphatic delivery. Her feet warming through the soles of her boots, Ji-hyeon, her Virtue Guard, and her Martial Guard cut their way through smoke and flesh as if they were the same.
"You see it?" Sullen asked Grandfather as they reached the upper edge of camp, the column of devils still hovering over the battlefield. He hoped they were just wild devils, anyway, and not something more material... an angry god, for example. Smoke was rising to join the swarm, but as they entered the maze of tents Sullen lost sight of the valley altogether, and couldn't tell if the black vapors were caused by a fire or something even less welcome.
"What?" said Grandfather, which was answer enough. "The smoke?"
"Nah, Fa, I—" Sullen began, but as they rounded a tent they nearly ran over a boy in a blue headband. The kid yelped, stumbling backward and firing his crossbow at them. The bolt went high, praise Rakehell for the luck he stole for his descendants, and Sullen skidded to a stop in front of the lad. "Ruddy hell, child, we're on your side! You could put a real hurt on someone, shooting off weakbows willy-nilly!"
The boy was still staring up in dread, and, following the kid's eye back over his shoulder, Sullen saw the line of Myuran prisoners coming down the mountain. That explained it, then; this runt thought the camp was being ambushed and had jumped at the first big shadow. "We captured them, kid, we took..."
But the kid wasn't looking at the hill behind them. The kid was looking up at Grandfather, who'd been too silent in the face of such bullshit, and then the first warm drops soaked through Sullen's hair, tickling his scalp.
"Ah, no, no, no," Sullen moaned, fumbling with the straps of the harness, but he knew before he even got them loose that Grandfather was too limp, an arm flopping against Sullen's face as he swung the old man down. Sullen had known it was coming for as long as he'd known what death was, but it wasn't supposed to happen this way, not for the man who'd taught him everything worth knowing, and a few more things besides. "Oh, _Fa_."
A few feathers jutted out of Grandfather's open mouth, the rest of the quarrel lodged in his palate and skull, the glistening arrowhead punched through the top of his head. Already he smelled like he'd been dead for weeks.
Brought down by one of the weakbows he so despised. Brought down by a boy whose life they had just bought back on the plateau, before Grandfather had even had the chance to sing for his son.
"I'm sorry," the kid squeaked, and, looking up, Sullen saw the boy was crying almost as hard as he was. He dropped the bow as Sullen rose to his full height, then turned to run, but not fast enough. Sullen pounced on the boy, whipped him to the ground, and crouched over him, hand tight around his throat. He squeezed, the kid pissing his pants, and Sullen wanted to stop, wanted to let the kid go, was even more scared of what he was doing to him than he was heartsick about Grandfather, but his hand just tightened as he whispered:
"I'm sorry, too."
Just when Maroto thought the worms were wearing off, the shit got all intense and crazy again, the Crimson infantry looking a mite more human now, but behaving even more devilish. As Purna wrenched her kakuri knife out of a soldier's collarbone and Maroto deflected a thrust from another who would have stabbed his ward, he saw that the soldiers farther in had stopped fighting and started eating the dead. Of all the lousy times for a Windhand flashback... Nothing seemed funny anymore, not the good kind of funny, anyway, and Maroto told himself he'd never sting again. Just like he usually did at this point in a bug-out, when things turned scary. Smoke seemed to be pouring from the ground wherever he took a step, the smell like burning hair and pungent semen, and he barely got his shield up in time to block a pike that would've plugged Purna.
"Gotta fall back," she panted. "We'll never find General Ji-hyeon in this mist. You see the others?"
"Nah," said Maroto, his tongue working normal again now that he'd sweated out some of the scorpion. Three furious Imperials blasted out of the smoke at them, and Maroto performed the trickiest dance of his life; it would've been easy enough, if he could brain them with a shield in clear conscience, but he didn't want to push his oath any more than he already had. So instead he put himself between Purna and the raging soldiers, shield up, shield over, shield down, the girl darting through his openings and tagging the soldiers. In all the excitement he caught a few shallow slashes and scrapes, but credit where due, when he rolled out of the way and Purna leaped forward to hack into the last man's face with her curved blade, he saw she didn't have a scratch on her. Then he started snickering again, kept laughing as he clambered back up and they shuffled through the curtains of smoke to take the stage, because he had finally figured out what role he was playing in this strange new drama.
He was Purna's devil.
Zosia wheezed along after Hoartrap through the camp, a stitch in her side the size of the Agrimonia Trench. Even the camp followers who usually laid low during the fighting lest they catch a stray arrow had come out to watch the baffling scene below, and a few had loaded heavy packs and were fleeing away up the slope, cutting out before things got any weirder. Zosia sympathized; she'd never seen Choplicker so happy, or Hoartrap so anxious. As the tents thinned out on the lower end of camp and they squeezed past the pickets, she saw that the black column of smoke rising from the battlefield was perfectly cylindrical, and extended as high as her eye could follow. Ripples of light began to appear in the heart of the pillar, and Zosia pinpointed the scent in the air she'd been trying to place the whole way down from the plateau: camping with Leib a dozen years before, they'd been caught out in the high country by a thunderstorm, and a bolt of lightning had blasted the stones close enough they could feel its energy tingling on their tongues and smell its hot tang.
The cylindrical cloud covered most of the valley, extending far enough outward to envelop the front lines, and Zosia saw that the Cobalt infantry in the rear were staring up at the black pillar in awe, weapons held limp when they were held at all. Hoartrap was cursing to wake the devils, and Zosia would have, too, if she'd had the breath—this was the worst deviltry she'd ever seen in thirty years of raising hell, the Chainwitches of the Imperial army calling up something that no mortal could hope to put down again... and she was running straight for it.
Then Hoartrap stopped so abruptly she almost bowled into him, the sorcerer drawing up short just at the base of the Lark's Tongue. The slack shoulders of the rear guard and barber surgeons and officers and the rest of the remaining Cobalt Company were lined up between them and the swirling column. Choplicker sat back and howled for all he was worth, tail beating the dust around them, and...
Pop. Not a loud one, either, like some firearms made, but more like the sound and sensation Zosia felt when she came down to the lowlands after a long spell in the mountains. And just like that, the wavering pillar of inky darkness and flickering light sucked down into the battlefield, like smoke drawn through a pipe. As the crown of the column plummeted down from the heavens, though, something must have changed upon the field, for instead of being pulled back into the earth with the rest of it, the remaining smoke billowed out across the valley, stinging Zosia's eyes and making Hoartrap cough.
"That's gone and done it," the sorcerer managed. "There's not a devil in my bag that's going to escape my wrath for this oversight. Someone in there knew this was coming, mark my words, someone smelled it on the wind but kept quiet."
"What _was_ that?" Zosia asked, Choplicker barking happily in response, headbutting her bottom to get her moving.
"I've got a pretty good idea," said Hoartrap. "But let's find out."
"Fucking devils," said Zosia, looking down at Choplicker. "First let's go find our friends. You willing to take me to Maroto and the rest?"
Choplicker strutted into the heavy clouds of smoke puffing up from the valley, and Zosia followed him down. No better guide for a tour of some new hell than your own personal devil.
" _Look. At. That_ ," breathed Brother Wan, still straddling Domingo but staring back at where the tower of blackness had collapsed to earth.
Domingo smelled it even before the wave of smoke rolling up the side of the valley reached them, his eyes watering as his nose recognized the orange sage oil Concilia had added to Efrain's bathwater when he was a child, when Domingo could still look at his wife with something other than desperation and his son with something more than disappointment. The grey shroud muffled the world, even the anathema atop him seeming remote and harmless as a memory of past failures.
"And the war's over," Wan said softly. "That which was prophesied in the Canticles has come to pass."
"What did you do?" Domingo asked just as softly, and because the hour was far too late for self-deception, he amended himself. "What did _we_ do?"
"We've saved the Star, Domingo." Milky tears ran off Wan's chin and landed on Domingo's red uniform. " _You_ saved the Star, by putting your faith in the Chain. Her Grace called it a weapon, because that was the only way you could understand it, but it was never a weapon. It was a gift, a gift to all mortals."
"I asked you what the fuck I did, you wretched monster!" Domingo's voice broke. "Stop talking Chainite madness and _tell_ me. _Please_. _What did I do?_ "
"Madness?" The fleeting softness of Wan's face set and his cheeks dried. "You still doubt her, even after all you've seen. All you've done."
"I just want to know," said Domingo, slumping back into his sweaty pillows, the monster that straddled him gazing down in scorn. "I just want to know."
"No you don't," said Wan. "You've never wanted to know. You've spent your whole existence denying the truth with one breath and demanding answers with the next. I was going to show you, I was going to take you through with me... But you're not worthy."
"You don't know, do you?" Domingo must be as mad as Wan, because it was so hard not to burst out laughing at this crazy, sad little monster who thought he had the whole game figured out. "You won't tell me because you don't even know what it is you've done!"
"I've saved the world, and now I'm going to pass through to my reward," said Wan. "But first I'm going to spare you from further pain. It will be... unpleasant, for the sinners left behind, and I think you have suffered enough in this life. You may despise me, Domingo, but I have nothing but pity for you."
Domingo groaned as the gaunt witchborn shifted his weight, sending more currents of grief through the colonel's broken leg. From his cassock Brother Wan had drawn the black knife Domingo had declined back on the Azgarothian border, when he'd dispatched the Immaculate prince. What a long time ago that seemed, back when the Immaculates' conquest of Linkensterne had seemed a crime worth killing over, back when Domingo still had ambitions beyond dying better than he was probably going to, now that his time was up. He wondered if the foreign prince's family would respond to the news of their child's cruel death the same way Domingo had, with fury instead of grief...
"Safe roads guide you to her breast," said Brother Wan, clumsy enough with his dagger that Domingo didn't hold much hope for a quick end to this. "Time to let the angels take you, Colonel."
"I doubt either of us will be seeing any angels," said Domingo, tensing every fiber of his broken body as Brother Wan leaned down to slit his throat.
The witchborn came in, close as a lover, and Domingo clobbered his soft temple with the brass hawkglass. Wan reeled to the side, lashing blindly with the dagger and clipping Domingo's cheek. The blade ran back along the bone and nicked his ear. That was just the bit of extra incentive Domingo needed, and he cracked the anathema a second time, harder still, the glass set in the brass tube exploding out in a bloom of crystals, and Brother Wan slumped on top of him, their foreheads knocking painfully together.
"A wise general never leaves the battlefield," Domingo told the limp monk. "And I never gave the boy anything he couldn't use as a weapon."
Brother Wan had dropped his knife over the edge of the wagon when he blacked out, and so it required a bit more time and commitment for the broken-legged, lame-armed colonel to do what needed doing, especially with the crick in his neck. One wouldn't think it, but that was the worst, like a thousand thorns jabbing into his spine as he rolled the anathema off him and then dragged himself upright in the wagon bed. The fumes were thicker now, like he'd snuck into the steamy bathhouse to steal a kiss from Concilia while Efrain splashed around the tub, laughing the bright, sharp laughter of children, a sound that had never agreed with Domingo.
He should rip up this bedding, use it to bind Brother Wan before he woke up. Interrogate him when he came to, using methods reserved only for traitors to the Crown. Get a straight answer out of the crooked man. But there was an awful lot of blood running off Domingo's flayed face, and who knew how long he'd be able to stay awake. Who knew how long he'd be alive. So Colonel Domingo Hjortt did the only judicious thing he could think of, and bashed away at the back of Brother Wan's head until he had no more strength to lift the broken hawkglass. Then he slumped back in the bloodied, befouled wagon bed, hissing at the songs his ruined body sang for him, and stared up into the hazy sky, hoping the smoke would clear and he could see the sun one final time before he went into what the superstitious called the First Dark, but what Domingo knew was nothing more nor less than the cold, cold ground.
# [CHAPTER
26](toc.xhtml#toc-chapter052)
Sullen held a boy of less than a dozen thaws to the ground, and choked him to death with one hand. Sullen smelled piss and shit, blood and old age, but that last was growing fainter by the breath, and as it faded he squeezed harder. The kid's eyes were bugging out, his legs flopping, feeble fingers latched onto Sullen's wrist. It was a dark task, but it needed doing, with Grandfather killed for no reason at all, murdered in a way to shame the ancestors. Vengeance had to be paid, and Sullen tightened his grip and looked away, for he took no pleasure in it.
"No." He dropped the boy as though he'd seized a snake and sat back on his haunches in the dusty lane between tents. The boy gasped, a dry, ugly noise that sounded like it hurt. And Sullen said it again, louder, trying to make it stick. "No!"
The whole reason they'd left the Savannahs was to find something better than the old ways, wasn't it? When you killed someone back home, you paid their family or you fought whoever came looking for revenge. Simple... but nothing seemed simple anymore. What good would come of killing this fool boy? What good would come of any of it?
"Sorry," the boy said it again, coughing on the word as he crawled backward on his arse, trying to get away, and, hearing that worthless word, Sullen wanted to jam it back down his neck. Hopping to his feet and advancing on him, he said:
"You think I give a _fuck_ if you're sorry? You killed my grandfather! I drag him all the way here, talk him into helping _you_ , your people, and that's how you repay him? Fucking _weakbow_?" He raised his foot to stomp the cowering boy before he caught himself again, stamped the earth instead. "What the fuck do I do now, huh? Leave him here, after all he did for me? Let you run away, after what you did for him?"
"Plee... plee... please," the kid stammered.
"I'm asking you a fucking question!" Sullen bellowed, feeling like his brain was going to boil out of his ears. He had been mad, once or twice, and always to bad result, but he'd never had the devils in him like this. "I don't have anyone else to ask! 'Cause you killed him! So _what do I do now_?"
"Ca-ca-crimson, or... Immmmmaculate?" said the kid, and Sullen realized he'd been ranting in the true tongue, and wherever this child came from, it wasn't the Noreast Arm. That was just as well, Sullen could rage in other languages than his own, though fishing around for the right words made him lose some of his momentum.
"You murdered my grandfather," he said in Immaculate. "You murdered him because... because you're a stupid fucking arsehole. So what do I do now? How can I let you go, when you did that to him? How can I face him, my other ancestors, when I stand at the door of Old Black's Meadhall? How?"
"Please," was all the kid managed, making Sullen wonder if the barrier hadn't been language, if this boy was just simpleminded. He looked back at Grandfather's limp form in the dust, hoping that even in death he could provide wisdom, but all he offered was an appetizing meal to the flies buzzing around his bloody mouth.
"All right," said Sullen, closing his eyes, telling himself he knew this hour would come... But predicting something and being ready for it aren't the same, not by a stretch. He'd always imagined Grandfather dying to save him, or some worthier person still, the old man sacrificing himself to great honor. Taking on a hundred enemies and making them pay dearly for one grey wolf that couldn't even stand on his own legs. Using his last breath to boast or crack a joke or maybe just say farewell to his grandson. That's how it would have happened in the sagas. Not like this. What kind of sad, disappointing song would this make?
The thing was, there was more going on right now than just what had happened to Grandfather. A lot more. This wasn't a fucking song, with Grandfather's death the dramatic end to a night's entertainment; wars didn't stop for one old man... Or did they? All that ruckus down in the valley had gone quiet, now that he pricked his ears that way, and the faint whiff of charcoal mixed with sweet rice reached his nose just before a grey cloud of smoke flooded up through the camp on the breeze. Craning his neck, he couldn't see any of the ghostly devils that had gathered over the battlefield, couldn't see the valley at all. Ji-hyeon was down there somewhere, and so was Uncle Maroto, and while his motives for wanting them alive couldn't be more different, want them alive Sullen surely did.
"All right."
"Alllll right?" The kid tried to get up but was shaking too badly.
"Yeah, all right," said Sullen, settling on his own way, since there was no one here to give him a better idea. "Grandfather there? You carry him up that hill. On your back. To the hump at the top. You make him a bed of tree branches and grass. Lay him on it. Feet toward the plains, head toward the mountain. Then you stay there until I come for you. Do that, I won't kill you."
The kid jerked his head up and down.
"If you don't, if I get up to that hump and find the both of you aren't waiting..." Sullen was going to leave it unsaid, but seeing that this fucking piece of shit was too thick not to murder honest folk volunteering to help out his own army, he spelled it out for him. "If you don't do all that, I'm going to run you down, anywhere you hide, and I'm going to murder you just as dead as Fa there. Only it won't be fast. It won't be easy. You'll be begging your gods for me to finish it, to let you go on and die. Yeah?"
The kid nodded fit to snap his own neck and save Sullen the bother.
"All right then." And because he couldn't help the living if he watched the dead, Sullen launched himself down through camp without sparing a backward glance for the kid or the flesh his grandfather had worn. He tried not to notice how light and free he felt, how nimbly he moved, without the weight of the old man on his back.
"Holy... holy," said Purna, staring agog into the wavering smoke. They had turned to face another snarling Imperial soldier, only to see him pulled wailing into the earth, along with most of the thick cloud. Maroto had hoped this was just the last hurrah of his worms, giving him a few last visuals, but apparently not. "What... what."
"Fucking bugnuts," he said, squinting into the foul mists and seeing that ahead of them there was not a single other person, not upright, not dead on the ground. After the clangor of an epic battle, the eerie silence of the vale fairly roared in his good ear, like he'd put it up to a hermit spider shell. "So that happened, huh?"
"What..." Purna said it again, maybe hoping for a better answer. "What?"
Maroto got a squirmy, cold feeling in his belly, staring at where all those people, living and dead, had just up and vanished, like the whole world had gone to bugs. To either side and behind them there were still corpses aplenty, and he knew from long experience that it was always better to take your chances with the mundane dead than the devilishly mysterious. Tossing away one of his battered shields and wiping the sweat and grime from his face, he said, "Fight's over, one way or another. Let's move."
Booking it away through the thinning waves of smoke, he kept a close watch for their friends, both among the other dazed figures lurching through the haze, and at their feet. Just before they got separated in the press he'd seen Hassan take a bad hammer to the back, but then the man had been swallowed by the blurring clash. He hadn't seen what happened to Din or Diggelby... But speak of the devils and watch them rise, here came Diggelby swaying through the smoke!
"Digs!" called Purna hoarsely. "Did you fucking see that shit?"
"The smoke?"
"No, dummy, the fucking Imperials!" said Purna.
"What about them?"
"They're gone!" Purna's voice had the ragged edge of someone who'd just seen their first true devil. Then again, Maroto had seen a lot of devils in his day, and whatever had happened back there definitely still bugged him right the fuck out. "Like, all of them! Or at least all the ones back there—they just... _went_ , right in front of us, and far as we could see the whole fucking army got took!"
"Sorcery," said Diggelby, in a tone that said it was _so_ passé. He waved them over. "Take a look."
Joining their friend, Maroto saw that Diggelby's armored caftan had lost most of its padding, the garment shredded to the skin in places, but other than a lot of blood caked on his person, he seemed to have come out all right. He held a flask in one shaking hand, and Prince was cupped in his other arm. The spaniel looked even worse than his master, a bloodied foreleg spasming, a cut on his snout, and his collar missing.
"A war monk?" said Purna, looking down at the half-dead man in robes curled at Diggelby's feet, his breath coming in shuddering gasps, a javelin jutting from his abdomen. "What does that prove?"
"We'll put a few questions to him," said Diggelby, passing the flask to a grateful Maroto. "See what's what. They call them 'Chainwitches,' so maybe he knows something about all this obvious witchery."
"Nah," said Maroto, both to Diggelby's suggestion and Purna's snatching the flask from his hand before he could take a second pull. "Why the devils would they do something that wiped out their folk 'stead of ours? Purna and me were right there when the crazy went down, and the Crimsons got the worst of it by a country league."
"Can't hurt to ask," said Purna, tossing Diggelby the flask and putting a boot onto the war monk to roll him onto his back.
"Careful there, weirdborn—" Thinking of Choi's sharp smile, Maroto amended himself. "Shit, I mean wildborn, _wildborn_ can be—"
"Maroto," said Diggelby peevishly, as if noticing him for the first time. "Maroto, where is my other shield?"
"Huh?" Maroto looked at the one shield he had left, which was no longer in any condition to be mounted in the nobleman's den once the war was won. "Oh balls, Diggelby, I totally forgot and—"
"Fucking bastard!" Purna yelped, staggering back from the prone Chainite, who had jabbed at her with a dagger. She gasped when her weight came down on her left leg.
"Told you to be careful," said Maroto, kicking the knife from the war monk's hand and snatching Diggelby's flask. "You tend that one and I'll see to Purna. Come on, girl, where'd he tag you?"
"I'm fine, I'm fine," said Purna, wobbling, trying to look at the back of her leg, and then she fell over. Maroto heard Diggelby grumbling as he drew his crystalline sword, a grunt and gurgle from the war monk, but didn't look back, his full notice on just how much red stuff was coming out of the back of Purna's thigh, leaking through the padded legging between the edge of her mail skirt and the steel cop protecting her knee. He fell to his knees beside her, rolling her on her side and slapping his hand on the narrow cut... But hot as her blood felt against his palm, ice began to spread through his chest—the pressure under his hand was bad, as bad as bad could get. She'd been stabbed, not slashed, and if her artery was nicked the girl would be dead in minutes. Maybe sooner.
"Diggelby!" he cried, trying to keep the terror out of his voice lest she catch it. "Your belt, Diggelby, right fucking now!"
"I'm fine, really," said Purna, trying to sit up on her elbow and slumping back down, blood flowing faster between Maroto's fingers. "Fucking jerk just... damn."
"Always talking me out of my belt, barbarian..." Diggelby started, but shut up as soon as he saw what had happened, stayed dead quiet as he slid down on the other side of Purna. A quiet Diggelby was not a reassuring portent. The fop fed his belt around her upper thigh with a junkie's steadiness, cinched it for all he was worth. The pressure barely lessened.
"I can get up," said Purna, voice quavering as she tried to see what they were doing. "I'm... fine."
Purna was dying fast, and there wasn't a fucking thing they could do to help.
"Hey, what's happened?" Zosia called, Choplicker having led her straight to a break in the smoke-choked valley. Given her devil's keen interest in sniffing the butt of a hurt spaniel that was inexplicably hanging out on the ruined battlefield, maybe he'd had ulterior motives. Beyond the wounded dog and the thing that pretended to be a dog, Maroto and one of his noble friends, Diggelby, kneeled over a fallen comrade. Purna, Maroto's cute, scrappy disciple—she hadn't recognized her at first, the girl too pale from all the blood covering her and her friends. "Shit, anything I can do to help?"
Maroto looked up at Zosia, obviously frightened out of his wits, and then, as though realizing this was all a nightmare and he would soon awake to find his friend unharmed, a rowdy grin lit up his dark, haunted face. Closing the last few feet of trampled grass, Zosia didn't see how the hells he could find any succor in her presence; she was worse at field surgery than he was, and the shuddering girl he held would soon be as dead as the countless unknown bodies she had stepped over in the course of getting to them.
"Zosia!" he said, sounding as close to broken as she'd ever heard him, which was saying something indeed. "Oh, thank every devil! Here, hold this, Diggelby, everything's going to be fine."
"Maroto, what the fuck!" Diggelby struggled to press his far smaller hands against Purna's slick red thigh as Maroto abandoned his post, lurching up and seizing Zosia's shoulders with his bloody hands. His face was right in hers, pupils filling his teary eyes, and he spoke with the measured composure of a bug veteran trying to convince a straitlaced stranger to lend him some silver.
"Shit, Zosia, Purna's real bad, you can see that..." He licked his chapped lips, gently squeezed her shoulders. "I know it's asking a lot, a whole lot, more than me or anyone's got any right to ask, yeah, but she's going to die, Zee, she's going to fucking die right here if you don't help her..."
Zosia's stomach dropped as she understood what he was driving at; even with Maroto managing to keep his eyes on hers instead of Choplicker, there wasn't a whole lot else he could possibly want from her.
"... and I swear, I fucking swear I'll do anything to make it up to you, break my vow to the queen, help you bind another, bind twenty more if you want, Hoartrap would help, I know it, so if you'd just—"
"I wish I could," said Zosia, making her words as precise as possible. "I can't."
Just like that, he got dangerous, friendly hands on her shoulders tightening down, fake smile turning into a genuine snarl. "Zee, I know it's asking a lot, and she's just one of thousands to get got today, _yes, of course_ , but you need to do this. Please. I'm fucking _begging_ you."
"And I'm telling you, it's not that I won't, it's that I _can't_ ," said Zosia, trying to keep her cool in the face of the heat he was throwing off. "He won't go. I offered him a way out, a long time ago, but he turned me down. He's not like other devils, he—"
"Try again, then, try it now," said Maroto, voice cracking. "Tell him you'll set him free if he saves her. Can't hurt to try, right? Maybe he couldn't before, but now, but now..."
Wouldn't that be a joke to wake the sleeping gods of the Sunken Kingdom with her laughter, if Choplicker refused to keep Zosia and Leib safe in exchange for his freedom, but took her offer now, for the life of some saucebox Zosia had spoken to once in her life? His very suggestion was absurd; even if Choplicker accepted and carried through, the world would be richer one smart-mouthed punk who'd get herself killed again soon enough, one way or another, and Zosia would have lost the greatest power known to mortals. If used wisely, a devil's wish could change the fates of empires, and Maroto expected her to dump hers on account of one girl he fancied?
"I'm sorry, Maroto, if I could help your girlfriend—"
"Try it!" he screamed, and then, realizing he'd shaken her, let go of Zosia's shoulders, tried to brush off the blood he'd smeared on her tunic. "Please, Zosia, she's not my girl, nothing like that, she's... she's my friend. She's my only real friend."
Maroto was blubbering now, and Zosia looked at the fallen girl, the fop trying to stanch her wound, and then her wicked devil, who was now giving the lapdog a look like he might eat it, if he thought nobody was paying attention. Quietly, Zosia said, "I'm your friend, Maroto, and I know how hard it is to let go—"
"You think you're still my _friend_?" He sneered. "You let me throw my life away on your account. Let me think _my friend_ had been murdered. Let me think _my friend_ needed someone to avenge her, keep her memory warm. You were a better friend dead than you ever were alive!"
Some of that stung, and some of it was horseshit for all kinds of reasons, but before she could stop herself the words were out of her mouth. Maybe she said it because she _was_ his friend, for all his problems, or maybe because she just wanted to prove to him that she'd been telling the truth. "Choplicker. You save Tapai Purna there, make her healthy and whole again, with no kinds of sinister twists to the deal, and I release you from your bond. Onetime offer, take it or leave it."
Choplicker glanced over, and Zosia held her breath...
And then the devil yawned, and turned back to acting all stiff and tough with the lapdog. It was an odd feeling, to be disappointed and relieved all at once, and hating yourself for your uncontrollable emotions in the bargain.
"See?" Zosia reached for Maroto's shoulder. "I wish I could—"
"What a load of shit," said Maroto, flinching away from her touch, uglier than she'd ever seen him. "You have to _want it_ , Zee."
"Excuse me?" Now Zosia was feeling her fire, too—he was in a place, obviously, but there were limits to how much she'd let go.
"You didn't want it, so it didn't work," said Maroto. "Everyone knows you have to want it, _especially_ the devils. So why don't you want to save her?"
"I do want it," said Zosia, hoping she meant it but not so sure anymore—what if Choplicker had sensed her reservations and taken that into consideration? What if he'd seen into her selfish heart, and knew this wasn't her one true wish? What if when she'd asked him to watch over her husband he had sensed some similar doubt? What if this was all her fault, instead of his?
"Liar. You fucking liar." Maroto shook his head, snot and tears on his grubby face, and he poked her in the chest, his eyes black as Gates and just as warm. "We're fucking _done_ , you and me. I gave up my life to help you, and you won't give up a fucking dog to help my friend? Fair enough, _Cold Zosia_ , but after I bury Purna I'm coming for you, and not even that devil of yours will be able to help. You're a fucking dead woman."
Maroto wasn't in his right mind, and he'd made some fair points, shitty as it was to admit, but the day some asshole talked to her that way after she'd tried loosing her devil to help him was the day she was fit for the grave. She bit her lip, nodded like she was considering his threat, then hurled herself forward, headbutting him in the chin. He stumbled backward and nearly tripped over his dying friend, then launched himself back at Zosia—only to be swept off his feet by a figure who came barreling out of the smoke, one of the few people to make the Flintlander look modestly proportioned. Hoartrap actually lifted Maroto, clenching him in a bear hug, and, looking at Zosia, called:
"I'll help him back to camp, you mind the children here."
"Fuckingfuckbastard!" Maroto thrashed to no avail as Hoartrap clumsily carried him off into the smoke. Zosia scowled at Choplicker; now that Maroto was but an angry echo in the miasma, she realized she had never seen him that unhinged before, and all her wrath fled, leaving her as hollow as she'd ever felt. All she could do for her old friend was watch someone he cared about bleed to death in the dirt for no good reason at all, so that was what she did.
What she tried to do, anyway, but looking back at Purna's blanched body, she saw that Diggelby had turned away, his red hands stroking his lapdog rather than fighting the inevitable. The blood still trickled out from Purna's thigh, and her chest fluttered, but she was going fast. Then Diggelby jerked his hands back with a little scream, falling backward on his ass as his dog started having a fit. Choplicker licked Zosia's hand, then plopped down at her feet with a whine, watching Diggelby's lapdog shake and shudder.
"What the fuck did you do to his mutt?" Zosia demanded, about at the end of her patience with her devil, but then Diggelby yelped again, and the worst stench imaginable overpowered the perfume of blood, metal, shit, and incense that permeated the ghostly battlefield. The fop's lapdog burst into green flames, and as it shook, burning hair came loose in stinking clumps, floating in the air like foul embers. What Zosia had thought was the poor animal squealing was its blackened skin roasting from the inside out, its boiling vitals whistling like a teakettle, and then the whole dreadful mass melted into the earth, giving off fluorescent vapors... vapors that snaked through the air, and plunged into Purna's nostril and mouth.
The effect was instantaneous, Purna's back arching and an earsplitting shriek blasting from her mouth, her eyes rolling back in her head. The blood on her leg began to sizzle, and black ichors bubbled up from the ground beneath her, climbing her thigh in serpentine streams and plugging the wound. No, not plugging it shut—flowing into it, the current increasing as she bucked on the ground. The stench of burned hair now mingled with that of wet dog, and as Purna screamed again it turned into a howl, an impossibly long, black tongue curling out of her mouth.
Then she went limp, shivering, but her chest was rising and falling in orderly fashion, the color had returned to her skin, and when Diggelby cautiously approached her to remove his makeshift tourniquet, they saw that the wound had healed, and instead of a scab or scar there blossomed a patch of snow-white fur.
"You saved her," said Zosia, hardly believing it even having seen it. "That dog of yours was a devil?"
"I guess so," said Diggelby sadly, looking at the toxic stain on the flattened grass where it had disappeared from the world of mortals, back to the First Dark. "My father, he bought Prince for me. He always said he was a devil, but I never really believed it; Prince was such an angel! And Baba is easily taken in by bold claims, so I just thought... But when I heard you two fighting about devils and wishes, I thought why not give it a go and—say!" He brightened, pointed at Choplicker. "Will you sell me yours? I'll give you a more than fair price, and since I suddenly find myself on the market..."
"Not a bad idea, actually," said Zosia, earning a reproachful glance from Choplicker. "But I'd get the better end of the deal—in case you didn't notice, he's defective. Now, let's get miracle girl here back to camp before Maroto goes any crazier."
It wasn't like any of the songs Ji-hyeon's second father would sing. It was like something out of her first father's sutras on the many kinds of hells. Intense and bizarre as it had gotten during the combat, after the explosive or whatever it was had gone off across the valley everything had taken on an ethereal sheen, and if not for her aching back and hand, she might have been able to pretend it was all a nightmare, if only for a few moments at a time. Might have been able to let herself pretend this wasn't all her fault.
They had been close enough to the perimeter that when the bomb or trick or spell went off, she had heard the sudden termination of thousands of raging voices, the quiet that followed even weirder than their early shouting, wailing, and chanting. As Choi led them steadily onward, the Crimson soldiers who appeared through the smoke became less frequent, until they only encountered Cobalt troops. It made little difference, though, the fight having left both armies, and that in and of itself was unnerving—if the mysterious weapon hadn't been detonated by either side, what had caused it? And if it was an explosion, why hadn't she heard anything more than a distant pop?
Hoartrap's meddling was still the only explanation that made some kind of sense, but before she confronted him about experimenting on her battlefield without her say-so, she wanted something to drink. Maybe a ten-year-long nap. Looking at her battered guards, though, she felt the opening murmurs of her guilty conscience. Upright though they were, Ji-hyeon could see that their wounds were grave enough that both Keun-ju and Choi might never walk out of the barber's tent. Even Fellwing had used the last of her strength to find Ji-hyeon's friends in the fray, guiding the wildborn to their mistress, and now lay softly hooting in the crook of Ji-hyeon's injured arm, too weak to fly. And what had it cost Ji-hyeon? A couple of fingers of her off hand.
As they hobbled through the ruined pickets and started up the rise toward camp, Ji-hyeon looked back at where the fighting had been worst. A break in the smoke revealed that a new topography had formed in the Lark's Tongue vale, the piled dead creating wide hill and dales as far as the haze let her see. There was more red than blue on the ground, and more blue than red upright, mechanically trying to line up all the Imperials who had surrendered after their command and the bulk of their army had vanished in a puff of smoke.
"Ji-hyeon, was this..." Keun-ju began, following her gaze across the fume-filled valley. "Is this something you've seen before, campaigning with the Cobalts?"
Ji-hyeon shook her head, but then that wasn't quite true. The random people wandering around in shock, too scared to think anymore... _that_ she had seen in the citizens of many of the towns they had sacked. And the smoke burning everyone's eyes and lungs, she'd delivered that at Geminides, when they'd sapped the wall of the castle to bust in the back. Then in Myura, Hoartrap had used deviltry and black magic to make the enemy officers go missing, although there had only been a few of them that time. And of course, of all the elements at work in this tapestry Ji-hyeon had helped weave, the one constant everywhere was death: dead friends, dead foes, dead animals, a dead land soaked in dead blood spilled with dead metal. So yes, she had seen this before, just never like _this_ , never all at once... And if she had planned better, if she had listened to Fennec and had them pull out instead of making a stand, none of this would have happened. What the hells was she doing out here in the heart of the Star, anyway, running around playing soldier with real people for her toys? Dismissing the counsel of her advisors and throwing herself down on the front line, where most of her bodyguard could be massacred to protect their child general? She hadn't seen Chevaleresse Sasamaso since her idiotic charge into the thick of it, nor the rest of her retinue...
"This is not your shame alone," said Choi, looking carefully at Ji-hyeon, as though she could really peer into her ward's thoughts just like Fennec always said. "Someone did this. Not you. We will hunt the truth."
"Of course we will," said Ji-hyeon, standing a little straighter and feeling it all the way from the goose egg coming up on her back down to the oozing rag Keun-ju had tied around her bitten hand. "First we discover where Fennec hid, since he didn't manage to keep up during our charge, and then... then..."
Ji-hyeon stared up at the blue tents arrayed on the hillside above her, tried to remember what was important and what was not, tried to consider everything that had just happened and how to proceed, but all she could think about was the look of feral abandon in the Imperial woman's eyes as she'd chewed off her fingers... That was something to focus on, anyway, and Ji-hyeon gestured with her crippled hand at the nearest white pavilion. "First thing we do is get tended by the barbers. Once we're there we'll have the officers brought in, figure out what happened, how many we lost, what our options are, with that other Imperial regiment no more than a few days out. Send sorties over to the Crimson camp and confiscate their supplies. Fennec can bide."
"Too well," said Choi, and they limped toward the busy sawbones, Ji-hyeon looking again over the murky field, wondering how many of the people who had trusted her when dawn broke that morning would never emerge from the smoke.
# [CHAPTER
27](toc.xhtml#toc-chapter053)
Hoartrap, you fucking piece of fuck shit, put me the fuck down right now or I'm going to devote my life to fucking you up, too! I'm not fucking crazy anymore!"
"What a reassuring statement," said Hoartrap, tightening his grip on Maroto. "Definitely not the sort of thing a raving madman would tell his captor."
"Who captured who?" Maroto said slyly, unable to keep from shaking with silent laughter. The bugs were definitely still in him, but even with their aid he was too exhausted to fight Hoartrap, straight bushed from lugging those two shields all over, running game for Purna's unappreciative arse, but then that thought brought him back around to what had happened to her, and he started squirming again. "Just let me see her! Just let me see her before you murder my only friend!"
"Nobody's murdering anybody. Not yet, anyway." Hoartrap muttered the last.
"This is 'cause she found out, isn't it?" And there it was, the blazing insight into Zosia's evil heart. "She found out I killed her husband, so she's revenging on me."
"Husband, you say," said Hoartrap, though he didn't sound interested, didn't sound like he believed a word, was just trying to pass the time as he lugged his heavy cargo through the spectral landscape of dead folk and broken weapons and arrows sticking up from the dirt, everything beyond their immediate vicinity cloaked in the rank black air. Normally, scavengers would be all over a field this ripe, the humans coming for gear and maybe parts to sell to medical students, the animals and devils coming for a meal, but not so much as a fly buzzed in the dismal wasteland. "Whose husband was it you killed, Maroto?"
"I didn't kill him," Maroto moaned, sick with remorse and anger and a whole lot of bad bugs. "I didn't mean to, I didn't, but you know how they are, they'll take what you say and they'll mess it all up, they'll take a good thing and make it bad, they'll find a way to get back at you, when all you did was set them free!"
"Mmmm," said Hoartrap, slowing his pace. "Crumbsnatcher, that's who did it?"
"Who else!" Maroto missed his rat so much, especially now; if he'd held on to him, he could have saved Purna. "I just wanted to see her again, that's all, I didn't know he'd make it happen so bad. And I was going to tell her, I was, that's why I came looking for her, but she already knows, she has to, why else would she be so cold? Why else would she murder my friend? It's payback, and I deserve it, but not Purna! Not her!"
"My my," said Hoartrap, coming to a stop and looking around, as if even he couldn't orient himself in this infernal valley. "That's quite the story. You're sure it's all true, not a nightmare some bug laid in your brain?"
"Call me a fucking liar, Hoartrap, call me a liar and see what happens!" Maroto tensed, then gave what Hoartrap had asked some serious consideration. Through the mists of the battlefield and the worms and the sting and everything else, he had to wonder, now that the question had been posed... "I'm sure about it being my fault, from what I asked Crumbsnatcher to do. Not sure about Zee knowing it was me, because I wanted to tell her, _want_ to tell her, 'cause she's got to know it wasn't the queen or the Chain or nobody but her old friend Maroto, but I didn't get a chance, and now... now Purna's dead, isn't she?"
"Did you tell her—Purna, I mean, or anyone else—about the terms of Crumbsnatcher's freedom? Someone else in camp Zosia could have heard it from?" Good old Hoartrap always knew the surest way to talk Maroto down when he'd worked himself up way too high; you just had to look at all the angles, and then sometimes you saw there was nothing to fret over.
"You're the first one I've told, ever," said Maroto, feeling relieved that Zosia couldn't know, and then shame at his relief. "No way she could know. Which means she didn't let Purna die as revenge, she let her bleed out because she's just a selfish old fucker who don't care about nobody but herself. I've got half a mind not to tell her at all, now, let her go barmy trying to figure out who sent the assassins, when all along it was—woof, what's the hurry?"
"Something I found over here that I want to show you," grunted Hoartrap, trotting off in a new direction. Through a gap in the smoke, Maroto saw the Lark's Tongue straight behind them, but when he tried to correct the old wizard's course he was reminded that they had something to see, at the center of the vale. Whatever it was, he doubted it was worth the bother; he was starting to crash pretty hard, but when they reached Hoartrap's destination he sobered up in one devil's breath of a hurry.
Hoartrap set him down on his own feet just as they stepped out of the smoke, and Maroto's knees almost went out on him as he surveyed the manifest impossibility. The miasma wouldn't cross the border of the enormous circular clearing, so here in the bull's-eye of what had been the battlefield was a perfect circle of fresh air, and beneath it, where crushed grass and kicked-up earth and a goodly many corpses ought to be, stretched a Gate. There were only six Gates on the Star, one for each Arm and the last in Diadem, everyone knew that... but here was a seventh, and it was wider than all the other six put together.
"This wasn't fucking here this morning," breathed Maroto, taking a step back from the edge where the flattened field gave way to absolutely fucking nothing. Made him feel ill, being this close to one, and he felt a powerful itch on his ankle. Looking down, he saw that the scorpion sting had started oozing grey slime down the side of his foot. Droplets peeled away from his skin and blew sideways into the Gate. "Where'd it come from?"
"I have a theory as to that," said Hoartrap, cracking his knuckles. "But I don't think you'll like it."
"Then you know what, don't even tell me. I've given myself enough black eyes, trying to see too far. If you think it's bad, I definitely don't—"
But then Hoartrap bum-rushed Maroto for the second time that day, carrying them both over the lip of the Gate.
It felt wrong, not having Grandfather's comforting weight on his shoulders, but then wrong was something Sullen would have to get used to. He slowed to a fast walk as he neared the edge of camp, not wanting to risk startling another kid into shooting his arse now that more and more roughed-up soldiers were moving between the tents. More than one of the grunts gave Sullen the iron eye, and he checked the cobalt handkerchiefs he'd tied on his bandolier, making sure his allegiances were right out there for everyone to see. There was a whole lot less singing and drinking than he'd expect out of returning victors, and given how idly they were all coming up the hill, they must have won, or come close enough—the fighting had stopped and they weren't being overrun by Imperials, so that seemed like it'd inspire a smile somewhere, anywhere... not a one. As he broke from the tight cluster of the camp and headed down past the white pavilions where most of the screaming was coming from, he saw the whole floor of the vale still blanketed in smoke, rising too high for him to see the far hills where the Crimsons had come in from the plains. He wondered if things were as grim on their side of the valley.
"Sullen!" Ji-hyeon. Fast as the relief bloomed at hearing her voice it wilted again, as he turned and saw how harmed she was. She looked like she'd been dunked in the giant bucket of chum from the Ballad of Count Raven and the Sea King, blood and bits of meat clinging to her from boots to forehead. The horned woman carried Ji-hyeon's helm for her, looking even more torn up than her mistress, and helping the general along was Keun-ju, the pretty boy's veil missing and his face caked in blood, a few shafts sprouting from his armor. They'd all made it out was what mattered, and Sullen sprinted over to meet the trio under the awning of a barber's tent. "Sullen, I'm so glad you're okay!"
"Oi," said Sullen, wanting to hug her, but reckoning that would've been low form even without her lover in the way, looking Sullen up and down like he was a butcher dubious if the animal before him was fit for consumption. Sullen wanted to tell Ji-hyeon straightaway about Grandfather, but with these two unfriendly strangers watching him, he just couldn't do it, and instead said, "You, um, you all right? All of you? Just missed you setting out, I guess. Sorry I couldn't help."
"We would have benefited from your presence," said Choi, not angry or mean about it, just telling it for what it was.
"Missed the whole engagement, did you?" said Keun-ju, and, not knowing if the barb he felt in the words was intentional or not, Sullen treated it as an honest question.
"Nah, she, uh, Zosia had us run up the mountain, to the hump up there? These... Myurans, they said, this regiment from Myura, they'd snuck around the back, and were trying to get us from behind, so we, you know. Stopped 'em."
"Must have been quite the clash," said Keun-ju, and Sullen finally kenned what this guy was driving at; unlike everyone else he'd passed coming down here, he didn't have a scrape on him, his clothes free of the blood, dirt, and the smoky stench that coated the rest of the Cobalts. That explained the looks he'd been getting from the soldiers he'd passed. "Were there many casualties?"
Sullen felt the straps of Grandfather's harness tighten across his chest, even though he'd taken them off and left them with the remains, and he took the first of three steps that would carry him to this smart-mouthed arsehole.
"Enough, Keun-ju," said Ji-hyeon, smiling wearily at Sullen. Her eyes were glassy, and she had the shakes even worse than most of the other troops he'd passed on the way down here. "That's great, Sullen. I wondered where the Myurans got to, since they weren't with the Fifteenth. I'll have Captain Zosia give me a full report, so don't worry about it now. I've got... I've got some other stuff to do first."
She lifted a bandaged hand, and he saw that the cloth was dark and sopping. Fellwing lay cradled in her elbow, the charcoal black owlbat now turned grey, and diminished somehow, but the devil would be fine, in time. It was feeding on something intangible that Ji-hyeon was giving off, he could tell somehow, and once it had enough strength to return to the air it would find plenty more nourishment in this place.
"Yeah, definitely, get yourself looked after," said Sullen. "Anything I can do? Not here, right, but just... anything?"
"Oh sure, lots," said Ji-hyeon, but then she just stared past Sullen at nothing at all, lips pursed.
"No one from Purna's squad arrived at command this morning," said Choi. "The general orders any able officers to report here, so if you know where she or your uncle is, you could tell them that."
Did he know where his uncle was? The eternal question. Whenever Sullen thought about how his uncle had abandoned the clan but not tried to help him and Grandfather, he would get a sad, sour stirring in his stomach, and his heartbeat would quicken unpleasantly. He felt the old symptoms now, but ignored them—he hadn't met Ji-hyeon and her people at the command tent in time, either, and big as the camp was, big as the fight had been, Maroto had probably just missed them, same as Sullen. He was around here somewhere, he wouldn't just disappear as soon as the threat of violence revealed itself... He wouldn't do that to Sullen again, not now that he'd finally tracked him down, and they were going to hear his explanation, just like Grandfather had always wanted. The old man had died for something after all, then: to give Sullen this opportunity.
"I'll find him. I'm good at that."
Keun-ju muttered something about what Sullen was good at, and he was glad he'd missed it, because Ji-hyeon looked to be having a tough enough day without Sullen beating her boyfriend's arse.
"Yeah, that would be helpful," said Ji-hyeon, sagging a little in Keun-ju's arms. "Thanks, Sullen."
"It's my honor, General," said Sullen, knowing a dismissal when he heard one, and wishing he was good for something other than chasing after his no-account uncle. "Feel better."
"Thanks, Sullen," she said again, but her eyes were back on nothing. "And thank your grandfather for me."
Sullen set off quick as he could, so she wouldn't see his face, wouldn't see that for a frost-cold boy from the Frozen Savannahs, he couldn't think about Fa without melting. He iced himself back over by focusing on the task at hand, what sometimes felt like the only task he'd ever known. Though his gut told him to look for his uncle back in the rear of the camp, hiding out in his tent, he decided to give Maroto the benefit of the doubt one last time, and started his search down on the hazy battlefield.
Instead of waiting for Hoartrap and Maroto to fall into it, the Gate swam up to catch them, and Maroto instinctively closed his eyes as he felt the textured blackness press its slick, cool membrane against his face and chest. It accepted him, and he was sinking into heaving mulch, fronds or cilia brushing against him, pushing him along, pulling him up, and just as he pondered if he'd rather drown in deviltry with his eyes closed or open, his ears popped and he felt solid ground beneath his feet, cool air on his skin.
After the Gate, the sensation felt all wrong, _he_ felt all wrong, unable to balance, and even as he tried to slowly lower himself to all fours lest he fall, his injured, overworked, and heretofore bug-numbed knee gave out on him. His eyes flashed open and his hands came up to break his fall, but he couldn't even see the ground as he toppled forward, the smoke thicker than ever. Hoartrap caught one of his arms and jerked him to the side, so instead of landing on his palms he cracked his ribs into toothsome rocks. Some improvement. He was about to roll away from the treacherous sorcerer, so he could spring up and pay him back proper for shoving Maroto into a fucking _Gate_ , like _that_ was ever acceptable, when a stern wind whipped up from the ground just in front of him, dispersing some of the smoke...
Not smoke. Fog. Sea fog, to be particular, as evidenced by the emerald waves crashing far below, against the dark ankles of the cliff he had nearly fallen over. He gingerly edged away from the rough precipice where he'd sprawled like a cat on a windowsill, and only when he had a few good feet between him and the cliff did he rise to his good knee and look around for Hoartrap. The sorcerer hadn't gone far, inspecting the bloated eucalyptus trees, sap-dripping vines, and greasy-looking bushes that closed in tight around the tiny scrap of open rock overlooking the sea.
Wherever they were, it was a very long way from the Lark's Tongue. The Bal Amon jungles, maybe. Hopefully. He knew how to get back from Bal Amon, once he'd thrown Hoartrap over the edge of the cliff. He tried standing up, but it wasn't happening, his equilibrium still trying its best to roll him into the sea. Woof.
"It's hard not to be impressed," said Hoartrap, turning back to Maroto.
"Well, I'll manage it somehow. Where in the bleeding holes I'm about to put in your face are we?"
"Your new home," said Hoartrap, fishing under his heavy robes and pulling out a foot-long centipede that had nested somewhere in the vicinity of his groin. When he was on a bender it took a lot to disincline Maroto from begging a hit off a bug, but that did it. Holding the unnaturally docile arthropod up in his fist and raising his other hand in the air, Hoartrap looked all set to carry out some more of his witchy shit, when he paused and gave Maroto a glum smile. "I do wish it had turned out different, Maroto. You were always my favorite."
"Are you going to kill me, is that what this is?" Maroto lurched up to his feet, then stumbled back down to a knee. "You promised, you treacherous dick! Back in Emeritus, when all that crazy shit with the Faceless Mistress happened, who stuck his neck out to save you? And this is the thanks I get?"
"Yes, Maroto, this _is_ the thanks you get," said Hoartrap, shaking the centipede at him. "More than I'd do for most. I swore I'd never kill you, and I take my oaths every bit as seriously as you do. You have nothing to fear from me. It's whatever creatures who dwell in the sea caves and jungles that I'd be concerned about, were I you."
Maroto looked down at his befouled, bedraggled armor, his single sandal, his empty knife sheath, and then raised his hands in disbelief. "You're breaking your oath, Hoartrap. This is murder."
"Oh tosh," said Hoartrap, crushing the centipede in his fist. "You're a resourceful boy, I'm sure you'll be back to troubling me in no time."
Maroto dove up from his crouch, hoping to take Hoartrap to the ground where his screwy balance wouldn't be as much of a detriment, but even moving in the right direction proved beyond him: instead of connecting with the sorcerer, Maroto landed beside him, squarely on a big succulent plant. By the time he'd removed himself from the spiny vegetation, Hoartrap was gone, only a ring of blackened rock and vegetation to mark where he'd disappeared.
Even when his balance finally returned, Maroto balked at blundering straight into the alien jungle. He was in that strangely sober liminal space between a powerful binge and an equally powerful hangover, and he didn't want to rush into anything. Instead, he limped back over to the cliff, dangled his legs over the side, and thought about Purna, and how she was dead right now, dead for nothing more than wanting a crack at glory and trusting him to show her the way. He sat there for a long time, feeling the sun-warmed limestone against his legs and watching the mist thicken, mourning her, missing her already. Then he rose wearily to his feet, and set out to kill every single person who had in any way contributed to his exile on this far-flung seascape, and to the death of his dearest friend. No excuses, no second chances. No devil in hell as bad as the Mighty Maroto, now that he sought vengeance for Tapai Purna.
"That's, uh, Tapai Purna, yeah?" said Sullen as he reached the two familiar figures who were carrying a third between them as they slogged up the hill toward camp. "Is she..."
"She's something," said Zosia. "But dead ain't one of 'em."
"Sturdy's the word I'd use," grunted the only member of Maroto's party who had always looked smooth and soft rather than tough and scarred. Diggelby, that was his name; no way Sullen would have come up with that handle on his own. He didn't look so smooth and soft anymore, and the little devil dog that he'd always carried around was nowhere to be seen. "Sturdy or, oof, well built—sounds nicer than heavy as lead shot. Be a chap and lend a hand?"
"Can't, on orders to bring my uncle to Ji-hyeon." Noticing Zosia's amused expression, Sullen explained, "Bring Maroto or Purna to the general, I mean, to give their reports. But Purna don't look able. She also wants you to tell her about the Myurans, ma'am."
" _Ma'am?_ " Zosia ignored the chuffing sound her devil made. "Don't you mean Captain Zosia?"
"I did mean that," Sullen said quick-like, anxious to be away. He didn't like her looking at him now any more than he had before, feeling more exposed than ever without Grandfather to literally cover his back. "Better be away, though—you two seen him around?"
"He went off into the smoke with Hoartrap," said Diggelby, looking back down to the hellish field. "If they're not back yet they must still be out there."
"Thanks," said Sullen, trying to get shy of Zosia as fast as possible. Having her watch him so closely felt much like being under the eyeless gaze of the Faceless Mistress; that he'd blundered into a feud between the two inscrutable, overly interested powers was a tragedy fit for the singers. "I'll sniff him out, then. Meantime, the general wants all able officers to report in at the barbers' tents, so you two could, um, do that."
"Sullen?" Diggelby looked in the dumps for the first time since Sullen had met the man.
"Yeah?"
"If you see Duchess Din and Count Hassan... We lost track of each other, and I don't know if they're back at the tents, or..."
"I'll keep a watch out for 'em," said Sullen, one of Maroto's cronies the last person he would have predicted himself relating to when this awful day had started.
"And if you find Maroto, give him a message," said Zosia.
"Sure," said Sullen, thinking maybe he should have learned Immaculate letters just like Grandfather always said, so he could've jotted down a list.
"Tell him to quit being such a scared little crybaby and get back to camp. I've got a surprise for him."
"Um... sure."
Zosia and Diggelby resumed carrying the unconscious girl up the hill, the silver-haired woman's devil dog giving Sullen the side-eye. Getting a gander at Purna as they hauled her past, she didn't look to have a mark on her, so she must've been knocked upside the head. Sullen hadn't previously noticed that the girl also had the blood of shamans, and he asked himself how'd he miss something obvious as that. If he was to survive on his own, he'd need to get out of his thick skull more, start paying attention to everything, instead of waiting for Grandfather to tell him what was what.
South a ways on the hillside, some folks with the red tabards, shields, or other heraldry of the Crimson Empire were sat on the ground, surrounded by soldiers in blue and being talked at by one of the many Cobalt captains whom Sullen hadn't met. He wondered what they'd do with them, or with the Myurans they'd captured on the mountain. Found himself hoping they'd just give them a word and let them off, like Silvereye had done with the unnamed pups who had climbed a rope of moonbeams up to her kingdom in hopes of earning their names. Kind of doubted it would play like that.
Coming down toward the point where the slope got real sharp just before leveling off into the valley, he figured this must have been where the worst of the fighting went down. Too many dead to count, and the living didn't look much better, some just standing there, blinking into the smoke, or sitting on top of corpses that might have been their friends, heads in their hands. The worst were the laughing ones, their strained cackles even less welcome in this solemn place than the moans and screams and sobs. The smoke flowed in high, thick currents down here, and Sullen stopped walking, contemplating the veiled valley from whence gloomy figures emerged like devils from darkness. Sullen felt like Rakehell, after he'd evaded the Eater of Mortals by hiding in the Land of the Coward Dead, watching the blind specters march past him in their everlasting retreat from the honor of the battlefield...
Except that was all a great heaping pile of shit, wasn't it? Sullen had seen enough fights by now to know a battlefield was the last place on the Star you'd find honor, only heartache and horror, which were hardly the same thing. And as for the rest of it, that was shit, too, Rakehell and Old Black, Boldstrut and Count Raven, the whole stinking pile of them. They were all just songs the Horned Wolves made up to boast about how great they'd been, back in the day—all those places their ancestors went, all the Star-shaking deeds they'd done, why hadn't anyone heard of 'em outside the Savannahs? Sullen had asked everywhere they went, hoping their travels would take them past the Altar of Plagues or the Kingdom of the Oblivion Eaters, but even after he'd gotten the hang of the Crimson tongue everyone just looked at him like he was a fucking idiot. _Are we anywhere near the Lake of Satsumo? There's a tomb someplace 'round there where my ancestor laid out Old Man Gloom and his child... No?_
Of course not. Because none of it was real, it was a stew of half-truths and full lies bards ladled out to quiet down unruly brats and feed the fancy of overgrown children like Sullen, who could recite a hundred sagas but didn't know enough about the real world to be of practical use to a single other person. If he'd spent more time taking things on their face instead of puzzling over their secret meanings or how they'd fit into the song of his days, maybe his life would have been a lot easier back in the Savannahs. Maybe Grandfather would still be with him. Maybe he'd have told Ji-hyeon what he thought of her before Keun-ju showed up, or even after, instead of avoiding her and hoping all the while she'd come to him. Maybe he'd have come at Zosia head-on, demanded to know if she was really planning to light up a whole city with liquid fire. Maybe he wouldn't be alone, utterly, completely alone, with not a soul to miss him if he never came back to the camp, never came back to the Savannahs, never went anywhere but into the barrow beside Grandfather.
Looking at the great wavering wall of grey mist before him, Sullen felt helpless as ever—where to begin, that was always the question. What was he supposed to do with himself, when his whole ruddy existence amounted to this, trying to find solid ground in a world of smoke and shadows? Nothing to do but what he always did, put his head down, wander ahead, and hope he either got lucky or somebody showed up to point the way for him. Like the Faceless Mistress had, far as that went—she was the one to tell him where to find his uncle, and if he hadn't run into her he'd still be wandering the Star, Grandfather in tow...
The colorless haze and the unnatural stillness of the place as Sullen pushed through the smoke brought Emeritus back to him, all right, what had seemed so dreamlike again as hard and real as the ache in his chest, the sob that still lurked in his throat. They'd had some good days in that place, him and Grandfather exploring a realm that almost made the old songs seem plausible. Here, in this unearthly field, he felt that same sense of giddy uncertainty, of being in a place between the real world and that of heroes, and he half expected the Faceless Mistress to appear behind the next bank of smoke. Wouldn't that be an ending to please any teller of tales, if his reflexive fear when he'd looked over from the hill and seen a flock of devils had been justified? If all the pandemonium and this sinister quiet that came after was the result of a vengeful god come to punish him for not following through on his quest, for raising spear and knife beside Zosia instead of against her?
"Stop it," he told himself, back to his old habits already. "It's not a song, Sullen."
"Oh, but all the Star's a song, isn't it?" came the melodious voice of Hoartrap, smoke sliding off his robes as he stepped atop a dead horse, took a bow. "Careful, laddie, I hear this field is crawling with Horned Wolves."
"Don't call me that," said Sullen, cursing himself for the careless wish that somebody would show up to help him. "Somebody" could mean a lot of things, and Grandfather used to say the only gods who listened were the tricksters. "Where's my uncle, witch? I know he was with you."
"And I know my dear Ruthless friend was with _you_ , last I saw him, and yet he is gone, too," said Hoartrap, eyeing the empty space over Sullen's shoulder. Oh, but it hurt that in Sullen's trek down through camp this witch was the only one to remark on Grandfather's absence—Ji-hyeon was in a bad way when she'd seen him, they all were, but still... "Perhaps they are off together, having some long overdue father-son bonding?"
"He..." Sullen closed his eyes and gulped down the foul air, poisoning the sob before it could hatch. Hoartrap was trying to distract him, was what was happening, and when he opened his eyes again they were clear. "My uncle Maroto was with you, witch. Do you deny it?"
"Of course not! He was in my company, yes, he was," said Hoartrap, hopping down from his perch on the dead horse and putting a hand over his breast. "I fear the Mighty Maroto is gone, Sullen of the Horned Wolf Clan."
" _Gone?_ " There it was, the last fucking stitch that held Sullen together snapping. "You mean dead, or you mean he _left_? If he's dead I'll see his body, _now_. If... if... if he..."
"I almost think you'd prefer him dead!" said Hoartrap.
"Fucking right I would!" Sullen was on top of Hoartrap before the witch could summon his devils or his brawn, and if Sullen hadn't needed answers more than he needed satisfaction he would have ripped the giant's arms off instead of merely shaking the shit out of him. "Where? Why? Where? _Why?_ "
"Let. Me. Go!" bellowed Hoartrap, and Sullen felt an evil warmth in his chest to see the witch lose his calm, if only momentarily. He did as he was asked, lifting his palms off the man's broad shoulders but not backing up an inch. Hoartrap didn't budge, either, his stale breath hot in Sullen's face. "Very well, very well, though I only know his motive, not his objective."
"Speak."
"I _am_ ," said Hoartrap haughtily, stepping around Sullen and bumping his shoulder, forcing him to walk alongside the witch lest he be walking after like an obedient devil. "You've met Purna, Maroto's disciple, haven't you?"
"Just saw Zosia and Diggelby carrying her up to the sawbones. What about her?"
"You mean she pulled through?" Hoartrap's giggle sounded as genuine as it was uncalled for. "Good for her, but no thanks to your uncle. She was gravely injured in the battle, but when she needed Maroto's help, he turned his back on her. He can be... exceptionally _cautious_ , your uncle, and I suspect his baser instincts got the better of him—none of us know what happened, all this smoke, all those Imperials blinking away to devils know where. It could spook anyone, and he said carrying her would slow them down."
Sullen tried to breathe, but nothing came in or out. He was so full of wrath there left no room for anything else, even air.
"Zosia fought him over the matter, right there with Purna dying on the ground at their feet. Fortunately for all parties I was able to overwhelm Maroto and escort him from the scene, which I suppose allowed Zosia and the pasha to carry Purna to safety. I walked with him a short way, whereupon he informed me he was done with all of us—he'd already sworn to kill Zosia, ask her if you don't believe me. I would have stopped him, but the truth is I owe Maroto my life from something that happened long ago, and could never bring myself to harm him. He's long gone by now, and didn't inform me of a destination."
They walked on in silence, and only when Sullen was positive a howl of rage wouldn't leave his lips, he quietly said, "You don't know where he went. But you tracked him before. You'll help me find him."
"I will, will I?" said Hoartrap, but one look from Sullen and he dropped the attitude. "Of course I will, Sullen, of course I will. But what you have to keep in mind about your uncle is that he gets this way sometimes, leaving his friends in a pinch. But he always comes back, tail between his legs, and we let it go because, well, we don't expect anything more from him. I think if you wait a day or two he'll come back to camp on his own, full of excuses for his bad behavior, promising to do better, finding loopholes in the oaths he swore against us in a moment of passion... the usual."
"Three days," said Sullen, as the smoke parted before them and he saw the Lark's Tongue high above, the Cobalt camp nestled on its knee, and the hump where his grandfather's corpse had better be waiting for him, if that kid didn't want to be eviscerated ere the moon rose. It was as though the fog inside him had burned away, too, from the least likely of suns; thanks to Hoartrap the Touch, Sullen had finally found a purpose that made sense, something he could follow through on without overthinking it, without doubting, without hesitation. What to do about Zosia and the Fallen Mistress, about Ji-hyeon, all that could wait until he'd done what most needed doing in all the world.
"He's not back in three days, I hunt him. He comes back sooner, we settle it then. There'll be no song swapping. No more of his treachery. Uncle Craven's fled his last fight."
# [CHAPTER
28](toc.xhtml#toc-chapter054)
At the third or maybe fourth polite whisper from the guards stationed just outside, Ji-hyeon hauled herself upright, temples pounding. Another whisper, and she gingerly disentangled herself from Keun-ju's bandaged limbs, taking stock of her tent. The kaldi warmer she had left burning revealed scattered clothes, busted armor, and dozens of stained dressings and washrags from where they'd changed one another's wrappings before collapsing into bed that afternoon. The poultice on her disfigured hand needed changing already, and she got queasy just looking at where her fingers should be.
"General," came the whisper again. Fennec. At last. "General! An emissary to see you!"
"Coming," she answered, pulling on a grimy skirt and jacket and groaning as her throbbing tailbone and bitten hand protested the exertion. Either the bugs they had given her for the pain had worn off or she was in an even worse way than she'd thought. Stuffing her hair back in what was probably a lopsided bun, she took another survey of the room and decided she just didn't care. If her visitor was the envoy who had announced his coming via owlbat while they'd been laid up in the barber's tent, he could choke on his indignation for all she cared... But, pausing at the flap, she changed her mind. No matter the point it would make, and as few shits as she had left to give, it was just too damn embarrassing. Old habits and such. She stepped into her slippers, hurried over and blew out the kaldi warmer, then quietly slipped out of the tent, careful not to let the guard's lantern light sneak in past her. It was after dark, but that was about all she could tell; it might have been anytime between sunset and dawn.
"Ah, General," said Fennec, rubbing his gloved paws together. "If we could talk inside, it is a matter of—"
"We'll walk and talk, gentlemen." She used her snottiest tone to address Fennec and the Imperial emissary at his side, the guards behind them exchanging a bemused look. "I need to stretch my legs."
Which was the truth; they felt like they'd been threshed by farmers with a personal vendetta against wheat, and hopefully a stroll would help.
"I think you can stretch later, Ji-hyeon," said the envoy, raising the visor on his owlbat-shaped helm. "I need a sit and a smoke, and your tent—"
"It's a little messy right now, Dad," she said, and, mad as she was at him, it was good to see his face. She hugged him, the studs of his armor cold through her hanbok. "I wondered if your old gear would still fit you!"
"It's possible I had it let out," admitted her second father, stroking her hair. The obvious pride on his face softened her a bit toward his betrayal... but only a bit. "Damned if you don't look the part. Fennec says that you've been a real handful, for him and the Imperials!"
"I bet he did," said Ji-hyeon, not terribly miffed—they both knew Fennec's biscuit was best buttered by whoever was closest to the plate. "You want to light your pipe before we get moving? There's a lookout spot I'd like to show you."
"You really aren't going to let me sit down for five minutes?" Had she actually missed that peevish note in his voice? "I sent word earlier, so you'd be ready for me—didn't you get it?"
"Oh, we got it," said Ji-hyeon, waving her bandaged hand at him and blinking away tears from even that little motion. "I've just been too busy waging your fucking war to set out kaldi for you like a good little girl."
"Oh, Ji," he said softly, reaching for her hand but thinking better of it. "Fennec told me, but... but what the devils were you doing out there, anyway? I've told you once I've told you a hundred times, a general leads from the rear, the rear! Fellwing's protection isn't some magical bubble you can step inside and then jump into a volcano! If you _ever_ —"
Ji-hyeon jabbed his chest with her good hand, got right in his face, and said, "If _you_ ever speak to me like that in front of my troops again, I'll have you run out of camp and close all future negotiations. Is that clear, Kang-ho?"
"Really, this is too much," he blustered, lifting her hand off his armor, when one of her guards took a step behind him, asked:
"General?"
"It's all right, soldier, the emissary is from foreign lands and his ways are strange. We'll acquaint him with Cobalt discipline soon enough." Ji-hyeon beamed at her father's gobsmacked expression. "Now, oh welcome ambassador, I am eager to hear the Empire's terms. The vantage point is this way, if you would be so kind?"
"Here, Kang-ho, mine's already packed," said Fennec, ever the peacemaker. In his glove he held out the thick briar billiard he was so proud of, the one whose mix of straight grain and birdseye made it appear to have two many-branched trees on the side of the bowl. "I believe you and the general have much to discuss, so the sooner we stop debating the location the better."
"Hmph," said her father. "I see you've done a fine job of keeping her in check."
"I live to serve my general," said Fennec with a bow, and as Kang-ho snatched the pipe away Ji-hyeon caught Fennec winking at her. If he thought a little ass-kissing now would spare him a harsh reproof for his desertion of the general's bodyguard during the Battle of the Lark's Tongue, the old fox was in for an even bigger surprise than her second father. Well, maybe not quite that big...
"I hope I didn't keep you," said Hoartrap, ever the gentleman as he flicked his fingers and the unlit lantern flared up, blinding Zosia after the dark of his tent. "If I'd known you wanted an audience, m'dear, I wouldn't have tarried. Oh, and you've brought my favorite little doggie-woggie in all the Star!"
Zosia was pleased to see her pep talk had done some good, for Choplicker didn't twitch, lying on the floor by her stool and watching the sorcerer as casually as he'd observe any other mortal. She puffed on the corncob pipe she'd bought off an old-timer earlier that evening, since she'd been fool enough to do the right thing and give Maroto back his briar. Someday she'd have to carve herself a real piece, but for now it was back to loaner pipes and cheap cobs.
"I'm in no hurry, Hoartrap, I've only got one more stop to make tonight."
"And here I hoped that handsome outfit was for my benefit," Hoartrap said wistfully, eyeing her dirndl. "Ah, but you've tied your apron wrong! If the knot's in the back like that everyone will think you're a mourning widow, Zosia. Let's move it around to the front, so the suitors will know you're available."
"If I tied it in the front they'd think I was a virgin," said Zosia, trying not to betray her annoyance with Hoartrap's damnable perceptiveness. "It's fine where it is."
"Well, whatever your status, you still look good in a dress, old friend. Far better than I did at your age."
"Oh, I'm sure your calves are as shapely now as they ever were," said Zosia. "Now, unless you've got any more beauty tips for me, why don't you pull up a seat, pack a bowl, and let's have us that blather you proposed the other day. I want to talk devils and secrets."
"I heard what happened with Diggelby's pet and dear Tapai Purna—was that the first time you've actually seen one set loose?" Hoartrap had a hard time keeping his eyes off Choplicker whenever the devil was around, Zosia could see that now. "Not pretty, I'd expect, but then passage from one world to another never is; death, birth, other roads..."
"Not pretty, but effective. She's good as new. More or less."
"I'd say improved. More or less." Hoartrap wasn't sitting, which was good, too—she was making him nervous. "Considering your options for our mutual friend, now that you've seen the efficacy of a devil's wish?"
"Hadn't occurred to me," said Zosia, and Choplicker drummed his tail on the dirt floor of the tent. "Not that he'd listen if I did."
A bark from the devil, and a chuckle from Hoartrap. "Yes, yes, I remember your difficulties in that regard. I've been pondering it, and I wonder if he isn't a special sort of creature, just as I've always said."
"A special wart on your vag is still a wart on your vag," said Zosia, and pulled in a mouthful of hot ash. She never could get the hang of cob pipes.
"You know, there are other ways of getting what you want than ordering one about." The pipe she'd made Hoartrap appeared in hand, already smoldering with the familiar aroma of cheap perfume and burning garbage. "Asking nicely. Begging. Offering something in trade beyond the usual terms."
"And here I thought you just ate them," said Zosia, and Choplicker growled at the laughing magician.
"I've never been lucky enough to catch one as fine as your specimen," said Hoartrap, puffing his pipe back to life. "But I have been looking into the transfer of devils. Our beloved general and her father put me onto the topic. I think I may have found a way, if you were so inclined, to take that troublesome fiend off your hands, in exchange for a more obliging devil. Maybe even several."
Choplicker's cold nose urgently nuzzled Zosia's dangling hand, and she rubbed his snout before wiping her damp palm on her checked apron. "You always were the helping kind, weren't you?"
"There's nothing I wouldn't do for a friend," said Hoartrap, blowing a smoke ring at Choplicker. The devil snapped at it.
"And what would you do with him, I wonder? Some sort of a roast?"
"Zosia, Zosia, Zosia," said Hoartrap. "I'd win the war, of course."
"All to help Ji-hyeon gain the Crimson Throne? That altruistic streak is going to get you into trouble someday."
"To help us all. The entire Star is in danger, or haven't you noticed? The Burnished Chain is too strong, its ambitions too grand. Do you have any idea what they called down this morning, what their ritual accomplished? It's too preposterous to even say aloud."
"I'd wondered where Ji-hyeon picked up her disdain for the church," said Zosia, her curiosity piqued despite her reluctance to be drawn into Hoartrap's schemes. "Is that why you murdered the war nun before I could talk to her? Sparing me the danger of an audience with a bound weirdborn?"
"I _knew_ it was eating you up, not knowing!" Hoartrap crowed. "You've finally mastered your temper, after all these years, but I knew you wanted to know!"
Zosia shrugged. "For all the good knowing has ever done me. But let's hear it all the same."
"Let's just say she was dangerous, and you're better off without her," said Hoartrap. "But getting back to the far more interesting issue of the evening, I've had a peek beyond the veil and those mad Chainites have—"
"Choplicker," Zosia said, heart pounding at what she was about to do. So much could go wrong... "Choplicker, I want Hoartrap to tell me the truth about why Sister Portolés came here, what she wanted me to know. I want it so bad that if he doesn't tell me, now, of his own free will, I grant you your freedom to secure the facts by any means necessary."
It went as quiet as the smoky valley in the tent, Hoartrap not doing a good job hiding his amazement... And then he chuckled, shaking his head. Zosia's gambit had fallen flat, as all of them did, when they involved her worthless, disobedient devil, and from here until the end of the Star she'd never again be able to put the screws to Hoartrap with the threat of an unfettered Choplicker.
"Oh, Zosia, you do keep me interested!" said Hoartrap. "A clever ploy, but devils don't work that way. I only wish that poor nun had told me something you'd find interesting, then—"
The lamp went out, its glass mantle exploding in the black tent, and the cacophony of a thousand bones splintering and snapping filled the air, the smell of lightning mingling with the scent of rich earth, and Zosia felt a wave of icy air brush past, her cheeks and shaking hands tickled by a thousand probing threads, and then—
"I'll tell, I'll tell," squealed Hoartrap. "Just call him off!"
Then the tent was still once more, though Zosia continued to feel minute pricklings all across her skin. After a few shaky breaths, Hoartrap tried an incantation, but stumbled over the words a few times before he calmed down enough to say them properly. When he finally completed it, light returned to the tent in the form of what appeared to be a small phosphorescent jellyfish floating in the air between them. Hoartrap stared down in horror at Choplicker, and Zosia had a look, too; same dog as ever, but his lips were pulled back in an uncanny approximation of a human smile. Strands of dog hair floated through the charged air, settling on everything, and Zosia brushed them off her dress, trying to slow her racing heart.
"You were saying?" she said, but it came out as a croak. She couldn't bear to look at Choplicker any longer, couldn't stop her legs from shaking like she'd missed a toehold climbing up a cliff. She'd almost gone and loosed the devil.
"Yes, yes, I was. I will. I am," whispered Hoartrap, still staring at her devil, and seeing Hoartrap so rattled was as thrilling as it was foreboding. What would have happened to the old sorcerer if he hadn't elected to come clean before Choplicker forced him?
"Let's hear it, then," said Zosia. "Starting with Portolés and everything she told you, and ending with whatever fell deviltry happened out there on the battlefield. Tell me that, and we'll call it a night."
"As you wish," said Hoartrap, finally taking a seat.
Kang-ho softened a bit when Ji-hyeon asked him about the family, and as they marched through the dark camp she felt an unexpected pang of homesickness. Come what may of the coming war, if every engagement resulted in such havoc as this one, Hwabun would remain apart from it all, safe from harm at the ends of the Immaculate Isles, and that gave her succor as they climbed the hill where she had parleyed with Fennec and Hoartrap but two nights before. Once the guards reached the crown of the hill and hung back out of earshot, though, her second father laid straight into her.
"All right, Ji-hyeon, you've had your fun," he said, puffing furiously on his borrowed pipe. "Now, just what the devils is the meaning of all this! You were supposed to use my silver to hire a crew big enough to secure the attention of a regiment or two, not the whole Crimson Empire! And now this... this _madness_ , provoking the Azgarothian regiment into open war? You're lucky Hoartrap was here to help you, or you'd never have carried it."
"Hoartrap didn't have anything to do with it," said Ji-hyeon, trying not to lose her temper; the louder she spoke, the worse her hand hurt. "We're still trying to figure out what happened—seems like a ploy by the Imperials that blew up in their faces. I've ordered everyone to stay off the field until that smoke clears and we can see what happened out there; it went dead quiet, right in the middle of things, and I've heard reports from soldiers close to the action that the earth opened up and swallowed the whole damned regiment. None of the Azgarothians or Myurans we captured are talking, if they even know what it was, but I've got one of my best captains interrogating the Azgarothian colonel as we speak."
"You took their colonel?" Her father sounded impressed in spite of his best efforts to the contrary. "How'd you manage that?"
"He was leading from the rear. When my people rode out to pillage the Imperial camp somebody found him hiding in a wagon on the far side of the vale."
"Well," said Kang-ho, trying to work up his ire again. "It still sounds like chance carried the day, such as it is, and by the look of things you gave up a lot more than you gained. How many heads did you lose?"
"Too many," said Ji-hyeon quietly. "Far too many."
"You're lucky, daughter, very, very lucky I arrived in time, and luckier still that my old buddy Waits is leading the regiment out of Thao. She still thinks we can work something out."
"She does, does she?" Ji-hyeon peered through the misty haze that still hadn't cleared off the vale. She wondered if it ever would, or if she would be forced to send a scouting party in to discover the truth behind the smoke. "Well, then I suppose you're both in for a disappointment, aren't you? There's been a change in plans, I'm afraid."
That got him flushed, all right, and for a moment he just scowled at Fennec, who shrugged and said, "You were the one who always said she took after you."
"Ji-hyeon..." her father began, but then a horn sounded from the direction of the command tent, two long blows to signal an arriving messenger. She sent Fennec to fetch the news, and as he left, her father tried again, his voice softer. "Ji-hyeon, listen to me. You've had your fun, but the reality is that you've gotten yourself in an awfully tight spot, and unless you want to have an unstoppable war on your hands by lunchtime, you need to get smart, and... and... oh no. No, no, no, Ji-hyeon, you're smarter than this!"
Evidently she wasn't doing as good a job of hiding her excitement as she'd thought. "It's too late, Dad. You offered me one role, which I thank you for, but I'm taking a better one."
"Ji-hyeon, I never would have let you go if I thought you'd be in real danger," said her father, looking down at her missing fingers. "This isn't a game anymore, this is—"
She socked him in the chin before she knew what she was doing. He stumbled back, more from surprise than the blow. She harried him, putting her face in his, and snarled:
"You and Fennec love saying that, but this was never a game! Never! People died, lots of people. Some of them I knew and some of them I didn't, but there was never a way for your plan to work without hundreds, hells, _thousands_ of people, innocent people, going to the grave. I've killed people, I've lost friends, and you lecture me about playing _games_? Fuck you, Kang-ho! Fuck you!"
He looked abashed. Nodded. Squatting down to pick up the pipe he'd dropped, he quietly said, "Please don't call me that. I'm still your friend, I hope, but I'm also one of your fathers. Call me names if you must, so long as 'Dad' is always one of them."
"Urgh!" She closed her eyes, breathed deeply, and when she opened them again she waved away the guards who had begun creeping closer. "Okay, _Dad_. But let's be real here. We both know what the stakes were. And now I'm raising them. Substantially."
"Hear me out, I beg you," he said in that pleading tone that always got under her first father's skin. "Let me broker a truce with the Empire. You said you know it's not a game, and I believe you, so you know that my plan involved a lot less risk for everyone. A lot less death. A lot less pain. I can get my people in the Empire back on board, if we act fast, color what happened here as unprovoked aggression by the Fifteenth. We can still take Linkensterne, which means you still have a choice to do the most good for the most people."
"We both know I don't have a choice anymore," she said, hoping reason would cut through his emotion. "Even if the Empire was willing to look the other way for this and every other crime I've committed against the Crown, I've got my own house to worry about. If I roll over and tell the troops we're teaming up with the Imperials they've been fighting all year just to take some shitty Immaculate border town, half of them would walk. The good half."
"They're mercenaries, Ji-hyeon, they'll do what you pay them to do." Her father smiled knowingly. "Don't pass the blame on this, Ji-hyeon—you want to take on the Empire, because you're young and ambitious and naïve enough to think you can swing it. Nothing more."
"There's a lot more," said Ji-hyeon angrily. "The Crimson Empire is a plague on the Star, and—"
"Oh please!"
"They are, and you fucking know it! The Black Pope rules in all but name after their last civil war, and what do you think that bodes? Her missionaries have been gnawing away at every Arm of the Star, and as soon as the Empire recovers from its infighting there isn't a power in the world that will be able to stop them. They've found a new way to win wars, Dad—by not fighting them. You get enough converts, and pretty soon the whole Star bows before Diadem... This could be the last chance for anyone to stop them!"
"Spoken like a true believer." Kang-ho shook his head. "Jun-hwan will never forgive me for singing you all those old songs."
"Listen to me, Dad, for once, listen! If I did things your way we'd have Linkensterne, a free state, a bastion of liberty... But for how long, before Diadem and all the Immaculate converts decide we're another Sunken Kingdom, in need of spiritual cleansing? We walk away now, when the fight's hard but not unwinnable, and we'll never have a second chance—never!"
"God of the Seas, but I was wrong about you," said Kang-ho, delivering the lowest blow yet doled out: "You're _exactly_ like your other father."
"Yes, well, say one thing for him, he never tried to murder my boyfriend." Ji-hyeon crossed her arms.
"Your what?" Her father looked honestly confused.
"Keun-ju! You stopped him from leaving with me, and would have had him executed, if Papa hadn't stopped you!"
And there was the recognition she was looking for. Kang-ho pulled on his pipe to stall for time, probably trying to decide between acting contrite or superior. Fortunately for him, he decided on the latter; Ji-hyeon preferred her second father when he was being an honest asshole rather than a deceitful charmer. "So Fennec spilled the rice, eh? Well, whatever the fox told you, yes, I kept Keun-ju on Hwabun, but I never planned on hurting him. To say nothing of an execution! Does that really sound like me?"
When she didn't answer, he said, "Look, you can ask him yourself, if you listen to reason and do things my way. Once we're all back on Immaculate soil, I'll send for him to meet us in Linkensterne, and you kids can carry on in whatever way you wish. What do I care if you want to piss on five hundred years of tradition and elope with your Virtue Guard? Jun-hwan may never forgive you for bringing such dishonor on our house, but _I'll_ always love you."
"So he's still safe on Hwabun?" This was fucking it, right here, if her dad lied to her one more time...
"Welllllll... no, no he's not," said Kang-ho guiltily. "But he's safe, I promise, he's with the best swordswoman the Star has ever known."
"Zosia?" When her dad gulped she poked his armor hard enough to feel the iron plates beneath the canvas coat. "The woman you tried to pay Chevaleresse Singh to murder? I wonder what instructions you gave her about how to deal with Zosia's companion?"
"How... Gods shit on my face, she's not..."
"One of my captains, now. I'm sure she'll be delighted to see you, catch up on old times."
He looked all around, as though the specter of Cold Cobalt was about to leap out of the darkness, and when he turned back to her there were tears in his eyes. "You're breaking my heart, Ji-hyeon."
"Just like you broke Grampa's heart, to hear you sing it."
"She'll murder me, Ji-hyeon, she'll fucking murder me, right here, in front of you!" She actually felt bad for her second father, even after all his bullshit, so she patted his shoulder and said:
"No she won't. Not without my order, and big a jerk as you've been, I'm not a monster." She hoped both clauses of her statement proved true before the end. "You wait here and think about whether you want to ride with us, against Samoth, or if you're going to get back on your horse and get the fuck out of my camp. But if you turn your back on me, Dad, I can't make any promises. Now, if you'll excuse me, I have to take a message from my captain."
It would have been nice for him to say something supportive, like maybe he was a teensy bit impressed at what an amazing general she obviously was, but instead he just stared at her, beyond words. Well, that would have to do for now—Fennec looked ready to drop from running up the hill. Her father stayed behind, watching her go, but when Fennec whispered the report in her ear, and then repeated it, as she commanded in a surprisingly steady voice, she was glad he hadn't left.
As she plodded back over to him, a wild giggle burst out of her, every ache in her body forgotten and the day's dire battle suddenly small. The expression on her face must have revealed something of the message's tenor, for her father looked as concerned as if both her arms had fallen off.
"What is it?" he asked. "What's happened?"
Her voice broke when she tried to speak, because even though she'd only met the man a handful of times, even though she'd fled the Isles in part to escape him, she never would have wished him harm beyond the sting of rejection. Who could have done such a thing? Other than her, of course.
"You're scaring me, Ji-hyeon, what's happened?"
"I..." Horribly enough, another giggle came out. "I..."
"What? What did you do?"
"I killed my fiancé," said Ji-hyeon, trying to remember what Prince Byeong-gu had even looked like. She recited the rest as precisely as it had been told to her. "I killed him, and I cut off his head, and I stuffed the white scarf he had worn in mourning for me into his mouth, and then I wrapped it all up in one of my Cobalt pennants and delivered it in a box to the Linkensterne garrison under cover of darkness."
Her father opened and closed his mouth several times, but when nothing came out she answered his unvoiced question:
"I mean, I didn't. Obviously. _No_. But tell that to Empress Ryuki; she's just declared war against the Cobalt Company. Oh, and offered governorship of Linkensterne to whoever brings her my head. So there's that."
Like everything else about her adventure in the Crimson Empire, it sounded so simple when she said it out loud. Instead of yelling at her, like she expected, her second father stepped forward and held her, and though her hand started hurting worse than ever and her back ached under his embrace, she did not join Kang-ho in shedding tears. She was too busy planning what to do next.
After her meeting with Hoartrap, Zosia had a powerful need to be away from Choplicker for a spell, and so before she entered the prisoner's tent she stopped in the darkness between campfires. Kneeling down, she scratched behind the monster's ears, scratched like she'd never scratched before. He groaned happily, licked her shaking hand.
"We've got a history, old devil," she told him. "I hope our future goes better for both of us. Now go treat yourself to whatever you want, so long as it harms no mortal."
He was off like an arrow, not giving her so much as a parting bark as he loped away. Zosia instantly regretted her carelessness—just what treat would he be able to secure for himself; how far might he range from their camp to obtain it?
Near on twenty-five years she'd had the devil bound to her, and after all this time she didn't know much more than she'd started with. Going forward she'd have to be a hell of a lot more specific with what she offered him, like she'd done in Hoartrap's tent. It had taken hours of pondering her wording before she'd dare to say it, and considering how well it had turned out, that had been a lesson, albeit an obvious one. Nothing with devils should be done rashly.
As she picked herself up, the chill of the looming winter cut through the dirndl she had not worn since the last time Efrain Hjortt had graced her with his presence. The dress no longer fit her as well, the woman who had sewn it with the help of her husband having a bit more weight on her bones, and a whole hell of a lot more on her heart. She tried to recall what Leib had said to her as they worked by the light of their hearth, what it was that had made her laugh so hard she'd pricked herself with the needle... She couldn't remember. Could barely remember the sound of his voice, though it had been but a year since he'd been taken from her. Murdered. In all that time, Zosia had spent far more hours intentionally _not_ thinking of him to spare herself the hurt than she had cherishing the good memories. Hardly seemed right. And now she had no earthly fucking idea why he had died; if Portolés had told the truth to Hoartrap and Queen Indsorith wasn't involved, then just what in every hell was she doing out here, waging war against the Crimson Empire? What had she been doing for the past year, if not preparing to avenge him?
Doing what she did best, apparently—making a lot of people dead for no damn reason at all.
The guards saluted as she approached the tent, probably having expected her earlier in the evening. Looking at the dark flap, she almost turned around and went back to her own tent, utterly drained now that the shock she'd suffered in Hoartrap's tent was wearing off. What a fucking day: climbing mountains, fighting Imperials, fighting her friends, trafficking with devils, and to top it all, learning credulity-straining revelations. That the first new Gate in recorded memory had opened right at their feet was dire enough, a signal that forces more powerful than she could imagine were actively seeking to reshape the world. The other part of the ceremony, though, the thing that Hoartrap believed was the true purpose of the Imperial sacrifice, with the opening of the Gate but a part of the price they paid to complete the ritual... could she really believe such a thing was even possible?
Yes, she decided, she had to. Hoartrap was in fear of more than his life when he'd told her everything. If he believed it had happened, then it had.
Which meant that the Star of today was unlike the Star of any day before it, stretching back for five hundred years. The world could never go back to what it had been this morning, when she'd bandied words with an avowed heretic digging the grave for a sister of the Chain. Word would spread quickly of the miracle that happened this morning, and then the entire Star would shudder before the supreme witchery of the Burnished Chain. Everyone would become a believer. What did Hoartrap say the Chainites called it? The Day of Becoming?
It almost made what had happened to Leib and everyone else in Kypck seem small. Almost convinced her to go check if Maroto had come back to camp yet, licking his wounds. She wanted to see the look on his face when he found out Purna was alive, and all because some spoiled fop from the old capital had been nicer to his dog than Zosia had been to hers. Almost made her stagger back to her tent, so she could bury her head in her cot and sleep for days, hiding in dreams that couldn't possibly be as mad as the waking world.
Almost, but the last time Zosia had put off interrogating a prisoner who would supposedly speak only to her the woman had been murdered in the night. It was time to get the truth out of Efrain Hjortt: assuming Portolés was right and Queen Indsorith hadn't sent him to Kypck, who had? The obvious suspect was the Burnished Chain, but Zosia was done with suspicions. She was ready for facts. When the Gate had opened beneath the Imperial army the entire Fifteenth Cavalry had disappeared along with most of their regiment, which meant Hjortt was the only one left alive from that day, save her.
A day hadn't passed that she hadn't cursed herself for not finishing the job, for giving Hjortt's people the chance to save him from the fire, but now she praised the stars overhead and the devils beneath them that she'd stuck a pin in him for another day. Who knew, depending on what he told her, she might not kill him now, either—wouldn't it be something, if every time she caught Efrain Hjortt he gave up some new secret, and then she could toss him back in for another day?
"Evening, Captain Zosia," said one of the guards as she shook off her thoughts and accepted his offered lantern. "He's in a bad way, barber ain't sure he'll live the night. He doesn't seem able to move much, but we chained him to a post to play it safe."
Just like they'd bound Sister Portolés, apparently; it was enough to make a girl wonder if somebody liked her, upstairs or down. Everything happens, according to the Chain, and maybe they were on to something. "Thanks. I won't be long."
Hjortt groaned as the light of Zosia's lantern reached the foot of his cot, and exhausted as she was, much as she'd thought she'd changed over the last year, the sound of his discomfort brought a smile to her face.
"Good evening, Colonel Hjortt," she said, taking her time crossing the room. An old trick for getting the prisoner's heart moving before you even started. "It's been a while, hasn't it? And yet it seems like only yesterday."
"A very long while, but not long enough," he said, his voice hardly anything like she remembered. "I wondered how it was possible... Even after everything, I wanted it to be true, but I had my doubts. But... but it's really you."
Zosia was glad she'd saved the dirndl for him. The light reached the top of the blankets, the prisoner closing his eyes from the glare, and she nearly dropped the lantern. Whoever this beat-up old man was, he wasn't Efrain Hjortt, and she came closer, holding the lantern up as though his wax disguise would melt away, revealing her nemesis. She could almost see a resemblance in his nose, despite all the bandages on his cheek. But then she was just confused, because she did recognize him, but hadn't seen him for so long she couldn't place it...
The Fifteenth. Of course. The fucking Fifteenth Regiment out of fucking Azgaroth.
"Nicely played, Cavalera," she said, sitting down on the edge of his cot and hooding the lantern so he could open his eyes again. Disappointed though she was at being tricked, she had to respect her adversary's cunning. "They pulled you out of retirement to lure me in, huh? The disinformation was a nice touch; I would've eventually gone after the Fifteenth Cavalry, but if I thought that awful boy was still in charge I'd never be able to resist."
He slowly opened his bloodshot eyes. They were wet with tears. He looked so old. "You... you remember me?"
"Remember you? Motherfucker, you rode me worse than every other regiment combined! Why do you think I ended up on that lunatic suicide mission to storm Diadem? You'd have kept us in the high country for years without getting a crack at King Kaldruut." Zosia shook her head in amazement. Twenty-odd years ago she had cursed his name almost as much as that of the king he served, but seeing him down all the days, she recognized that he'd just been playing his part, the same as she had played hers. He'd always fought fair, too, which was more than could be said for most of his peers. "Domingo Cavalera, Colonel of the Fifteenth Regiment out of Azgaroth. I understand you probably don't believe me, given the circumstances, but by the six devils I bound, it's damn good to see an old face."
"Forgive me if I don't share your sentiment," he growled, blood leaking through the bandage on his face.
"Shit, let me get that," said Zosia, dabbing his chin with her sleeve, unable to stop smiling. What she wouldn't have given to see him laid low like this back in the day, but now... now she just felt bad for him. He was just like her, a relic of days gone by trotted out for one last job. "This is ridiculous, keeping you in irons in your condition. I'll have them unlock you immediately. Anything else I can bring you, Colonel Cavalera? Food, drink, smoke? A bug for the pain? Anything at all, I'll fetch it myself."
"Yes," he said, the words falling hard as a hammer shaping a sword. "You can give me back my son's thumbs."
Zosia froze. " _What?_ "
"His thumbs, woman—you took them, didn't you? Bad enough you burned him like a witch, but he went into the crypt looking like a fucking thief."
Zosia stared at her old opponent, tried to speak... but nothing came out.
"And it's Hjortt now, Domingo Hjortt. I kept my wife's name, even after she left."
"Colonel... Hjortt?" Zosia sank back down to the ground, and seemed to keep sinking, all the way down to the lightless reaches beneath the earth, where the Flintlanders say the First Dark gave birth to all the monsters and devils of the world, the worst of which were named mortals. She couldn't open her eyes, couldn't do anything but let out a long, miserable sigh. She had killed Efrain Hjortt after all, had killed him first, and hadn't even realized it. Now that the hour had arrived, Zosia found herself unable to keep the promise she had made to him back in Kypck—not a single tear fell to mark the passing of the young colonel who had set her on this blood-drenched road, the path that had seemed so obvious a year before now lost in shadow.
And now she was the only one left alive from that day in Kypck, with no more answers than she had started with. She would never hear from Efrain Hjortt's lips who had sent him, because she had been so convinced she had known that she hadn't even asked him before cutting off his thumbs and setting him on fire. Leib forgive her, she was every bit as mad a monster as her enemies had always said. It didn't matter if it was an empire or a village, everything Zosia touched fell into ruin—even if the younger Hjortt were here to give her one answer, she knew that behind it would be the deeper truth that her husband and the rest of his village were killed because of Zosia. If she had never gone to Leib after abdicating the Crimson Throne, never convinced him to retire with her to his childhood home, he and every other villager who had died in the massacre would still be alive. That was why the six devils were first drawn to her, before she and her Five Villains bound them: because no matter where she went or what she tried to do, Zosia sowed misery and death.
Opening her eyes and staring into the dark at the corner of the tent, she at last understood why Choplicker hadn't granted her wish to protect her and Leib all those years ago. Not even a devil can save you from yourself.
"Will you tell me something?" Domingo asked her, sounding just as tired and heartbroken as she was. When she shrugged her heavy shoulders in response, he said, "Out there on the field... what happened? What did I unleash, letting those Chainites perform their ritual?"
"That?" Zosia looked over at Domingo and saw her grief and guilt reflected back on his wracked features. At least it wouldn't be lonely in hell. "Oh, not much. Just the end of the world."
"Oh," said Domingo, as though he'd rather expected that but still wasn't happy to hear it. "Well, where does an unrepentant old sinner go from here, then?"
"Where do you think?" said Cold Zosia, because there was only one direction left, and only one way to get there. "We go down swinging."
# EPILOGUE
The sloop cut through the fog, no one aboard making a sound lest the Immaculate turtle ships be right on top of them in the pale miasma. You had to be just as ruthless as a pirate to sign on as a customs officer, and twice as greedy, so it wasn't surprising the two turtles hadn't given up the chase even when it became apparent where the smugglers were fleeing to. What did surprise the captain of the vessel renamed the _Queen Thief_ was that the Immaculates had followed them into the eternal fogbank that hovered over the sea where the Sunken Kingdom had vanished so many hundreds of years past. Usually Immaculate ships were too skittish to get anywhere near the perpetual storms of the Haunted Sea... but then again, most smugglers were too smart to risk it, too.
Whether there was actually a continent-swallowing whirlpool at the heart of the rain and fog, as the old salts claimed, made little difference, since a scant mile into the mists the seas grew so high and rough that even a much larger ship than the _Queen Thief_ could be tipped in short order. The captain knew, because she had fled here once before under similar circumstances, and been followed in similar fashion, only to give their pursuers the slip once things got choppy. As if to warn her against future trespass, the fog had lifted just enough for them to see the customs ship capsized by a massive wave, the screams of her crew drowned out by the turbulent sea and the crack of furious lightning. Yet the captain wasn't the superstitious type, and so she'd tried the same trick twice... only to find the Immaculates hot on her heels, and the Haunted Sea calmer than a stoned sloth underneath all the mist.
"Cap'n Bang," the lookout hissed down from the crow's nest. "Got a glimpse through the glass when that breeze blew through, and they're coming in on either side. No hope of turning in time."
"Hells," said Bang, chewing on her pipe. "Can you get a look north?"
"North?" Dong-won, her boatswain, turned the color of the fog. "Cap'n, I know it looks calm now, but..."
"Sew buttons on your butt, Bosun," said Bang with more bravado than she felt. "You give me a clear sea and I'll sail it, no questions asked. It clear up there, Hae-il?"
The lookout said nothing, but his hawkglass fell from the mist-obscured crow's nest. Bang neatly caught it out of the air and tucked it into her belt. Trying not to look as impressed with herself as she felt, she hissed, "Hae-il. Hae-il!"
When the lookout didn't reply, Bang nodded up at the crow's nest. Dong-won took a step back, raising his palms, but with another hard nod at the mast, Bang cajoled him into climbing. She slapped his rump as he went up, just so he'd remember who was boss the next time an order was given.
"He's fainted dead away, Cap'n," Dong-won called down a moment later.
"Well, there's a welcome omen," muttered Bang. "What do your hungry gull eyes see, Bosun?"
"See, Cap'n? Not much. It's clouded up again. Here, I'll see if I can wake him up," said Dong-won.
"Double time, Bosun, double time," said Bang, and took another long draw on the pipe she'd stolen from Cobalt Zosia herself. Well, given the toll of years and all, she ought to be called Silver Zosia these days, but credit where deserved—the cutty smoked better than any pipe Bang had ever set her lips to. "Bosun?"
"Oh shit," Dong-won moaned. "Oh shit, oh shit, oh shit."
"Another welcome omen," said Bang, trying to bluff herself through the sardine scales rising on her neck. "What's the song, Bosun? Sea monster? Whirlpool? What?"
"Uhhhhhh," said Dong-won, followed by what sounded suspiciously like a prayer to the Sea God. Bang didn't like prayers on her boat; it was asking for trouble from whatever gods you left out. Knowing two in the crow's nest was already tight, she shoved her way past her nervous crew, down to the front of the boat. Snapping out the hawkglass, she peered over the prow in imitation of the crane figurehead just below her.
Thick as the fog had been a moment before, as soon as she put her eye to the hawkglass Bang was blinded by sunlight reflecting on wet rock or metal. Stowing the instrument and rubbing her eye in irritation, she looked back up to see what blasted spit of rock was threatening her ship now... and nearly lost her grip on the prow. Her jaw dropped wide as a customs officer's pocket. Zosia's pipe fell from her teeth, but treasured though the cutty was, Bang didn't even notice.
The _Queen Thief_ broke through the last few curtains of fog, and instead of a storm or maelstrom at the heart of the Haunted Sea, there was an entire coastline. They'd come perilously close to the sea cliffs that rose a thousand feet into the air, the island steaming in the bright sunshine and light breeze. Impressive as all this was, what smacked Bang square in the gob were all the enormous caves yawning in the cliffs, caves from which swarmed enormous, many-legged creatures the likes of which she'd never conceived, even in harpyfish dreams. The monsters dove down into the calm sea, one close enough to splash sense back into the captain.
"Tack!" Bang yowled, running back across her ship, slapping any of her stunned crew in striking range. "Tack, you poltroons, tack tack tack! Get us out of here!"
Already, though, Bang could hear the scratch-scratch-scratching of something at the hull... After all these centuries, the Sunken Kingdom of Jex Toth had returned, and she hadn't come back alone. Off the starboard bow, Zosia's bobbing pipe was knocked under by a violent splash, and sank into the busy darkness.
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# Contents
1. COVER
2. TITLE PAGE
3. WELCOME
4. DEDICATION
5. PART I: OF MORTAL WISHES
1. CHAPTER 1
2. CHAPTER 2
3. CHAPTER 3
4. CHAPTER 4
5. CHAPTER 5
6. CHAPTER 6
7. CHAPTER 7
8. CHAPTER 8
9. CHAPTER 9
10. CHAPTER 10
11. CHAPTER 11
12. CHAPTER 12
13. CHAPTER 13
14. CHAPTER 14
15. CHAPTER 15
16. CHAPTER 16
17. CHAPTER 17
18. CHAPTER 18
19. CHAPTER 19
20. CHAPTER 20
21. CHAPTER 21
22. CHAPTER 22
23. CHAPTER 23
24. CHAPTER 24
25. CHAPTER 25
26. CHAPTER 26
6. PART II: AND THE DEVILS TO GRANT THEM
1. CHAPTER 1
2. CHAPTER 2
3. CHAPTER 3
4. CHAPTER 4
5. CHAPTER 5
6. CHAPTER 6
7. CHAPTER 7
8. CHAPTER 8
9. CHAPTER 9
10. CHAPTER 10
11. CHAPTER 11
12. CHAPTER 12
13. CHAPTER 13
14. CHAPTER 14
15. CHAPTER 15
16. CHAPTER 16
17. CHAPTER 17
18. CHAPTER 18
19. CHAPTER 19
20. CHAPTER 20
21. CHAPTER 21
22. CHAPTER 22
23. CHAPTER 23
24. CHAPTER 24
25. CHAPTER 25
26. CHAPTER 26
27. CHAPTER 27
28. CHAPTER 28
29. EPILOGUE
7. ORBIT NEWSLETTER
8. COPYRIGHT
# Navigation
1. Begin Reading
2. Table of Contents
# Copyright
The characters and events in this book are fictitious. Any similarity to real persons, living or dead, is coincidental and not intended by the author.
Copyright © 2015 by Alex Marshall
Cover design by Lauren Panepinto
Map design © Tim Paul
Cover © 2015 Hachette Book Group, Inc.
All rights reserved. In accordance with the U.S. Copyright Act of 1976, the scanning, uploading, and electronic sharing of any part of this book without the permission of the publisher constitute unlawful piracy and theft of the author's intellectual property. If you would like to use material from the book (other than for review purposes), prior written permission must be obtained by contacting the publisher at permissions@hbgusa.com. Thank you for your support of the author's rights.
Orbit
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First ebook edition: April 2015
Orbit is an imprint of Hachette Book Group, Inc. The Orbit name and logo are trademarks of Little, Brown Book Group Limited.
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The publisher is not responsible for websites (or their content) that are not owned by the publisher.
ISBN 978-0-316-27799-0
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# Table of Contents
1. Cover
2. Title Page
3. Copyright
4. Preface
5. Acknowledgements
6. Introduction
7. Section I: Fundamental skills
1. Chapter 1: Accountability
1. Aim of this chapter
2. Regulation and registration
3. Healthcare assistants and assistant practitioners
4. Responsibilities and accountability
5. Delegation
6. Related aspects and terminology
7. Summary
8. References
2. Chapter 2: Communication in healthcare
1. Aim of this chapter
2. Why good communication is important
3. Definition of communication
4. Communication methods
5. Strategies to improve communication
6. Related aspects and terminology
7. Common problems or communication barriers
8. Skills for the Health Care Certificate
9. Summary
10. References
11. Addendum
3. Chapter 3: Psychological well-being
1. Aim of this chapter
2. What is meant by psychological care?
3. Psychological assessment in the healthcare setting
4. The importance of psychological care in the healthcare setting
5. Strategies to optimise psychological well-being
6. Pharmacological (drug-related) options
7. Non-pharmacological options
8. Therapeutic sense of self
9. Common problems
10. Summary
11. References
4. Chapter 4: Documentation and record keeping
1. Aim of this chapter
2. The importance and purpose of documentation in relation to clinical skills
3. Confidentiality in records and documentation
4. Types of documentation
5. Legal aspects relating to documentation
6. Common problems
7. Related aspects and terminology
8. Strategies to improve standards of record keeping
9. Summary
10. References
8. Section II: Core clinical skills
1. Chapter 5: Pulse
1. Aim of this chapter
2. What is a pulse?
3. Relevant anatomy and physiology
4. Related aspects and terminology
5. Factors affecting the pulse rate
6. Terminology
7. Automated devices
8. Fetal heartbeat
9. Documentation
10. Common problems
11. Summary
12. References
2. Chapter 6: Blood pressure monitoring
1. Aim of this chapter
2. What is blood pressure?
3. Reasons for monitoring blood pressure
4. Who requests the test?
5. Who can take a BP reading?
6. What is done with the readings/information?
7. Relevant anatomy and physiology
8. Related aspects and terminology
9. Terminology
10. Korotkoff's sounds
11. Equipment
12. Sites for recording blood pressure
13. Taking blood pressure
14. Documentation
15. Common problems
16. Summary
17. References
3. Chapter 7: Temperature
1. Aim of this chapter
2. What is temperature?
3. Reasons for measuring temperature
4. Normal limits
5. Relevant anatomy and physiology
6. Related aspects and terminology
7. Terminology
8. Taking a temperature reading
9. Route
10. Taking a temperature reading
11. Documentation
12. Common problems
13. Summary
14. References
4. Chapter 8: Pulse oximetry
1. Aim of this chapter
2. What is an oxygen saturation reading?
3. Who can perform the test?
4. Reasons for recording an oxygen saturation level
5. Relevant anatomy and physiology
6. Related aspects and terminology
7. The mechanics of pulse oximetry
8. Equipment
9. Normal readings
10. Using a pulse oximeter
11. Documentation
12. Common problems
13. Summary
14. References
5. Chapter 9: Respiratory care
1. Aim of this chapter
2. What is respiratory care?
3. Relevant anatomy and physiology
4. Upper respiratory system
5. Lower respiratory system
6. Recording a respiratory rate
7. How to measure and record a respiratory rate accurately
8. Measuring and recording a peak expiratory flow rate
9. Performing suctioning
10. Related aspects and terminology
11. Common problems
12. Summary
13. References
14. Addendum
15. Reference
6. Chapter 10: Urinalysis and faecal occult blood testing
1. Aim of this chapter
2. Reasons for performing urinalysis and FOB tests
3. Relevant anatomy and physiology
4. Urinalysis testing
5. Faecal occult blood testing
6. Related aspects and terminology
7. Common problems
8. Summary
9. References
10. Addendum
7. Chapter 11: Urinary catheterisation and catheter care
1. Aim of this chapter
2. Urinary catheterisation
3. Relevant anatomy and physiology
4. Types of catheterisation
5. Patient preparation for catheterisation
6. Insertion technique
7. Catheter care
8. Sampling
9. Removal of catheter
10. Related aspects and terminology
11. Terminology
12. Common problems
13. Summary
14. References
8. Chapter 12: Venepuncture
1. Aim of this chapter
2. Reasons for performing venepuncture
3. Relevant anatomy and physiology
4. Common sites for venepuncture
5. Infection
6. Hand hygiene
7. Aseptic (sterile) technique
8. Health and safety
9. Environment
10. Performing the skill: requirements and technique
11. Related aspects and terminology
12. Common problems
13. Summary
14. References
9. Chapter 13: Blood glucose monitoring
1. Aim of this chapter
2. What causes diabetes?
3. Reasons for performing blood glucose measurement
4. Relevant anatomy and physiology
5. Related aspects and terminology
6. Blood glucose levels
7. Hypoglycaemia
8. Hyperglycaemia
9. Common problems
10. Summary
11. References
10. Chapter 14: Fluid balance and intravenous maintenance
1. Aim of this chapter
2. Reasons for monitoring fluid balance
3. Related anatomy and physiology
4. Electrolytes
5. Related aspects and terminology
6. Fluid balance charts
7. The intravenous route
8. Care of the cannula
9. Discontinuing an IV infusion
10. Common problems
11. Summary
12. References
9. Section III: Complex clinical skills
1. Chapter 15: Medicines
1. Aim of this chapter
2. The role of healthcare assistants and assistant practitioners in relation to medicine administration
3. Types of medicines
4. Medication prescribing and legal aspects
5. Related aspects and terminology
6. Common medications
7. Errors in administration and adverse reactions
8. Summary
9. References
2. Chapter 16: Peripheral intravenous cannulation
1. Aim of this chapter
2. Reasons for cannulation
3. Why perform peripheral IV cannulation
4. Relevant anatomy and physiology
5. How to insert and remove a peripheral IV cannula
6. Environment
7. Performing peripheral IV cannula: requirements and technique
8. Patient education for peripheral IV cannulation
9. Related aspects and terminology
10. Common problems/potential complications of peripheral IV cannulation
11. Summary
12. References
3. Chapter 17: Recording a 12-lead Electrocardiograph (ECG)
1. Aim of this chapter
2. Relevant anatomy and physiology
3. The cardiac conduction system
4. Reasons for recording a 12-lead ECG
5. How to perform a 12-lead ECG
6. Related aspects and terminology
7. Common problems and actions
8. Summary
9. References
4. Index
10. End User License Agreement
## Pages
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## Guide
1. Cover
2. Table of Contents
3. Preface
4. Introduction
5. Section I: Fundamental skills
6. Begin Reading
## List of Illustrations
1. Chapter 2: Communication in healthcare
1. Figure 2.1 Briefly look at Figure 2.1. What can you see? It might depend on your perspective. Refer to the end footnote on this page.
2. Chapter 4: Documentation and record keeping
1. Figure 4.1 The diabetic care pathway. Source:
3. Chapter 5: Pulse
1. Figure 5.1 Sites for taking a pulse.
2. Figure 5.2 Structure involved in initiation of a pulse.
3. Figure 5.3 Rhythm strip for normal heartbeat – 'sinus rhythm': note the regular pattern and shape of each wave. Source: NHS Lothian (2008). Reproduced with permission from NHS Lothian.
4. Figure 5.4 An increased heart rate – tachycardia: note that the waves are closer together. Source: NHS Lothian (2008). Reproduced with permission from NHS Lothian.
5. Figure 5.5 Bradycardia – slow heartbeat: note the regular pattern of the wave, but the spacing is far wider than the strips in Figure 5.3 and 5.4, giving a slower heart rate. Source: NHS Lothian (2008). Reproduced with permission from NHS Lothian.
6. Figure 5.6 Taking a radial pulse.
7. Figure 5.7 Observation chart with 'normal' and 'irregular' pulse charted. Source: NHS Lothian (2008). Reproduced with permission from NHS Lothian.
8. Figure 5.8 TPR (temperature, pulse and respiratory) chart with apex (A) and radial (R) pulse charted. Source: NHS Lothian (2008). Reproduced with permission from NHS Lothian.
4. Chapter 6: Blood pressure monitoring
1. Figure 6.1 Internal structure of the heart.
2. Figure 6.2 An automated blood pressure measuring machine.
3. Figure 6.3 Inappropriate positioning for a blood pressure recording. The arm should be supported on a pillow and below heart level.
4. Figure 6.4 A TPR (temperature, pulse, respiratory rate) chart with blood pressure readings charted. Source: NHS Lothian 2008. Reproduced with permission of NHS Lothian.
5. Figure 6.5 TPR (temperature, pulse, respiratory rate) chart with erect (standing: E) and supine (lying: S) blood pressure readings charted. Source: NHS Lothian 2008. Reproduced with permission of NHS Lothian.
5. Chapter 7: Temperature
1. Figure 7.1 Body temperature at different sites on the body. (Adapted from Torrance and Semple 1998.)
2. Figure 7.2 Location of the hypothalamus and medulla oblongata within the brain.
3. Figure 7.3 Heat production and heat gain from the skin.
4. Figure 7.4 Heat loss from the skin.
5. Figure 7.5 Negative feedback mechanism to control body temperature. (Adapted from Tortora and Derrickson (2011) and Dougherty and Lister (2011).)
6. Figure 7.6 Electronic thermometer. Produced with kind permission from Cardinal Health.
7. Figure 7.7 TPR (temperature, pulse and respiratory rate) chart with temperature recordings. Source: NHS Lothian 2008. Reproduced with permission of NHS Lothian.
6. Chapter 8: Pulse oximetry
1. Figure 8.1 A pulse oximeter with probe in situ.
7. Chapter 9: Respiratory care
1. Figure 9.1 The respiratory system.
2. Figure 9.2 Muscles of respiration.
3. Figure 9.3 Peak flow meter with disposable one-way mouthpiece. Source: Photograph by I Lavery.
8. Chapter 10: Urinalysis and faecal occult blood testing
1. Figure 10.1 Urinary system.
2. Figure 10.2 Digestive system.
3. Figure 10.3 Example of a test recording slip. Source: Photograph by I Lavery.
4. Figure 10.4 A faecal occult blood (FOB) specimen card. Source: Photograph by I Lavery.
5. Figure A10.1 The Bristol Stool Form Scale. Source: Used under CC-BY-SA 3.0 Unported https://creativecommons.org/licenses/by-sa/3.0/deed.en.
9. Chapter 11: Urinary catheterisation and catheter care
1. Figure 11.1 Male bladder and urethra.
2. Figure 11.2 Female bladder and urethra.
3. Figure 11.3 Catheter bag and outlet valve.
4. Figure 11.4 Catheter.
5. Figure 11.5 Sterile pack. Source: Photograph by I Lavery.
6. Figure 11.6 Belly bag. Source: Photograph by I Lavery.
7. Figure 11.7 Sampling ports.
10. Chapter 12: Venepuncture
1. Figure 12.1 Common sites (upper arm).
2. Figure 12.2 Vacuum tubes.
3. Figure 12.3 Insertion technique example.
4. Figure 12.5 Insertion technique.
5. Figure 12.4 Winged device and adaptor.
6. Figure 12.6 Example of blood culture set.
7. Figure 12.7 Adaptor.
11. Chapter 13: Blood glucose monitoring
1. Figure 13.1 Pancreas shown in relation to the kidneys, duodenum and adrenal glands.
2. Figure 13.2 Maintenance of blood glucose. Adapted from Tortora and Derrickson (2006), Marieb and Hoehn (2007) and Thibodeau and Patton (2007).
3. Figure 13.3 Advantage blood glucose meter by Roche. Source:
4. Figure 13.4 Site for blood glucose sampling.
5. Figure 13.5 Blood specimen for blood glucose testing.
12. Chapter 14: Fluid balance and intravenous maintenance
1. Figure 14.1 Fluid regulation in the body. Source: Thibodeau 2009. Reproduced with permission of Elsevier.
2. Figure 14.2 Fluid balance chart. Source: NHS Lothian 2008. Reproduced with permission of NHS Lothian.
3. Figure 14.3 Cannula with intravenous line attached.
4. Figure 14.4 Spiking an IV bag.
5. Figure 14.5 Filling the drip chamber.
6. Figure 14.6 Priming the IV line.
7. Figure 14.7 Discontinuing an IV line.
13. Chapter 15: Medicines
1. Figure 15.1 Compliance aid for medication delivery.
2. Figure 15.2 A 'spacer' inhaler.
3. Figure 15.3 Nasal cannula.
14. Chapter 16: Peripheral intravenous cannulation
1. Figure 16.1 Venous anatomy of upper arm.
2. Figure 16.2 Hand veins.
3. Figure 16.3 Cross-section of vein.
4. Figure 16.4 Example of cannula.
5. Figure 16.5 Inserting the cannula. Source: Photograph by I Lavery.
6. Figure 16.6 Device in place. Source: Photograph by I Lavery.
15. Chapter 17: Recording a 12-lead Electrocardiograph (ECG)
1. Figure 17.1 Electrical conducting system of the heart.
2. Figure 17.2 The QRS complex.
3. Figure 17.3 Electrode and lead placement for standard 12-lead ECG: (a) Limb electrode placement and (b) electrode placement on the chest.
4. Figure 17.4 Example of sinus rhythm.
## List of Tables
1. Chapter 2: Communication in healthcare
1. Table 2.1 Checklist for effective communication
2. Chapter 3: Psychological well-being
1. Table 3.1 Body's autonomic responses
2. Table 3.2 Stress response symptoms
3. Table 3.3 Stages of grief and possible outcomes
4. Table 3.4 Non-pharmacological options
3. Chapter 4: Documentation and record keeping
1. Table 4.1 Examples of records
2. Table 4.2 Competency framework: record keeping
4. Chapter 5: Pulse
1. Table 5.1 Procedure for taking a manual pulse reading
2. Table 5.2 Procedure for taking a pulse reading using an automated machine
3. Table 5.3 Pulse rates in relation to age
4. Table 5.4 Procedure for taking an apex pulse recording
5. Table 5.5 Recording apex and radial heartbeats
6. Table 5.6 Competency: recording a pulse rate
5. Chapter 6: Blood pressure monitoring
1. Table 6.1 Blood pressure classification
2. Table 6.2 Korotkoff's sounds
3. Table 6.3 Procedure to measure blood pressure with mercury, aneroid or electronic machines
4. Table 6.4 Procedure for lying (supine) and standing (erect) blood pressure recordings First ensure that you follow the procedures detailed in Table 6.2 for the specific machine that you are using
5. Table 6.5 Sizes of cuff
6. Table 6.6 Common problems when taking a blood pressure reading
7. Table 6.7 Competency framework: recording a blood pressure
6. Chapter 7: Temperature
1. Table 7.1 Factors affecting heat production
2. Table 7.2 Grades of pyrexia
3. Table 7.3 Summary of the advantages and disadvantages of different methods
4. Table 7.4 Summary of the advantages and disadvantages of different sites for measuring body temperature
5. Table 7.5 Procedure for taking a temperature reading using either a mercury or electronic thermometer
6. Table 7.6 Procedure for taking a temperature reading using a tympanic thermometer
7. Table 7.7 Procedure for taking a temperature reading using a temporal artery thermometer
8. Table 7.8 Variance in temperature range dependent on site
9. Table 7.9 Thermometry competency: practical assessment form
7. Chapter 8: Pulse oximetry
1. Table 8.1 Procedure for recording an oxygen saturation level
2. Table 8.2 Practical assessment form: competency framework for recording SpO2.
8. Chapter 9: Respiratory care
1. Table 9.1 Children's respiratory rate and age
2. Table 9.2 Assessment for suctioning
3. Table 9.3 Suction pressures
4. Table 9.4 Competency framework: recording a respiratory rate
5. Table 9.5 Competency framework: recording a peak expiratory flow rate (PEFR)
6. Table 9.6 Competency framework: suctioning
9. Chapter 10: Urinalysis and faecal occult blood testing
1. Table 10.1 Significance of substances in the urine
2. Table 10.2 Competency framework: urinalysis testing
3. Table 10.3 Competency framework: faecal occult blood (FOB) testing
10. Chapter 11: Urinary catheterisation and catheter care
1. Table 11.1 Catheter selection
2. Table 11.2 Paediatric catheter sizes
3. Table 11.3 Catheterisation procedure
4. Table 11.4 Intermittent self-catheterisation procedure
5. Table 11.5 Problem solving
6. Table 11.6 Competency framework: indwelling catheterisation
7. Table 11.7 Competency framework: intermittent catheterisation competency – patient/carer
8. Table 11.8 Competency framework: intermittent catheterisation by healthcare assistant
9. Table 11.9 Competency framework: sampling competency
11. Chapter 12: Venepuncture
1. Table 12.1 Summarising possible considerations for vein choice
2. Table 12.2 Guide to good venepuncture practice: vacuum system
3. Table 12.3 Specific actions and observations during the procedure
4. Table 12.4 Guide to good practice and winged device (butterfly) insertion
5. Table 12.5 Blood cultures: good practice guide
6. Table 12.6 Competency framework: venepuncture
12. Chapter 13: Blood glucose monitoring
1. Table 13.1 Procedure for taking blood glucose measurements using a capillary blood sample
2. Table 13.2 Symptoms of hypoglycaemia
3. Table 13.3 Treatment for hypoglycaemia
4. Table 13.4 Treatment for hyperglycaemia
5. Table 13.5 Complications of diabetes
6. Table 13.6 Competency – blood glucose monitoring
13. Chapter 14: Fluid balance and intravenous maintenance
1. Table 14.1 Regulator of fluid balance
2. Table 14.2 The procedure for priming an intravenous (IV) line
3. Table 14.3 Procedure to discontinue an intravenous infusion
4. Table 14.4 Common problems with gravity infusion sets
5. Table 14.5 Competency framework: record clinical observations (fluid balance)
6. Table 14.6 Competency framework: record clinical observations (intravenous (IV) maintenance, including priming and discontinuing an infusion (IVI))
14. Chapter 16: Peripheral intravenous cannulation
1. Table 16.1 Key preventative interventions
2. Table 16.2 Cannula choice guidance
3. Table 16.3 Preparation for procedure
4. Table 16.4 Specific actions and observations during the procedure
5. Table 16.5 Maintenance and care of the intravenous (IV) cannula after insertion
6. Table 16.6 Specific nursing actions during procedure – removal
7. Table 16.7 Practical assessment form: competency – peripheral IV cannulation
15. Chapter 17: Recording a 12-lead Electrocardiograph (ECG)
1. Table 17.1 Procedure for recording a standard 12-lead ECG
2. Table 17.2 ECG recording common problems
3. Table 17.3 Competency framework competency: recording a standard 12-lead ECG
# Clinical Skills for Healthcare Assistants and Assistant Practitioners
**Angela Whelan and Elaine Hughes**
Faculty of Health and Social Care, Edge Hill University, UK
**Second Edition**
This edition first published 2016 © 2016 by John Wiley & Sons Ltd
First edition published 2009 by Paula Ingram and Irene Lavery
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The contents of this work are intended to further general scientific research, understanding, and discussion only and are not intended and should not be relied upon as recommending or promoting a specific method, diagnosis, or treatment by health science practitioners for any particular patient. The publisher and the author make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of fitness for a particular purpose. In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of medicines, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each medicine, equipment, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. Readers should consult with a specialist where appropriate. The fact that an organization or Website is referred to in this work as a citation and/or a potential source of further information does not mean that the author or the publisher endorses the information the organization or Website may provide or recommendations it may make. Further, readers should be aware that Internet Websites listed in this work may have changed or disappeared between when this work was written and when it is read. No warranty may be created or extended by any promotional statements for this work. Neither the publisher nor the author shall be liable for any damages arising herefrom.
_Library of Congress Cataloging-in-Publication Data_
Names: Whelan, Angela, 1962- , author. | Hughes, Elaine, 1969- , author. | Ingram, Paula, 1969- Clinical skills for healthcare assistants. Preceded by (work):
Title: Clinical skills for healthcare assistants and assistant practitioners / Angela Whelan and Elaine Hughes.
Description: Second edition. | Chichester, West Sussex ; Hoboken, NJ : John Wiley & Sons Inc., 2016. | Preceded by Clinical skills for healthcare assistants / Paula Ingram and Irene Lavery. 2009. | Includes bibliographical references and index.
Identifiers: LCCN 2015045703 | ISBN 9781118256411 (pbk.)
Subjects: | MESH: Nursing Care–methods | Nurses' Aides | Great Britain | Handbooks
Classification: LCC RT41 | NLM WY 100 FA1 | DDC 610.73–dc23 LC record available at <http://lccn.loc.gov/2015045703>
A catalogue record for this book is available from the British Library.
Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books.
Cover image: © Monkey Business Images Ltd/Getty
# Preface
The Francis Report highlighted the importance of a workforce that was not only caring and compassionate but able to provide care that is underpinned by knowledge. The basis of the broad, generic role that is undertaken by many healthcare workers has alignment with this view of the future nurse and has been included within the Skills for Health and the Skills Certificates.
This book provides background knowledge on the day-to-day care that is provided by those working in caring environments. Clinical skills are fundamental to the role of the care worker, and as the role of the care worker progresses the expansion of the skills that can be undertaken as part of their role continues.
To address this, the book covers both fundamental clinical skills as well as the more complex ones that generally require specific training within the workplace to complete. Therefore this book is aimed at those already engaged in care work and new students in health and social care in a variety of clinical settings and can be used as a resource that will guide the reader through the clinical skill itself through to self-assessment.
Elaine Hughes & Angela Whelan
# Acknowledgements
The production of this second edition has been a long and winding road and we would like to acknowledge the work of both Paula Ingram and Irene Lavery in the original book.
The continued support and encouragement form our families, especially Ged and Ruth Whelan, Owen Gallagher and Les McNee has been unwavering, for which we are very grateful.
Enthusiasm from friends and colleagues has been continuous and we would like to offer special thanks to Karen Ellis, Aintree University Hospital Trust, Beth Spencer and Debbie Chadwick, Edge Hill University for their help and support.
Angela Whelan & Elaine Hughes
# Introduction
The book has been split into three sections:
1. **1.** **Section 1** covers fundamental skills applicable to all staff, and is essential as a prerequisite before performing all clinical skills.
2. **2.** **Section 2** contains core clinical skills, which includes most of the clinical skills required for clinical practice that are often taught at a local level.
3. **3.** **Section 3** outlines complex clinical skills, which require more in-depth training and may be restricted to specialist areas of practice, and that often require the direct supervision of registered nurses.
Each chapter has the same structure, starting with the aims and objectives of the chapter, followed by the explanation of why the skill is performed, relevant anatomy and physiology, related aspects and terminology, how to perform the skill and common problems. Throughout each chapter case studies and Think about it boxes relating to the topic will be included, encouraging the reader to apply them to their own practice. The final section addresses both self- and formal assessment where required.
The use of checklists, pictures and clear, concise theory is aimed at making the book a comprehensive yet easy to read resource for all.
# Section I
## Fundamental skills
# Chapter 1
Accountability
# Learning objectives
* Identify the current plans regarding regulation of healthcare assistants and assistant practitioners
* Define accountability
* Relate accountability to the healthcare assistant and assistant practitioner role
* Describe the duty of care and how it relates to negligence
* Discuss consent
* List the key elements of the Mental Capacity Act
## Aim of this chapter
The aim of this chapter is to enable healthcare assistants and assistant practitioners to understand the issues and concept of accountability relating both to their role and to others around them.
This chapter covers accountability and issues surrounding accountability in relation to clinical skills. Healthcare assistants, healthcare support workers and assistant practitioners form an integral part of the contemporary flexible 'nursing family' (RCN 2004). A substantial proportion of essential nursing care is now delivered by the unregistered branch of the nursing family with some personnel such as assistant practitioners undertaking work previously performed by registered staff (RCN 2012). Registration and regulation of healthcare assistants, health support workers and assistant practitioners continues to be debated (Vaughan et al. 2014)
## Regulation and registration
Registration refers to the process by which professionals such as nurses are registered with a regulatory body. Registered staff are professionally accountable to their respective regulatory bodies, for example nurses are accountable to the Nursing Midwifery Council (NMC) and allied health professionals to the Health and Care Professions Council (HCPC). Regulation refers to a set of rules that members are required to follow by law (Law Commission et al. 2012: 68): for example, nurses are regulated by the NMC and legally have to follow the rules set out by that specific body; for nurses, therefore, the NMC is the main focus for regulatory accountability (NMC 2015b). The Nursing Midwifery Council regulates nurses and midwives in England, Wales, Scotland and Northern Ireland and exists to protect the public. They set standards of education, training, conduct and performance so that nurses and midwives can deliver high-quality healthcare throughout their careers. The NMC makes sure that nurses and midwives keep their skills and knowledge up to date and uphold a set of professional standards. There is a clear and transparent processes used to investigate nurses and midwives who fall short of those standards. In the event of a serious error, professional misconduct, failure to respect professional boundaries or unethical conduct, a registered nurse is held accountable and can be removed from the register. The NMC hold a register of nurses and midwives allowed to practise in the UK (NMC 2015b).
## Healthcare assistants and assistant practitioners
Both assistant practitioners and healthcare assistants remain unregistered and without a regulatory body, unlike registered nurses. They do, however, have codes of conduct and it is imperative practitioners become familiar with them.
In Scotland, since 2011 all new HCAs have been required to meet induction standards and comply with a code of conduct, while employers are required to sign up to a code of practice (Scottish Government 2010). In Wales there is an All Wales Code of Conduct for healthcare support workers (Welsh Assembly Government 2011). In addition, the Hywel Dda Health Board introduced a code of conduct for healthcare support workers, along with an employers' code of practice 'to provide an assurance framework for public protection' (Horner 2012; Hywel Dda Health Board 2015). A voluntary register, but no mandatory regulatory system, exists in Northern Ireland. In England, the Coalition Government rejected the recommendation made in Robert Francis's report into the failings at the Mid Staffordshire Foundation Trust (Francis 2013), that recommended all healthcare support workers should be regulated. Instead Camilla Cavendish (DH 2013b) was asked by the Secretary of State to review and make recommendations on the recruitment, learning and development, management and support of healthcare assistants and social care support workers. The resulting report, published in July 2013, found that the preparation of healthcare assistants and social care support workers for their roles within care settings was inconsistent, and one of the recommendations was the development of the Care Certificate. In the absence of registration and a regulatory body, all unregistered health and social care workers are recommended to read the chapters of this book and consider them alongside and in addition to the Care Certificate. Local codes have also been developed, please become familiar with your local policy and code(s)
Skills for Health and Skills for Care published the Code of Conduct (2013) for healthcare support workers and adult social care workers. Although this code is voluntary it is seen as best practice. This Code of Conduct sets the standard of conduct expected of healthcare support workers and adult social care workers, outlining the behaviour and attitudes that are expected of those working in health and social care settings to provide safe, compassionate care and support (Skills for Health and Skills for Care 2013).
The role of the assistant practitioner operates at band 4 or above and has emerged since it was first introduced in the Northwest of England in 2002 to cover a number of professions and settings. This role was introduced in the UK to complement the work of registered professionals, working across professional boundaries, and now performs many tasks previously undertaken by registered staff (Vaughan et al. 2014). Skills for Health (2009: 1) defined the role of the Assistant Practitioner as:
> An Assistant Practitioner is a worker who competently delivers health and social care to and for people. They have a required level of knowledge and skill beyond that of the traditional healthcare assistant or support worker. The Assistant Practitioner would be able to deliver elements of health and social care and undertake clinical work in domains that have previously only been within the remit of registered professionals. The Assistant Practitioner may transcend professional boundaries. They are accountable to themselves, their employer, and, more importantly, the people they serve.
# Think about it
Identify other professional groups within your clinical area and find out about the professional bodies to which they report. What are your thoughts about registration? What advantages do you think are attached to registration and are there any negatives?
## Responsibilities and accountability
Accountability and responsibility are words that are often used interchangeably by health professionals as though they have the same meaning (Griffith 2015). Responsibility means _having control or authority over someone or something_ (Griffith and Tenegnah 2010). Carvallo et al. (2012) identify responsibility as accepting a task or duty that you have been given and accepting that task willingly. So it can be seen that responsibilities are linked to your role, which means you require training and assessment of the necessary knowledge, skills, values and ability to undertake a particular task or duty. In order to be responsible, Dimond (2011) asserts it is also necessary to have legal knowledge, as ignorance of the law is no defence. So as an HCA or AP you are responsible for your practice and for ensuring the interventions undertaken are in the best interests of your patients. Responsibility equates to the duty of care in law. Scrivener et al. (2011) explain that the duty of care applies whether the task involves bathing a patient or complex surgery – in each case there is the opportunity for harm to occur. In this context, the question that arises concerns the standard of care expected of practitioners performing these tasks. This is the legal liability the practitioner owes to the patient. By accepting the responsibility to perform a task the practitioner must ensure the task is performed competently, at least to the standard of the ordinarily competent practitioner in that type of task.
### Accountability
Accountability is crucial to the protection of the public and individual patients and is a complex concept to understand (Griffith and Tengnah 2010). Nurses are bound by the NMC to be accountable (NMC 2015a). Dimond (2011) reports four arenas of accountability relating to registered nurses:
1. **1.** Accountable to the Public via criminal law and criminal courts.
2. **2.** Accountable to the Patients via civil law, civil courts.
3. **3.** Accountable to the Employer via contract of employment, employment tribunal.
4. **4.** Accountable to the Profession via NMC, Conduct and Competence Committee.
Mullen (2014) points out that HCAs and APs are not accountable to a professional body, but they are accountable to the other arenas. Additionally there are also general responsibilities related to accountability laid out for all staff in the NHS Constitution (see Boxes 1.1 and 1.2 for a summary of responsibilities relating to accountability (Mullen 2014)). Put quite simply, Griffith and Tengnah (2010) define accountability as 'being answerable for your personal acts or omissions to a higher authority with whom you have a legal relationship'.
# Box 1.1 Accountability
Code of Conduct for Healthcare Support Workers and Adult Social Care Workers
(Skills for Health and Skills for Care 2013)
## Guidance statements
As a healthcare support worker or adult social care worker in England, you must:
* Be honest with yourself and others about what you can do, recognise your abilities and the limitations of your competence and only carry out or delegate those tasks agreed in your job description.
* Always behave and present yourself in a way that does not call into question your suitability to work in a health and social care environment.
* Be able to justify and be accountable for your actions or your omissions – what you fail to do.
* Always ask your supervisor or employer about any issues that might affect your ability to do your job competently and safety. If you do not feel competent to carry out an activity, you must report this.
* Comply with your employers agreed ways of working.
* Report any actions or omissions by yourself or colleagues that you feel may compromise the safety or care of people who use healthy and care services and. If necessary, use whistle blowing procedures to report any suspected wrongdoing experiences, activities and people across the NHS.
# Box 1.2 NHS Constitution staff responsibilities
A summary of the areas related to accountability
* You have a duty to accept professional accountability and maintain the standards of professional practice as set by the appropriate regulatory body applicable to your profession or role.
* You have a duty to act in accordance with the express and implied terms of your contract of employment.
* You have a duty not to discriminate against patients or staff and to adhere to equal opportunities and equality and human rights legislation.
* You have a duty to protect the confidentiality of personal information that you hold.
* You have a duty to be honest and truthful in applying for a job and in carrying out that job.
Remember: you are still 100% accountable for your acts and omissions.
### Areas of accountability
#### Public
Accountability to the public would involve a breach of criminal law and prosecution through the criminal courts (Dimond 2011). An example of this would be if an HCA or AP caused the death of a patient through their practice. The individual would be prosecuted through the criminal courts for that crime.
#### Patients
Civil law is actionable in the civil courts and may or may not be a crime (Dimond 2011). Individuals can take out legal proceedings against any healthcare professional, including healthcare assistants and assistant practitioners. The organisation will take responsibility for this under a concept known as vicarious liability that will be discussed later, providing the worker has followed policies and procedures. The law imposes a duty of care on a practitioner in circumstances where it is reasonably foreseeable that the practitioner could harm a patient through their action or failure to act (Cox 2010). Healthcare assistants are legally accountable to the patient for any errors that they may make through civil law (RCN 2011). An example here could be if, during cannulation, a healthcare assistant hit a nerve and caused pain, and the patient wished to take legal proceedings.
#### Employer
Mullen (2014) points out that HCAs and APs are accountable to their employer and as such are expected to follow their contract of duty, to work within the domain of their job description and to follow the codes of responsibility and behaviour, as laid out in the recent code of conduct for healthcare workers (Skills for Health and Skills for Care 2013) (Box 1.1). It is vital, therefore, that you have an up-to-date copy of your job description and that you are competent and trained to undertake the tasks, behaviours and responsibilities described (Mullen 2014). The need for job/role clarification is essential as employers need to ensure the right processes are in place and staff are trained with the right skills (Vaughan et al. 2014)
## Delegation
The Oxford English Dictionary (2012) defines delegation as, 'entrusting a task to another person'. HCAs and APs may be delegated or allocated tasks by another member of staff (usually, but not always from a registered practitioner) or they may delegate a task to somebody else (i.e. they are the delegator) (Mullen 2014). The RCN (2011) states:
> If a practitioner such as a registered nurse should delegate a task, then that practitioner must be sure that the delegation is appropriate. This means that the task must be necessary; and the person performing the delegated task, for example a HCA or nursing student, must understand the task and how it is performed, have the skills and abilities to perform the task competently and accept responsibility for carrying it out.
Delegation must always be appropriate and in the best interest of the patient. Simply put, if you are delegated a task, you must have been trained and assessed as competent to undertake that job. If this is not the case, you must inform the person delegating the task to you. Equally, if you are delegating a task to somebody else you must ensure they are competent to perform that task. It is essential that delegation is appropriate, and the principles of delegation adapted from the RCN document (RCN 2011) are shown in Box 1.3.
# Think about it
A registered nurse (RN) delegates the task of taking a patient's temperature using a tympanic thermometer (this measures the temperature in the tympanic membrane in the ear). You have never seen the piece of equipment before. What would your response be? Do you think that this is an appropriate task to delegate?
# Box 1.3 Principles of delegation
* Delegation must always be in the best interest of the patient and not performed simply in an effort to save time or money
* The support worker must have been suitably trained to perform the task
* The support worker should always keep full records of training given, including dates
* There should be written evidence of competence assessment, preferably against recognised standards such as National Occupational Standards
* There should be clear guidelines and protocols in place so that the support worker is not required to make a clinical judgement that they are not competent to make
* The role should be within the support worker's job description
* The team and any support staff need to be informed that the task has been delegated (e.g. a receptionist in a GP surgery or ward clerk in a hospital setting)
* The person who delegates the task must ensure that an appropriate level of supervision is available and that the support worker has the opportunity for mentorship. The level of supervision and feedback provided must be appropriate to the task being delegated. This will be based on the recorded knowledge and competence of the support worker, the needs of the patient/client, the service setting and the tasks assigned (RCN et al. 2006)
* Ongoing development to ensure that competency is maintained is essential
* The whole process must be assessed for the degree of risk.
Delegation is the process by which a registered practitioner can allocate work to a healthcare assistant who is deemed competent to undertake that task, and the worker then carries the responsibility for that task. Registered practitioners are accountable for ensuring you have the knowledge and skill level required to perform the delegated task. The healthcare assistant is accountable for accepting the delegated task, as well as being responsible for their actions in carrying it out.
# Think about it
In relation to these principles, identify and reflect on the tasks that are delegated to you within your own organisation. Seek out any local policies and procedures that are in place to define the tasks that can be undertaken following competency based training.
Choosing tasks or roles to be undertaken by a healthcare assistant is actually a complex professional activity; it depends on the registered practitioner's professional opinion and, for any particular task, there are no general rules (RCN 2011). The NHS Constitution (Department of Health (DH) 2013), however, applies to registered practitioners who are additionally accountable to their regulatory body for ensuring that the standards of practice, patient care and treatment meet the regulator's standards. The concept of delegation is included within all professional bodies' codes of conduct that the registered practitioner is required to follow (Mullen 2014). For example: Standard 11 of The Code, (NMC 2015a) requires nurses to:
> Be accountable for your decisions to delegate tasks and duties to other people
>
> To achieve this, you must;
1. **11.1** only delegate tasks and duties that are within the other person's scope of competence, making sure that they fully understand your instructions
2. **11.2** make sure that everyone you delegate tasks to is adequately supervised and supported so they can provide safe and compassionate care, and
3. **11.3** confirm that the outcome of any tasks you have delegated to someone meets the required standard.
There are a number of aspects to consider in conjunction with the competence of the healthcare assistant and assistant practitioner in relation to the activity to be delegated.
## Related aspects and terminology
### Competence
Skills for Health develop National Occupational Standards (NOS) to set clear standards for a wide range of activities for healthcare workers. NOS describe the skills, knowledge and understanding needed to undertake a particular task or job to a nationally recognised level of competence. They cover key activities undertaken within the occupation in question under all the circumstances that the job holder is likely to encounter. HCAs and APs must develop the competencies required within their role to a given standard. The introduction of the Care Certificate has already been discussed and is available from SFH's website <http://www.skillsforcare.org.uk/Standards/Care-Certificate/Care-Certificate.asp>.
### Vicarious liability
Vicarious liability means that the employer is accountable for the standard of care delivered and is responsible for employees working within agreed limits of competence appropriate to the abilities of that employee. Therefore, to remain covered by an employer's vicarious liability clause, the HCA or AP must only work within this area of assessed competence and within the responsibilities of their role and job description. This principle operates to make an employer liable, along with the employee, for any negligence caused by the employee provided that they are operating within the organisation's policies and procedures (Samanta and Samanta 2011). For example, you have performed venepuncture (the taking or drawing of blood) from a patient, having completed all the appropriate education and competency required by your employer. Unfortunately, the next day the patient has bruising at the site. As you had followed all policies and procedures, should the patient sue, the organisation would take responsibility for your actions.
### Indemnity insurance
Where employers are vicariously liable for the actions of their staff, they need to have insurance to cover the risks of clinical negligence claims arising from employee carelessness. Individual practitioners remain legally accountable for their actions but it is rare for injured patients to sue them rather than their employers (Cox 2010).
The Health Care and Associated Professions (Indemnity Arrangements) Order 2014 No. 1887 (2014) states 'each practising registrant must have in force in relation to that registrant an indemnity arrangement which provides appropriate cover for practising as such'. The NMC Code (2015) standard 12 reflected these new arrangements stating that registered nurses must:
'12.1 make sure that you have an appropriate indemnity arrangement in place relevant to your scope of practice.'
This means, if a patient sues the employing hospital for negligence due to a nurse or healthcare assistant causing injury, the organisation would cover the nurse under vicarious liability (see above). However, the patient can also decide to sue the nurse or healthcare assistant as a separate case and, in this instance, indemnity insurance would pay for the practitioner's legal costs and the compensation paid to the patient. While this currently refers to regulated healthcare professionals, there is discussion as to whether HCAs, APs and other support workers will also require mandatory indemnity insurance. Some union membership includes indemnity insurance; it is advisable that you check whether you are currently covered.
### Duty of care and negligence
The term 'duty of care' is used to describe the obligations implicit in the roles of all health or social care workers and is not something that can be opted out of (Mullen 2014). The RCN (2011) guidance highlights the importance of 'duty of care', a term that is described clearly: 'The law imposes a duty of care on practitioners, whether they are HCAs, APs, students, registered nurses, doctors or others, when it is "reasonably foreseeable" that they might cause harm to patients through their actions or their failure to act' (Cox 2010; RCN 2011). Where a patient or relative is dissatisfied with the care received from either an organisation or an individual, they can sue for clinical negligence. So, HCAs and APs have a duty of care and therefore a legal liability with regard to the patient. Mullen (2014) clearly identifies that HCAs and APs are responsible for:
* Always making the care and safety of patients your first concern.
* Ensuring that the task is necessary and in the patient's best interest.
* Ensuring your level of practice is of the standard that is expected of your role and the tasks that you perform.
* Keeping your practice and knowledge up to date.
* Always respecting the public, the patients, the clients, carers, NHS staff and partners in other organisations.
* Demonstrating your commitment to team working by cooperating with your colleagues in the NHS and in the wider community.
* Reporting to the registered professional members of the team any concerns, changes, and developments about the patients/clients.
* If you as an HCA or AP supervise the work of other junior members of the team, you need to be sure that what you ask them to do is within their capability and that you are accessible and supportive.
* If you supervise the work of other junior members of the team, that you report any concerns about their performance to your line manager.
### Reasonable care
Reasonable care is the level of care which an ordinary and reasonable person would use under comparable circumstances. In the law, it is used as a standard to assess liability. If it can be demonstrated that someone had a duty of care and failed to exercise reasonable care, that person can be held negligent and may be liable for damages. On the other hand, if someone exhibited reasonable care and something happened anyway, this person would not be considered negligent.
### Standards of care
The law imposes a duty of care on practitioners, whether healthcare support workers, registered nurses, doctors or Allied Health Professionals (AHPs), in circumstances where it is 'reasonably foreseeable' that they might cause harm to the patients through their actions or their failure to act (Cox 2010). This applies whether a complex task is being performed or whether the HCA or AP is bathing a patient and injure a patient through a careless act. The law imposes a standard of care in relation to each task and this standard applies no matter where patients receive treatment and is irrespective of the carer's qualifications. The legal standard of care is judged by that of the ordinarily competent practitioner performing the particular task or role. Should practitioners fall below this standard of care, they breach their duty of care.
### Consent
In 2009, the Department of Health published the second edition of the _Reference Guide to Consent for Examination or Treatment_ (the guide is currently under review, 2015). The Guide describes the process of seeking consent, the importance of establishing whether the person has capacity to give consent, what constitutes valid consent, the form that consent might take and the duration of that consent. It highlights the need to ensure that the consent is given voluntarily and that sufficient information has been imparted to allow valid consent to be made (DH 2009).
The Guide (DH 2009) further identifies that it is a general legal and ethical principle that valid consent must be obtained before starting any treatment, physical investigation, or providing personal care, for a person. This principle reflects the right of patients to determine what happens to their own bodies, and is a fundamental part of good practice. A healthcare professional (or other healthcare staff) who does not respect this principle may be liable both to legal action by the patient and to action by their professional body. Employing bodies may also be liable for the actions of their staff.
Consent is clearly enshrined within the various codes of conduct so that you are working in partnership with patients at all times and that agreement is clearly documented within patient records. For the nursing family, obtaining consent is an opportunity to deliver care, using good communication and interpersonal skills to discuss the procedure fully with the patient, which may involve reassurance and support especially if the procedure is new to the patient, they are anxious or they have had a previous bad experience. Where possible, choose a quiet environment where you will not be interrupted and give the patient plenty of time to be able to ask questions.
Once you are happy that the patient fully understands the procedure and any possible complications, this should be documented. It is important to remember that the patient may refuse to consent: this is their right which must be respected.
There are a number of legal cases that are identified within the Guide (DH 2009) that are worth reading to gain an understanding of the importance and consequences of gaining consent.
### Capacity
Capacity means the ability to use and understand information to make a decision, and communicate any decision made. Taylor (2013) points out that it is generally presumed in law that adult patients have the capacity to make decisions, unless there is evidence that they do not (Parliament 2005). A decision made by a patient with capacity must be respected, even if it appears unwise or irrational. A patient may want to sign their own discharge; while not logical to us, this patient may have other priorities such as drug or alcohol misuse or they may want to make some arrangements before being admitted from the Accident and Emergency Department. Although hospitals and other healthcare providers have a legal obligation to provide adequate care for their patients (Cassidy v Ministry of Health, 1951), patients do not generally have to accept any offer of treatment.
It can be very frustrating to respect the patients' rights to autonomy, and healthcare practitioners can feel frustrated by what they see as a foolish or reckless decision. They may also feel uncomfortable knowing that a failure to provide care may lead to liability in civil law (negligence) or a criminal charge of gross negligence manslaughter if the patient dies as a result (R v Adomako, 1994). Ethical awareness and an earnest desire to deliver care in the best interest of the patient can cause healthcare workers to worry about the implications of following a patient's wishes, particularly if the patient has refused potentially life-saving treatment. There is always the worry of what might happen to the patient and of potential legal reprisals.
Capacity must be assessed by the health professional who is seeking consent. The issues to be set decided by any assessment are set out in s. 3(1) Mental Capacity Act 2005. These are whether or not the patient is able to:
1. **a.** understand the information relevant to the decision,
2. **b.** retain that information,
3. **c.** weigh that information as part of the process of making the decision, or
4. **d.** communicate his decision (Gallagher et al. 2012).
Where there is cause to question a patient's decision-making capacity, it can be difficult to decide the best course of action if they refuse treatment. In these situations, cases can be referred for a court declaration on the lawfulness of a proposed course of action (Taylor 2013).
### Mental Capacity Act (2005)
The law applies to adults over the age of 16 years in England and Wales and is designed to protect and empower individuals who may lack the mental capacity to make their own decisions about their care and treatment. Examples of people who may lack capacity include those with:
* dementia;
* a severe learning disability;
* a brain injury;
* a mental health condition;
* a stroke;
* unconsciousness caused by an anaesthetic or sudden accident.
If a person has one of the above conditions it does not necessarily mean they lack the capacity to make a specific decision. Someone can lack capacity to make some decisions (for example, to decide on complex financial issues) but still have the capacity to make other decisions (for example, whether they want or need paracetamol for a headache). The person who would normally assess capacity is the person who would implement the decision if the person had capacity and agreed. For example, a surgeon would assess an individual's capacity with regards to surgery.
The HCA and AP need to have an understanding of what mental capacity is and recognise that these are potentially vulnerable people, ensuring they are fully safeguarded and remain at the centre of decision-making. Please check your local policy and if you have any uncertainties discuss this with your manager. The RCN (2013) in their document Making it Work: Shared Decision-making and People with Learning Disabilities discuss shared decision-making, which is a process by which people with learning disabilities, their families, carers and healthcare professionals work in partnership to decide on tests, treatments, management or support packages, based on clinical evidence and the person's informed choices. This process will very often involve the person's family, supporters and those closest to the person with a learning disability; the aim is to reach an agreement on the best course of action while at the same time acting in the person's best interests. The RCN emphasise the work of Coulter and Ellins (2011: 11) that:
> The most important reason for practising shared decision-making is that it is the right thing to do. Communication of unbiased and understandable information on treatment or self-management support options, benefits, harms, and uncertainties is an ethical imperative and failure to provide this should be taken as evidence of poor quality care.
#### Scotland
The Adults with Incapacity (Scotland) Act 2000 permits intervention in the affairs of an adult only if:
> The person responsible for authorising or effecting the intervention is satisfied that the intervention will benefit the adult and that such benefit cannot reasonably be achieved without the intervention. (s.1(2))
>
> The term adult means a person who has attained the age of 16 years (s.1 (6))
Gallagher et al. (2012) point out the important difference between the Scottish Act and the Act governing England and Wales is the purpose of any intervention – it will 'benefit' the person in Scotland and be in their 'best interests' in England and Wales. Both Acts and relevant Codes of Practice set out similar matters to be taken into account in assessing capacity and in deciding benefit/best interest.
Lack of capacity may occur, with particular reference to mental illness or inability to communicate because of physical disability. It may be the case that you are the first person to notice a loss of capacity in a patient and, in these instances, further advice and help should be sought.
# Think about it
Identify patients in your care with possible disabilities that might reduce their capacity. What do you think you can do and what policies should you be aware of?
If the patient is deemed incapable of giving consent then treatment will be strictly undertaken in relation to the Incapacity Act or the Mental Health (Care and Treatment) (Scotland) Act 2003. Part 5 of the Adults with Incapacity Act (relating to medical treatment and research) allows treatment to be given to safeguard or promote the physical and mental health of an adult who is unable to consent.
In England, the Department for Constitutional Affairs published a factsheet in April 2004 that summarises the key principles of the then Mental Incapacity Bill (now renamed the Mental Capacity Bill). The key principles from this are adapted in Box 1.4.
# Box 1.4 Key principles of incapacity (adapted from Department for Constitutional Affairs 2004)
* An assumption of capacity: every adult has the right to make their own decisions and must be assumed to have capacity to do so unless it is proved otherwise.
* Capacity is decision specific: a new assessment must be taken each time that a decision is to be made and no blanket label of incapacity is allowed.
* Participation in decision-making: everyone should be encouraged and enabled to make decisions with help and support given to allow an expression of choice.
* Individuals must retain the right to make what might be seen as eccentric or unwise decisions.
* All decisions must be in the person's best interests, giving consideration to what the person would have wanted.
* Decisions made on behalf of someone else should be those that are least restrictive of their basic rights and freedoms.
www.dca.gov.uk/menincap/mcbfactsheet.htm
## Summary
The need for healthcare assistants and assistant practitioners to gain an understanding of accountability and related issues cannot be over-emphasised. It is vital to have an up-to-date copy of a job description, to ensure they have the education and training required to safely and competently deliver care. While healthcare providers have a responsibility to offer the best care possible, it is important to remember that patients have the right to refuse it.
# Case study 1.1
A patient requires a specimen of blood to be taken. You are asked to perform this task. You have had training and done a couple of supervised practices, but have not yet had your final assessment. You take the blood with no injury to the patient. Would this be acceptable, stating your rationale?
# Case study 1.2
Mrs Phillips, a 58 year old, requires an indwelling urinary catheter inserted, but has refused before.
Discuss how you proceed to try to gain her consent. Are there issues about her capacity that you should consider?
# Self-assessment
**Assessment** | **Aspects** |
---|---|---
Code of Conduct | _Have you read and understood your Code of Conduct?_ | **Achieved ✓**
Accountability | _Have you considered all aspects of this section?_ | **Achieved ✓**
| To whom are you accountable? |
| The different areas of accountability |
| The healthcare assistant role and delegation |
| The assistant practitioner role and delegation |
| Vicarious liability |
Patient | _Have you considered all aspects of this section?_ | **Achieved ✓**
| Duty of care and negligence |
| Reasonable care |
| Standards of Care |
| Consent |
| Capacity |
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19. Nursing and Midwifery Council (NMC) (2015b) Our role [online]. Available at: <http://www.nmc.org.uk/about-us/our-role/> (accessed 15 April 2015).
20. Oxford English Dictionary (2012) _Oxford English Dictionary_. Oxford: Oxford University Press.
21. Parliament (2005) _Mental Capacity Act_. London: Stationery Office. Available at: www.opsi.gov.uk.
22. Royal College of Nursing (RCN) (2004) _Full Health Care Support Worker_. London: RCN. Available at: <https://www.rcn.org.uk/membership/categories/category30> (accessed 3 March 2015).
23. Royal College of Nursing (RCN) (2006) _Intercollegiate Paper: Supervision, Accountability and Delegation of Activities to Support Workers: A Guide for Registered Practitioners and Support Workers_. London: RCN.
24. Royal College of Nursing (RCN) (2011). _Accountability and Delegation: What You Need to Know_. London: RCN. Available at <http://www.rcn.org.uk/__data/assets/pdf_file/0003/381720/003942.pdf> (accessed 30 April 2015).
25. Royal College of Nursing (RCN) (2012) _The Nursing Team: Common Goals, Different Roles_. London: RCN. Available at: <http://www.rcn.org.uk/__data/assets/pdf_file/0010/441919/004213.pdf> (accessed 30 April 2015)
26. Royal College of Nursing (RCN) (2013) _Making it Work: Shared Decision-making and People with Learning Disabilities_. London: RCN.
27. Samanta A and Samanta J (2011) Patient safety in secondary care. In: Tingle J and Bank P (eds) _Patient Safety, Law Policy and Proceedure_. London: Routledge, pp. 128–136.
28. Scottish Government (2010) _Healthcare support workers – mandatory standards and codes_. Edinburgh: Scottish Government. Available at: www.healthworkerstandards.scot.nhs.
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# Chapter 2
Communication in healthcare
# Learning objectives
* Define effective communication in relation to healthcare settings
* Discuss the importance of communication in effective team working in clinical practice
* Identify appropriate communication methods and their application to practice
* List barriers to communication and identify solutions
## Aim of this chapter
The aim of this chapter is to explore communication methods and challenges within the healthcare setting. This will enable the reader to maximise their skills in communicating with patients, families, carers, colleagues and the interprofessional team.
## Why good communication is important
The importance of communication is reflected by professional bodies such as the Nursing Midwifery Council (NMC) who recommend that communication is integrated into the education of healthcare practitioners. Communication and interpersonal skills are highlighted as Standards for Competence and are part of the essential skill clusters for registered nurses (NMC 2013). Furthermore, the Code (NMC 2015) clearly states the importance of communication in Statement 7: that to practise effectively you communicate effectively. Similarly, The Code of Conduct for Healthcare Support Workers and Adult Social Care Workers in England, developed by Skills for Health (2013: 7), states that you should 'Communicate in an open and effective way to promote the health, safety and wellbeing of people who use health and care services and their carers'. Patient-centred healthcare revolves around the implementation of effective communication (Hayes and Collins 2013) and healthcare assistants and assistant practitioners, as part of the nursing family, are at the heart of the communication process. Casey and Wallis (2011: 35) nicely sum up the importance of communication when they write: 'Communication is central to human interaction. Without it, people cannot relate to those around them, make their needs and concerns known or make sense of what is happening to them.' The Department of Health (2010) clearly identifies that staff should communicate effectively with each other to ensure continuity, safety and quality of healthcare for all (DH 2010).
Communication is possibly the most important skill you can develop, but it is a vast and complex topic and so this chapter focuses on helping healthcare assistants and assistant practitioners improve and develop their communication skills in the context of their roles. Look at Figure 2.1. What can you see? What you see will depend on your perspective.
**Figure 2.1** Briefly look at Figure 2.1. What can you see? It might depend on your perspective. Refer to the end footnote on this page.
Source: www.creativethink.com. 1990. Reproduced with permission of Von Oech.
Figure 2.1 is either a bird, or a question mark, or if you turn it upside down it's a seal juggling a ball on its nose.
Self-knowledge and understanding, that is being self-aware, help us to gain insight into our values and beliefs that mould us as individuals. By becoming self-aware (Iggulden and Sharples 2009) we can develop the understanding we need to have empathy with other people and see things from their perspective; an important facet of communication, especially when we can see why communication is important from somebody else's perspective.
## Definition of communication
We tend to take communication for granted; we understand the word, but it is not that easy to define. Oxford Dictionary Language Matters defines communication as 'the imparting or exchanging of information by speaking, writing, or using some other medium', which fails to express its complexity. Schiavo (2013) discusses the difficulty of defining communication, emphasising the importance of behavioural, social, and organisational aspects of communication. Although the focus of this chapter is on work settings, consider the difference with respect to a social, everyday lifestyle communication and a work-related communication. Hayes and Collins (2013) also point out the complexities of communication that relate to how organisational communication feeds directly into the attitudes, relationships and behaviours of staff working within.
Different types of relationships determine the appropriate style of communication, for example how we talk with our family will differ from how we talk with our manager, and so some choices of communication are already made for us by the situation or the context.
# Think about it
This is a useful point to stop and consider why we need to communicate.
Communication is essential:
* to give instructions;
* to ask for information;
* to express needs and feelings;
* to exchange ideas and thoughts;
* to entertain;
* to give and seek reassurances;
* to share experiences.
The NMC (2015) states that patients should be informed about their care and that information should be shared appropriately. In order to achieve this, Standard 5 of the Code (NMC 2015) states that you must:
1. **5.1** respect a person's right to privacy in all aspects of their care
2. **5.2** So communication is two way, with sender(s) and receiver(s), with the purpose of passing on a message with information; therefore it needs to be to the right person/people, at the right time and in language that is comprehensible to all.ake sure that people are informed about how and why information is used and shared by those who will be providing care
3. **5.3** respect that a person's right to privacy and confidentiality continues after they have died
4. **5.4** share necessary information with other healthcare professionals and agencies only when the interests of patient safety and public protection override the need for confidentiality, and
5. **5.5** share with people, their families and their carers, as far as the law allows, the information they want or need to know about their health, care and ongoing treatment sensitively and in a way they can understand. (NMC 2015: 6)
Communication is often the main complaint in healthcare, and in 2012 the then newly appointed health service ombudsman, Julie Mellor, reported 'careless', 'insincere' and 'unclear' communication had fuelled a surge in complaints against the NHS in England. These complaints can affect the quality of a patient's care, and this is why this book suggests that communication is a fundamental skill.
## Communication methods
Let us now review some key aspects of communication in healthcare.
# Think about it
What methods of communication are used in healthcare – make a list of them.
McEwen and Harris (2010) propose that communication is made up of three intricately woven parts: verbal, non-verbal and paralinguistic or paraverbal modes. All three modes are usually used together. Mehrabian's (1981) classic research into body language and non-verbal communication found that:
* only 7% of a message is conveyed by the actual words we speak;
* 38% is by paralinguistic features (e.g. tone and pitch);
* 55% is by other non-verbal factors.
So we can see that attention to non-verbal methods is crucial.
Thus, when communicating, it is important that actions match words because that is what people see; for example, smiling when saying 'Hello, pleased to see you', and not frowning, because the receiver might misunderstand the message. In fact the sender may be frowning because it is a very sunny day and they can't see the other's face clearly, but the receiver will see the frown and may think 'He doesn't really want to talk to me'. The importance of this approach is borne out by the introduction of the ' _hello_ my name is' campaign, which was started by Dr Kate Granger in 2013 following her experience as a patient.
### Non-verbal communication
# Think about it
Non-verbal communication is often classified as body language, so name three ways of communicating using body language:
1. **1.**
2. **2.**
3. **3.**
Dickson et al. (1997) in their classical text highlighted the six main functions of non-verbal communication:
1. **1.** Replacing speech.
2. **2.** Complementing the verbal message: this is considered the main function of non-verbal communication.
3. **3.** Regulating and controlling the flow of communication, for example nodding, and eye contact to indicate continue speaking.
4. **4.** Providing feedback, as above.
5. **5.** Helping define relationships between people, for example a white coat to denote a role such as a doctor.
6. **6.** Conveying emotional states.
Components of non-verbal communication include: touch, proximity, orientation, posture, body movements, facial expressions, eye contact and appearance.
#### Touch
Healthcare professionals are increasingly wary of touching patients, other than when undertaking a task such as dressing a wound. In healthcare, however, touch is therapeutic and one of the most powerful ways that we have of communicating non-verbally (McEwen and Harris 2010). Here culture and gender issues may arise, and so the healthcare assistant should observe the patient for cues as to comfort and acceptance. Kitching (2012) highlights the importance of touch in caring for vulnerable patients. However, if you read and consider the scenario in Box 2.1, Sara could have sat down with Annie and held her hand while they had the same conversation, and certainly then Annie would have felt really listened to and cared for.
# Box 2.1 Scenario
It is 07:15 on a busy Saturday shift in an acute hospital ward, when Mrs Annie Wilson, a 54-year-old patient with acute asthma, rings her bedside buzzer.
Healthcare assistant Sara Smith goes into the single room in response to the buzzer.
_Annie:_
'Thank goodness, you've come.'
_Sara:_
'Hello Annie, what's the problem?'
_Annie:_
'I can't breathe.'
_Sara:_
'Can't breathe? Oh dear, let me check your oxygen.'
_Annie:_
'I'm so frightened, I haven't slept a wink.'
_Sara:_
'Why are you frightened, Annie?'
_Annie:_
'Because of my asthma, I feel I can't breathe, like I'm choking.'
_Sara:_
'Now, Annie, you know you are on treatment for your asthma and you are safe in hospital as we are around all the time.'
_Annie:_
'I still feel like I'm choking, it's terrible...'
_Sara:_
'I'm sure it must be. What can I do to help make you feel better? Would it help if I put on your fan as it's a bit stuffy in here?'
_Annie:_
'I was cold and it made too much noise.'
_Sara:_
'Let's try it, and I'll get you a blanket. How would that be?'
_Annie:_
'OK, if you think that'll help. Don't leave me please.'
_Sara:_
'I am only going to get you a blanket.'
#### Proximity
Proximity is about space, and Dickson et al. (1997) suggest that in Western cultures we have four zones:
1. **1.** Intimate zone of 0–50 cm.
2. **2.** Personal zone of 50 cm–1.2 m.
3. **3.** Social/consultative zone 1.2–3.5 m.
4. **4.** Public zone 3.5 m and above.
They further noted, interestingly, that in healthcare, patients' personal space and even intimate space is regularly invaded by staff, often without seeking the patient's permission, and they say that this can increase the vulnerability and loss of control that a patient feels in healthcare. Thus always consider when approaching the patient, particularly if about to undertake a clinical skill, that they should be allowed to give permission; for example ask, 'Is it alright if I take your blood pressure?' Then the healthcare assistant can proceed and the patient feels in control of the situation.
#### Orientation
Orientation is about where and how the communication takes place. Thus, when talking to a patient in a wheelchair, consider the level and where possible make sure that you communicate at eye level and so sit down too. Often in healthcare we talk over objects, for example the patient is on one side of a desk or bed and the healthcare assistant is on the other; this artificial barrier can affect the quality of communication too, so consider how to minimise this.
#### Posture
Posture includes how one stands or sits, looking relaxed and interested, for example leaning forward to listen. This links to orientation and, again, if a patient is in bed and we approach them to talk, remember that we are towering above them and this can look very dominating or controlling, and so sit down.
#### Body movements
Body movements are a powerful means of conveying non-verbal communication; imagine if Sara (see Box 2.1) had stood with her arms folded during the conversation, what message would Annie have picked up? Probably that Sara does not care or is not interested. However, body language can be misunderstood, as Sara may have had her arms crossed because she was tired and cold after a long night shift.
Be aware also that cultural variances might play a part, for example hand gestures in some cultures might offend; Sobiechowska (2010) states that cultural or ethnic experience and heritage may imbue us with strong beliefs about a number of matters, for example the role of women or the capacity of gender. Similarly, Hindle (2003) uses the example of a gesture that we commonly use in the UK for OK, which is a circle made with our index finger and thumb; with the other fingers pointing up, this means to a Tunisian 'I am going to kill you'. The NMC (2015: 7) states that to communicate effectively one must use 'a range of verbal and non verbal communication methods and consider cultural sensitivities, to better understand and respond to people's personal health needs'.
#### Facial expressions
Think of facial expressions: one example has already been used with frowning, but our faces are often said to tell a story, as we roll our eyes we may not even realise that we are doing so. So, when someone says, 'I see you're unhappy about my idea', it is because of the cue that they have observed; but cues can be misread, so, for communication to be effective, it is about all aspects of communication working together, delivering the same message.
#### Eye contact
Many suggest that the eyes are a powerful means of communicating non-verbal messages, for example the child misbehaving becomes aware of a glare from a parent and swiftly knows that she is in trouble! Eye contact can include or exclude. Toocaram (2010) also points out that some people with severe learning disabilities may be able to point to symbols or pictures to explain how they are feeling (e.g. the Wong Baker visual analogue pain chart that uses faces) and what they want or need. Good eye contact and 'eye pointing' can become meaningful and communicative and can speak volumes.
#### Appearance
Finally, appearance is a means of communicating non-verbally, for example how we dress may reflect our mood or task. In a hospital setting we often ask the patient to get undressed and take away that form of expression (communication). Think of dressing for a night out with friends versus a first date; I bet that your wardrobe choice is very different!
So non-verbal cues can be important for the observant healthcare assistant; for example while taking a venous sample of blood, the healthcare assistant notices that the patient is looking away and is restless – this body language may tell the healthcare assistant that the patient is nervous or frightened and so they can give reassurance and explanations.
### Tone in communication
Now let us briefly think about tone and its importance in effective communication; again vigilance and self-awareness are necessary. How do we sound to others? If we speak loudly because a person is hard of hearing, will they hear the tone as angry? In healthcare a conversation might be carried out over the phone with a patient's family member so consider how much of the message is lost if they can hear only the tone and words.
Email is another form of communication. Kraszewski (2010) highlights the advantages of communication via email as being cheaper, faster, more convenient and less obtrusive than a phone call. Email also allows the recipient time to consider and think about their response while providing a written record of communication, enhancing record keeping. However Kraszewski (2010) does advise caution: the use of humour may cause offense and lead to misunderstanding, plus there is the possibility of sending the email to an incorrect recipient. Although email lacks the subtlety of tone, there are a series of symbols to denote expressions such as a smiley face ☺ or :) which may not be appropriate in a formal email. The NMC (2015: 16) requests to 'use all forms of spoken, written and digital communication (including social media and networking sites) responsibly, respecting the right to privacy at all times'. More guidance on the use of social media and networking sites can be found at: www.nmc-uk.org/guidance.
In terms of healthcare, Crow (2010) reports that professionals often use jargon, abbreviations and acronyms that are meaningless to patients, carers and even their colleagues in other departments. This jargon can help us to be specific in our work, but the choice of words can create confusion to others. Imagine that you have been sent a clinic appointment and are a young teenager, so, on arrival at the reception, you ask for Nurse Led, because printed at the top of your appointment card is Nurse Led Clinic. This is an example of jargon and, if the receptionist finds it funny and laughs while explaining, the tone may cause the young teenager to become embarrassed or even angry, resulting in a total breakdown in communication and creating a humiliated and possibly angry patient.
### Verbal communication
The written word is still classed as verbal communication. There are many advantages to written language as it allows distribution and uniformity of instruction and information, and so can be re-read and thought over or reflected upon and is also a permanent record.
# Think about it
Consider restrictions on the effectiveness of the written word. Write down what these might be.
People's reading skills need to be considered: can they read – have they lost their spectacles or is the font size too small, are they literate (able to read), do they have dyslexia (disorder in reading or writing), is the information too technical, or is English not their first language? All these factors will affect the quality of the written word as a means of communication, which the NMC (2015) emphasises in statement 7.2: 'take reasonable steps to meet people's language and communication needs, providing, wherever possible, assistance to those who need help to communicate their own or other people's needs'.
No matter whether care plans are computer held or paper copies, the writing needs to be legible, clear, concise and understandable. There are a number of tools available to help you to improve the readability of any piece of work including the Gunning FOG Index and the SMOG Readability Formula. Both tools are similar and relate to the use and length of words and simple sentence structure. Writing is explored in more detail in Chapter 4 in relation to record-keeping purposes.
## Strategies to improve communication
This section reviews some of the challenges facing effective communication in healthcare.
# Think about it
What might be barriers to effective communication in healthcare?
Let us consider the three aspects related to communication (each of these aspects is reviewed in the scenario in Box 2.1):
* the sender;
* the receiver(s);
* the situation: includes environmental factors.
# Think about it
What recommendations might you suggest to enhance the conversation in Box 2.1?
Let us pause here and think over the short conversation:
* Is there evidence of active listening?
* Is there evidence of open questions?
* Is there evidence of any leading questions?
* Is this conversation effective?
## Related aspects and terminology
### Active listening
Active listening is a process and the most important aspect is to _accept_ what is heard, so that the conversation is heard from the sender's (e.g. in Box 2.1, the patient Annie's) point of view (McEwen and Harris 2010). The receiver is listening for clues – words or phrases – that say what the sender is feeling and expressing. Listening is therefore crucial for effective communication.
Table 2.1 figures SOLER, a theory that was developed by Gerard Egan who describes techniques for active listening. In the form of non-verbal communication, SOLER theory can be valuable when helping another person and can make that person feel cared for, involved in what is going on, feel respected and understood. SOLER theory can also be learned by anyone who wishes to become a better listener.
**Table 2.1** Checklist for effective communication
**SOLER** | **Achieved ✓**
---|---
Sit **S** quarely in relation to the patient |
Maintain an **O** pen posture |
**L** ean slightly towards the patient |
Maintain reasonable **E** ye contact with the patient |
**R** elax (sit comfortably and supported) |
Source: Egan 1990. Reproduced with permission of Cengage Learning.
In Annie's case she says, 'I'm frightened' and the receiver (Sara) shows that she has heard by acknowledging this; one way is to repeat the word or phrase, so Sara replies, 'Why are you frightened?' Here Sara has used Annie's word and asked her a question to allow her to expand on this initial statement; this is defined as an 'open' question.
### An open question
An open question is phrased in a way that invites the other person to open up and say more, and usually starts with what, why, how, when or where. The framing of questions is crucial; Harris and McEwan (2010) maintain that if people are asked open-ended questions and are rushed, they may respond more freely. Using a non-judgemental approach coupled with active listening is important. Closed questions, which usually require a yes or no answer or confirmation of details, such as 'Tell me your name', are useful for confirming what is known or for being specific. In this situation it is more helpful to allow Annie 'space' to tell you why she is frightened. 'How' is a useful way of starting a question, but take care because this can sometimes lead to one-word answers, for example 'How are you feeling?' 'Tired!' Harris and McEwan (2010) also remind us it is important to know when to refer an issue on to others, especially when dealing with sensitive issues.
### Leading questions
This links to leading questions; the risk with these is getting the answer that was wanted and maybe not what was needed, for example 'You do want to get up now, don't you?' There was an example in Box 2.1 with the fan suggestion and, although it may be helpful, Sara has possibly missed the cue about Annie's fear of choking. So care must be taken to use questions that allow the person to expand and go beyond a simple statement.
In one author's experience, a real conversation led to the identification that the patient thought that if she fell asleep her breathing would become poorer and so her oxygen levels would drop, and she would then fall into a coma and die. Only through open questions did we arrive at this fear and so were able to discuss and allay it.
## Common problems or communication barriers
There are a numerous barriers to effective communication; Toocaram (2010) highlights the challenges faced in caring for disadvantaged and vulnerable groups of people, including those with learning difficulties, physical difficulties, sensory deprivation and cross-cultural issues. Furthermore we have to consider prejudice and stereotyping that may affect communication – and that includes our own. Consider a normal shift: think of how much time you could spend with one patient, compared to how much time you actually have. Are there any resource issues, are you feeling stressed by targets to meet or staff shortages? What kind of mood are you in; perhaps you had an argument before you came into work? And can you really fit all that you need to do into one day? Are there any organisational or professional barriers? Hayes and Collins (2013) recognise the necessity for cultivating the ability to professionally disagree with colleagues without personally offending them, which can impact on the organisation, the team, the individual as well as, perhaps most importantly, the patient. Good communication is an ongoing process particularly in stressful situations where it can be difficult to see the non-verbal messages of the patients with whom we mostly communicate (Kourlouta and Papathanasiou 2014).
When nursing, communication requires:
1. **1.** Being self-aware – what are we doing, why and how.
2. **2.** Developing the knowledge that informs our behaviour and our skills. There are formal courses or you can access resources and undertake some self-directed study. Have a chat with your manager and/or your clinical educator.
3. **3.** Be clear – if you are not certain and muddled, you are not going to communicate anything other than your own lack of ability. If you are clear, you will have more confidence and present yourself in a positive manner.
### Physical barriers
Other barriers to effective communication might relate to a patient's condition, for example Annie may find talking difficult due to her asthma and acute breathlessness. Other factors that may affect the patient's ability to communicate or understand communication range from poorly fitting dentures, poor hearing, to poor sight or maybe not wearing hearing aids or glasses.
Conditions such as cerebral vascular accidents (stroke) may affect a patient's speech (dysphasia) and also a patient may be less able to process a conversation, or the words that they choose may not be appropriate or 'fit' the conversation. A stutter or other form of speech impediment may cause poor communication. A patient who suffers from dementia or acute confusion may be unable to process a message and so responds less appropriately, as could a patient with a brain or head injury or illness, and the patient in an intensive setting on a ventilator will also have a communication challenge. A learning disability may impede or hinder the ability to understand and process a message. You must communicate any concerns you have if you believe a patient is vulnerable or at risk and needs extra support and this is clearly identified in Statement 17 of the Code (NMC 2015).
We also need to consider environmental barriers. These will depend on the environment; however, broadly we might consider noise as a barrier, for example machines bleeping, other people talking, trolleys clattering.
Allied to this might be the lack of privacy, especially in a hospital setting. Lighting and room space are other factors and, in the community setting, environmental factors may include other family members or pets!
If it is too cold or hot people can become distracted, blocking effective communication. Talking to someone while you stand in front of a window can create a shadow over your face and poor-sighted or hearing-impaired or deaf people will lose the ability to see your face and your mouth, and so limit their ability to 'see' the conversation.
Case study 2.1 will help in consideration of some environmental aspects.
# Case study 2.1
Mr Wang, a Chinese man in his 60s, is being admitted to his bed in the ward. Part of the admission requires asking about his bowel habits; he appears not to understand the question and answers with a 'yes'.
What action might the healthcare assistant admitting him need to consider?
Possible factors might be that the patient is embarrassed in a public place, is hard of hearing or does not understand English. Never assume anything.
The options available to the healthcare assistant would again depend on the setting, but there might be a private room where he could be admitted. If hearing were identified as a problem, writing the question down could possibly help. If English were not his first language, a professional (trained) translator could help. It is recommended not to use family members or friends even when their English is good, because this may breach confidentiality and also cause embarrassment between the family or friends and the patient. Harris and McEwen (2010) note that translators maybe required when communicating with people for whom English is not their first language. In this case, it is important to clarify the role of the interpreter or translator and to address the patient, not the translator.
Some situations might be aided with the use of pre-prepared cards with symbols and words; however, these would have limited application. A drawing instead of words may also assist, but take care not to patronise or use inappropriate pictures.
So, environmental barriers need careful attention, including:
* layout;
* lighting;
* ventilation;
* distractions in the area.
All these are known to affect communication, for example if the lighting is poor a patient with a sight problem might not be able to see and so communication may break down.
## Skills for the Health Care Certificate
In the wake of the Francis Inquiry into the Mid Staffordshire NHS Foundation Trust, Camilla Cavendish was appointed to undertake an independent review of healthcare assistants and support workers across health and social care. Consequently a partnership was formed led by Health Education England, working closely with Skills for Care and Skills for Health. The partnership developed the standards and framework for the delivery of the Care Certificate, with guidance from the Department of Health and its Cavendish Governance Assurance Board. Standard 6 of the Care Certificate (Skills for Health 2015) is about Communication, which incorporates themes discussed within this chapter. Further information about the Care Certificate can be found at www.skillsforhealth/qualifications@skillsforhealth.org.uk.
## Summary
All of the points below are embedded within the Code of Professional standards of practice and behaviour for nurses and midwives (NMC 2015: 1) which 'set the standards that patients and members of the public tell us they expect from healthcare professionals'. A healthcare professional:
* is respectful of the person being talked to;
* is clear;
* does not use jargon, technical words or abbreviations;
* is empathic and sensitive to the receiver's (patient) needs;
* takes account of the receiver's abilities/disabilities.
# Self-assessment
Table 2.1 is a simple checklist that would aid any communication and ensure it is effective.
## References
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2. Crow J (2010) Communication: the essence of care. In: Kraszewski S and McEwen A (eds) _Communication Skills for Adult Nurses_. London: McGraw Open University Press, pp. 37–54.
3. Department of Health (2010) Essence of Care 2010: Benchmarks for Communication <https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/216695/dh_119973.pdf> (last accessed 15 March 2015).
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12. McEwen A and Harris G (2010) Communication: fundamental skills. In: Kraszewski S and McEwen A (eds) _Communication Skills for Adult Nurses_. London: McGraw Open University Press, pp. 1–22.
13. Mehrabian A (1981). _Silent Messages: Implicit Communication of Emotions and Attitudes_ , 2nd edn. Wadsworth, Belmont, California. Available at: <http://www.kaaj.com/psych/smorder.html> (accessed 6 February 2015).
14. Nursing Midwifery Council (2013) Standards for Competence for Registered Nurses. Available at: <http://www.nmc.org.uk/globalassets/siteDocuments/Standards/Standards-for-competence.pdf> (accessed 10 February 2015).
15. Nursing & Midwifery Council (NMC) (2015) The Code. _Professional Standards of Practice and Behaviour for Nurses and Midwives_. London: NMC.
16. Oxford Dictionary Language Matters (online) Available at: <http://www.oxforddictionaries.com/definition/english/communication> (accessed 30 March 2015).
17. Schiavo R (2013) _Health Communication: From Theory to Practice_ , 2nd edn. London: John Wiley & Sons.
18. Skills for Care & Skills for Health (2013) Code of Conduct for Healthcare Support Workers and Adult Social Care Workers in England www.skillsforcare.org.uk & www.skillsforhealth.org.uk (accessed March 2015).
19. Skills for Health (2015) The Care Certificate Framework (Assessor) Health Education England, Skills for Care and Skills for Health.
20. Sobiechowska P (2010) Communication in learning and teaching. In: Kraszewski S and McEwen A (eds) _Communication Skills for Adult Nurses_. London: McGraw Open University Press, pp. 123–142.
21. Toocaram J (2010) Communication in learning and teaching. In: Kraszewski S and McEwen A (eds) _Communication Skills for Adult Nurses_. London: McGraw Open University Press, pp. 90–106.
22. Von Oech R (1990) _A Whack on the Side of the Head_. London: HarperCollins Publishers.
## Addendum
### Gunning FOG Index (Gunning 1952)
Gunning FOG Index: from <http://en.wikipedia.org/wiki/Gunning-Fog_Index>, accessed 27/02/08 and permission obtained from wikipedia. Also available at: www.tasc.ac.uk/sdev1/drobis/profcom/fog.htm (accessed 11 January 2006).
Step 1 | Count out a 100-word passage. Make sure that the passage ends with a full stop, even if you go slightly above or below exactly 100 words
---|---
Step 2 | Find the average sentence length by dividing 100 by the number of sentences in the selected passage, e.g. 8 sentences = 100 ÷ 8 = 12.5
Step 3 | Count the number of words with three or more syllables (e.g. syllables). This number gives you the percentage of 'hard words' in the passage, e.g. 9
Don't count | Proper nouns, e.g. Irene, Paris
| Combinations of easy words such as typewriter or newsletter
| Verb forms with ends: es, ing or ed, e.g. transmitted
| Jargon familiar to your reader
Step 4 | Add the average sentence length (Step 2) to the number of 'hard words' (step 3), e.g. 12.5 + 9 = 21.5
Step 5 | Multiply the total in Step 4 by 0.4 to get the reading level for the passage, e.g. 21.5 × 0.4 = 8.6
Note | Easy reading range is 6–10. The average person reads at level 9. Step 5 score was based on a sample from this chapter
Remember, when writing, that the aim is to be understood, so keep to the KIS principle = keep it simple. Aim for a reasonable FOG score, because the last thing we need is the lack of clarity and confusion that we often get with fog!
# Chapter 3
Psychological well-being
# Learning objectives
* Describe the importance of psychological assessment and care in health and well-being
* Discuss the importance of psychological care when undertaking clinical skills
* Identify the psychological factors that may affect the patient's well-being
* Review strategies to optimise psychological well-being when providing healthcare
## Aim of this chapter
The aim of this chapter is to explore the importance of the psychological health and well-being of the people in our care. This will allow the healthcare assistant to consider the patient in a holistic and compassionate manner when supporting people and undertaking clinical skills in the workplace.
## What is meant by psychological care?
Consideration of the patient's psychological health and well-being is essential in delivering holistic, person-centered care. Maslow discussed the concept of human motivation in 1943 and this has often been used as the foundation for discussion of holism in nursing. Maslow's Hierarchy of Needs clearly identifies how all the elements of the person's life need to be fulfilled to achieve what he defines as 'self actualisation' or to feel as a whole person. Maslow's (1943) theory provided the basis for the Activities of Living Model (Roper et al. 1985) which is often used in Adult and Child settings to assess patients' needs. The underpinning concept of this model was to provide care that was holistic in nature, focusing on the biopsychosocial elements of the individual's needs across the lifespan. Frequently the biological aspects of nursing are focused on, for example, the performance of a task such as undertaking venepuncture. However it is essential that the psychological elements of care are not forgotten when providing high-quality, compassionate nursing care as this allows nurses to add the human dimension to care in understanding their patients' behaviour in response to health and illness.
Walker et al. (2012) describe psychology as the study of human behaviour, thought processes and emotions. However, when psychological care is discussed it can have many dimensions all rooted within the individual's 'behaviour'. Psychological care can range from caring for people with mental health disorders (psychiatry and psychology) to health psychology, which looks at behaviour responses in health and illness (Taylor 2009; French et al. 2010) and holism. Therefore this chapter will review how a fundamental psychological assessment can be undertaken and how this can aid the healthcare assistant to ensure that the patient receives a holistic package of care, enhancing the patient experience.
# Think about it
If you were being admitted to hospital, what aspects of care and treatment might make you anxious?
Individuals are unique, so assessment is critical to identify their concerns or fears. When patients are admitted to hospital or attend a GP surgery, they may be experiencing stress, which could result from their illness, fear of the unknown, fear about painful treatments or concerns over the impact that a potential illness may have on their life, family, work and social community. The skill for the healthcare assistant is to identify and support a patient through this stressful period, and to do that they must first ensure that they have a clear understanding of patient's holistic needs and their concerns.
## Psychological assessment in the healthcare setting
Consider, as Mitchell (2007) describes, patients entering a strange and often sterile environment such as a hospital, where they will probably be partially undressed, for example for 12-lead ECG, and unsure about what is happening or about to happen. They will be waiting for instructions and procedures (often unpleasant) from a variety of healthcare staff (many strangers to them), all the while trying to retain information and ask questions. It is known that anxiety can prevent people from retaining information and for this reason it is important to check the patient's understanding of any nursing procedure before it is undertaken.
Mitchell (2007) identifies that the belief in one's own ability to cope with a stressful situation or challenging demand is often based on past experiences. Therefore, when assessing the patient pre-procedure, the healthcare assistant should identify this and the ways in which the patient may cope or maintain control over their own health, particularly if they have a long-term condition; for example through the use of music or reading for relaxation before investigations or surgery, or patients could continue to manage their own blood sugar tests. _Please check that this is acceptable policy locally_.
Mitchell (2007) also suggests considering environmental factors, noting that the friendliness of staff is crucial, especially in busy, sterile clinical areas because they often feel impersonal and unfriendly. These thoughts have been fundamental to care since the publication of the Francis Report (Francis 2013) and have been central to the adoption of the 6 Cs in nursing (DH 2012) as well as in NHS core values (DH 2013) and quality strategies such as the 15 Steps Challenge (Williams 2013), which was born from a mother stating that she could tell what kind of care her daughter would receive within 15 steps of walking onto a ward. The principles contained within the 6 Cs, the NHS core values and the 15 Steps Challenge can all help to ensure that care and compassion is at the heart of care delivery in any health and social care settling and reduce feelings of anxiety that many patients will have.
Noise can often increase stress and distract patients (and staff), and although distraction can be a strategy to help patients cope, here it may be a problem, for example when the healthcare assistant explains the preparation for a 12-lead ECG and the patient misses important information because of distraction or background noise making it difficult for them to hear or concentrate.
Preparation of children and their families is essential in healthcare. The psychological care of the child is paramount and reduces stress and anxiety before procedures and helps to prevent further distress when clinical skills are undertaken. Part of the preparation may be undertaken by a play specialist. The role of the play specialist is to work with children and families to prepare them for procedures and help develop mechanisms to cope with anxiety, as structured play is known to improve recovery times (Howard 2013; Stonehouse 2014). However, the point of preparation is equally important, and those working in children's settings should be aware of the developmental stage of the child. For some children, preparation too far in advance can cause greater anxiety and this should be discussed with the child's parents or guardians (Trigg and Mohammed, 2010)
Parents' knowledge of how their children react to stressful situations will help the healthcare assistant determine the appropriate timing of the preparation, as well as which coping strategies would be most useful. Crowley (2014) suggests that having a knowledge of child development is important in preparing children for tests and clinical interventions. This can be used during the preparatory period and communication with the child and parents adjusted accordingly. Before any procedure such aspects must be considered because they will help the healthcare assistant identify and plan or offer strategies to help the patient cope.
## The importance of psychological care in the healthcare setting
### Psychological factors
Some factors have already been mentioned, for example fear and stress; however, there is a range of factors that the healthcare assistant should consider.
#### Stress
The symptoms of stress are based on the body's autonomic nervous system response (fight or flight) of arousal. Table 3.1 shows the body's autonomic responses.
**Table 3.1** Body's autonomic responses
**Body organ/system** | **Effect**
---|---
Heart and cardiac system | Heart rate and blood pressure increases
Lungs | Respiratory rate and depth of breathing increases
Liver | Glucose is released for muscular activity
Brain | Blood re-routed here to aid decision making
Eyes | Pupils dilate to aid visualisation of threat
Stomach and digestive system | Blood diverted to the major organs
Skin | Blood diverted – leads to pallor and sweating
Adapted from Walker et al. (2012) and Clancy and McVicar (2009).
Clancy and McVicar (2009) state that a person's response to stress is individual to them and therefore subjective. However, what is clear is that the individual responds in a cognitive, behavioural and physiological way to their stressor (Walker 2012). In the healthcare environment, stress can affect many patients. The role of the healthcare worker is important in helping patients develop coping strategies. It has long been recognised that the more information a patient is given, the more anxiety levels are reduced. This is particularly relevant in pre-operative patients where direct care is often provided by healthcare assistants. Spending extra time listening to patients and recognising their fears can reduce stress and anxiety levels (Renouf et al. 2014: Mendes da Mata 2014). Stress is also known to have direct effects on the immune system, which may delay recovery for some patients, and the importance of health promotion around lifestyle can have a positive impact on recuperation (Walker 2012). Walker et al. (2012) identified a range of symptoms from the stress response, which is discussed in Table 3.2.
**Table 3.2** Stress response symptoms
**Aspects** | **Symptoms**
---|---
Physiological | Altered sleep pattern, e.g. insomnia, waking early or not getting to sleep
| Indigestion, nausea, diarrhoea, constipation
| Headaches, muscle tension
| Panic attacks
| Increased heart rate
| Weight loss or gain
Cognitive | Feeling a failure, low self-esteem or confidence
| Worrying a lot, perhaps about things that didn't normally matter
| Not wanting to be bothered, apathetic about issues
| Difficulty in making decisions, forgetfulness
Emotional | Feeling upset, crying more than normal
| Feeling irritable or short tempered
| Unreasonable behaviour or negative attitude
| Fears that are not rational
| Tiredness
| Loss of being able to see life in a fun way or loss of sense of humour
Behavioural | Irregular eating habits, e.g. comfort eating, not eating at all or overindulging
| Taking time off for minor illnesses (which would not normally result in absence)
| Using stimulants, e.g. drugs, alcohol, tobacco
| Withdrawing from usual activities, e.g. not seeing friends or going out as much
| Being accident prone
Adapted from Walker et al. (2012) and Clancy and McVicar (2009).
Often patients can be unaware of the effects of stress until careful questioning, commonly at admission but also before some procedures, when the healthcare assistant checks that the patient understands the procedure.
# Think about it
Look through the clinical skills in the other chapters and list the ways that stress and anxiety might affect the tests or results, the patient's response to the test itself or your ability to undertake the test with an anxious patient
#### Pain
Walker et al. (2012) describe pain as not only a physical experience but an emotional one too. From childhood, pain is associated with injury and acts as a warning that something has gone awry with the body (Brooker and Waugh 2013). With children, pain can be very difficult to assess as they may not have the verbal ability to communicate, yet pain can be associated with stress, fear and anxiety (Trigg and Mohammed 2010).
Walker et al. (2012) suggest that pain-related fear is often more disabling than the pain itself. Both adults and children may experience anticipatory pain before a procedure and become stressed and anxious. This can have an effect on the procedure, for example inserting a cannula in a patient who is tense is likely to be more painful and can lead to avoidance behaviour (Solowiej 2010) unless this is recognised and managed.
Chronic pain is associated with a range of psychological problems, for example depression and social isolation (Brooker and Waugh 2013). Chronic pain can have effects on both adults and children. The child with chronic pain can become isolated from their peer groups and pain can potentially delay their development, while pain in an adult can have a wide-ranging impact on their holistic well-being and affect many aspects of their lives (Brooker and Waugh 2013; Trigg and Mohammed 2010). It is not within the scope of this book to explore this area in depth, but some aspects are worth reviewing relating to the patient's response to healthcare.
#### Phobias
Walker et al. (2012) describe phobias as irrational fears that lead to avoidance. Brooker and Waugh (2013) state that both adults and children can develop a phobia towards needles which is influenced by prior experiences. For this reason, when undertaking any clinical skill it is essential to assess each patient and provide as much information as the patient requires to prevent the development of healthcare-associated phobias. It should also be noted that the healthcare assistant should ensure that each patient is given enough time to discuss any fears they may have around a procedure.
#### Panic or anxiety
This is described as a consequence of uncertainty and unpredictability. It is often the result of a new situation, for example emergency admission to hospital, where the person lacks the appropriate information, or the ability to make sense of what's happening, for example a patient with dementia (Walker et al. 2012).
#### Confusion
Confusion can occur for several reasons within the healthcare setting and having an understanding of the reason for confusion will assist the healthcare assistant in helping patients to make a recovery or undertake a clinical skills. Patients may be confused because of their clinical condition, for example because of diabetes, epilepsy, dehydration, medication or dementia. For those who have any form of dementia, taking them from familiar surroundings can make confusion worse and good communication skills are essential when caring for any patient who is confused. It should also be noted that it may be necessary to change the method of communication to meet the patient's needs (Nazarko 2014).
#### Culture
Culture can be interpreted in different ways and can be linked to religion. However, countries also have their own cultures with associated beliefs and norms of behaviour and this can influence how a patient may react to healthcare (Brooker and Waugh 2013). Therefore healthcare assistants need to be respectful of their patient's cultural values, especially where privacy and dignity is concerned, without making assumptions (Trigg and Mohammed 2010; Brooker and Waugh 2013). Brooker and Waugh (2013) point out that the acceptance of healthcare can be based on cultural beliefs, for example around blood transfusions, certain medications that are animal derivatives or the preference of traditional therapeutic interventions such as herbalism or acupuncture.
However, in terms of pain and pain expression, there is evidence to suggest that culture plays a role in the patient's experience of pain. Yet Brooker and Waugh (2013) point out that when an individual is away from their original culture their response to pain changes. Although the relevance of culture in the experience of pain is useful for the healthcare assistant to acknowledge, it should also be pointed out that this can lead to stereotyping of specific cultures and therefore care should be taken to prevent this from occurring (Trigg and Mohammed 2010).
#### Grieving process
In 1969, Elisabeth Kubler-Ross identified five stages of grief that could encompass different types of behaviour: denial and isolation, anger, bargaining, depression, and acceptance (Kubler-Ross 1989). Table 3.3 outlines this process.
**Table 3.3** Stages of grief and possible outcomes
**Stage** | **Possible outcome examples**
---|---
Denial and isolation | 'I can't possibly have bowel cancer, I feel well'
Anger | 'It's all your fault, you should have sent me for tests sooner'
Bargaining | 'If I could turn the clock back I would eat better food and stop smoking and this cancer would never have happened'
Depression | 'I can't cope with this, what if I need surgery, how will my family manage without me if I die?'
Acceptance | 'Now that the operation is scheduled I feel less uncertain as I know this cancer will be gone soon and I can focus on getting better again'
Throughout the stages the person who experiences loss will attempt to find meaning, enabling adaptation to the new status quo (Neimeyer et al. 2011).The final stage is often described as acceptance, as the person comes to terms with loss, but timeframes vary considerably and may not necessarily follow any logical progression. A patient may react to bad news, such as being told that they have a heart condition after tests such as a 12-lead ECG and blood tests, in different ways, so it may be helpful to be aware of these stages. This can help the healthcare assistant to respond in a supportive and caring manner, and to suggest or offer coping strategies.
#### Conflict
This may occur as part of grieving or anxiety about the loss of family member or because of a diagnosis. Showing compassion and empathy to patients can help avoid conflict and where this does occur the use of good communication skills can help deescalate the situation.
## Strategies to optimise psychological well-being
Many patients, particularly those with long-term conditions, can be affected psychologically by their health. It is important for healthcare assistants to ensure effective communication with their patients at all times and this can act as a signpost to help patients cope with their condition. Some patients may benefit from adopting mindfulness techniques to help them cope with their illnesses, and these techniques can then be utilised by the patients when in stressful situations such as in a healthcare environment (Coffey et al. 2010).
### Communication
Effective and compassionate communication is an essential skill for all healthcare assistants. Part of this is active listening skills that will enable the patient to be clearly understood by those caring for them and can help build a therapeutic relationship (Boyd and Dare 2014). Healthcare assistants need to be able to communicate with patients in a language they understand without technical jargon as this will help reduce anxiety. Working in a multicultural and inclusive society will inevitably bring healthcare assistants into contact with patients who either do not speak English or communicate via sign language. As all patients have a right to information about their condition, and a lack of information can cause anxiety, in instances such as this the local policy should be followed regarding the use of interpreters (Boyd and Dare 2014).
### Information
When providing children with information it is essential that this is done in a truthful way. If a clinical skill you are undertaking is likely to hurt then telling the child this will help to form a trusting relationship (Trigg and Mohammed 2010). Information provides a greater understanding of the procedure for children and their families and helps eliminate fear (Dawson et al. 2012). As Trigg and Mohammed (2010) point out, age friendly and accurate information is particularly important with children as their active imaginations and lack of knowledge can actually cause a greater level of fear. It should also be noted that stress can prevent retention of information in both children and adults and therefore it can be useful to repeat information to ensure it is understood and retained (Mohammed and Trigg 2010).
In addition, the person's cognitive ability will also determine how information is provided, and for those patients with learning disabilities information may need to be given in manageable chunks with the support of the key worker (Brooker and Waugh 2013). Pre-information can be helpful, to prepare the patient in advance of the procedure, for example for catheterisation. Information can allow a patient more control, choice and understanding of what is happening, which is why many of the chapters identify patient education aspects, for example peripheral cannulation. A review of Chapter 2 may also be of value.
Thus, the intent of effective communication and appropriate information is to have a patient who is aware and reassured about what is happening or going to happen.
### Assessment
Careful assessment includes both communication and information; this is not just to inform, educate and gain consent, but also to ensure that all factors have been assessed, both physically and psychologically.
Trigg and Mohammed (2010) and Dawson (2012) suggest that assessing the readiness of both the parents and child to undergo any clinical skill can help the healthcare assistant to prepare them more effectively. Methods that can be used to assess readiness and prepare families could include photographs, play with actual equipment, videos of clinical areas and pre-admission clubs where available.
These methods may help identify the child's, as well as the parents', understanding and acceptance of the procedure, and allow healthcare staff to assess what strategies might be most suited to the child, for example if a child shows fear of a catheter, discuss the use of local anaesthetic gel and clinical holding (see Chapter 11).
In adults Dougherty and Lister (2011) noted the use of open questions (discussed in Chapter 2) to assess psychological care needs such, as:
* How have you been feeling since your treatment?
* What concerns you most about your health?
* What do you find helps you to relax the most?
### Patient involvement
It is now embedded in healthcare that all patients have a fundamental human right to make their own decisions and participate within their own healthcare (McKinnon 2013). The exceptions to this would be those who are not deemed to have mental capacity or are of a young age (McKinnon 2014). This is particularly important in terms of gaining consent when undertaking clinical skills. Here the patient can make choices that are appropriate to their own needs, such as when a test will be undertaken or even whether to have it at all. This is very closely linked to the provision of information and all patients have the right to be fully informed in their care as well as a participant in their choices (McPeake et al. 2014).
# Think about it
You are preparing a 13-year-old boy for a peak flow test. How could you check out his understanding of the procedure?
### Timing/pacing
As mentioned earlier, ensuring that the patient has the right information and communication at the right time are important. Mitchell (2007) highlights this and points out that the healthcare assistant must ensure that the patient is not too sleepy, for example under post-procedure sedation or following an epileptic seizure, as they may not be able to fully absorb the information that is given.
This is particularly important when dealing with children, as different age ranges will be able to process information at varied rates. The healthcare assistant needs to be aware of their level of development and adjust the timing and pacing accordingly (Crowley 2014).
## Pharmacological (drug-related) options
_Medicines that may be used might be limited to registered nurses or doctors only; please check your local policies_.
Hands et al. (2010) state that children undergoing venepuncture, can suffer from both physical and psychological stress and suggest that local anaesthetics, such as creams/gels, should be used in venepuncture and cannulation in children – which must be prescribed and administered by an authorised healthcare professional. Zempsky (2008) also discusses non-invasive needle-free local anaesthesia called iontophoresis, which uses a mild electric current to numb the area before cannulation or venepuncture. Please check your local policy about this equipment and its use.
Sedation is another pharmacological option. However it does have the side effects of patients becoming too drowsy to respond, and in research from intensive care settings it has been found that sedation can have negative long-term effects on a person's psychological health (Croxall et al. 2014).
One final option may be the use of general anaesthesia; however, this is unlikely to be used for any of the clinical skills listed and discussed within this book.
_It should be noted that pharmacological options are unlikely to be within the scope of a healthcare assistant_.
## Non-pharmacological options
There are several options for patients to utilise before, during and after any treatment or tests. Trigg and Mohammed (2010) suggest the use of distraction, guided imagery and visualisation, and relaxation techniques. Brooker and Waugh (2013) suggest that similar strategies can be employed by adults, which may include relaxation, distraction, hypnosis, imagery and massage where appropriate for the patient's condition. Table 3.4 lists the options.
**Table 3.4** Non-pharmacological options
**Option** | **Action**
---|---
Massage | Can be helpful for all ages, but only if patient wishes and is not contraindicated by their condition; can reduce pain and anxiety, and increases relaxation
Guided imagery | Most effective with adults and children 8 years and over. The patient imagines a positive place or setting, e.g. playing on a beach, sitting by a gently flowing river
Relaxation | Works well with adults and older children because they can be taught to breathe slowly and relax different muscle groups; younger children can be asked to slowly blow out imaginary birthday candles; relaxation can work well with soothing music that is chosen by the patient. However, recordings that provide the sound of birds chirping, waves rolling or soft heartbeat can be very soothing to small infants
Distraction | Can be provided through reading, music, conversation or through play – specifically with children
Visualisation | Positive thoughts can dispel false or unfounded fears, and similar to guided imagery, patient thinks of a personal positive situation
Hypnosis | Helps to reduce pain perception and aids relaxation. Should only be attempted by a trained hypnotherapist
Adapted from Brooker and Waugh (2013) and Trigg and Mohammed (2010).
## Therapeutic sense of self
Mitchell (2007) describes this as the beneficial effects that the presence of a healthcare worker, such as an assistant, can have on a patient, especially in the acute care setting. This is due to the support and reassurance that a healthcare assistant can provide, offering supportive, positive communications and providing some coping strategies; for example, a patient with a fear of needles before sampling (venepuncture) is supported by the healthcare assistant using a breathing technique and topical local anaesthetic gel. Having a partner or friend present while waiting can help ease anxiety and, in some cases, such as children or a patient with a learning disability, being present (if willing and it is suitable) during a procedure may also help. With children, a parent can hold the child while the procedure is carried out, for example insertion of a peripheral cannula or blood being sampled from a finger for blood sugar testing. The presence of a friend, parent or family member can often reassure, and make the person, especially a child, feel safe. Walker et al. (2012) noted the importance of social support, which offers a sense of belonging gained from family and friends.
This aspect should not be overlooked, and it is often the presence of a healthcare assistant, or any other healthcare staff, that is of great benefit to the patient's psychological well-being. It is also good practice with many invasive procedures; acting as a chaperone and being able to answer questions, or just _being there_ , can be a huge relief to an anxious patient.
### Instrumental support
Walker et al. (2012) suggest that this is about offering practical and tangible support. This could include signposting them to self-help groups where patients can receive support to take control of their own health. The healthcare assistant should also be wary about offering advice as it is essential that patients make their own decisions around healthcare or patients can become passive in managing their own conditions.
## Common problems
As noted earlier by Mitchell (2007), when the patient's physical needs are met, but their emotional and psychological ones are not, holistic care is not being provided. The patient may not respond to treatment or communications in the manner expected (Walker et al. 2012). The patient's feeling of loss or anxiety may lead to unexpected behaviours, which could cause disruption in a healthcare setting, for example coping with anger can be threatening to the healthcare assistant and others because this behaviour, if not handled effectively, may escalate into verbal or physical aggression where knowledge of conflict resolution would be advantageous. Likewise, the patient who withdraws due to confusion or fear will also pose a challenge to all healthcare staff, and effectively care, compassion and communication are essential.
Staff may lack confidence in assessing psychological needs, but by use of open questions, as suggested by Dougherty and Lister (2011), the healthcare assistant can invite patients to discuss any fears or concerns that they have. From this initial dialogue, the patient, together with the healthcare assistant, can identify what strategies are available and suitable. An associated aspect is recording this information, because many staff may not recognise documentation as an essential part of practice (Skills for Care & Skills for Health 2013). This is an area where the healthcare assistant must ensure good practice and record any communications promptly and clearly. These should be factual reports and not contain subjective statements.
## Summary
This chapter has a narrow focus of just clinical skills; we acknowledge this and suggest that the reader explores wider aspects of psychological care. It is not within the scope of this book to explore mental health issues, but further reading around this area may be beneficial to your practise as a healthcare assistant and ultimately patient care.
If you do not know the patient, some mental health symptoms may be 'masked' or hidden by the process of admission and undergoing procedures, particularly invasive ones such as peripheral cannulation (inserting a cannula). If you have any concerns about your patient's psychological well-being, always seek advice from a registered practitioner.
# Case study 3.1
Mr Helmut Jung has been admitted as an emergency with chest pain, while on holiday from Germany. He is 66 years old and seems to speak reasonable English. His wife is back at the hotel, calling his family in Hamburg and gathering his medicines and nightclothes. He is in pain and very anxious.
You have been asked to prepare him for a standard 12-lead ECG procedure. What aspects would you need to consider to help prepare him psychologically?
_You do not need to understand the actual procedure of recording a standard 12-lead ECG for this task_. This asks you to consider the situation and the psychological preparation required.
# Self-assessment
**Assessment** | **Aspects** | **Achieved ✓**
---|---|---
Psychological care | _Have you considered all aspects of this section?_ |
| Patient assessment |
| Psychological factors |
| Coping strategies |
| Problems and reporting concerns |
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# Chapter 4
Documentation and record keeping
# Learning objectives
* Identify why accurate and prompt records are essential
* Outline the standards for good record keeping
* Discuss the types of documentation in relation to clinical skills
* Describe legal requirements in relation to record keeping
## Aim of this chapter
The aim of this chapter is to explore the standards required for patient documentation and record keeping, focusing on records and documentation relating to clinical skills, such as recording observations on the T, P, R (temperature, pulse and respiration) chart. The importance of recording and maintaining accurate and prompt records along with legal aspects are also discussed.
## The importance and purpose of documentation in relation to clinical skills
Beach and Oates (2104) describe health records as documented evidence about the care and treatment patients receive, including care plans. They are not only written communications between colleagues about patients and evidence of care, but are also clinical tools, enabling continuity of care and the setting of goals and plans to deliver care. From a governance and commissioning perspective, health records also provide evidence that care is meeting quality and safety standards set and monitored by regulators in addition to the contractual requirements set by commissioners (Unite the Union 2014).
As a member of the wider healthcare team, the healthcare assistant (HCA) and assistant practitioner (AP) or student nurse is personally accountable for good record keeping so that they can document their care. The HCA or AP should only be delegated a task if they fully understand what is being asked of them, they have had relevant training, are competent and the task is within their scope of practice. The Code (NMC 2015) emphasises the responsibility of registered nurses when delegating tasks. Furthermore, in relation to record keeping and documentation, the Code (NMC 2015: 9) states that to keep clear and accurate records you must:
1. **10.1** complete all records at the time or as soon as possible after an event, recording if the notes are written some time after the event
2. **10.2** identify any risks or problems that have arisen and the steps taken to deal with them, so that colleagues who use the records have all the information they need
3. **10.3** complete all records accurately and without any falsification, taking immediate and appropriate action if you become aware that someone has not kept to these requirements
4. **10.4** attribute any entries you make in any paper or electronic records to yourself, making sure they are clearly written, dated and timed, and do not include unnecessary abbreviations, jargon or speculation
5. **10.5** take all steps to make sure that all records are kept securely, and
6. **10.6** collect, treat and store all data and research findings appropriately.
In relation to clinical skills, records are maintained in order that a patient's condition can be observed and monitored, for example the record of a patient with diabetes would contain information about blood sugar levels in the urine or blood. These ongoing records, at defined times such as before meals, will allow the patient to receive the correct treatment. In a person with diabetes, this might be to adjust the dose of insulin that the patient receives. Hutson and Millar (2009) and NMC (2015) emphasise that record keeping should not be viewed as something that is done if time allows and that they should be written as soon as possible after the procedure. Recording vital signs such as temperature, pulse and blood pressure can determine future actions. The HCA or AP must understand why these particular signs have to be checked and recorded. A blood pressure record may be 'routine' as part of a general observation of the patient's condition; which is different from a patient returning from major surgery, where a change in blood pressure may indicate an internal bleed.
As noted above, records ensure that members of the healthcare team are aware of what is happening to that patient, of any treatment(s) that they are receiving, and the effects – both positive and negative – for example, whether analgesia (pain medication) has reduced pain or not. The NMC (2015: 9) states you must keep clear and accurate records relevant to your practice and you must attribute any entries you make in paper or electronic records to yourself, making sure they are clearly written, dated and timed, and do not include unnecessary abbreviations, jargon or speculation. Hutson and Millar (2009) point out that individual Trusts and organisations may have their own local policy about which abbreviations can be used. Care should be taken, however, as any mistakes in their meaning may have serious repercussions. Beach and Oates (2014) suggest writing should be clear and succinct, in short sentences using simple words and sticking to the facts.
Effective records allow staff to monitor patients over 24-hour periods for every day that they receive healthcare (NMC 2015). If a patient was suffering from chest pain and part of the care was to have the patient's vital signs observed (e.g. temperature, pulse and respiratory rate), and they received an analgesic, monitoring can help develop a picture of the patient's response to the treatment. Thus, if the pain were not responding to the analgesic, the pulse and respiratory rate could remain elevated, showing the potential need for more analgesia. Only through keeping accurate records and reviewing them on an ongoing basis can healthcare staff provide the most effective and responsive care possible. Dougherty and Lister (2011) emphasise that documents help in assessing patients and can hold a baseline (a reading that acts as a reference for future readings) of data, for example BP, and allow ongoing monitoring of a patient's condition and needs. This is crucial as a patient's condition can be unpredictable and complex.
Dougherty and Lister (2011) identified examples of subjective statements in records (Table 4.1).
**Table 4.1** Examples of records
**Poor example** | **Good example**
---|---
Upset today | Patient states: 'feeling upset'
Appears depressed | Patient says: 'I am concerned about my treatment and how it will affect me'
Source: Adapted from Dougherty 2011. Reproduced with permission of Wiley Blackwell.
One of the challenges in healthcare is the variety of staff involved in any one patient's care and the fact that the information each person needs to carry out their role varies; this means confidentiality must be considered. The Data Protection Act 1998 and the Freedom of Information Act (FOIA) 2005 are important, and healthcare assistants must be aware of the impact that these acts have on their role. It is important to remember that the Data Protection Act 1998 gives patients the right to access personal information held about them. Hutson and Millar (2009) point out that confidentiality, security and access to records are governed by legislation not only from the UK but also from the European Convention on Human Rights. The various legislation is incorporated within local policies, therefore it is important to read these and be aware of when and to whom information is made available or withheld.
Information sharing is vital to safeguarding and promoting the welfare of children and young people. A key factor identified in many serious case reviews (SCRs) has been a failure by practitioners to record information, to share it, to understand its significance and then take appropriate action. In March 2015, HM Government produced non-statutory advice – Information Sharing Advice for Practitioners Providing Safeguarding Services to Children, Young People, Parents and Carers to support practitioners in the decisions they take when sharing information to reduce the risk of harm to children and young people. Please check your local policies relating to safeguarding, documentation and information sharing.
## Confidentiality in records and documentation
Healthcare assistants must always be aware that information might be accessed by the patient and in some cases friends or visitors – for example via the TPR chart as it is often hanging on a patient's bed or wall. When patients are being admitted, they should be informed that data (their personal details) is shared with other members of the healthcare team where relevant to ensure that they receive the best care possible.
The patient should be reassured that these confidential notes are kept safe and, with the development of computerisation, given added reassurance that these are password protected, so only staff who have authorisation can access their records. Always consider the security of this information: do not leave a patient's records (e.g. nursing or case notes) lying around or walk away from a computer if it is on and still open at a patient record. Check what documents can be left safely at a patient's bedside, such as a urine chart or peak flow chart. _Please check your local policy_.
Improper use of social media, especially Facebook, is leading to disciplinary action against staff at a number of English trusts. Figures released to Guardian Healthcare show that 72 separate actions were taken by 16 trusts against staff that inappropriately used social media between 2008–09 and October 2011. The data, released in response to freedom of information (FoI) requests, reveals Facebook to be the main medium for misdemeanors. The largest number of incidents took place in 2010–11, indicating the growing use of social media and the difficulties it presents to the NHS.
# Think about it
Consider who needs the patient records and why they are necessary.
## Types of documentation
The key aspect with regard to documentation is to _check your local practice area_ and identify what is deemed acceptable and has been approved. In relation to clinical skills, focus would be on charts for recording TPR, urinalysis, peak flow, blood glucose levels, faecal occult blood (FOB) tests and patient care plan/case notes for recording, for example, peripheral intravenous cannulation: date, time, site, cannula gauge, reason for insertion, any issues and signature. The standard 12-lead ECG record is often noted on the recording itself and stored securely within the patient's record – local variations may apply. _Always check your local policy_.
Another type of documentation that may be used is a care pathway or integrated care pathway (ICP). The development of clinical protocols, care pathways, patient-held records or shared documentation emerged to help improve the patient's experience of care and service delivery. Dougherty and Lister (2011) noted that these offer a consistent method of assessment, which enables communication among the various healthcare staff. Beach and Oates (2014) identify that the aim of a care plan is to enable the team providing care, as well as the author of the plan, to meet the assessed needs or goals of the person receiving care. The care plan needs to be current, accurate and evidence based, with SMART (specific, measurable, achievable, realistic and timed) objectives (refer to Figure 4.1 for an example).
**Figure 4.1** The diabetic care pathway. Source:
Reproduced with kind permission of Suzanne Delaney, Diabetic Nurse Specialist, NHS Lothian.
The chapters in Section 2 of this book explore a range of clinical skills; within each there is a review of the knowledge and skills necessary to perform the procedure(s) (clinical skill(s)) safely and competently. All require competent record keeping.
# Think about it
What clinical skills will you be required to undertake? Consider what types of records or documentation you will need to maintain in your practice area.
## Legal aspects relating to documentation
The underpinning principle in record keeping is that _if it has not been recorded, it has not been done_. Documentation and records are therefore essential legal documents that should record and support individual actions, while maintaining a conversation between the multidisciplinary team about the patient. The Department of Health (DH 2006) stipulates that all individuals who work for NHS organisations are responsible for any records they create or use in the performance of their duties. Furthermore, any record an individual creates is a public record. Dimond (2011) states a legal document is 'any document requested by the court', which includes patient records. Therefore it is essential to follow local policy and ensure documentation is accurate and of the highest standard possible. Local policies about record keeping and documentation should reflect relevant legislation and regulations as well as national and regional/organisational policy. Local policy should also reflect the national policies on information governance, confidentiality, information security, records management and the NHS constitution (DH 2003, 2006, 2007, 2013a, 2013b).
Those working in regulated care settings, such as care homes, should adhere to the standards set by the relevant regulator. In England, care is regulated by the Care Quality Commission under the Health and Social Care Act 2008 (Regulated Activities) Regulations 2010, and in Scotland care is regulated by Health Care Improvement Scotland. Regulation 20 of the Health and Social Care Act 2008 (Regulated Activities) Regulations 2010 stipulates, 'that service users are protected against the risks of unsafe or inappropriate care and treatment arising from a lack of proper information about them by means of the maintenance of an accurate record in respect of each service user, which shall include appropriate information and documents in relation to the care and treatment provided to each service user'. Effectively this means that whether you work within or outwith the NHS, record keeping and documentation must be of a high standard.
Caldicott Guardians was set up within the NHS to oversee access to patient identifiable information and should be seen as the gatekeeper for patient information held within a healthcare setting (Hutson and Millar 2009). In England, Wales and Northern Ireland this role is mandatory and is usually undertaken by a senior clinician, but it is only advisory in Scotland. This person is also responsible for the protection of and uses of patient identifiable information by staff, and for the developing and monitoring policies of interagency disclosure. The Caldicott principles (Department of Health 2013a) are
1. **1.** Justify the purposes.
2. **2.** Don't use personal confidential data unless it is absolutely necessary.
3. **3.** Use the minimum necessary personal confidential data.
4. **4.** Access to personal confidential data should be on a strict need-to-know basis.
5. **5.** Everyone with access to personal confidential data should be aware of their responsibilities.
6. **6.** Comply with the law.
7. **7.** The duty to share information can be as important as the duty to protect patient confidentiality.
# Think about it
Who is designated to release patient records in your organisation? If a patient asks to see their documents, what is your local policy and what would you do?
Beach and Oates (2014) also highlight that clinical records have been discussed in several recent serious case reviews and public inquiries, including the reviews of NHS complaints (Clywd and Hart 2013); the Liverpool Care Pathway (Neuberger 2013); the reviews of care at the University Hospitals of Morecambe Bay NHS Foundation Trust (Care Quality Commission (CQC) 2012) and Mid Staffordshire NHS Foundation Trust (Mid Staffordshire NHS Foundation Trust Inquiry 2010; Francis 2013) – all of which related poor practice to poor record keeping, including incomplete and inconsistent records, inaccurate recording of patient information and discussions with patients and families, and poor recording of transfer information.
## Common problems
The quality of nursing documentation has consistently been found to be failing to meet recommended standards (Prideaux 2011). Bridget Dimond (2011) has noted the following common errors in record keeping:
* Date, time and signature omitted.
* Inaccuracies/lack of name, date of birth, address, NHS number.
* Lack of evidence of discussions/agreement with patient.
* Illegible handwriting.
* Lack of entry in the record when an abortive call/visit has been made.
* Ambiguous abbreviations.
* Record of phone calls (e.g. to social services) that omitted the name and designation of the recipient (e.g. social worker).
* Covering up errors.
* Absence of relevant information.
* Inaccuracies, especially of date.
* Delay in completing the record, sometimes more than 24 hours have elapsed before the records are completed.
* Record completed by someone who did not deliver the care.
* Unprofessional terminology, for example 'dull as a doorstep'.
* Meaningless phrases, such as 'lovely child', 'appears', 'slept well', 'encouraged'.
* Opinion mixed with facts.
* Reliance on information from others without identifying the source.
* Subjective not objective comments, for example 'normal development'.
* Main dataset fields on the Patient Administration System (PAS) incomplete.
## Related aspects and terminology
The main areas of concern in relation to information governance are consent, information sharing and confidentiality (Beach and Oates 2014). Therefore it might be useful at this point to revisit Chapter 4 and then consider this terminology in relation to your record keeping and documentation.
## Strategies to improve standards of record keeping
### Electronic records and standardised approach
Both unitary (single) patient records and electronic formats are becoming the 'norm', which has the potential to standardise format, minimising confusion, giving uniformity and allowing staff to record information in a recognisable way that is easy to locate and act upon (Dougherty and Lister 2011; Beach and Oates 2014). This approach allows information to be shared, reducing duplication and repetition, which is better for the patient who does not have to repeat name, address, DOB, and so on over and over. Another advantage of electronic records is that they can be shared promptly across healthcare teams, for example a GP can send a patient's records when they are being admitted to hospital. This can allow data to be compared, for example the peak flow record of a patient with asthma will allow staff to monitor and observe changes (e.g. deterioration from home/baseline) and response to treatment (Dougherty and Lister 2011). Beach and Oates (2014), however, emphasise the importance of not sharing passwords and logging out of computers following use.
### Good time-management skills
Time constraints and workload are often cited as reasons for poor documentation; as previously stated, the recording of care is an integral part of care, not an add on, using and developing good time-management skills will help to allocate time for documentation.
### Cultural change
The UK Government's health information strategy (DH 2012), arising from the 'no decision about me without me' approach (DH 2010), reflects the move away from healthcare providers being in sole control towards a more involved approach including patients and service users in decisions about their health and care. As of 2015, GP practices offer patients access to online services, communication with the practice and personal records (Royal College of General Practitioners (RCGP) 2013).
### Audit and education/training
Regularly auditing documentation acts as an incentive for staff to maintain a good standard of record keeping and also provides evidence of areas of poor practice so that measures can be taken to improve performance. Education and training are important, organisations need to ensure that staff know what to do and are giving adequate training to enable them to do the job
# Think about it
How could you audit your records? What formal audit process and tools does your organisation use relating to record keeping?
## Summary
Record keeping is not something separate from clinical care but is the documented reflection of the care provided, and together they co-exist and are integral to holistic practice (Prideaux 2011). Healthcare assistants and assistant practitioners must recognise the importance of good documentation and record keeping. Very simply, to conclude and sum up this chapter: health records should demonstrate and be a part of high-quality patient care.
Hutchinson and Sharples (2006) described a model called HORUS, indicated within the NHS's Connecting for Health, which is used as the basis for a competency checklist (Table 4.2).
**Table 4.2** Competency framework: record keeping
**Competency** | **First assessment/reassessment**
---|---
Steps | Demonstration/supervised practice | Date/competent signature
**Record keeping** | Date/signed | Date/signed | Date/signed | Date/signed | Date/signed |
| 1 | 2 | 3 | 4 | 5 |
Information was | | | | | |
1. **1.** **H** eld securely and confidentially
2. **2.** **O** btained fairly and efficiently
3. **3.** **R** ecorded accurately and reliably
4. **4.** **U** sed effectively and ethically
5. **5.** **S** hared appropriately and lawfully
| | | | | |
Supervisors/Assessor(s): | | | | | |
Source: Hutchinson 2006. Reproduced with permission of RCN Publishing Company.
# Case study 4.1
John Simms is a healthcare assistant in your team. He reports to you that he was recording Mr Jung's urinalysis results in his records when he realised that he had written this information in the wrong record. He has been working in your clinical area for only six weeks and is unsure what he should do. What would you advise?
# Self-assessment
**Assessment** | **Aspects** | **Achieved ✓**
---|---|---
Records | _Have you considered all aspects of this section?_ |
| Purpose and importance of accurate records |
| Access to and completion of appropriate records |
| Types of documentation in practice area |
| Ensuring security and safety of information |
Patient | _Have you considered all aspects of this section?_ | **Achieved ✓**
| Consent aspects |
| Confidentiality |
| Patient education, e.g. access to health records |
## References
1. Beach J and Oates J (2014) Maintaining best practice in record-keeping and documentation. _Nursing Standard_ **28** (36): 45–50.
2. Care Quality Commission (2012) _Investigation Report. University Hospitals of Morecambe Bay NHS Foundation Trust_. London: CQC.
3. Clwyd A and Hart T (2013) _A Review of the NHS Hospitals Complaints System: Putting Patients Back in the Picture_. London: The Stationery Office.
4. Department of Health (DH) (2003) _Confidentiality: NHS Code of Practice_. London: The Stationery Office.
5. Department of Health (DH) (2006) _Records Management: NHS Code of Practice, Parts 1–2_. London: The Stationary Office.
6. Department of Health (DH) (2007) _NHS Information Governance: Guidance on Legal and Professional Obligations_. London: The Stationery Office.
7. Department of Health (DH) (2010) _Equity and Excellence: Liberating the NHS_. London: The Stationery Office.
8. Department of Health (DH) (2012) _The Power of Information: Putting All of Us in Control of the Health and Care Information We Need_. London: The Stationery Office.
9. Department of Health (DH) (2013a) _Information: To Share or Not to Share. The Information Governance Review_. London: The Stationery Office.
10. Department of Health (DH) (2013b) _The NHS Constitution for England_. London: The Stationery Office.
11. Dimond B (2011) _Legal Aspects of Nursing_ , 6th edn. Harlow: Pearson Education Limited.
12. Dougherty L and Lister S (eds) (2011) _The Royal Marsden Hospital Manual of Clinical Nursing Procedures_ , student edn. Oxford: Blackwell Publishing.
13. Francis R (2013) _Report of the Mid Staffordshire NHS Foundation Trust Public Inquiry: Executive Summary_. London: The Stationery Office.
14. Hand T and Casey A (2012) Delegating Record Keeping and Countersigning. Royal College of Nursing Records. Available at <http://www.rcn.org.uk/__data/assets/pdf_file/0003/472719/Delegating_and_countersigning_records2012.pdf> (accessed 26 March 2015).
15. The Health and Social Care Act 2008 (Regulated Activities) Regulations (2010) Available at: www.legislation.gov.uk/search?title=The+Health+and+Social+Care+Act+2008+%28Regulated+Activities%29+Regulations+2010&year=&number=&type=uksi (accessed April 2015).
16. HM Government (2015) _Information Sharing Advice for Practitioners Providing Safeguarding Services to Children, Young People, Parents and Carers_. Crown copyright, London.
17. Hutson M and Millar N (2009) Recording keeping. In: Iggulden H, MacDonald C and Staniland K (eds) _Clinical Skills. The Essence of Caring_. London: McGraw Hill, pp. 27–54.
18. Hutchinson C and Sharples C (2006) Information governance: practical implications for record-keeping. _Nursing Standard_ **20** (36): 59–64.
19. Mid Staffordshire NHS Foundation Trust Inquiry (2010) _Independent Inquiry into Care Provided by Mid Staffordshire NHS Foundation Trust_. January 2005 – March 2009. Volume I. London: The Stationery Office.
20. Neuberger J (2013) _More Care, Less Pathway: A Review of the Liverpool Care Pathway_. London: The Stationery Office.
21. Nursing and Midwifery Council (NMC) (2009) _Record Keeping – Guidance for Nurses and Midwives_. London: NMC.
22. Nursing and Midwifery Council (NMC) (2015) _The Code Professional Standards of Practice and Behaviour for Nurses and Midwives_. London: NMC.
23. Prideaux A (2011) Issues in documentation and record-keeping. _British Journal of Nursing_ **20** (22): 1450–1454.
24. Royal College of Nurses (RCN) (2012) Record Keeping (online) Available at: <http://www.rcn.org.uk/development/health_care_support_workers/professional_issues/record_keeping> (accessed April 2015).
25. Royal College of General Practitioners (2013) _Patient Online: The Road Map_. London: RCGP.
26. Unite the Union (2014) _Record Keeping and Documentation: A Guide for Health Professionals_. London: Unite the Union.
# Section II
## Core clinical skills
# Chapter 5
Pulse
# Learning objectives
* Define what a pulse is
* Explain how a pulse is initiated by the heart
* List the different locations where a pulse can be felt
* Identify common factors that can affect the pulse rate
## Aim of this chapter
The aim of this chapter is to understand how a pulse is generated and felt within the body, the common sites and factors influencing its rate, rhythm and amplitude (strength).
## What is a pulse?
A pulse can be felt where an artery is near the surface of the body and lies over a bone or another firm background. A pulse is the rhythmic expansion of the artery wall as it is stretched by a wave of blood that is pumped through the vessels with each heartbeat (Waugh and Grant 2010; Thibodeau and Patton 2007; Rawlings-Anderson and Hunter 2008). The heartbeat occurs when the ventricle of the heart (see 'Relevant anatomy and physiology') pumps blood into the aorta, which is already full with blood, and then into the arterial system (Maddex 2009). In normal cardiovascular health, one heartbeat corresponds to one pulse beat (Maddex 2009).
### Reasons for performing a pulse reading
A pulse rate is often requested as part of 'routine' observations. It can be taken as a baseline (a reading taken that acts as a reference for future readings), to monitor changes in a patient's condition (e.g. after surgical intervention) or to check that medication is working correctly (e.g. after administration of a medication to correct an abnormal heartbeat (Marieb and Hoehn 2007).
## Relevant anatomy and physiology
The pulse is strongest in the arteries closest to the heart, becoming weaker in the arterioles and then disappearing altogether in the capillaries (Tortora and Derrickson 2011). The most common location for taking a pulse reading is the radial site (located inside of the wrist and underneath the thumb). It is often the first choice because many patients are familiar with this site and it is easily accessible and non-invasive. However the choice of site will often vary with the patient and the presenting clinical situation. If the patient was acutely unwell, perhaps with a condition that reduces blood volume – such as shock, haemorrhage or a collapse with unknown cause – a pulse may not be easy to palpate at sites away from the heart because blood will be directed to the major organs. In such instances the radial pulse may be weak or difficult to find and the carotid or femoral site would be more appropriate (Figure 5.1). In children under the age of 2 the heartbeat is usually auscultated (listened to) via a stethoscope at the apex of the heart. In adulthood the apex can be located on patients' left-sided chest wall in the space between the fifth and sixth ribs (fifth intercostal space) on a line with the midpoint of the left clavicle (collar bone) (Herbert and Sheppard 2005) (Figure 5.1). In children up to the age of 7 the location of the apex beat can be found at the fourth intercostal space (Kyle 2008). Listening to the apex is deemed more appropriate because the vessel walls in neonates and infants are not fully developed, making palpation difficult. However, it is good practice in children's nursing to check for the presence of the brachial pulse (Ball and Bindler 2008). Pulses in the lower legs are usually palpated only when assessing the circulation (flow of blood) to the limbs, which may be affected by vascular problems or after surgery or trauma to the limbs (Maddex 2009).
**Figure 5.1** Sites for taking a pulse.
In some patients locating a pulse may prove challenging, despite them being clinically well. This can be due to slightly unusual anatomy or the presence of cardiovascular disease. It is also a skill that can prove difficult initially and practise is recommended, especially when accessing the carotid pulse, because locating this may be necessary in an emergency situation.
# Think about it
Ask your friends and family if you can practise taking their pulse at various sites. Note the difference in the pulses, including the rate, rhythm and strength (amplitude). Is there anything that might be causing these differences?
The heart generates an electrical impulse that causes it to contract (the muscles within the heart structure shorten and pulls inwards, compressing the chambers). Figure 5.2 shows the important structures involved in generating this impulse. The sinoatrial (SA) node is often described as the natural 'pacemaker' of the heart because it initiates impulses of contraction (Waugh and Grant 2010). This causes the atria (Figure 5.2) to contract, which then stimulates the atrioventricular (AV) node. The Purkinje fibres then convey this impulse to the apex of the myocardium, where the wave of ventricular contraction begins pumping blood into the pulmonary artery and aorta, resulting in a heartbeat and pulse (Waugh and Grant 2010).
**Figure 5.2** Structure involved in initiation of a pulse.
## Related aspects and terminology
Maddex (2009) suggests that the following be considered when obtaining a pulse.
### The rate of the pulse
This indicates the frequency of contraction of the left ventricle and is affected by age, exercise, stress, injury and disease. In acute practice patients may have hypovolaemic shock, which is a circulatory disturbance where there is usually a reduction in blood volume. This leads to a rapid, thready pulse which is a characteristic sign of shock (Scales and Pilsworth 2008; Boulanger and Toghill 2009).
### The amplitude
This indicates the strength of the ventricular contractions. A weak contraction may not generate a pulse at the limbs (peripheral) or, if present, it may be weak. It can also occur when there is a lack of blood volume, for example if the patient is bleeding heavily or dehydrated. Where a full and bounding pulse is felt, this may be indicative of complications such as anaemia, heart failure or the early stages of septic shock (Jevon and Ewens 2007).
### The rhythm
The rhythm of the pulse is determined by assessing the regularity of the pressure waves from the heart and can assist in establishing whether the heart is beating regularly (Rawlings-Anderson and Hunter 2008). In health, the heartbeats with regular coordinated contractions, which is referred to as sinus rhythm (Marieb and Hoehn 2007). An irregular pulse can be caused by problems in the heart's conduction system, such as atrial fibrillation where the chambers of heart fails to contract together (Marieb and Hoehn 2007).
When listened to through a stethoscope, the sound of the heartbeat comes primarily from blood turbulence caused by closing of the heart valves, although only the first two are loud enough to be heard through a stethoscope (Tortora and Derrickson 2010). The sounds are heard as 'lubb dupp', followed by a pause, with the pause interval reducing when the pulse increases (Tortora and Derrickson 20101).
# Point for practice
As anxiety can increase the pulse rate, before taking a pulse try to ensure that the patient is as relaxed as possible. Ensure that the patient is fully informed as to why the pulse is being taken and give reassurance if necessary. If the patient is unduly anxious, consider a delay to provide them with time to settle into the surroundings and relax before the pulse is recorded
## Factors affecting the pulse rate
Pulse rates can alter due to many factors, both physical and psychological, and may indicate conditions that are life threatening, for example cardiac arrest, or long-term cardiac conditions such as angina. Factors that increase and decrease pulse rates are the following:
* Exercise: this increases the heart rate (Marieb and Hoehn 2007).
* Anxiety: a patient's heart rate can increase due to anxiety.
* Medication: some medication can both increase and decrease heart rates.
* Trauma: the loss of blood and fluid volume causes the heart to beat faster to circulate the fluid around the body.
* Pain: this can cause an increase in heart rate.
* Infection.
* Cardiac abnormalities; for example, if atherosclerosis (build-up of plaque) is present in the arteries, this can influence the pulse rate (Maddex 2009).
* Circulation problems.
* Temperature: increased body temperature (pyrexia) will increase the pulse rate (Jevon and Ewens 2007), whereas decreased body temperature (hypothermia) will decrease it (Waugh and Grant 2010).
* Reduced consciousness: coma will decrease the pulse rate.
* Fitness: if a person is very fit, the heart becomes very efficient and a lower pulse rate can deliver the required blood to the body.
* Metabolic diseases: these affect the body's metabolic rate, for example over/underactive thyroid.
* Breathing pattern: in some patients inspiration (breathing in) can increase the pulse rate due to changes in intrathoracic pressure (Rawlings-Anderson and Hunter 2008).
* Smoking can increase the heart rate as this can cause a narrowing of the arteries.
* Age: see Table 5.3.
# Think about it
Take your resting pulse rate. Now run on the spot for 2 minutes and take your pulse again.
What implications do you think this may have for patients attending the GP surgery or hospital?
How would you ensure that you are measuring an accurate pulse rate for your patient?
## Terminology
* _Irregular pulse_ : this is a pulse that does not have a clear pattern and may have 'gaps' as if beats were being omitted. Because this cannot be detected on standard automated machines, it is important that pulse readings should be taken manually as relevant clinical information can otherwise be missed (Boulanger and Toghill 2009).
* _'Normal' pulse_ : the normal adult heart rate is between 60 and 100 beats/min, but at rest is usually between 60 and 80 beats/min depending upon the individual (Waugh and Grant 2010). When assessing a patient's pulse, it is important to look at what is considered 'normal' for every individual, bearing in mind the many factors discussed previously. Figure 5.3 shows the normal pattern of a pulse on an electrocardiograph (ECG) reading (see also Chapter 17).
* _Tachycardia_ : this is an increased pulse rate of over 100 beats/min (Maddex 2009; Rawlings-Anderson and Hunter 2008). Atrial tachycardia relates to an increased rate in the upper chamber of the heart. On an ECG this would be seen as having an increased number of contractions on the strip (Figure 5.4).
* _Bradycardia_ : a reduced heartbeat of less than 60 beats/min (Maddex 2009; Rawlings-Anderson and Hunter 2008). This will result in a decreased number of contractions shown on the ECG (Figure 5.5).
* _Weak pulse_ : this is when the pulse is not strong on palpation with two fingers placed over the site.
* _Thready pulse_ : this is when the palpated pulse is weak and can be irregular.
* _Fibrillation_ : a condition of rapid and irregular contractions (Dougherty and Lister 2011).
* _Respiratory sinus arrhythmia_ : a harmless increase in the pulse rate due to inspiration (breathing in) can be seen in patients with good cardiovascular health (Woods et al. 2005).
**Figure 5.3** Rhythm strip for normal heartbeat – 'sinus rhythm': note the regular pattern and shape of each wave. Source: NHS Lothian (2008). Reproduced with permission from NHS Lothian.
**Figure 5.4** An increased heart rate – tachycardia: note that the waves are closer together. Source: NHS Lothian (2008). Reproduced with permission from NHS Lothian.
**Figure 5.5** Bradycardia – slow heartbeat: note the regular pattern of the wave, but the spacing is far wider than the strips in Figures 5.3 and 5.4, giving a slower heart rate. Source: NHS Lothian (2008). Reproduced with permission from NHS Lothian.
The contraction of the heart, which gives rise to a pulse, can be shown on ECG readings (see Chapter 17). The strips in Figures 5.3–5.5 show how normal, fast and slow pulses affect the ECG. It is not the intention that individuals read ECGs (see also Chapter 17); these are merely to show how the pulse rate presents with different pulse values.
If a pulse is being taken manually, a watch or clock with a second hand is required. The pulse should always be taken manually for a baseline, because use of an automatic monitor (e.g. Dinamap™, Critikon™) does not highlight the amplitude (depth), volume or whether it is regular (Boulanger and Toghill 2009). Always seek advice as to which method of recording the pulse is being requested if not for a baseline recording. The procedure for taking a manual pulse is shown in Table 5.1 (note that for apex and radial pulse, this is shown in Table 5.5).
**Table 5.1** Procedure for taking a manual pulse reading
**Action** | **Rationale**
---|---
Wash hands with soap and water or cleanse with alcohol gel | To prevent the spread of infection
Inform the patient and gain verbal consent (for children parent or guardian consent is required) | The patient is fully informed and has given consent voluntarily
Ensure access to a watch or clock with a second hand | To ensure accurate timing
Choose the site (usually radial) and, if necessary, explain the reasoning to the patient | Choose an appropriate site dependent on clinical presentation
Children aged under 2 will require the apex site to be used (see Table 5.1)
For the radial pulse: place the first, second or third fingers along the appropriate artery and press gently (Figure 5.6) | The fingertips are sensitive enough to feel the pulse accurately
To record a manual pulse rate, count the number of beats for 60 seconds. The number counted will be the actual pulse rate, e.g. if 84 beats are counted in 60 seconds the pulse rate would be 84 | This is more accurate than counting for 15 seconds and multiplying by 4 because it allows enough time for irregularities or other defects to be detected (Dougherty and Lister 2011)
Document the reading as per local policy and any other details, e.g. missed beats, irregular or thready pulse (Figure 5.7) | To ensure accurate record keeping and for good communication
Help patient to redress, if necessary | To maximise patient comfort and dignity
Reassure patient if necessary | Patient comfort
Report to nurse in charge | Patient may require further management
## Automated devices
Pulse recording is a feature on many machines including automated blood pressure machines (see Chapter 6) and pulse oximetry machines (see Chapter 8). The machine takes the reading automatically without the user needing to palpate (feel) the pulse. To ensure accurate readings the following points should be considered:
* The machine should be clean, appear undamaged and have been serviced regularly (usually annually, but check local policy). When the machine is switched on it may do a self-test, and if any error codes are displayed the machine should not be used.
* The machine must be used in accordance with the manufacturer's instructions and appropriate accessories used where applicable; for example, a blood pressure cuff or the finger probe of the pulse oximiter.
* Competency based training should be completed before unsupervised use of the device on a patient to ensure correct placement of the accessories and competent use of the device.
* Some machines will have a timespan in which they make an assessment before showing the pulse rate. This means that, in some instances, the pulse rate given by the machine will be the pulse rate 5–10 seconds before the reading is shown.
* If the pulse is very fast or irregular, the pulse rate or abnormality may not be detected.
* Where patients have poor circulation to their arms or legs, for example peripheral vascular disease, an inaccurate reading may be obtained due to poor blood flow.
* If the patient moves while the reading is being taken, this may interfere with the signal, and movement may be wrongly interpreted as a heartbeat.
* A pulse should always be checked manually to ensure that it relates to the wave/pulse generated by the machine.
The procedure for taking a pulse rate using a machine is described in Table 5.2.
**Table 5.2** Procedure for taking a pulse reading using an automated machine
**Action** | **Rationale**
---|---
Wash hands with soap and water or cleanse with alcohol gel | To prevent the spread of infection
Inform the patient and gain verbal consent | The patient is fully informed and has given consent voluntarily
Collect the appropriate machine and, where applicable, accessories. Ensure that the machine is clean and in good working order, and has been serviced as per local policy | To ensure machine is in good working order before use
Ensure that user has had competency training with the machine being used | Correct accessories are essential for the machine to function accurately
To ensure that the machine is operated as the manufacturer intended
Apply the machine to the appropriate site, e.g. BP machine to arm, pulse oximeter probe to finger | To allow reading to be taken
Note the value of the recording, taking the patient's physical well-being and other observations into consideration, e.g. temperature, BP, pallor (colour) of patient | To assist in identification of incorrect recordings
Document the reading as per local policy (Figure 5.7) | To ensure accurate record keeping and for good communication
Help patient to redress, where necessary | To maximise patient comfort and dignity
Reassure patient if necessary | Patient comfort
Report to nurse in charge if abnormal | Patient may require further management
When taking a pulse reading, either manually or with a machine, it should also be remembered that the value of the pulse measurement should be assessed together with other observations of the patient, including the following:
* Assess the patient's circulation; if the patient's hands are cold this could indicate poor circulation and if competent to do so a capillary refill time (CRT) test can be done to establish this.
* Is the patient alert? Assessment of the patients AVPU score (alert, responds to voice, responds to pain only, unconsciousness) can be performed if one is competent to do so.
* What are the values of other observations that have been performed, for example BP and temperature recordings? A correlation between these may indicate a more serious clinical condition such as shock or haemorrhage.
* In Acute Hospital Trusts these measurements are the basis of the Early Warning Score (EWS), which is a track and trigger score recommended for use by National Institute for Health and Clinical Excellence (NICE 2007).
The role of the healthcare assistant will be to report findings, not to diagnose conditions, and therefore any reading that is unexpected or outside the expected range should be reported to a registered nurse to allow further investigation and/or management.
## Fetal heartbeat
In both infants and children, the normal heartbeat range is higher than that of adults (Rawlings-Anderson and Hunter 2008). Before being born, a baby's heartbeat can be heard by using a stethoscope or an electronic machine. The value is around 150 beats/min, which is significantly higher than in adults (see Table 5.3).
**Table 5.3** Pulse rates in relation to age
**Age** | **Average heart**
---|---
| **rate (beats/min)**
Fetus | 160
Newborn | 140
1–12 months | 120
12 months–2 years | 110
2–6 years | 100
6–12 years | 95
Young person | 80
Adult | 80
Adapted from Trimby (1989).
### Neonates and young children
Once born, babies continue to have an increased heartbeat up until adolescence, with the pulse rate gradually decreasing until a more constant reading is reached in adulthood (see Table 5.3). As mentioned earlier, a stethoscope is used to hear the apex heartbeat of a child under the age of 2 because, if taken manually, the rapid pulse rate and small area for palpation result in inaccurate data (Dougherty and Lister 2011). The procedure for taking an apex beat is detailed in Table 5.4.
**Table 5.4** Procedure for taking an apex pulse recording
**Action** | **Rationale**
---|---
Wash hands with soap and water or cleanse with alcohol gel | To prevent the spread of infection
Inform the patient and gain verbal consent (for children parent or guardian consent will be required) | The patient is fully informed and has given consent voluntarily
For very young children involving a play specialist may be helpful | Practising the procedure on, for example, a soft toy may reduce anxiety in the child and increase compliance
Collect equipment: watch/clock, and stethoscope; the stethoscope must be in good condition with clean, well-fitting earpieces. clean the stethoscope as per local policy | So procedure can be performed without delay
If the stethoscope is contaminated this presents an infection risk. If the stethoscope is broken it will not perform the function adequately
Draw the screens | To protect patient privacy and dignity
Check that the stethoscope is positioned correctly | Smooth and accurate facilitation of the procedure
Count the number of apex beats heard in 1 minute. The number counted will be the pulse rate, e.g. if 120 beats are counted in 60 seconds the pulse rate would be 120 | This is more accurate than counting for 15 seconds and multiplying by 4 because it allows enough time for irregularities or other defects to be detected (Dougherty and Lister 2011)
Document the reading and any other details as per local policy, e.g. missed beats or irregular (Figure 5.7). Note that it may not be necessary to write apex or abbreviate to 'A' on individual readings as this may be documented at the top of the chart | To ensure accurate record keeping
Patient may require further management
Help patient to redress, where necessary | To maximise patient comfort and dignity
Reassure patient if necessary | Patient comfort
Report to nurse in charge if abnormal | To ensure correct clinical management of the patient
### Apex and radial pulse measurement
Where patients have a pulse deficit, that is an atrial fibrillation (AF) where the heartbeat does not match the heart rate at the radial pulse, apex (heart) and radial (wrist) pulses may be taken together to assess the number of beats that are not transmitted. This will require two people, with a watch that both individuals can see, and a stethoscope for the person assessing the apex beats. The procedure is shown in Table 5.5.
**Table 5.5** Recording apex and radial heartbeats
**Action** | **Rationale**
---|---
Wash hands with soap and water or cleanse with alcohol gel | To prevent the spread of infection
Inform the patient and gain verbal consent | The patient is fully informed and has given consent voluntarily
Collect equipment: watch/clock, stethoscope – the stethoscope must be in good condition with clean, well-fitting earpieces, clean as per local policy as per local policy | Allow the procedure to be performed without delay
If the stethoscope is contaminated this presents an infection risk. If the stethoscope is broken it will not perform the function adequately
Draw the screens | Patient privacy and dignity
Both individuals should be able to see the watch and agree when they will start counting beats | To ensure that the same time period is used to count the heartbeats.
Check that the stethoscope is positioned correctly and that a radial pulse is felt | Smooth facilitation of the procedure
Procedure commences with staff agreeing when counting will start, e.g. when the second hand gets to 12 we will count for a minute, or one person can also control the procedure by saying 'start' and 'stop' | To ensure that the same time period is used to count the heartbeats
Document the reading; this will involve using either different colours, e.g. blue/red, or different letters, e.g. A (for apex) or R (for radial) as per local policy (see Figure 5.8) | To clearly identify which reading relates to apex and radial recording
Help patient to redress, where necessary | To maximise patient comfort
Reassure patient if necessary | Patient comfort
Report to nurse in charge if abnormal | To ensure correct management of the patient
This is a skill that may require practise, especially when assessing the apex heartbeat, and competency should be achieved in this skill before performing it on a patient. In patients with AF the apex reading will always be higher than the radial pulse because some contractions may not be strong enough to transmit the pulse wave to the radial pulse (Figure 5.6). It is because of this that beats can become lost, resulting in a deficit between pulse and apex measurements (Jevon 2007).
**Figure 5.6** Taking a radial pulse.
## Documentation
The pulse may be recorded in the patient's notes (these may be held by the patient if they are in the community). In a hospital setting, the recordings will be noted on either a temperature, pulse and respiratory chart (TPR) or a EWS chart; the readings often take the form of a graph (see Figure 5.7), where the A (atrial) and R (radial) are clearly marked (Figure 5.8). Many Trusts' record keeping policies state that records should be made in black ink so they can easily be photocopied should the need arise. Therefore advice should be sought from the registered nurse regarding the approved workplace method of documentation.
**Figure 5.7** Observation chart with 'normal' and 'irregular' pulse charted. Source: NHS Lothian (2008). Reproduced with permission from NHS Lothian.
**Figure 5.8** TPR (temperature, pulse and respiratory) chart with apex (A) and radial (R) pulse charted. Source: NHS Lothian (2008). Reproduced with permission from NHS Lothian.
## Common problems
Problems of ensuring an accurate pulse rate can be divided into those concerning technique, patient and equipment.
### Technique
The technique is one that will require practise, especially when accessing sites other than the radial pulse. Both the thumb and forefinger have pulses of their own and are very sensitive, therefore practitioners must be aware that this can be confused for the patient's pulse (Dougherty and Lister 2011). Recognising and having the confidence to report an irregular pulse rate will also require practise and the healthcare assistant should work to their code of practice and seek help when unsure (WUTH 2011). Competency based training should be completed before performing this task independently to ensure that the correct technique is performed.
### Patients
Where patients have an underlying condition, such as poor circulation, the pulse may be more difficult to find at the radial site and other sites may prove more successful. If the patient is acutely unwell as a result of, for example, a major haemorrhage (blood loss), this will reduce the circulating blood volume and may make the radial site difficult to palpate. In preparation for a pulse rate being taken the patient should not have exercised or smoked before the procedure; if they have done so the reading may not be accurate (Rawlings-Anderson and Hunter 2008).
### Equipment
Equipment being used should have been serviced, should be clean and when switched on should not display any error codes. Local policy will dictate when a machine can be used but it is not recommended if performing the reading for the first time on a patient because irregularity, depth and amplitude cannot be identified, as mentioned earlier. If the reading obtained does not appear correct, the pulse rate should be taken manually to check. When taking a pulse manually it is essential that a watch with a second hand is used to enable the pulse to be taken for a full 60 seconds. Universal precautions should always be taken before and after contact with a patient and hands should be washed with soap and water or cleaned with alcohol gel using the Ayliffe technique.
## Summary
A pulse should always be taken manually for the first time to feel its depth and ensure that it is regular. Subsequent readings can be taken using automated equipment if the pulse is regular and stable according to your workplace policy. As with all other clinical skills, users must be competent in a pulse measurement and understand the factors that influence its value before practising this skill independently on patients. Table 5.6 is an example of a competency framework for recording pulse.
**Table 5.6** Competency: recording a pulse rate
**Pulse** | **First assessment/reassessment** |
---|---|---
**Steps** | **Demonstration** | **Date/competent/signature**
| Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
Pulse – manual | | | | | |
1. **1.** Describe what a pulse is and how the heart initiates this
2. **2.** List the sites for taking a pulse with rationale
3. **3.** Describe activities that affect the pulse rate
4. **4.** State the difference in pulse rate for different age groups
5. **5.** Collect equipment for manual or automated device
6. **6.** Correctly identify the patient and explain procedure, and give an effective explanation about the procedure
| | | | | |
**Recording pulse** | **Demonstration** | **Date/competent/signature**
| 1 | 2 | 3 | 4 | 5 |
1. **7.** Demonstrate accurate recording for manual and/or automated machine
2. **8.** Demonstrate tidying away of equipment if applicable
3. **9.** Complete appropriate documentation applicable to the clinical area
| | | | | |
# Case study 5.1
Mr Gary Johnstone has been admitted for planned investigations to his knee. He is 28 years old and enjoys playing sport competitively. He is fairly relaxed about his admission. His pulse rate is taken and it is 48. What factors do you think are influencing his pulse rate?
# Case study 5.2
Mrs Celia Jones is 45 years old, married with two children, and has come into hospital for investigations into suspected stomach cancer. She explains that she has had to rush here after dropping her children at school. Her pulse rate is 104. What factors do you think are influencing her pulse rate and what further actions would you take?
# Self-assessment
**Assessment** | **Aspects** | **Achieved ✓**
---|---|---
Patient | _Have you considered all aspects of this section?_ |
| What initiates a heartbeat? |
| The possible sites to take a pulse |
| The normal pattern of a pulse on an ECG and how a slow/fast heartbeat alters the pattern |
Procedure | _Have you considered all aspects of this section?_ | **Achieved ✓**
| Factors that can affect the pulse reading |
| The factors that should be taken into consideration if using an automated device to take a pulse reading |
| Recording and reporting concerns |
## References
1. Ball J and Bindler R (2008) _Pediatric Nursing. Caring for Children_ , 4th edn. London: Pearson.
2. Boulanger C and Toghill M. (2009) How to measure and record vital signs to ensure detection of deteriorating patients. _Nursing Times_ **105** (47): 10–12.
3. Dougherty L and Lister S (eds) (2011) _The Royal Marsden Hospital Manual of Clinical Nursing Procedures_ , 8th edn. Oxford: Blackwell Publishing.
4. Herbert R A and Sheppard M. (2005) Cardiovascular function. In: Montague SE, Watson R and Herbert RA (eds) _Physiology for Nursing Practice_ , 3rd edn. London: Baillière Tindall, pp. 383–463.
5. Maddex S (2009) Measuring vital signs In: Baillie L (ed.) _Developing Practical Adult Nursing Skills_ , 3rd edn. London: Hodder Education, pp. 116–157.
6. Jevon P (2007) Cardiac monitoring part 4: Monitoring the apex beat. _Nursing Times_ **103** (4): 28–29.
7. Jevon P and Ewens B (2007) _Monitoring the Critically Ill Patient: Essential clinical skills for nurses_ , 2nd edn. London: Blackwell.
8. Marieb E M and Hoehn K. (2007) _Human Anatomy and Physiology_. San Francisco: Benjamin Cummings.
9. Kyle T (2008) _Essentials of Pediatric Nursing_. Philadelphia: Lippincott Williams and Wilkins.
10. NHS Lothian (2008) _Observations Chart_. Edinburgh: NHS Lothian.
11. National Institute for Health and Clinical Excellence (NICE) (2007) _CG50 Acutely Ill Patients in Hospital_. London: NICE.
12. Rawlings-Anderson K and Hunter J (2008) Monitoring pulse rate. _Nursing Standard_ **22** (31): 41–43.
13. Scales K and Pilsworth J (2008) The importance of fluid balance in clinical practice. _Nursing Standard_ **22** (47): 50–57.
14. Thibodeau G A and Patton K T (2007) _Anatomy and Physiology_ , 6th edn. St Louis, MO: Mosby Elsevier.
15. Tortora G J and Derrickson B (2011) _Principles of Anatomy and Physiology_ , 13th edn. Hoboken, NJ: Wiley & Sons.
16. Trimby B (1989) _Clinical Nursing Procedure_. Philadelphia, PA: JB Lippincott.
17. Waugh A and Grant A (2010) _Ross and Wilson Anatomy and Physiology in Health and Illness_ , 11th edn. Edinburgh: Churchill Livingstone.
18. Woods S L, Sivarajan Foelicher E, Underhill Motzer S and Bridges E (2005) _Cardiac Nursing_ , 5th edn. Philadelphia, PA: Lippincott, Williams & Wilkins.
19. WUTH (2011) _Code of Conduct for Assistant Practitioners_. Wirral England.
# Chapter 6
Blood pressure monitoring
# Learning objectives
* Discuss the anatomy and physiology of the heart and its major vessels, relating this to blood pressure measurement
* List the factors that affect blood pressure readings
* Identify why lying and standing blood pressure readings are taken
* Identify the correct method for taking blood pressure
* Identify how to document blood pressure readings correctly
## Aim of this chapter
The aim of this chapter is to review the principles for undertaking blood pressure (BP) monitoring, the related anatomy and physiology, and the skills required to measure, record and report findings.
## What is blood pressure?
Blood pressure can be defined as the force or pressure that the blood exerts on the walls of the blood vessels (Waugh and Grant 2010; Tortora and Derrickson 2011).
## Reasons for monitoring blood pressure
Blood pressure is taken to obtain a baseline (a reading that acts as a reference for future readings) or as an ongoing measure of cardiovascular (heart) function in order to make comparisons, aid diagnosis and evaluate the management of medical conditions. It is also used to screen patients for underlying disease or complications, or as a precaution for side-effects to certain medications (e.g. the contraceptive pill).
## Who requests the test?
A BP reading can be requested in the community setting by a GP, practice nurse or community nurse. This may be part of patients' care when they are discharged from hospital, or to assess their health in relation to a long-term condition, for example hypertension (high blood pressure) as a result of heart disease. In an acute setting, such as a hospital, doctors or nursing staff may request blood pressure to be taken due to the patient's clinical presentation, or it may be part of a specific routine, such as admission procedure or after surgical intervention. Other professionals may also take a reading as part of an assessment, for example an occupational therapist or physiotherapist taking a reading to assess a patient after a history of frequent falls.
## Who can take a BP reading?
Any healthcare professional can undertake BP measurement, the most important criteria being that they are competent in the skill. Incorrect recordings or poor technique in blood pressure measurement can result in inappropriate treatment or undiagnosed conditions that may have a severe effect on the patient's health. Accurate blood pressure readings, on the other hand, can give important clues about health and well-being, and NICE (2011) recommends that patients with suspected or confirmed hypertension who are appropriately trained use home blood pressure monitoring devices to accurately record their blood pressure, which may influence treatment more appropriately.
## What is done with the readings/information?
'Routine' BP recordings will be written in different documents, depending on the purpose of the recording and whether in hospital, the GP surgery, the community or the patient's own home. The documentation may take the format of patient records (can be held by the patient, e.g. antenatal notes during pregnancy), admission documentation, care plans, care pathways or as a specific chart for observations – commonly referred to as a TPR (temperature, pulse and respiratory rate) chart or in acute settings an EWS chart (early warning system). (The recording on the TPR chart is shown in Figure 6.4.) If the result is outside 'normal' parameters for the patient (see notes later) the reading must be verbally reported to the nurse in charge immediately.
## Relevant anatomy and physiology
### Structure of the heart
The heart is best described as a pump and to assist this function it is made almost entirely of muscle (Figure 6.1). This muscle works automatically, thus it does not need the brain to tell it to work but does so under what is known as 'involuntary action'. The heart is situated in the thorax (chest cavity) between and in front of the lungs (Waugh and Grant 2010). It is centrally placed but tilted, which is why the heartbeat is heard to the left, and is roughly the size of a fist (Tortora and Derrickson 2011; Thibodeau and Patton 2007).
**Figure 6.1** Internal structure of the heart.
Within the heart, there are two top chambers known as the right and left atria and below two further chambers known as the right and left ventricles (Thibodeau and Patton 2007) (Figure 6.1). The right atrium receives blood that does not contain oxygen (deoxygenated) from throughout the body. The deoxygenated blood enters the right atrium from the superior vena cava, which brings blood from the top half of the body, the inferior vena cava, which carries blood from the bottom half of the body and the coronary sinus, which is a collection of vessels that drains blood from the heart into the right atrium. The blood then passes into the right ventricle under pressure through the tricuspid valve. After the blood leaves the right ventricle it is then taken to the lungs via the pulmonary arteries where the lungs add oxygen to the blood. Once the blood has combined with oxygen (oxygenated blood) it is returned to the heart via the pulmonary veins to the left atrium. Again, under pressure it enters the left ventricle through the mitral valve. The oxygenated blood is then expelled from the left ventricle through the aortic valve into the aorta to supply oxygen and blood to the tissues. This results in the left side of the heart having oxygenated blood and the right side deoxygenated blood. The two sides are completely separated by the septum so the blood cannot meet, resulting in the heart functioning as two pumps (Tortora and Derrickson 2011). An independent blood supply delivers blood to the heart muscle itself.
The amount of blood ejected from the ventricle in one contraction is called the 'stroke volume', and this volume is estimated to average 70 millilitres (ml) per beat in the average adult (Tortora and Derrickson 2011). To estimate the cardiac output, this is multiplied by the heart rate, giving the amount of blood ejected from the left ventricle in one minute (Box 6.1) (Jevon and Ewens 2007). Non-invasive blood pressure (involves a machine being applied externally) gives an early sign of a fall in cardiac output (Jevon and Ewens 2007).
# Box 6.1 Cardiac output formula
Example
A man has a heartbeat of 72 and a stroke volume of 70 ml (millilitres) Cardiac output = Heart rate × Stroke volume 72 × 70 = 5040 ml/min or 5.04 litres per minute (l/min)
### The role of valves within the circulatory system
There are four sets of heart valves, two sets guarding the openings between the atria and ventricles (the tricuspid and mitral valves), and two located inside the pulmonary artery and aorta (called the aortic and pulmonary valves or semilunar valves collectively). Thibodeau and Patton (2007) describe heart valves as mechanical devices that permit the flow of blood in one direction only.
Defective heart valves can cause heart murmurs and this leads to regurgitation (blood leaking backward through the valve when it should be closed). Diagnosis can result after unusual sounds are first heard through a stethoscope before, between or after normal heart sounds, or they may mask the normal heart sounds (Tortora and Derrickson 2011). These sounds are commonly known as 'innocent heart murmurs', because they do not present any health problems at all and the sounds are made by the blood circulating through the heart's chambers and valves, or through blood vessels near the heart. Heart murmurs can be common in children, often disappearing later in life (Tortora and Derrickson 2011).
However some people can develop problems with their valves. Valves that narrow and reduce blood flow have valve stenosis, while valves that fail to close properly have valve incompetence. Valve incompetence allows blood to flow backwards, these are often called 'leaky valves'. The degree of valve incompetence varies with the individual and can have different effects on the body. Because of this some valve problems will not require treatment and for others valve replacement will be necessary.
### The cardiac cycle
The heart maintains constant circulation by a series of events known as the cardiac cycle (Waugh and Grant 2010). The cycle consists of atrial systole, which is when the atrium contracts lasting around 0.1 second, followed by ventricular systole, contraction of the ventricles that lasts around 0.3 s. Finally complete relaxation of both atria and ventricles occurs, lasting 0.4 s. It is this sequence of contraction and relaxation of the heart muscle that allows blood to flow around the body.
When the left ventricle contracts and pushes blood into the aorta, the resulting pressure is called the systolic blood pressure. This is the maximum pressure of the blood against the wall of the artery (Waugh and Grant 2010). It is expressed as the top figure when quoting blood pressure (think of a fraction: this is the first number above the line). When complete cardiac diastole occurs and the heart is resting following the ejection of blood, the pressure within the arteries is called diastolic blood pressure (the bottom number below the 'fraction' line). This is the minimum amount of pressure exerted against the wall of the artery, after closure of the aortic valve (Marieb and Hoehn 2010). An example of a blood pressure reading is shown in Box 6.2.
# Box 6.2 Example of how a blood pressure is written
Arterial blood pressure is what is commonly referred to as blood pressure and is measured in millimetres of mercury (mmHg) using a sphygmomanometer or electronic device (Marieb and Hoehn 2010). When measuring blood pressure for the first time it is good practice to take a reading from both arms. It can then be determined if there is a discrepancy in the reading and when this occurs the arm with the highest reading should be used for measurement (British Hypertension Society 2006). It should also be noted that NICE (2011) recommends that readings with a discrepancy greater than 20 mmHg systolic require further investigation. Any discrepancies should be reported to the nurse in charge as this may indicate that the patient has an undiagnosed medical condition. This should also be documented in the patient's records.
### Normal blood pressure
Blood pressure can fluctuate within a wide range and still be considered within normal limits. Normal systolic pressure should be between 100 and 140 mmHg and diastolic between 60 and 90 mmHg (Waugh and Grant 2010). Often there can be variance in the definition of normal BP with individual BP fluctuating (Wallymahmed 2008). Systolic readings of around 120 mmHg and diastolic of about 80 mmHg are considered 'normal'. However people with a reading at the high end of the normal range – with a systolic blood pressure between 135–139 mmHg systolic and a diastolic reading between 85–89 mmHg – are likely to benefit from lifestyle advice, with 'at risk' patients requiring medication to control their blood pressure further (Joint British Societies 2005).
## Related aspects and terminology
### Maintenance of normal blood pressure
Blood pressure is maintained within normal limits through fine adjustments by the body with a number of factors affecting the value recorded; this is detailed in Box 6.3.
# Box 6.3 Factors affecting blood pressure readings
* **Blood volume** : this relates to the amount of blood that is circulating around the body. Where the blood volume is reduced dramatically, such as haemorrhage (rapid blood loss), this causes a drop in BP. Tortora and Derrickson (2011) state that even losses of 10 per cent or more, for example in instances of trauma, haemorrhage or severe dehydration, can result in a fall in BP.
* **Peripheral resistance** : this relates to the pressure that is presented against the flow of blood and can reduce the efficiency of blood returning to the heart.
* **Elasticity of the artery walls** : this is how much 'give' the blood vessels have; and in cases of stenosis (narrowing of the artery) of the vessels elasticity is lost (Waugh and Grant 2010). Atherosclerosis, commonly called 'hardening of the arteries', is a build-up of fat and cholesterol deposits within the vessels. This directly affects the elasticity of the arteries and it is caused by lifestyle factors that are related to diet and smoking and may be influenced by a previous family history (Clancy and McVicar 2009).
* **Respiratory centre** : when this centre is stimulated in the brain, particularly during inspiration, the blood pressure will rise (Jevon and Ewens 2007).
* **Nicotine** : as nicotine is a vasoconstrictor (reduces the diameter of the blood vessel), the BP increases (Jevon and Ewens 2007).
* **Age** : Clancy and McVicar (2009) reports that BP increases throughout the lifespan thus affecting the 'normal reading' for any specific patient. In addition, arteries harden with age and therefore an increase in BP is also expected.
* **Gender** : men generally have higher BP than women (Clancy and McVicar 2009).
* **Weight** : obesity is a risk factor in the development of hypertension.
* **Emotional factors** : stress, fear, anxiety and excitement can all increase a person's blood pressure (Maddex 2009). This is due to the body's 'fight or flight' response caused by release of adrenaline from the adrenal glands (Tortora and Derrickson 2011). Although relaxation has been shown to be beneficial for patients' emotional well-being, Dickinson (2008) has identified that relaxation therapy does not reduce blood pressure to a level that is statistically significant.
* **Diet/medications** : high salt intake has been shown to increase blood pressure (ERPHO 2008) while diuretics can also reduce BP by decreasing sodium content in the blood through filtration in the kidneys and by decreasing circulatory volume (Tortora and Derrickson 2011).
* **Time of day** : BP is known to be lowest in the morning, rising throughout the day, reaching its peak in the afternoon, and then falling in the evening. This is linked to the body's own circadian rhythm and research suggests that taking antihypertensive medication at bed time may improve patient's blood pressure levels during the day (Hermida et al. 2011).
* **White coat hypertension** : this is when the individual's BP is consistently higher when measured in a hospital or community practice setting rather than the individual's home, due to anxiety or fear of the medical environment. NICE (2011) acknowledges this importance in its guidelines in suggesting how to determine accuracy of blood pressure readings
* **Gravity** : with postural hypotension the systolic BP can fall more than 20 mmHg within three minutes of standing (Sathyapalan et al. 2011). This is also known as 'orthostatic hypotension'. Baroreceptors, which are situated throughout the body and monitor changes in BP, raise the BP with increased stimulation (Valler-Jones and Wedgbury 2005). However, if this mechanism is lost, for example after prolonged bed rest, the patient may faint on standing (Jevon and Ewens 2007). (See 'Lying and standing BP measurement.')
* **Hormones** : there are also various hormones that affect BP and aid its regulation by altering cardiac output, changing systemic vascular resistance or adjusting the total blood volume, for example the hormones renin and aldosterone from the kidneys (Tortora and Derrickson 2011).
* **Family history** : this can be related to coronary heart disease, which can cause resistance to blood flow and increased peripheral resistance as mentioned earlier (Loscalzo et al. 2008).
* **Sleep** : this is when systolic BP is at its lowest (Hermida 2011).
## Terminology
### Hypertension
Hypertension is an elevation in the blood pressure and may be acute or chronic. It is based not on one reading but on readings that are taken over several days, and where the value exceeds the upper limits of what is considered normal for the patient (NICE 2011). Hypertension increases the risk of having a stroke or heart attack and can be a result of lifestyle choices, stress, anxiety or recent strenuous activity. The National Institute for Health and Clinical Excellence (NICE) defines hypertension as elevated BP above 140/90 mmHg (NICE 2011) (see also Joint British Societies 2005). If the BP reading is higher than 140/90, NICE (2011) guidelines suggest that further readings should be taken through home ambulatory blood pressure monitoring (ABPM), where two measurements per hour while the patient is awake should be taken. This can also be determined through home blood pressure monitoring (HBPM), where the community team visit patients twice a day for a period between four and seven days to establish trends in blood pressure to enable an accurate diagnosis to be made.
### Hypotension
This refers to when the systolic BP is below 100 mmHg and can be the first indicator of shock in an acutely ill patient (where vital body processes shut down in response to a reduction in blood volume), the result of good physical health, caused by medications such as beta blockers, severe congestive cardiac failure or a heart attack affecting a large part of the myocardium (Dougherty and Lister 2011). It can also indicate that there is not sufficient pressure to pump blood around the body. As the blood carries the oxygen with it, organs can become under-perfused and this can cause the individual to faint (see 'Postural hypotension').
### Postural or 'orthostatic' hypotension
The symptoms of postural hypotension may be dizziness and in some instances fainting. When this occurs BP is measured when the patient is both standing (erect) and lying (supine), to detect a deficit when the patient stands up. Postural hypotension is defined as a reduction in blood pressure measurement of at least 20 mmHg systolic when the patient stands compared to their blood pressure when lying down (Sathyapalan et al. 2011). The procedure for measuring lying and standing blood pressure is shown later in Table 6.4.
The British Hypertension Society (2004), supported by the World Health Organization, classify blood pressure in Table 6.1.
**Table 6.1** Blood pressure classification
**Category** | **Systolic BP (mmHg)** | **Diastolic BP (mmHg)**
---|---|---
Optimal blood pressure | <120 | <80
Normal blood pressure | <130 | <85
High normal blood pressure | 130–139 | 85–89
Grade 1 hypertension (mild) | 140–159 | 90–99
Grade 2 hypertension (moderate) | 160–179 | 100–109
Grade 3 hypertension (severe) | >180 | >110
Isolated systolic hypertension (grade 1) | 140–159 | <90
Isolated systolic hypertension (grade 2) | >160 | <90
### Twenty-four-hour monitoring
Monitoring a patient's blood pressure over a 24-hour period can be done for various reasons that include where patients:
* have suspected white coat hypertension (where blood pressure is normal away from healthcare practitioners but increases in their presence);
* have fluctuating BP readings (Hypertension Influence Team 2007);
* have a BP that is poorly controlled despite medication (Hypertension Influence Team 2007);
* require an initial diagnosis of hypertension (NICE 2011).
The device used is called an ambulatory monitor, which means that the patient is fully mobile while the device is recording the BP at regular intervals. This has the advantage of monitoring the patient's BP while they are participating in normal daily activities.
## Korotkoff's sounds
When taking a BP reading manually, sounds known as Korotkoff's sounds are listened for to establish a reading. These can only be heard through a stethoscope during deflation of the inflated cuff. The five phases are in Table 6.2.
**Table 6.2** Korotkoff's sounds
**Phase** | **Description**
---|---
1 | This is the systolic blood pressure. It is heard as repetitive, faint yet clear tapping sounds, which gradually increase in intensity
2 | This is the softening of sounds, which may sound like blowing or swishing
3 | This is the return of sharper and perhaps crisper sounds that do not regain the intensity of phase 1
4 | This is where a distinct muffled sound is heard, which may become soft and blowing
5 | No sounds are heard. This is the diastolic blood pressure
Adapted from O'Brien et al. (2003).
In most instances all phases will be heard; however, Williams et al. (2004) state that if, during phase 5, the reading reduces to zero, phase 4 should be used. The British Hypertension Society (BHS 2006) and Dieterle (2012) state that this can occur in pregnancy; if so phase 4 sounds should be used for the systolic reading. It is essential that the skill of taking BP is both practised and assessed to ensure that the technique is correct and that the phases are heard correctly as this is an essential aspect of practice in obtaining an accurate reading.
Care must be exercised when taking patients' BP to ensure that efforts are taken to reduce anxiety, and that a period of time has elapsed after activity and smoking as they both influence the BP value.
## Equipment
Blood pressure is taken with a manual mercury sphygmomanometer, an aneroid sphygmomanometer or a fully automatic device (see Table 6.3 for the procedure). When using any equipment, it is necessary before use to check that the machine has been serviced as per local policy and appears in good working order. It is also essential that the correct size of cuff be used to ensure accuracy of the BP readings. Table 6.5 shows correct sizing of cuffs.
**Table 6.3** Procedure to measure blood pressure with mercury, aneroid or electronic machines
**Action** | **Rationale**
---|---
_1. The patient_ |
Explain the procedure to patients, paying particular attention to informing them of the tightness of the cuff and the need to stop eating, talking and moving during measurement (Dougherty and Lister 2011; Wallymahmed 2008) | To fully inform the patient, gain verbal consent and cooperation
The patient should not have been participating in strenuous activity for 30 minutes before taking the reading (Jevon and Ewens 2007) | This would give an inaccurate reading
Let the patient rest for 5 minutes before the procedure (Wallymahmed 2008) | Anxiety will give an inaccurate reading
Wash and dry hands (Jevon and Ewens 2007) | Prevent the spread of infection
_2. Equipment/accessories_ |
Ensure that the machine is in good working order, has been serviced as per local policy and is clean | To ensure accuracy of the machine
Choose an appropriate cuff (for both the type and model of the machine and the patient) | BP cuff should be appropriate for the patient (see Table 6.5) to ensure accuracy. The equipment should be in good condition
A stethoscope will be required for a manual reading and must be in good condition with clean, well-fitting earpieces | To ensure that it is fit for purpose and to prevent infection
Bladder length should be 80% of the arm's circumference but no more than 100% (Wallymahmed 2008) | To ensure accurate readings
**For mercury** position the manometer within 1 metre of the patient with the level of the mercury clearly visible and resting at the zero level (Wallymahmed 2008) | To ensure that the scale is easily visible (Wallymahmed 2008)
**For aneroid** , ensure that the dial can be seen when operating the machine |
_3. Patient_ |
Expose the arm to the shoulder, removing tight or restrictive clothing (British Hypertension Society 2006; Jevon and Holmes 2007) | Restrictive clothing may produce inaccurate readings
The arm should be supported at the level of the heart; a pillow is ideal (Jevon and Holmes 2007; Wallymahmed 2008) | To ensure accuracy of the reading (see Box 6.1)
The same arm should be used each time to allow comparison | To ensure consistency if there is a variance between arms. The arm with the highest reading should be used (NICE 2011)
The bladder cuff should encircle the arm just above the antecubital fossa (crook of the elbow) 2.5 cm above the brachial artery (Dougherty and Lister 2011). The centre of the bladder cuff should be positioned over the brachial artery at the point of maximum pulsation (Dougherty and Lister 2011). It is recommended that a space of two fingers should be evident between the cuff and where the stethoscope is placed | To ensure correct placement
Connect the cuff tubing to the manometer tubing and loosen the valve of the inflation ball | To ensure smooth facilitation of the procedure
_4. Procedure_ |
**For mercury/aneroid** : to estimate systolic blood pressure – palpate the brachial artery which can be located in the middle of the arm at the inner elbow, slightly inwards towards the body. By placing two or three fingers at this site the pulse can be found, as it is the site of maximum pulsation (Dougherty and Lister 2011). Inflate the cuff until pulsation disappears. Inflate a further 10 mmHg and release the valve slowly, taking a note of the reading on the mercury column when the brachial pulse returns | Provides an estimate of the systolic pressure
Deflate the cuff completely allowing all the air to escape | Residual air in the cuff many give an inaccurate reading
Palpate the brachial artery and place the diaphragm of the stethoscope lightly over the site. Inflate the cuff to 30 mmHg above previous estimated systolic pressure | Excessive pressure can distort sounds or make them persist for longer
Listen through the stethoscope releasing the valve on the cuff by approximately 2–3 mmHg/s (Wallymahmed 2008) | At faster rates of deflation if using mercury it may fall too quickly, resulting in an inaccurate reading
When the first sound is heard the level should be noted; this is the systolic pressure. Continue to deflate the cuff and, at the point that the sounds disappear altogether, this is the diastolic pressure | Ensure knowledge of Korotkoff's sounds (see Table 6.3)
BP should be measured to the nearest 2 mmHg (Wallymahmed 2008) | Provides a more accurate reading
**Electronic device** : |
Switch on the device and press start | To obtain the reading
Read the systolic and diastolic blood pressure as displayed on the machine but ensure the reading is consistent with patient's overall general condition | To ensure that the reading is accurate and the machine functioning correctly
_5. Documentation_ |
Document the systolic and diastolic BP on the appropriate chart (Figure 6.1) | To ensure record of BP reading is available
Report any abnormal readings to nurse in charge or medical staff | To allow further intervention where necessary
_6. Remove equipment_ |
Remove the cuff and make the patient comfortable | Patient comfort
Return the equipment to appropriate store, cleaning as per local policy if required. Plug in electronic device | To allow equipment to be in good working order for next patient
If the cuff is too small, the reading could be falsely high and if too large a cuff is selected the reading could be too low (SCENIHR 2009).
### Mercury sphygmomanometers
Standard mercury sphygmomanometers are becoming less common as mercury presents a health and safety hazard – and since 2009 they have been removed from the market for purchase – but those already available in the clinical setting can continue to be used if they are in a good state of repair (MHRA 2009). Because of the risk associated with mercury leakage the procedure for dealing with this should be detailed in local policies and procedures within organisations that use mercury sphygmomanometers. To ensure accurate readings using a mercury sphygmomanometer, it is important that the following points should be noted:
* Ensure that the gauge of the manometer which contains mercury is kept in a vertical position as this will result in an overestimation of the blood pressure reading (SCENIHR 2009; Dougherty and Lister 2011).
* The control valve must tighten and loosen easily and not leak because this would cause an underestimation of the systolic pressure and overestimation of the diastolic pressure (Jevon and Holmes 2007).
* The rubber tubing and bladder centre should be intact and not perished (Dougherty and Lister 2011).
* Deflation of the cuff should be slow at a rate of 2–3 mmHg per second (Jevon and Holmes 2007).
### Aneroid sphygmomanometer
This device is commonly used in the community and sometimes patients may have these in their own homes. It works by measuring the cuff pressure using bellows connected to a cuff via rubber tubing, and the pressure is transferred to a dial to give the reading (Dougherty and Lister 2011). Like any other sphygmomanometer, these machines must be calibrated correctly as they can result in inaccurate readings due to damage that is not visible to the user. Therefore, the patient's clinical presentation should also be considered, and readings rechecked using another machine if they do not correlate with the BP reading obtained. To promote accurate readings in these machines it is recommended that:
* the indicators sit at the '0' correctly before use (Dougherty and Lister 2011);
* the faceplate is not damaged; commonly it can be cracked, which will affect readings (Dougherty and Lister 2011);
* the rubber tubing is not defective or leaking (Dougherty and Lister 2011).
### Automated devices
An alternative to the manual sphygmomanometer is the use of automated devices, which can be fixed or portable. An example of one model is given in Figure 6.2. They are sometimes referred to as monitors, with some models capable of taking ECG (electrocardiograph), pulse and pulse oximetry readings. The machines can operate by battery, mains power or both. Some machines have functions allowing BP readings to be measured at regular intervals, for example every 15 minutes, and may have a facility to store the readings. It is essential that the machine is used in the way that the manufacturer intended, so individuals must ensure that they are taught how to use it correctly and refer to the manufacturer's instructions. The machine displays the systolic and diastolic values, and in some instances the mean value that is referred to as the 'mean arterial pressure'. The machine measures the blood pressure by detecting pressure oscillations (waves) in the cuff, which are generated by arterial wall movement, with each arterial pulsation beneath an occluding cuff. The amplitude (depth) of the oscillation depends on the relationship between the cuff pressure and the arterial BP, reaching a maximum when the cuff pressure equals the mean arterial pressure. Therefore, if the pulse is weak, thready or irregular the reading may not be accurate, and NICE (2011) recommends that the reading should be checked with a manual sphygmomanometer. Validated automated devices can also be used by patients for home blood pressure monitoring where patients are known to have hypertension and for ABPM (NICE 2011).
**Figure 6.2** An automated blood pressure measuring machine.
## Sites for recording blood pressure
* Either arm, situating the cuff on the upper arm using the brachial artery (most common) to hear the Korotkoff sounds.
* At the wrist where the radial and ulnar arteries are situated, placing the cuff on the forearm; this would not be expected from a healthcare assistant.
* The foot, placing the cuff above the ankle where the dorsalis pedis artery is situated; this would not be expected from a healthcare assistant.
* On the thigh where the cuff is placed in the centre of the thigh and the Korotkoff sounds are listened for at the popliteal artery. However this would not be expected from a healthcare assistant.
## Taking blood pressure
The cuff is usually placed on the upper arm at the heart level for both adults and children, with the thigh used only when the upper arm cannot be used, and this would not be expected of a healthcare assistant without further training. When using all BP measuring machines the arm should be supported for optimum readings to be obtained (Jevon and Ewens 2007). Figure 6.3 shows inappropriate positioning for taking a BP reading.
# Think about it
Get someone who has completed competency based training for blood pressure to take your blood pressure. How did it feel? Did the cuff become uncomfortable? Imagine how this could feel for your patient group. Is there any way you can help to improve their experience here?
**Figure 6.3** Inappropriate positioning for a blood pressure recording. The arm should be supported on a pillow and below heart level.
As mentioned earlier, where a patient has a variance in lying and standing BP a reading should be obtained for both lying and standing. Where the patient has a history of fainting or collapse when standing it is recommended that another person be available to ensure patient safety. Table 6.4 details the procedure for lying and standing BP measurement.
**Table 6.4** Procedure for lying (supine) and standing (erect) blood pressure recordings First ensure that you follow the procedures detailed in Table 6.2 for the specific machine that you are using
**Action** | **Rationale**
---|---
1. **1.** Explain the procedure and rationale to the patient
| To fully inform the patient, gain verbal consent and cooperation
1. **2.**
For lying (supine) blood pressure:
Lie the patient down for 5 minutes (Jevon and Holmes 2007)
| To prepare the patient for the procedure and ensure an accurate reading. It may also relax the patient
1. **3.** Complete the procedure as per Table 6.4 dependent on the device being used
| To ensure that an accurate reading is obtained
1. **4.**
Document the reading ensuring that you are recording it for lying (supine) reading (Figure 6.1)
Leave the cuff in place
| Accurate record of the BP reading
Preparation for the next part of the procedure
1. **5.** Allow the patient to stand for 1 min, supporting the patient where necessary (Jevon and Holmes 2007)
| To ensure that an accurate reading is obtained. Supporting the patient will ensure patient safety should they fall
1. **6.**
Complete the procedure as per Table 6.4
Document the reading ensuring that you are recording it for standing (erect) reading (Figure 6.5)
| To ensure that an accurate reading is obtained. Either a code of E (erect) and S (supine) should be recorded on the chart or in some workplaces it is common to record (L) lying and S (standing) (Figure 6.5)
1. **7.** Explain the readings to the patients if they want this information
| To ensure that the patient is fully informed and allow further information to be given, where necessary
# Think about it
What factors would you consider when taking a blood pressure reading on a patient who is agitated and who has an intravenous infusion (drip) in place? What other groups of patients might you need to adapt your practice for?
The Joint British Societies (2005) summarise the main points regarding BP measurement using a standard mercury sphygmomanometer or semiautomated device as follows:
* Use a properly maintained, calibrated and validated device.
* Measure sitting BP routinely: standing BP should be recorded at the initial estimation in patients who are older or have diabetes.
* Remove tight clothing, support the arm at heart level, ensure that the patient's hand is relaxed and avoid talking during the measurement procedure.
* Use a cuff of appropriate size (see Table 6.5).
* Read BP to the nearest 2 mmHg.
* Measure diastolic BP during disappearance of Korotkoff sounds (phase 5).
* Take the mean of at least two readings; more readings are needed if marked differences between initial measurements are found.
* Do not treat on the basis of an isolated reading.
**Table 6.5** Sizes of cuff
**Indication** | **Bladder width × length (cm)** | **Arm circumference (cm)**
---|---|---
Small adult/child | 12 × 18 | <23
Standard adult | 12 × 26 | <33
Large adult | 12 × 40 | <50
Adult thigh cuff | 20 × 42 | <53
Source: Hypertension Influence Team 2007. Reproduced with permission of British Hypertension Society.
## Documentation
### Charting blood pressure readings
Once the systolic and diastolic BP values have been obtained they should be recorded promptly. If they need to be charted on an observation chart, this takes the format of a graph. Despite variations of the chart being available, the principles are the same. The systolic pressure is marked by an arrow at the top and the diastolic value by an arrow at the bottom. The space between the readings is drawn in a dotted line. After several readings have been charted this method allows trends to be seen clearly. Figures 6.4 and 6.5 show examples of charts with BP readings recorded.
**Figure 6.4** A TPR (temperature, pulse, respiratory rate) chart with blood pressure readings charted. Source: NHS Lothian 2008. Reproduced with permission of NHS Lothian.
**Figure 6.5** TPR (temperature, pulse, respiratory rate) chart with erect (standing: E) and supine (lying: S) blood pressure readings charted. Source: NHS Lothian 2008. Reproduced with permission of NHS Lothian.
# Think about it
A blood pressure reading is taken with a cuff that is too large for the patient. How do you think this will affect the readings obtained? What implications might this have for the patient's treatment?
## Common problems
Common complications can occur when using non-invasive blood pressure devices and it is important to identify these promptly and then reporting them to the nurse in charge to ensure patient safety. Box 6.4 shows the common complications.
# Box 6.4 Common complications of non-invasive blood pressure measuring devices
* Swelling at the site where the cuff is placed, known as limb oedema, can occur (Jevon and Ewens 2007).
* Friction blisters can occur if the blood pressure machine is used very frequently causing irritation at the site (Jevon and Ewens 2007).
* Nerve damage can occur to the nerves within the arm, known as ulnar nerve palsy (Jevon and Ewens 2007).
* Excessive bruising and even wounds can result due the frequent overinflation of the cuff where the patient is receiving anticoagulant therapy that 'thins' the blood (e.g. heparin or warfarin) or due to peripheral neuropathy in diabetes (Uzun 2012).
Many patients who are having a BP recorded have underlying diseases or are receiving medical intervention that will need to be taken into account when considering a suitable site. Box 6.5 summarises some of the main considerations.
# Box 6.5 Inappropriate sites and rationale
* **Intravenous infusion running:** taking blood pressure on this arm could interfere with fluid delivery.
* **Pulse oximetry machine being used** : taking BP on the same arm will alter the readings, because blood flow will be occluded.
* **Fistula/shunt** : shunts are used for renal dialysis and taking BP at this site may cause damage to the shunt.
* **Trauma** : where there has been injury to a site that could be used for BP measurement the cuff could cause further injury.
* **Atrial fibrillation** (increased heartbeat in the top chamber of the heart): some automated devices provide unreliable readings, and in such instances another type of device should be used (NICE 2011).
* **Previous stroke with residual damage to one side** : the patient's circulation may be affected or the arm is limited in movement or sensation.
* **Lymphoedema** : this is swelling that can be due to many causes, for example mastectomy with lymph node removal, and taking a BP reading could damage an area that is already swollen.
* **Arthritic limb** : the patient may have arthritis in the arm(s) resulting in correct positioning being problematic and causing discomfort and pain.
* **Circulatory problems** : where circulation in the arms is affected this may result in inaccurate readings.
To ensure accurate BP readings it is essential that the patient be prepared, the equipment be in good working order and the healthcare assistant be competent in the skill. Table 6.6 summarises the common operator and equipment problems when taking a BP reading.
**Table 6.6** Common problems when taking a blood pressure reading
**Problem** | **Action to reduce inaccurate readings**
---|---
Poor technique of the user (Wallymahmed 2008) | Ensure that, before undertaking the procedure, competency based training and assessment have been completed in line with local policy
Machine malfunction | Report to appropriate personnel (e.g. medical physics, servicing department or manufacturer). Do not use the machine
Equipment has tape applied to secure | Report and do not use the damaged piece of equipment
Use of an incorrectly sized cuff (Wallymahmed 2008) | This is essential for accurate readings and an appropriate sized cuff should be sought (see Table 6.5)
Failure to ensure that the mercury column is initially at zero (Wallymahmed 2008) | Always ensure that the mercury column is initially at zero before commencing the procedure
Patient has tight clothing on | This will give an inaccurate reading and clothing needs to be removed
The arm is not correctly supported | If the arm is unsupported the muscles may contract, leading to a rise in diastolic blood pressure (Wallymahmed 2008). Incorrect positioning during the procedure can lead to an error rate as high as 10% (Jevon and Ewens 2007)
Blood pressure cuff comes off when reading taken | This can be due to the wrong size of cuff and the arm circumference should be re-measured and the correct cuff used
In other instances, the Velcro on the cuff may be worn and ineffective and will need to be replaced
Cannot 'hear' blood pressure sounds | Ensure that all equipment is working. Palpate pulse and ensure that the stethoscope is at the correct pulse point. Seek assistance if unsure.
Patient complains that it is sore to take blood pressure | Do not pump cuff up too high unless patient has hypertension. Use estimated systolic value (see Table 6.4) or previous readings to act as a reference
Movement causes noise and inaccurate readings | Ask the patient to remain still or if the patient cannot do this, ask colleague to assist you
Rounding up readings to the nearest 5 or 10 mmHg (Wallymahmed 2008) | Document the exact reading that is obtained
## Summary
An understanding of how the body controls blood pressure can help link theory to practice. It is essential that BP be taken with equipment on which the healthcare assistant has completed competency based training because the recordings can affect patient management. Abnormal or unusual recordings for the patient should always be reported to ensure prompt management where necessary.
Blood pressure measurement is an area of healthcare assistant practice with the potential to make a real difference to the patient's quality of life and lifespan (Thornett 2007). Table 6.7 is an example of a competency framework for blood pressure measurement.
**Table 6.7** Competency framework: recording a blood pressure
**(BP)** | **First assessment/reassessment**
---|---
**Steps** | **Demonstration** | **Date/competent/signature**
| Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
Blood pressure | | | | | |
1. **1.** Describe what is blood pressure and the relationship with the heart
2. **2.** State sites for recording blood pressure with rationale
3. **3.** State examples of inappropriate sites for a healthcare assistant
4. **4.** State the normal range for blood pressure readings
5. **5.** Describe systolic and diastolic pressure
6. **6.** Describe some factors affecting blood pressure
7. **7.** Describe the procedure for manual, aneroid and automated devices, including choice of sites
8. **8.** Describe maintenance of all pieces of equipment, including reporting faults
| | | | | |
(BP) | First assessment/reassessment
**Recording blood pressure** | **Demonstration** | **Date/competent/signature**
| Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
1. **9.** Describe the procedure for dealing with mercury spillage (if applicable)
2. **10.** State when to report/ask for assistance
3. **11.** Collect all equipment
4. **12.** Demonstrate correct identification of patient, effective explanation and communication in relation to blood pressure recording
5. **13.** Demonstrate accurate recording using: (a) automatic blood pressure machine, (b) mercury sphygmomanometer and/or (c) aneroid sphygmomanometer
6. **14.** Demonstrate correct documentation of the recording
7. **15.** Demonstrate tidying away of equipment including cleaning
# Case study 6.1
Mrs Wooley has come to the well woman clinic for a check up. As part of the process you are asked to take her observations. In your surgery you use an automatic machine and her blood pressure reading is 145/95 and you also notice her pulse is irregular. What might be causing this high reading and what actions would you take regarding her observations?
# Case study 6.2
Mr Jones has lung cancer and is admitted for pain control and dehydration. He is emaciated (thin) and frail, and has an intravenous infusion running. His blood pressure is being taken with a mercury sphygmomanometer and a standard size adult cuff is being used. The readings are not what you would expect given his condition. What actions would you take to ensure that the readings are correct?
# Self-assessment
**Assessment** | **Aspects** | **Achieved ✓**
---|---|---
Patient | _Have you considered all aspects of this section?_ |
| What blood pressure actually measures in the patient |
| What the systolic and diastolic pressure represent |
| The factors that affect blood pressure |
| The role of the cardiac cycle |
Procedure | _Have you considered all aspects of this section?_ | **Achieved ✓**
| Selecting equipment |
| Suitable sites |
| Patient information |
| Documenting and reporting concerns |
## References
1. British Hypertension Society (2004) Guidelines for management of hypertension: report of the fourth working party of the British Hypertension Society, 2004 – BHS IV. _Journal of Human Hypertension_ **18** : 139–185.
2. British Hypertension Society (2006) Fact File 01/2006. Blood Pressure Measurement. Available at: www.bhsoc.org/bhf_factfiles/bhf_factfile_jan_2006.doc (accessed 1 March 2008).
3. Clancy J and McVicar A. (2009) _Physiology and Anatomy for Nurse and Healthcare Practitioners: A Homeostatic Approach_ , 3rd edn. London: Arnold Hodder.
4. Dougherty L and Lister S (eds) (2011) _The Royal Marsden Hospital Manual of Clinical Nursing Procedures_ , 8th edn. Oxford: Blackwell Publishing.
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# Chapter 7
Temperature
# Learning objectives
* Identify the normal temperature range and describe how body temperature is controlled
* List the factors that affect heat production and heat loss
* Identify the symptoms and causes of increased and decreased temperature
* Describe the different devices that record temperature and how they work
* Describe how to take and record an accurate temperature
## Aim of this chapter
The aim of this chapter is review the principles and practice surrounding temperature measurement and its related physiology.
## What is temperature?
Body temperature is the balance between heat loss and heat production (Clancy and McVicar 2009). To ensure that a constant temperature is maintained, a fine balance between heat produced in the body and heat lost to the environment is essential (Waugh and Grant 2010). The body's core temperature is the optimum temperature for the body's organs to function, and the range varies between 36 °C and 37.5 °C (Tortora and Derrickson 2011). The shell temperature is the temperature near the body surface (Tortora and Derrickson 2011). Figure 7.1 shows the body temperature at different sites.
**Figure 7.1** Body temperature at different sites on the body. (Adapted from Torrance and Semple 1998.)
## Reasons for measuring temperature
* To determine a baseline (a reading against which future readings can be compared) on admission to hospital (Dougherty and Lister 2011).
* To monitor fluctuations in temperature (Dougherty and Lister 2011).
* To identify changes in a patient's condition so treatment can be planned accordingly (Dougherty and Lister 2011).
* To ensure patient safety (McCallum and Higgins 2012).
* To identify potential disease or infection (Jevon 2010).
## Normal limits
In normal health, despite changes to external temperature, the body is able to maintain a core temperature around 37 °C (Tortora and Derrickson 2011). However, an individual's temperature can safely range from 36 °C to 37.6 °C without homeostasis being affected (Clancy and McVicar 2009). Because treatments can be based upon temperature recordings, it is essential that readings are accurate and reported as necessary.
## Relevant anatomy and physiology
Temperature is controlled by a temperature-regulating centre in the hypothalamus, which is situated in the brain. It is responsive to the temperature of circulating blood and the vasomotor centre in the medulla oblongata, which controls the diameter of blood vessels. This controls heat loss and gain (Waugh and Grant 2010). Figure 7.2 shows the location of the hypothalamus and medulla oblongata within the brain.
**Figure 7.2** Location of the hypothalamus and medulla oblongata within the brain.
The body also has thermoreceptors (sensors) in the skin and mucous membranes that send signals to the hypothalamus stimulating the production or loss of heat. This results in the body being able to regulate temperature. It is therefore vital that our body temperature be kept within fairly strict limits. This is done via a negative feedback system and is known as homeostasis or the 'constant internal environment' (Clancy and McVicar 2009) (see Figure 7.5 later in text).
## Related aspects and terminology
In order to understand temperature regulation, both heat production and loss need to be understood.
### Heat production
All living cells produce heat during metabolism: in muscles when they are active and continuously by the liver. It can also depend on the body's metabolic rate (the rate at which the body uses energy). Factors that affect heat production are included in Table 7.1.
# Think about it
What effect do you think prolonged exposure to either a hot, humid desert environment or a cold, snowy, freezing climate would have on body temperature?
**Table 7.1** Factors affecting heat production
**Factor** | **Rationale**
---|---
Metabolic rate | The basal metabolic rate produces heat, which in turn directly affects the body's temperature (Clancy and McVicar 2009)
Exercise | Exercise is known to increase the metabolic rate. Furthermore, during strenuous activity the basal rate can increase by up to 15 times, increasing up to 20 times for elite athletes (Tortora and Derrickson 2011). Immobility and age can have the opposite effect, with individuals needing to add layers of clothes for warmth (Turnball and Petty 2013; Sund-Levander and Grodzinsky 2010)
Sweat gland activity | Reduced sweat gland activity preserves heat that would normally be lost by evaporation (see heat loss)
Goosebumps/ shivering | Goosebumps occur when the muscles surrounding the hair follicles contract, causing the raising of the hair to trap a layer of air around the body and prevent heat loss. If this is ineffective, shivering often follows
| Shivering involves intense, muscular contraction and relaxation cycles. This physiological response to cold produces heat which directly increases body temperature (Clancy and McVicar 2009)
Hormones/disease | The main hormones relating to temperature control are those from the thyroid, predominantly thyroxine (T4). In the case of an overactive thyroid, where there is increased hormone production, individuals may have a higher than normal body temperature. An underactive thyroid results in the opposite with a reduced metabolic rate and a reduced temperature (Mulryan 2010)
| In times of stress, adrenaline and other hormones may be released, which can also increase the metabolic rate and produce heat (Tortora and Derrickson 2011). Other conditions that affect temperature include hypoglycaemia (low glucose level in blood) and adrenal insufficiency (adrenal glands are situated on top of the kidneys)
Infection | The body responds to infection by releasing pyrogens that change the hypothalamus reset point, having the effect of increasing body temperature (Clancy and McVicar 2009). For every degree centigrade increase in body temperature, the metabolism increases by around 10% (Tortora and Derrickson 2011)
Eating | Eating and digesting food can increase the metabolic rate up to 10–20%, with a higher increase for protein-based meals than that for carbohydrates and lipids (Tortora and Derrickson 2011)
Age | Neonates have an underdeveloped thermocentre in the brain and require intervention to ensure that heat loss is minimised, e.g. extra clothing, including a hat to reduce heat loss from the head. In low birth weight neonates, current practice advocates placing the infant into polythene bags to prevent rapid heat loss (Turnball and Petty 2013). In children the metabolic rate (in relation to their size) is double that of an older person, due to growth (Tortora and Derrickson 2011). In older people the metabolic rate is lower and there is a decreasing incline to sweating, which contributes to the body temperature generally being lower (Sund-Levander and Grodzinsky 2010)
Gender | Metabolic rates tend to be higher in males than females, which in turn increases the temperature (Tortora and Derrickson 2011)
Body shape | Larger individuals will have a higher basal rate due to an increase in surface area, therefore increasing the body temperature (Tortora and Derrickson 2011)
Pregnancy/ breast-feeding | Pregnancy and breast-feeding increase the basal metabolic rate and can have a direct influence on temperature (Tortora and Derrickson 2011)
Menstruation | Immediately prior to ovulation the body's temperature can reduce by up to 0.5 °C due to a reduction in progesterone. Following ovulation temperature returns to normal (Clancy and McVicar 2009).
Medications/ alcohol | Some medications can increase the basal rate and temperature, e.g. amphetamines (Tortora and Derrickson 2011). Antidepressants, sedatives and tranquillisers have the opposite effect and can reduce the body temperature
| Alcohol does not promote heat production and may suppress the body's warning of low or high temperatures due to altered consciousness and awareness
Environmental factors | In hot climates, a reduction in the basal metabolic rate occurs and the body reduces heat production in an effort to cool the body. Heat loss through sweating also occurs (Clancy and McVicar 2009)
Time of day | The body's natural variance, which causes hourly fluctuations, is known as the circadian rhythm. This is influenced by sleep patterns (e.g. day/night shift workers) with the higher recording of temperature in the hours after awakening and before retiring. This has implication for the basal metabolic rate which reduces during sleep (Clancy and McVicar 2009)
When looking after patients, many factors may influence metabolic rate and temperature control. The skin can gain heat by radiation, for example through sunlight; this heat is then absorbed deep down into the subcutaneous layers and blood vessels (Clancy and McVicar 2009). Figure 7.3 shows how the skin controls heat production and heat gain.
**Figure 7.3** Heat production and heat gain from the skin.
### Heat loss
Most heat loss from the body occurs through the skin (Figure 7.4), although small amounts are lost in expired air, urine and faeces (Waugh and Grant 2010). Heat is lost from the skin when heat is conducted to the skin surface. It is then lost by radiation, or mixed with sweat to be lost by evaporation.
**Figure 7.4** Heat loss from the skin.
The methods of heat loss are evaporation, conduction, radiation and convection, and each is described in turn.
#### Evaporation
Evaporation is the conversion of a liquid into a vapour. In the human body, evaporation of water requires heat energy to be used, causing heat to be lost primarily from the skin (Tortora and Derrickson 2011). An increase in temperature stimulates the sweat glands, which secrete sweat on the surface of the body via ducts. The evaporating sweat then cools the skin and the body loses heat (Waugh and Grant 2010).
# Think about it
Can you think of a time when your body sweated or shivered? How did this make you feel?
Evaporation is of particular importance in high environmental temperatures when it is the only method that cools the body (Tortora and Derrickson 2011). Loss of heat by evaporation can also occur from the deeper layers of the skin to the surface of the body, from mucous membranes and during breathing. Here the individual is unaware that evaporation is occurring, and this is known as insensible loss (Waugh and Grant 2010). Insensible loss is often used when calculating fluid balance charts to ensure that all fluid loss is considered (see Chapter 14).
#### Conduction
This is the transfer of heat to any substance in direct contact with the body (Tortora and Derrickson 2011). It accounts for a relatively small amount of heat loss and examples include clothes or jewellery taking up heat from the skin. Hot and cold drinks as well as hot and cold baths can also cause the body to conduct (Tortora and Derrickson 2011).
#### Radiation
Radiation is the transfer of heat via infrared rays between a warmer and a cooler object without physical contact, for example the sun. In cool environments the body loses a greater percentage of heat loss from the skin by this method than through conduction and evaporation combined (Clancy and McVicar 2009). In hot environments no heat is lost by this route, but may be gained by heat radiating to the skin (Tortora and Derrickson 2011).
#### Convection
This is movement of heat away from a surface by movement of heated air or particles (Tortora and Derrickson 2011). A cool fan or convection heater would fulfil this purpose by circulating and moving the air. Another example would be getting out of a hot bath, which would have provided heat to the body, and then the heat being quickly lost via a cool breeze from an open window (Tortora and Derrickson 2011).
# Think about it
What nursing actions are taken to promote heat loss due to an increase in temperature in a patient and how do they work? Are there any particular patients you would take care with when reducing temperature?
Temperature control is essential for the well-being of the human body and this maintenance is done by constantly checking, and if necessary altering, systems. This cycle is called a negative feedback mechanism and is shown in Figure 7.5.
**Figure 7.5** Negative feedback mechanism to control body temperature. (Adapted from Tortora and Derrickson (2011) and Dougherty and Lister (2011).)
## Terminology
* _Core temperature_ : the temperature deep within the body supplying the major organs (Clancy and McVicar 2009).
* _Shell temperature_ : the temperature near the body surface, including the skin and the subcutaneous layers (Tortora and Derrickson 2011).
* _Hypothermia_ : lowering of the body's core temperature to 35 °C or lower (Maddex 2009).
* _Pyrexia_ : a temperature >37.5–38.9 °C (Dougherty and Lister 2011).
* _Hyperthermia_ : a core temperature >40.0 °C (Dougherty and Lister 2011).
### Hypothermia
This is when the body's temperature is <35 °C and mechanisms to increase heat production are ineffective (Maddex 2009). The body's metabolic rate is reduced in an attempt to try to preserve heat (Clancy and McVicar 2009). The causes of hypothermia are shown in Box 7.1.
# Box 7.1 Summary of causes of hypothermia
* Renal dialysis due to heat loss from the blood leaving the body and dialysate entering (Ronco and Ricci 2008).
* Anaesthesia (Tanner 2011).
* Burns as the body is unable to regulate surface temperature (Clancy and McVicar 2009).
* Extreme or overwhelming cold, for example exposure to a cold environment (Clancy and McVicar 2009)
* Low metabolic rate, especially in older people and in hypothyroidism (Clancy and McVicar 2009).
* Rapid blood transfusion (Vasiliki 2011).
* Metabolic conditions, such as hypoglycaemia (low blood sugar) and adrenal insufficiency (Dougherty and Lister 2011).
* Medications that alter the perception of cold, increase heat loss by vasodilatation or inhibit heat generation, for example alcohol, paracetamol, antidepressants (Dougherty and Lister 2011).
Patients may shiver due to being cold as the body attempts to increase its metabolic rate and therefore produce heat (Clancy and McVicar 2009). In these cases a warming blanket may be sufficient to raise the temperature, or in extreme cases warmed fluids may be used to raise core temperature (Mains 2008). If the temperature continues to drop, shivering is replaced by muscle rigidity and cramps, and blood pressure and heart rate begin to slow (Clancy and McVicar 2009). In extreme hypothermia, confusion, loss of consciousness or cardiac problems can occur, leading to death if the temperature falls to <25 °C (Clancy and McVicar 2009).
### Pyrexia
The term pyrexia relates to an increase in the body's core temperature (Dougherty and Lister 2011). Patients with pyrexia often appear flushed, and as the body attempts to lose heat they can feel hot to the touch. Pyrexia can be divided into three grades and these are shown in Table 7.2.
**Table 7.2** Grades of pyrexia
**Grade** | **Temperature (°C)** | **Details**
---|---|---
Low grade | 37 to 38 | Indicates an inflammatory response as a result of mild infection, allergy or disturbance of body tissue. Can also be due to trauma, surgery, malignancy or blood clots (thrombosis)
Moderate-to-high grade | 38–40 | Caused by a wound or other infections (e.g. respiratory or urinary tract)
Hyperpyrexia | ≥40 | Bacteraemia (the presence of bacteria in the blood), damage to the hypothalamus or high environmental temperatures
Source: Adapted from Dougherty (2011). Reproduced with permission of Wiley Blackwell.
Leach (2009) suggests that in half of patients that have a high temperature this is related to an infection that is either bacterial or viral in origin. Where there is an increase in temperature but no infection evident, the causes for the increase in temperature are known as non-infective causes of pyrexia and hyperthermia (Dougherty and Lister 2011). Causes of non-infective pyrexia and hyperthermia are shown in Box 7.2. Occasionally people who have very high temperatures will feel cold and begin to shiver, and this is known as a 'rigor'. The reason for this is that the hypothalamus becomes confused and resets itself to a higher point. The body then attempts to heat itself to meet this point by shivering in the same way it does when it is cold. When this reset point is met it is then that the patient stops shivering and begins to feel hot. This increase in body temperature due to infection is the body's own response of killing any bacteria in the body (Clancy and McVicar 2009).
# Box 7.2 Non-infective causes of pyrexia/hyperthermia
* Alcohol withdrawal.
* Medications (including recreational drugs such as ecstasy).
* Allergic drug or transfusion reaction.
* Reaction to vaccines (common in neonates and children).
* Exercise.
* Gout.
* Trauma.
* Heat stroke or heat exhaustion.
* Hyperthyroidism (overactive thyroid), this causes an increase in metabolic rate.
* Malignancy (cancer).
* Status epilepticus (constant fitting).
* Stroke/heart attack (myocardial infarction).
* Central nervous system damage.
* Vasculitis (inflammation of a blood vessel).
* Surgery.
* Environmental factors – hot and humid surroundings/too many layers of clothing.
(Adapted from Dougherty and Lister 2011.)
Often patients with high temperatures will be given medication to reduce their temperature (antipyrexial medication) and a fan (to promote air circulation), or be sponged with cool, slightly warm water (tepid sponging), which will aim to cool the surface of the skin. The evidence for these routine interventions is limited, and it is suggested that giving antipyretics for high temperatures prevents the body's own defence mechanisms from working effectively as well as masking symptoms (Leach 2009). Care should also be taken when using fans and they should not be used in the chill phase as this can cause an increase in temperature due to shivering (Jevon 2010). However, if the patient is feeling hot provision of a fan with indirect air circulation across the skin can be beneficial in terms of patient comfort. Tepid sponging can have similar effects to fan cooling and cause patients to shiver. NICE (2007b) also recommend that tepid sponging should not be carried out on children as there are no proven benefits. If the temperature continues to rise, dehydration can occur as a result of loss of fluid through sweating, and convulsions can occur (particularly common in the under-5 age group). Following this, body proteins (enzymes), which are involved in chemical reactions, are disrupted, affecting the chemical reaction in the body, leading to death at 44–45 °C (Tortora and Derrickson 2011).
## Taking a temperature reading
There are various methods of taking a temperature reading and each is discussed in turn. The equipment that you use will often depend on whether it is suitable for the patient and its availability in the clinical area. Recommended good practice is that the same site and method are used where possible and that this information is documented for future reference (Sund-Levander and Grodzinsky 2010). A summary of the advantages and disadvantages of each method is shown in Table 7.3. However, it should be noted that no one method or site is viewed as best, with many authors disagreeing about the accuracy of different methods and sites (Farnell et al. 2005; El-Radhi and Patel 2006; Mackechnie and Simpson 2006; DeVrim et al. 2007; Sund-Levander and Grodzinsky 2010).
**Table 7.3** Summary of the advantages and disadvantages of different methods
| **Advantages** | **Disadvantages**
---|---|---
Mercury | Can be reused for groups of patients | Mercury is actively discouraged due to the health and safety risk
| | Risks of cross-infection with poor cleaning techniques
| | Can be inaccurate if used incorrectly
Electronic | Quick, easy to use | Cost implications re-disposables
| Disposable cover for each measurement, promoting infection control | Machine requires maintenance
| | When using the machine with an oral probe, because of the weight of the probe it needs to be held in place
Tympanic | Quick, accurate and easy to use | Cost implications re-disposables
| Disposable cover for each measurement, promoting infection control | Machine requires maintenance and calibration
| | Not suitable for children under 4 weeks
| | Can be used only in the ear for tympanic membrane use
Chemical | Totally non-invasive | Cost implications re-disposables
| Disposable for each patient | Requires storage at below 30 °C (Maddex 2009)
Temporal artery | Quick |
| Can be used on all age groups | Has been shown to be inaccurate compared to other methods of temperature measurement
The main methods are the following:
* Mercury thermometer – oral/axilla or rectal.
* Tympanic thermometer.
* Electronic thermometer.
* Chemical (dots).
* Temporal artery.
### Mercury thermometer
Mercury thermometers have been withdrawn from sale since 2009 due to the risks of environmental contamination with spilt mercury. However, mercury thermometers still within use in the workplace and in a good state of repair can be used where there is no other alternative (MHRA 2013). There are different types of mercury thermometer available, namely oral (for oral or axillary use) or rectal (for rectal use, often with a red bulb to distinguish between oral and rectal) and a low reading thermometer (for hypothermic patients), which can be used at any site, but has a lower range starting at 24 °C.
### Tympanic thermometers
Tympanic thermometers operate by sensing body heat through infrared energy given off by the tympanic membrane in the ear (Mains 2008). The only site for this method is the ear canal and DeVrim et al. (2007) report that, as the tympanic membrane and the hypothalamus share a common blood supply, it is a valid indicator of core temperature. Ear canal size, presence of wax, operator technique and the patient's position can potentially affect the accuracy of the readings; however, the literature surrounding this is inconclusive (Sund-Levander and Grodzinsky 2010; Mains 2008).
In addition, maintenance of the machines is essential and it is particularly important that they are calibrated correctly, because failure to do so results in the reading being unreliable, with measurements continually becoming less accurate as more readings are taken (Mackechnie and Simpson 2006). The thermometer can calculate the temperature at the tympanic membrane, but can also convert it into the reading at the skin surface, oral or core by using the 'mode' button. To ensure that accurate readings are obtained it is essential that healthcare assistants understand this function. Models and manufacturers do vary, so check locally with regard to the model used in practice.
### Electronic thermometer
This is an electronic or digital machine with a probe, which can be used orally, rectally or in the axilla. Sahib El-Radhi (2013) suggests that digital thermometers record a temperature in less than a minute, which is generally indicated by an audible beep, making this a much quicker method of temperature measurement. They also have plastic sheaths to cover the probes that are aimed at reducing the risk of infection; however, the thermometer should still be decontaminated between each patient use. Maintenance and knowledge of how to use the machine is essential to ensure accurate temperature measurement. Figure 7.6 shows an electronic thermometer.
**Figure 7.6** Electronic thermometer. Produced with kind permission from Cardinal Health.
### Chemical thermometer
These are thin plastic strips that have 50 small dots of thermosensitive chemicals, which change colour with increasing temperature (Maddex 2009). They should be stored at below 30 °C and can be used orally or in the axilla (Maddex 2009). It is essential to ensure that they are placed correctly; where the axillary route is being used, the dots must placed next to the inner part of the body, in contact with it. For either oral or axilla use it is essential that the thermometer be left in place for one minute orally and three minutes for axillary (Sahib El-Radhi 2013). They are disposable for each patient and non-invasive and can therefore reduce the risk of cross-infection.
### Temporal artery thermometer
This is a hand-held non-contact thermometer that takes a reading after the probe has been scanned along the forehead. The machine uses an 'arterial heat balance method' to take a reading by measuring the temperature of the skin surface over the artery and the ambient temperature, and then calculating the arterial temperature. However, sweat produced during fever can cause this type of thermometer to give inaccurate results, as can changes in the ambient room temperature (Sahib El-Radhi 2013). A study undertaken by Hamilton et al. (2013) compared the results of tympanic and temporal artery temperature measurements. Here it was found that the incidence of temporal thermometers misclassifying pyrexial patients as having a normal temperature were about three times higher than tympanic. Therefore this method of temperature measurement may have implications for the diagnosis and treatment of patients. In summary, there are many methods of taking a temperature recording. However, all equipment must be used as intended by the manufacturer, including correct placement and timing, otherwise inaccurate recordings will be obtained.
## Route
The choices of sites for temperature measurement are oral, rectal, axilla, tympanic membrane and temporal artery. A summary of the advantages and disadvantages of each site is given in Table 7.4.
**Table 7.4** Summary of the advantages and disadvantages of different sites for measuring body temperature
**Sites** | **Advantages** | **Disadvantages**
---|---|---
**Oral:** requires the probe tip to be placed in the mouth in the sublingual pocket, which is under the tongue (Mains 2008) | Easily accessible, no undressing required | Sublingual pocket must be used or inaccurate results will be obtained
| | The patient cannot talk while the procedure is being performed and it is not suitable for breathless patients because it is important that the lips close around the thermometer (Sund-Levander and Grodzinsky 2010)
| | It is also unsuitable for patients who have disease or pain/discomfort in the oral mucosa because the thermometer may cause further pain or discomfort
| | Not suitable for children under 5, confused or unconscious patients, because they may bite the probe or be unable to hold in place
| | When timing the duration, the thermometer must remain in place for an accurate reading; this is a source for error because it is often not left in situ for long enough, giving inaccurate readings
| | When using mercury thermometer, if the glass breaks this causes a hazard (MHRA 2013)
| | This route is unsuitable for patients who have recently had a hot or cold food or drink, or smoked (Mains 2008).
**Rectal:** involves placement of the probe 4 cm into the rectum in adults | Useful if the patient has peripheral shut-down (poor circulation at extremities) | Invasive and can be embarrassing for patients
Not suitable for neonates because of incidence of rectal perforation (DeVrim et al. 2007)
Sund-Levander and Grodzinsky 2010) | | The presence of soft stools can alter recordings (Sund-Levander and Grodzinsky 2010)
| Useful only if other sites are not possible | Not suitable if any rectal disease or irritation is evident (Sund-Levander and Grodzinsky 2010)
**Tympanic:** the probe is inserted into the ear canal (see Table 7.3) | Non invasive
Very quick – takes 3 seconds
Suitable for most adults and children (Mains 2008)
Value not influenced by food, drink or smoking | Correct placement not always achieved
Localised temperature can affect results, e.g. cool air or placement against a pillow (which will generate heat) before measurement can affect results
**Axilla:** where the thermometer is placed under the arm | Non-invasive | Often not left in for sufficient time when using mercury thermometers
| Patient can talk while in place | Vasoconstriction (blood vessels narrow) or chilled skin give inaccurate readings (Sund-Levander and Grodzinsky 2010)
| | Can prove difficult to hold in place for the required duration, especially for children, confused patients and the elderly
**Temporal artery:** requires the device to be 'stroked' across the centre of the forehead from the midline to the lateral hairline and then placed behind the earlobe, in the soft depression below the mastoid | Non-invasive
Quick
Value unaffected by eating, drinking or smoking | Correct placement will require some education
Limited research available currently
When choosing the site for recording temperature, factors such as previous sites, the equipment available and an assessment of the patient should all be considered. The procedure to obtain recordings is given next.
## Taking a temperature reading
First, taking a temperature reading using a mercury thermometer is discussed at oral, rectal or axillary sites. The equipment required is shown in Box 7.3.
# Box 7.3 Equipment needed to take a temperature recording with a mercury thermometer
* Vessel containing thermometer.
* Alcohol swabs.
* Tissue (for rectal use).
* Lubricant (for rectal use).
* Watch that is capable of timing in minutes.
The procedure for taking a temperature reading using a mercury or electronic thermometer device is shown in Table 7.5, taking a tympanic temperature reading is shown in Table 7.6 and temporal artery thermometer reading is shown in Table 7.7.
# Think about it
Which methods and sites do you think would be suitable for the following patients: a frail, thin older patient; an unconscious patient; a baby of 11 months; and a child aged 10 years? What are the reasons for your choices?
**Table 7.5** Procedure for taking a temperature reading using either a mercury or electronic thermometer
**Action** | **Rationale**
---|---
1. Explain the procedure to the patient fully, including reason for test and to gain verbal consent | Patient fully understands why test is being performed and the procedure, and has agreed to participate
2. Check whether the patient has had food or drink or has smoked in past 20–30 minutes. _Oral only_ | To ensure accurate reading
3. Wipe thermometer with alcohol swab.
Check that mercury is at base of thermometer
Place cover over an electronic probe | Prevent cross-infection
To ensure accurate reading
4. Place the thermometer | To ensure correct positioning of the thermometer for accurate reading
**For oral:** place the bulb of the thermometer in patients' mouths under the tongue in the sublingual pocket and ask them to close their lips around it |
**For axillary:** place the bulb fully under the arm of the patient with the arm across the chest to hold it in place |
**For rectal:** lubricate the thermometer with lubricating jelly; place 4 cm into the rectum (Sund-Levander and Grodzinsky 2010) |
5. Leave in place for 3–5 min
Electronic thermometer will beep. | To ensure accurate reading
6. Remove the thermometer
If rectal site is used immediately wipe both the patient's rectum and the thermometer with tissue
Document and/or report reading | Patient comfort
Report abnormal findings immediately to nurse in charge as further care may require planning.
Documentation provides a legal record
7. Wipe with alcohol – start at the end held by the nurse and wipe in a rotating manner towards the bulb end | Prevent cross-infection
Shake the thermometer so that the mercury returns to the base | Thermometer ready for use next time
Remove the plastic cover on an electronic probe and dispose in clinical waste |
Replace probe in correct position for storage (electronic) |
**Table 7.6** Procedure for taking a temperature reading using a tympanic thermometer
**Action** | **Rationale**
---|---
1. Explain the procedure to the patient fully, including the reason for test and to gain verbal consent | Patient fully understands why test is being performed and procedure, and has agreed to participate.
| Note that not suitable for children under 4 weeks old (NICE 2007b) and the correct size probe should be used for accurate readings (Mains 2008)
2. Ensure that the patient is not positioned in a draught or that the ear has been against a pillow | May affect readings
3. Do not use ears that have been reported as sore | May affect placement and accurate readings
4. Apply a new probe cover each time the machine is used | As per manufacturer's instructions
| Prevent cross-infection
| Provide accurate readings
5. Position thermometer as per manufacturer's instructions | Optimal reading
6. Scan the ear, and then listen for audible beep | Confirms reading has been taken.
| A measurement may not be the same in the left and right ear due to physiological differences so record which ear the reading has been taken from
7. If reading is not valid, repeat | Wait at least 2 min before repeating a measurement in the same ear to reduce an artificially low reading from 'draw down', caused by placing the probe tip into the ear canal and reducing its internal temperature
8. Report any abnormal findings | To plan further management
**Table 7.7** Procedure for taking a temperature reading using a temporal artery thermometer
**Action** | **Rationale**
---|---
1. Explain the procedure to the patient fully, including reason for test, and gain verbal consent | Patient fully understands why test is being performed and procedure, and has agreed to participate
2. Run or 'stroke' the scanner across the centre of the forehead from the midline to the lateral hairline, depressing the button constantly throughout. A disposable cover may be used in some models | To record an accurate temporal artery temperature
Prevention of cross-infection
3. Touch behind the ear lobe, in the soft depression below the mastoid | To account for any differences in the temperature in the temporal artery due to sweat (the temperature would be lower)
4. Release the button and read the temperature from the display window | To view reading
5. Report any abnormal findings | To plan further management. Patient safety
6. Dispose of cover if being used or clean as per manufacturer's instructions | Prevent contamination
| Ready for use
The temperature recorded at different sites will give various different readings, rectal measurements giving the highest because it is deeper in the body, followed by tympanic, with oral methods recording the lowest value. Table 7.8 summarises the variance in temperature dependent on the site.
**Table 7.8** Variance in temperature range dependent on site
**Body site** | **Normal temperature range (°C)**
---|---
Oral | 36.9–37.1
Tympanic | 36.9–37.1
Rectal | 37.0–37.5
Axilla | 36.5–37.0
(Adapted from Clancy and McVicar (2009).)
## Documentation
The temperature recording must be documented in either the patient's case notes or on an observation chart depending upon the area of practice. Temperature recordings on an observation chart are usually documented in a graph (Figure 7.7). In Acute Hospital Trusts temperature measurements are part of the Early Warning Scoring system (track and trigger systems) recommended by NICE (2007a). A baseline recording, often done on admission to hospital, will act as a reference for what is 'normal' for that patient. As temperature can vary due to the site, documenting the site where the temperature is taken from, as well as the actual reading, is recommended (Jevon 2010).
**Figure 7.7** TPR (temperature, pulse and respiratory rate) chart with temperature recordings. Source: NHS Lothian 2008. Reproduced with permission of NHS Lothian.
Abnormalities should always be reported to the nurse in charge, so further management can be planned where necessary. However, the reading should also be taken together with how the patient looks and feels: for example is the patient feeling hot/clammy, are they red in the face, hot or cold to the touch, shivering or is the body rigid? This helps ensure that inaccuracies are identified and, if necessary, checked by another method or route.
## Common problems
Problems relating to thermometry can be split into three areas: the patient, the equipment and the technique.
### The patient
Specific routes have disadvantages and limitations as mentioned in Table 7.4. If there is any doubt as to where exactly the thermometer should be placed, for example the sublingual pocket, further advice should be sought. Where possible the patient should also be actively involved in using any specific routes that may improve patient comfort, for example the rectal route would not be a preference for most people unless it was specifically indicated.
### The equipment
As with all pieces of equipment the thermometer should be clean, in good working order and serviced (where applicable). Only dedicated disposables should be used and multiple uses of, for example, probe covers should never occur.
### The technique
The specific technique in relation to both the type of thermometer and the route should be fully understood before commencing the procedure. Competency based training should also be undertaken in line with local policy.
## Summary
It does not matter which route or site is used to record temperature, the most important thing is that it is accurate and that understanding of the variables of the different sites and external factors are taken into account. How the patient looks and feels should also be taken into consideration when assessing the patient's temperature, thus ensuring that the recording obtained represents true clinical symptoms. Table 7.9 gives an example of a competency framework for recording temperature.
**Table 7.9** Thermometry competency: practical assessment form
**Competency: record temperature** | **First assessment/reassessment**
---|---
**Steps** | **Demonstration** | **Date/competent signature**
| Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
Recording temperature | | | | | |
1. **1.** State normal range for body temperature (°C)
2. **2.** Define the terms pyrexia and hypothermia
3. **3.** State different sites for recording temperature
4. **4.** Describe different types of thermometers used and rationale
5. **5.** Describe the common problems with each type
6. **6.** Describe how you would prepare a patient for each method and gain consent
| | | | | |
**Steps** | **Demonstration** | **Date/competent signature**
| Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
Recording temperature | | | | | |
1. **7.** Describe the procedures for the models of thermometer being used in your practice
2. **8.** Identify and justify the use of documentation
3. **9.** State when to ask for assistance/report findings
4. **10.** Describe safe disposal and cleaning of the equipment following use
5. **11.** State when to ask for assistance/report findings
Supervisors/Assessor(s):
# Case study 7.1
Archie is an active 12-month-old boy. His temperature is taken with a tympanic thermometer and shows that it is within the normal range. However, he is very hot and clammy.
You suspect the reading may be incorrect. Why?
# Case study 7.2
Mrs Jones had abdominal surgery two days ago. She has a temperature of 39.5 °C. What actions do you think you should take and what are the possible causes of the increased temperature (pyrexia)?
# Self-assessment
**Assessment** | **Aspects** | **Achieved ✓**
---|---|---
Patient | _Have you considered all aspects of this section?_ |
| Why is temperature recorded? |
| What mechanism does the body have to control temperature? |
| Give some causes of increased/decreased temperature |
| List some factors that affect heat loss and gain in the body |
Procedure | _Have you considered all aspects of this section?_ | **Achieved ✓**
| Describe the different methods of recording temperature |
| List the sites and rationale for each |
| Documentation |
## References
1. Clancy J and McVicar A (2009) _Physiology and Anatomy: A Homeostatic Approach_ , 3rd edn. London: Hodder Arnold.
2. DeVrim I, Kara A, Ceyhan M, et al. (2007) Measurement accuracy of fever by tympanic and axillary thermometry. _Pediatric Emergency_ **23** (1): 16–19.
3. Dougherty L and Lister S (eds) (2011) _The Royal Marsden Hospital Manual of Clinical Nursing Procedures_ , 8th edn. Oxford: Blackwell Publishing.
4. El-Radhi A S and Patel S (2006) An evaluation of tympanic thermometry in a paediatric emergency department. _Emergency Medicine Journal_ **23** : 40–41.
5. Farnell S, Maxwell L, Tan S, et al. (2005) Temperature measurement: comparison of non-invasive methods used in adult critical care. _Journal of Clinical Nursing_ **14** : 632–639
6. Hamilton P A, Marcos L S and Secic M (2013) Performance of infrared ear and forehead thermometers: a comparative study in 205 febrile and afebrile children. _Journal of Clinical Nursing doi_ : 10.1111/jocn.12060 (last accessed 9 May 2013).
7. Maddex S (2009) Measuring vital signs. In: Baillie L (ed.) _Developing Practical Nursing Skills_ , 3rd edn. London: Hodder Education, pp. 116–157.
8. Jevon, P (2010) How to ensure patient observations lead to effective management of patients with pyrexia. _Nursing Times_ **106** (1): 16–18.
9. Leach R (2009) _Acute and Critical Care Medicine at a Glance_. Oxford: Wiley-Blackwell.
10. Mains, J A (2008) Measuring temperature. _Nursing Standard_ **22** (39): 44–47.
11. Mackechine C and Simpson R (2006) Traceable calibration for blood pressure and temperature monitoring. _Nursing Standard_ **21** (11): 42–47.
12. McCallum L and Higgins D (2012) Measuring body temperature. _Nursing Times_ **108** (45): 20–22.
13. Mulryan C (2010) Disorders of the thyroid function. _British Journal of Healthcare Assistants_ **4** (5): 218–222.
14. MRHA (2013) Mercury in medical devices. Available at: <http://www.mhra.gov.uk/Safetyinformation/Generalsafetyinformationandadvice/Product-specificinformationandadvice/Product-specificinformationandadvice%E2%80%93M%E2%80%93T/Mercuryinmedicaldevices/index.htm> (accessed 9 May 2013).
15. NHS Lothian (2008) _Observations Chart_. Edinburgh: NHS Lothian.
16. NICE (2007a) _CG50, Acutely Ill Patients In Hospital_. London: NICE.
17. NICE (2007b) _CG47 Feverish Illness in Children: Assessment and Management of Children Younger than Five Years of Age_. London: NICE.
18. Ronco C and Ricci Z (2008) Renal replacement therapies: physiological review. _Intensive Care Medicine_ **34** : 2139–2146.
19. Sahib El-Radhi A (2013) Temperature measurement: The right thermometer and site. _British Journal of Nursing_ **22** (4): 208–211.
20. Sund-Levander M and Grodzinsky E (2010) What is the evidence base for the assessment and evaluation of body temperature? _Nursing Times_ **106** (1): 10–13.
21. Tanner J (2011) Inadvertant hypothermia and active warming for surgical patients. _British Journal of Nursing_ **20** (16): 966–968.
22. Torrance C and Semple M (1998) Practical procedures for nurses. Recording temperature 1, no 6.1. _Nursing Times_ **94** (2): insert 2p.
23. Tortora G J and Derrickson B (2011) _Principles of Anatomy and Physiology_ , 13th edn. Hoboken, NJ: Wiley & Sons.
24. Turnball V and Petty J (2013) Evidence-based thermal care of low birthweight neonates. Part one. _Nursing Children and Young People_ **25** (2): 918–922.
25. Vasiliki K (2011) Enhancing transfusion safety: nurses role. _International Journal of Caring Sciences_ **4** (3): 114–119.
26. Waugh A and Grant A (2010) _Ross and Wilson Anatomy and Physiology in Health and Illness_ , 11th edn. London: Churchill Livingstone.
# Chapter 8
Pulse oximetry
# Learning objectives
* Describe how a pulse oximeter works and produces a reading
* State the reasons for measuring and recording oxygen saturations
* List the conditions and factors that can affect readings
* Identify suitable sites for the probe
* Describe how to take and record an oxygen saturation reading
## Aim of this chapter
The aim of this chapter is to understand how pulse oximetry measures the oxygen saturation levels in blood, its significance and its application in practice.
## What is an oxygen saturation reading?
Pulse oximetry is a non-invasive method of measuring the oxygen saturation of arterial blood. Oxygen saturation is expressed as the percentage of haemoglobin (a component of red blood cells, see relevant anatomy and physiology) that is saturated with oxygen (Maddex 2009; Collins 2009).
## Who can perform the test?
Only individuals who are taught how to use the machine correctly and have obtained a clinical competency should undertake this clinical skill. Local guidelines and policies should also be followed. Abnormal findings, or a change in the patient's 'normal' reading, should be recorded and reported immediately to the nurse in charge.
## Reasons for recording an oxygen saturation level
* As part of lung function assessment in patients with long-term pulmonary (lung) disease such as COPD (Chronic Obstructive Pulmonary Disease) (Peate 2007).
* To monitor unstable cardiac conditions (e.g. cardiac failure or heart attack) (Maddex 2009).
* When transporting patients who are unwell and require oxygenation assessment (NICE 2007).
* To monitor the effectiveness of oxygen therapy or respiratory medication such as nebulisers (Higginson and Jones 2009; Maddex 2009; Dougherty and Lister 2011)
* Before, during and after procedures that may require sedation/anaesthesia, or that may cause potential respiratory depression (WHO 2008; Maddex 2009).
* To reduce the need for frequent arterial blood sampling in acute care (BTS/SIGN 2012).
When measuring the oxygen saturation levels in a patient, the overall condition and other vital signs should also be considered. This then allows review of the entire clinical presentation and not just the value of the reading in isolation. Preston and Flynn (2010) suggest that nurses should undertake observations such as pulse oximetry on an individual basis and use this to provide safe care for their patients whilst following NICE (2007) guidelines.
Pulse oximetry is useful for identifying patients who have a reduced level of oxygen in their blood (hypoxaemia). This is particularly relevant in acute settings where supplementary oxygen may be prescribed to correct this and prevent further deterioration of the patient's condition (Jevon and Ewens 2012; Collins 2009). Monitoring of pulse oximetry can help the healthcare practitioner to identify at an early stage those patients who are at risk of becoming cyanotic (Maddex 2009). Cyanosis leads to a bluish discolouration around the lips, mucous membranes of the mouth and at the nail beds. However, cyanosis is a late sign of hypoxia where oxygen saturation will have fallen to around 80–85% before discolouration occurs (Jevon and Ewens 2012; Casey 2011). It is also important that healthcare practitioners observe their patients and do not just take their oxygen saturations, as restlessness, confusion and agitation can be early indicators of clinical deterioration (Jevon and Ewens 2012). Reduced oxygen in arterial blood (hypoxaemia) can still occur without reduced oxygen to the skin and membranes (cyanosis). This occurs where the concentration of haemoglobin is low or the capillaries do not receive enough blood, sometimes referred to as not being well perfused (Jevon and Ewens 2012).
# Think about it
Have you seen a pulse oximeter used in your clinical area? If so can you remember why the oxygen saturation level was being measured for your patient?
## Relevant anatomy and physiology
Haemoglobin is the oxygen-carrying part of red blood cells (Dougherty and Lister 2011). The red blood cells are specifically designed by having a biconcave shape, which is a round curved shape, to maximise the available surface area. Each haemoglobin molecule has four oxygen binding sites. When oxygen binds with haemoglobin it is referred to as oxyhaemoglobin, and when all haemoglobin sites have oxygen molecules attached they are described as fully saturated (WHO 2011).
The amount of haemoglobin that combines with oxygen can be influenced further by various factors, including blood pH, temperature and carbon dioxide levels (WHO 2011). When certain levels of these substances are present, the oxygen will be at its optimum, that is the best possible level for oxygen uptake. This is known as the oxygen dissociation curve. The oxygen saturation reading is a measure of the percentage of haemoglobin molecules saturated with oxygen, but does not indicate the actual number of red blood cells (Dougherty and Lister 2011).
## Related aspects and terminology
* _Hypoxia_ : diminished oxygen in tissues.
* _Cyanosis_ : bluish or purple coloration of the skin and mucous membranes due to excess carbon dioxide and insufficient oxygen in the blood (Casey 2011).
* _Hypoxaemia_ : insufficient oxygenation of blood (Maddex 2009).
* _Haemoglobin_ : the pigment contained in red blood cells, which is used to carry oxygen (Collins 2009).
* _Oxyhaemoglobin_ : haemoglobin combined with oxygen molecules (Maddex 2009).
* _Plethysmographic waveform_ : the visual representation of the pulse wave on a pulse oximeter machine. This represents the quality of the pulse at the point where oxyhaemoglobin saturation is being measured (Jevon and Ewens 2012)
## The mechanics of pulse oximetry
The Beer–Lambert Law states that the concentration of an unknown solute dissolved in a solvent can be determined by light absorption (Chan et al. 2013). Therefore, pulse oximetry works on the principle that blood saturated with oxygen is a different colour from blood depleted of oxygen (Dougherty and Lister 2011). Thus, oxygen saturation can be estimated over a period of time by measuring the difference between light absorption of full and empty capillaries (Collins 2009). To assist this process, the pulse oximeter probe consists of two light-emitting diodes (one red and one infrared) on one side of the probe. These transmit red and infrared light through body tissue, usually a fingertip or ear lobe, to a photodetector on the other side of the probe (Collins 2009). The amount of light that is absorbed by the red blood cells allows the microprocessor in the machine to determine the oxygen saturation of the patient (Jevon and Ewens 2012). Figure 8.1 shows an adult pulse oximetry probe. A pulsatile flow is required and the oximeter calculates this over a number of pulses (Maddex 2009; Chan et al. 2013). Therefore a good blood flow to the vessels is required for an accurate reading.
**Figure 8.1** A pulse oximeter with probe in situ.
### Advantages of pulse oximetry
Previously the only method of measuring the concentration of arterial blood would have been arterial blood gases. Sampling arterial blood either involves drawing blood from an arterial line, a line that is inserted into the main vessel of the heart (often used in the intensive care unit), or sampling from an artery using a needle. Sampling from an artery is a highly skilled procedure, mostly carried out by medical staff and nurses with additional training; carries complications of increased risk of infection and bruising; and is often painful (Maddex and Valler-Jones 2009). A sample from an arterial line is pain free for the patient but also carries the risk of infection. It is not expected that a healthcare assistant would undertake this procedure, but check local policy. The sample can either be sent to a lab for analysis or be tested in specialist areas where blood gas analysers are located. If the machine is within a unit or clinical area, it requires personnel to be trained in both its use and the interpretation of its findings. Therefore it can be seen that pulse oximetry is quick, generally reliable and cost effective and can be undertaken by a range of suitably trained healthcare personnel.
### Limitations of pulse oximetry
As pulse oximetry measures only haemoglobin oxygen saturation and not haemoglobin concentration, the patient can still have a depleted amount of oxygen (hypoxia) despite a 'normal' pulse oximetry reading (Jevon and Ewens 2012). It should also be remembered that pulse oximetry does not provide an indication of the adequacy of ventilation, carbon dioxide retention, partial pressure of oxygen or respiratory rate (Casey 2011; Collins 2009; WHO 2011). However, it is still an invaluable monitoring tool in a variety of clinical settings as long as its uses and limitations are fully understood (Maddox 2009). The accuracy of the pulse oximiter is dependent upon the frequency of calibration, usually within +/- 2% for saturations >90%, with the accuracy falling at saturation levels lover than 80% (Casey 2011).
## Equipment
Pulse oximeters are either non-invasive units or are fully integrated into a patient monitoring system, such as those found in critical care areas or electronic blood pressure machines. Some may record the pulse rate and this may be seen visually as a waveform. A pulse oximeter should not be used to take a pulse because the reading would give the rate of the pulse only and would not give important information such as the volume and rhythm. Therefore, use of a pulse oximeter is predominantly to measure haemoglobin oxygen saturation (WHO 2011).
## Normal readings
Normal levels are usually between 95 and 100%, but depend on individual patients (Dougherty and Lister 2011; Collins 2009; WHO 2011). However, in the acutely ill patient this may vary between 94 and 98%, while a fall below 90% is classed as a clinical emergency (Jevon and Ewens 2012; WHO 2011). Alarms can be set depending on individual patients' clinical presentation, but guidance should be sought as to both the levels that should be set and whether local policy allows healthcare assistants to do this. It is essential always to record the oxygen therapy being received by the patient together with the readings, and to the clinical condition of the patient. A sustained trend of falling oxygen saturation levels is clinically important and should always be reported promptly (Dougherty and Lister 2011). Some conditions can affect readings, so the patient's medical history should be considered before carrying out the procedure (see Box 8.1 for possible factors).
# Box 8.1 Factors affecting oxygen saturation readings
## Poor circulation
This can be due to peripheral vascular disease or vasoconstriction (narrowing of blood vessels), low temperature (hypothermia) or low blood pressure (hypotension) (Dougherty and Lister 2011). All can give low readings due to the reduced blood flow. This results in a decreased pulsatile flow which is necessary for the pulse oximeter to calculate the reading (Preston and Flynn 2010). Arterial constriction or shock can also cause readings to be low (Chan et al. 2013). To ensure accurate readings it is recommended that the probe be placed where there is a good blood flow.
## Carbon monoxide
The presence of carbon monoxide (CO) in blood can give falsely normal readings because the CO combines with O2 to form carboxyhaemoglobin. This substance is bright red, similar to oxyhaemoglobin; as both compounds have a similar absorbence, this results in the pulse oximeter being unable to distinguish between oxygen and carbon monoxide in the red blood cells providing a 'normal' reading. This can be a result of expose to gas, cigarette smoking, exhaust fumes or exposure to smoke from house fires (Chan et al. 2013; Casey 2011). In these instances pulse oximetry should not be relied upon (Jevon and Ewens 2012).
## Tricuspid valve incompetence (heart valve failure)
Inaccurate readings are obtained due to the machine not being able to differentiate between arteriolar and venous pulsation (Casey 2011). Further advice should be sought as to whether pulse oximetry should be used.
## Anaemia
High oxygen saturation can be recorded but inadequate oxygen is actually perfusing (getting into) the tissues due to the reduced number of haemoglobin molecules (Chan et al. 2013; Dougherty and Lister 2011). Advice should be sought to identify the appropriateness of pulse oximetry for these patients.
## Atrial fibrillation
This is a fast heartbeat from the top chamber of the heart that interferes with the pulsatile signal (Maddex 2009). If this is an intermittent problem it may still be possible to obtain accurate readings, so further advice should be sought.
## Parkinson's disease or seizures
An incorrect reading may be obtained due to the tremor associated with Parkinson's disease or the irregular movement caused by seizures or shivering (Dougherty and Lister 2011). Both conditions can cause interference and artefacts (disturbance) and therefore give inaccurate readings. However Chan et al. (2013) suggest that newer pulse oximeters have improved processing and can take account of movement and give accurate readings.
## Altered red blood cell shape
As mentioned earlier, blood cells are biconcave in shape to promote oxygen uptake. Sickle cell disease and some medications (e.g. anaesthetic agents) alter the shape of red blood cells and will alter readings (Casey 2011; Chan et al. 2013). Therefore caution and further advice should be sought both in the interpretation of these readings and as to whether pulse oximetry is appropriate for these patients.
## Using a pulse oximeter
Before performing the skill, ensure that you have received approved training and undertaken supervised practice in line with local policy. It is also advisable to consult the manufacturer's directions for the make and model in use (Dougherty and Lister 2011).
It is essential that the correct cable and probe be used with the appropriate machine (for accurate recordings. The machine should have been serviced in the past year (a PAT or medical devices sticker will be in place with a date), should be visibly clean and, when switched on successfully, should go through a series of self-tests with no error codes (see 'Common problems'). If an error code or abnormality is noted, report the fault and use another machine. Jevon and Ewens (2012) suggest that if there are problems getting a reliable trace or reading that the skin at the site where the probe is to be placed could be rubbed to improve circulation, using a different site to place the probe or changing the probe or the pulse oximiter itself for a different machine.
# Think about it
Set up a pulse oximetry machine on yourself, rotating the site and type of probe where possible.
What reading would you expect to get and why?
### Pulse oximetry probes
There are multiple sites where a probe can be placed, which depend on both the probe being used and the individual patient. The correct probe and its size for the site is essential in both children and adults. For infants, probes that attach to the palms and soles of the feet are available, and in a study by Das et al. (2010) it was found that in children with cyanotic heart disease the sensor on the sole of the foot is the most accurate of all probes.
In adults the probe is dependent on the site intended by the manufacturer, but possibilities include probes suitable for fingers or toes, and specialist ear probes. The cable should also be loose, so movement will not disrupt the sensor, and the clip should be attached to the shoulder of the patient. Finally, a headband is also available and this requires the cable to be looped around an ear and tucked in. This may not be available in every clinical area. To reduce the risk of hospital acquired infection, single-patient use probes are available in some clinical areas; however, the reusable probe has the advantage of being quick to use and cost effective (Chan et al. 2012).
If the pulse oximetry reading requires continuous monitoring, the patient's preference may be taken into account or, in the case of confused or agitated patients, a site that is out of vision may be best.
Whatever site is chosen, only an appropriate probe for the machine being used should be in place. Tape, to hold the probe in place, should not be used as this can cause pressure or thermal (heat) damage to the extremity (Dougherty and Lister 2011; Jevon and Ewens 2012). Where the site is used for continuous monitoring this should be checked and rotated at least 2-hourly to prevent any pressure damage resulting from prolonged use at any one site (MRHA 2010). Where the patient is unable to flex the fingers voluntarily, this may result in stiffness, and the site may need to be changed more frequently (Jevon and Ewens 2012).
The probe should be visually examined before use to ensure that it is not broken or dirty (Collins 2009). Replace the probe if it is faulty and always refer to the manufacturer's recommendations for cleaning. If it is proving difficult to obtain a trace, warm and rub the skin to improve the circulation (Jevon and Ewens 2012). Table 8.1 describes the procedure for recording an oxygen saturation level using a pulse oximeter.
**Table 8.1** Procedure for recording an oxygen saturation level
**Action** | **Rationale**
---|---
1. Explain the procedure to the patient and gain verbal consent. Document | The patient will fully understand the procedure and consent to participate
2. Check that the equipment has been serviced, is in good working order and clean, and has designated accessories (lead/probe) | The machine should be serviced as per local policy to ensure that an accurate reading is obtained
A clean probe will prevent cross-infection
Correct accessories essential for accurate readings
3. Ensure the patient is warm and comfortable | If the patient is cold they could have decreased peripheral blood flow that can reduce blood flow (and give a low reading)
If the patient is shivering this can interfere with the signal
If the patient is comfortable they will be more relaxed, especially if having continuous monitoring (Dougherty and Lister 2011)
4. Wash hands and put on a clean apron (Dougherty and Lister 2011) | Prevent cross-infection
5. Select a suitable site for the probe and place as per manufacturer's instructions | Ensures accuracy of reading
6. Switch the machine on and check function; should beep with each detected pulse or waveform (Dougherty and Lister 2011) | Accurate pulse detection
Shows the patient that the procedure is painless and checks the machine
7. Record both the oxygen therapy (where applicable) and SpO2 reading – reporting any abnormal readings. This may be a change for the patient or out with 'normal' limits | To provide a legal record of the measurement
The nurse in charge may want to reset alarms/parameters to identify changes in recorded saturation levels (Collins 2009). If set incorrectly, alarms can be a nuisance if constantly activated
8. Remove the probe, if using for routine or intermittent observation (and when appropriate for continuous monitoring)
When continuously monitoring, ensure that cable is positioned as safely as possible and probe secured if necessary
Return to check probe is not causing any complications. Rotate site every 2 hours | Patient comfort
For health and safety round the bed space
To prevent damage to the patients skin (Jevon and Ewens 2012)
9. Clean the equipment, in line with local policy
Return to equipment store; plug in to recharge if appropriate. | Prevent cross-infection
To recharge the machine ready for use
## Documentation
Ensure that any oxygen therapy that the patient is receiving is recorded together with the pulse oximetry reading. This can allow medical staff to make decisions about the continued use of supplementary oxygen therapy as prolonged unnecessary use of oxygen can be harmful. Likewise, avoid taking oxygen saturation levels when the patient has just been suctioned (a catheter inserted into the windpipe to remove secretions), because this will give a false reading (see Chapter 9).
Pulse oximetry recordings may be documented in the patient's case notes if the patient is in the community or on TPR/MEWS/NEWS charts if in hospital.
## Common problems
Errors in pulse oximetry readings can be due to many different variables, some of which can be reduced to promote a more accurate trace. They have been split into three different areas, namely those caused by light transmission, pulse detection and actual use of the equipment.
### Light transmission/absorption
As mentioned previously and shown in Figure 8.1, the finger probe consists of two parts, with one side receiving the light source and the other being a photodetector. If bright light, either artificial or sunlight, is picked up readings can be affected (WHO 2011). If the reading is an intermittent recording (i.e. not continuously in place), consider closing a curtain or switching off the fluorescent lights until the reading has been taken. In instances where the light is necessary for treatment, for example phototherapy to treat jaundiced babies or in operating theatres, the probe should be covered to ensure accurate readings (WHO 2011; Fouzas et al. 2011). Nail varnish also causes problems with transmission and patients who have nail varnish in place should be asked if they would mind removing it to obtain accurate readings (Dougherty and Lister 2011). There is some evidence to suggest that false nails interfere with the light source and may provide inaccurate readings (Fouzas et al. 2011).
Other factors that affect the transmission of light, and cause low readings, include the presence of dried blood on the skin, substances such as engine oil on the hands or heavily nicotine stained fingers (Collins 2009; Jevon and Ewens 2012). Chan et al. (2013) noted that intravenous dyes used in imaging affect light transmission, and individuals using pulse oximetry should seek advice about how long these agents are active for to enable measurements to be taken when they are no longer active.
### Pulse detection
Jevon and Ewens (2011) and Dougherty and Lister (2011) discuss the fact that movement, including shivering, may cause interference in the signal or the probe to become dislodged. In some instances another site may produce a better trace, for example an ear or toe, and for intermittent readings supporting the probe in place may be beneficial.
### Equipment use
As with all pieces of equipment, the pulse oximeter should have been serviced as recommended by the manufacturer and local policy. When the device is switched on it should perform a self-test and not display any error codes; this ensures the accuracy and reliability of the machine (Maddex 2009).
If the machine is dropped or broken, as with other pieces of equipment, suitably qualified staff should check it – local policy will dictate whether this is an in-house department or the manufacturer. The correct accessories, for example probes, should be used for each specific machine and the accessories checked to ensure that they are clean and for signs of damage.
Measuring oxygen saturation levels on the same arm as a BP cuff or venous line can disrupt the machine's ability to measure the pulse as the flow of blood allows the pulse oximiter to determine its reading (Jevon and Ewens 2012; Dougherty and Lister 2011). The pulse reading should match the patient's heart rate; if this is not the case it may indicate that not all pulsations are being detected and another machine should be sought as this can affect the accuracy of the reading
## Summary
Pulse oximetry, when used appropriately, is a good way of accurately measuring oxygen saturation levels. Where the role of the healthcare assistant involves taking these readings it is essential that competency based training is undertaken in accordance with local policies and procedures for the specific device that is in use. Table 8.2 provides a competency framework for recording SpO2 levels.
**Table 8.2** Practical assessment form: competency framework for recording SpO2.
**Steps** | **First assessment/reassessment/demonstration** | **Date/competent signature**
---|---|---
| Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
Recording oxygen saturation levels ( _S_ pO2) | | | | | |
1. **1.** State normal range for _S_ pO2 as a percentage
2. **2.** State what oxygen saturation levels actually measure and the limitations
3. **3.** Define the terms cyanosis and hypoxia
4. **4.** State different sites for recording oxygen saturation
5. **5.** List common causes of inaccurate recordings, caused by disease processes and the equipment
6. **6.** Describe different types of models in use
7. **7.** Describe appropriate sites and the reasons for these choices
8. **8.** Describe how you would prepare a patient for obtaining an oxygen saturation reading and gaining consent
9. **9.** Describe the correct procedure for recording oxygen saturation
10. **10.** Describe safe disposal and cleaning of the equipment following use
11. **11.** Identify and justify the use of documentation
12. **12.** State when to ask for assistance/report findings
Supervisors/Assessor(s):
# Case study 8.1
Mrs Semple is a frail 86-year-old woman who has been admitted to hospital with hypothermia (low temperature). She is shivering and requires her oxygen saturation levels to be monitored.
What equipment would you consider for her and what factors would affect your decision? What might affect the readings of the pulse oximeter?
Describe some of the reassurances and special precautions that should be taken for her.
# Case study 8.2
Baby Ben is aged 8 months and has been admitted with a respiratory problem (suspected pneumonia). He is to be started on a pulse oximeter for continuous monitoring.
What factors affect the equipment and site choices for him? What special precautions should also be taken for him to ensure that no harm comes to him during his treatment?
# Self-assessment
**Assessment** | **Aspects** | **Achieved ✓**
---|---|---
Patient | _Have you considered all aspects of this section?_ |
| The purpose of the red and infrared lights used to measure oxygen saturation |
| The diseases that can affect pulse oximetry readings |
| Advantages and disadvantages of pulse oximetry |
| The indications for pulse oximetry use |
Procedure | _Have you considered all aspects of this section?_ | **✓**
| What the normal limits for pulse oximetry are |
| The possible sites and types of probe available |
| Documentation of readings |
## References
1. BTS/SIGN (2012) British Guidelines on the Management of Asthma. Available at: <http://www.sign.ac.uk/pdf/sign101.pdf> (last accessed 20 May 2013).
2. Casey G (2011) Pulse oximetry: What are we really measuring? _Kai Tiaki Nursing New Zealand_ **17** (3): 24–29.
3. Chan E, Chan M and Chan M (2013) Pulse oximetry: Understanding its basic principles facilitates appreciation of its limitations. _Respiratory Medicine_ **107** : 789–799.
4. Collins T (2009) Pulse oximetry. In: Smith S, Price A and Challiner A (eds) _Ward-Based Critical Care_. M&K Publishing: Keswick.
5. Das J, Aggarwal A and Aggarwal N (2010) Pulse oximeter accuracy and precision at five different sensor locations in infants and children with cyanotic heart disease. _Indian Journal of Anaesthesiology_ **54** (6): 531–534.
6. Dougherty L and Lister S (eds) (2011) _The Royal Marsden Hospital Manual of Clinical Nursing Procedures_ , 8th edn. Oxford: Blackwell Publishing.
7. Fouzas S, Pirifitis K and Anthracopoulos M (2011) Pulse oximetry in paediatric practice. _Paediatrics_ **128** : 740–752.
8. Higginson R and Jones B (2009) Respiratory assessment in critically ill patients: airway and breathing. _British Journal of Nursing_ **18** (8): 456–461.
9. Jevon P and Ewens B (2012) _Monitoring the Critically Ill Patient_ , 3rd edn. Oxford: Blackwell Publishing.
10. Maddex S (2009) Measuring vital signs. In: Baillie L (ed.) _Developing Practical Adult Nursing Skills_. London: Hodder Arnold, Chapter 4.
11. Maddex S and Valler-Jones T (2009) Assessing physical health and responding to sudden deterioration. In: Baillie L (ed.) _Developing Practical Skills_ , 3rd edn. London: Hodder Arnold.
12. MRHA (2010) _Top Tips for Pulse Oximetry_. MRHA: London.
13. NICE (2007) _Acutely Ill Patients in Hospital_. London: NICE.
14. Pete I (2007) Caring for the person with chronic obstructive pulmonary disease, part 2. _British Journal of Healthcare Assistants_ **4** (7): 347–349.
15. Preston R and Flynn D (2010) Observations in acute care: evidence -based approach to patient safety. _British Journal of Nursing_ : doi 10.12968/bjon.2010.19.7.47446.
16. WHO (2008) Surgical Safety Checklist. Available at: <http://who.int/patientsafety/safesurgery/ss_checklist/en/> (accessed 20 May 2013).
17. WHO (2011) _Pulse Oximetry Training Manual_. WHO: Geneva.
# Chapter 9
Respiratory care
# Learning objectives
* Discuss the anatomy and physiology of respiration
* Identify the reasons for recording a respiratory rate and accurately perform this skill
* List the reasons for measuring peak flow and discuss how to safely carry out the procedure
* Discuss suctioning techniques and safety aspects
* List the terms related to respiratory care
* Discuss the role of the healthcare assistant in respiratory care
## Aim of this chapter
The aim of this chapter is to identify the anatomy and physiology relating to respiration, and explore the recording of a respiratory rate and a peak flow. Suctioning techniques will also be discussed.
## What is respiratory care?
The respiratory system is made up of the nose, pharynx, larynx, trachea, bronchi and lungs (Tortora and Derrickson 2011) (Figure 9.1).
**Figure 9.1** The respiratory system.
If there is a problem at any point in the system this may result in the patient feeling breathless. This chapter describes the role of a healthcare assistant in assessing and assisting a breathless patient through the observation, recording and reporting of respiratory rate and/or peak flow.
The treatments commonly associated with respiratory care, such as oxygen therapy or nebulisers, are explored briefly in Chapter 15; however, this may not be part of a healthcare assistant's accepted role and your workplace policy should be checked.
## Relevant anatomy and physiology
The main function of the respiratory system is to supply the body with oxygen and remove carbon dioxide through the process of inspiration (breathing in) and expiration (breathing out) (Maddex 2009).
The lungs are the organs of respiration and are situated in the thoracic cavity. Therefore breathing can be defined as air moving in and out of the lungs and their associated structures. Air enters through the mouth and nose, and passes via the pharynx (throat), larynx (voice box), trachea (windpipe), bronchi and bronchioles into the air sacs called alveoli (Tortora and Derrickson 2011). Gas exchange takes place in the alveoli, which have been likened to a bunch of grapes. Their surface area is approximately 70 m2 in an adult, and if spread out flat are equivalent to the surface area of a football pitch (Tortora and Derrickson 2011). The respiratory system is in two sections: the upper respiratory system refers to the nose, pharynx and associated structures; whereas the lower respiratory system refers to the larynx, trachea, bronchi and lungs (Tortora and Derrickson 2011).
## Upper respiratory system
The nose has two parts: external and internal (Tortora and Derrickson 2011):
1. **1.** External: a supporting framework of bone and cartilage, covered with muscle and skin and lined by mucous membrane.
2. **2.** Internal: the nasal cavity is split by the nasal septum, which divides into a right and left side.
When air enters the nostrils it passes through the vestibule (just inside the nostrils), which is lined by skin, containing coarse hairs that filter out large dust particles. Air that is passed through the nose is filtered, but also warmed and moistened (humidified).
### The pharynx (throat)
This is a funnel-shaped tube about 13 cm long, which lies behind the nasal and oral cavity, above the larynx and just in front of the cervical vertebrae. The pharynx functions as a passageway for air and food, provides a resonating chamber for speech sounds, and houses the tonsils, which help eliminate foreign invaders (Tortora and Derrickson 2011).
## Lower respiratory system
### Larynx (voice box)
This is a short passageway that connects the pharynx with the trachea, and the wall of the larynx is made of cartilage (Tortora and Derrickson 2011). When small particles, such as dust, smoke, food or liquids, pass into the larynx a cough reflex occurs to expel the material.
Normally, the epiglottis (a large leaf-shaped piece of elastic cartilage) is able to move up and down like a trap door (leaf portion), so during swallowing the larynx rises and allows the free edge of the epiglottis to move up and down and form a lid; therefore liquids and foods are routed into the oesophagus and kept out of the larynx and lungs.
### Trachea (windpipe)
This is a tubular passage for air, about 12 cm long and 2.5 cm in width (Tortora and Derrickson 2011). It is found in front of the oesophagus, and extends from the larynx to the bronchi, which then split into a right and left primary bronchus.
### Bronchi
When the trachea divides, a right primary bronchus (windpipe) goes into the right lung and a left primary bronchus goes into the left lung. The right main bronchus is more vertical, shorter and wider than the left, so any aspirated object, for example foodstuffs, is more likely to enter and lodge in the right primary bronchus. On entering the lungs, the primary bronchi divide to form smaller bronchi. This extensive branching from the trachea resembles a tree trunk with its branches and is commonly called the bronchial tree (Tortora and Derrickson 2011).
### Lungs
These are a pair of cone-shaped organs lying in the thoracic (chest) cavity, separated from each other by the heart. The lungs have two layers of serous membranes called the pleural membrane which encloses and protects each lung. Between these membranes is a small space called the pleural cavity that contains a lubricating fluid secreted by the membranes. This fluid reduces friction between the membranes. Each lung is subdivided into lobes. The right lung has three lobes while the left lung has two (Tortora and Derrickson 2011).
### The alveoli and gaseous exchange
Within the lungs are alveoli where gaseous exchange takes place; it is estimated that the lungs contain 300 million alveoli. A chemical called surfactant is secreted within the alveoli which prevents the surfaces within them from sticking to each other during the expiration phase (Clancy and McVicar 2009).
Breathing is regulated in the brain and has both conscious and unconscious control. Conscious control is when a patient takes an extra breath or a deeper inspiration, whereas most breathing is unconscious – we just do it without thought. The regulation of breathing is managed by the respiratory centre, which responds to the gas levels in the blood, usually oxygen and carbon dioxide and also hydrogen. The centre monitors gas levels, and in normal respiration is driven by the increase in the carbon dioxide level, which triggers nerve impulses down to the respiratory muscles and stimulates respiration (Tortora and Derrickson 2011).
In patients with a chronic lung disease, for example chronic obstructive pulmonary disease (COPD), over time the body adapts to a constantly elevated level of carbon dioxide (CO2) and therefore the respiratory centre switches to respond to a drop in the oxygen (O2) level. This is one reason why any acutely ill respiratory patient needs careful observation and monitoring of blood gases, and accurately and carefully titrated (dosed) O2 therapy. Too high a level of O2 would remove the respiratory drive in these patients, when the respiratory centre fails to trigger the respiratory muscles and the patient stops breathing (Clancy and McVicar 2009).
To aid breathing we have both principle and accessory muscles of respiration (Figure 9.2). The principle muscles consist of the diaphragm situated under the lungs and the intercostal muscles between the ribs. The accessory muscles consist of the abdominal muscles and the muscles above the ribcage into the shoulder and neck (Clancy and McVicar 2009). It is the expansion of these muscles that help breathless patients make their breathing more effective (Clancy and McVicar).
**Figure 9.2** Muscles of respiration.
Breathing can be affected by many factors: disease – infection, lung cancer, asthma; emotional state – stress, fear leading to hyperventilation (overbreathing); position – cramped or slouched will restrict breathing; trauma – accident to the brain or chest, or surgery; and exercise.
## Recording a respiratory rate
### Why and when a respiratory rate is observed, assessed and recorded
* On admission and before procedures – to provide a baseline record to compare later recordings (NICE 2007).
* When a patient's condition changes, for example feeling unwell, becomes breathless, complaining of pain or injury.
* To monitor response to treatments/medications, for example oxygen, morphine, inhalers.
* Before specified medications for baseline, for example blood administration.
* To monitor changes in oxygenation or respiration, for example someone with asthma.
### What do you observe?
Massey and Meredith (2010), and Dougherty and Lister (2011) identify the importance of observing rate, depth, pattern, sound, regularity/rhythm and colour when assessing respirations.
#### Rate
When assessing the respiratory rate, you need to know the expected normal rate for a person's age group (Dougherty and Lister 2011; Cook and Montgomery 2010). The baseline rate on admission or before procedures/medications will allow comparison. However, the respiratory rate varies according to age, size (build) and gender, and other demands, such as exercise; discussed in more detail below (Wild and Peate 2012).
The normal adult respiratory rate is 12–18 breaths/min (Dougherty and Lister 2011), while Maddex (2009) suggests this can vary with age, gender and size (Table 9.1).
**Table 9.1** Children's respiratory rate and age
**Age (years)** | **Respiratory rate (breaths/min)**
---|---
Newborn | 30–60
<1 | 30–45
1–2 | 25–35
2–5 | 25–30
5–12 | 20–25
>12 | 15–25
Adapted from Syers (2008); Cook and Montgomery (2010).
Stress, fear, anxiety and exercise will increase the respiratory rate and this is normal. Let us consider a patient on admission; they may be anxious, have rushed to get to the appointment on time, or be in pain, and these factors may have affected the respiratory rate. Therefore this recording may not be a true baseline.
Both high and low respiratory rate should raise concern and be recorded and reported immediately to the nurse in charge (Wild and Peate 2012). The nurse should be aware of normal and abnormal ranges in order to act on their findings and ensure patient safety. A raised respiratory rate (tachypnoea) in an adult would therefore be over 20 breaths/min and a decreased respiratory rate (bradypnoea) is considered if the rate is below 8–10 breaths/min (Massey and Meredith 2010; Dougherty and Lister 2011).
We have noted that some factors, such as stress and exercise, can increase the rate, however some respirator conditions such as asthma, COPD and cardiac tamponade can also cause patients to have an increased respiratory rate (Massey and Meredith 2010; Wild and Peate 2012).
Bradypnoea can be caused by certain conditions, such as a brain tumour, or treatments, like morphine, which are known to depress (reduce) the respiratory rate and this is the reason why a patient newly started on any opioid (i.e. morphine) will have their respiration monitored. A rate of 10 or below must always be reported promptly (Massey and Meredith 2010; Wild and Peate 2012).
# Think about it
Mrs Winifred Johnson is 57 years old and has been admitted for a bronchoscopy to investigate her persistent cough.
You are asked to record her observations and you measure her respiratory rate at 30 breaths/min.
What factors might you need to consider?
What action might you take?
#### Depth
Observation of the depth of breathing is useful as this can give an indication of ventilation (Maddex 2009).
Deep rapid breaths (hyperventilation) are often associated with anxiety or panic attacks. If prolonged, a patient will start to feel dizzy and faint; this is a result of a drop in the CO2 level, and you can help by encouraging the patient to breathe slowly in and out of a paper bag (this allows the patient to re-breathe the exhaled CO2 and so stabilises them). Slow shallow breaths (hypoventilation) can occur with some drugs, such as morphine, and will also lead to poor gas exchange and insufficient oxygen. Dougherty and Lister (2011) state that normal breathing is effortless, automatic and regular. The depth is the volume of air moving in with each respiration, and in an adult this is about 500 ml (Maddex 2009).
#### Pattern
As noted before, normal breathing is effortless, so, if a patient is having difficulty breathing (dyspnoea), you might observe irregular, noisy breaths and also possibly the use of the accessory muscles of respiration (neck and abdominal muscles). Changes in the pattern of respiration are often found in disorders of the respiratory centre in the brain (Dougherty and Lister (2011).
Therefore, assessment should include the pattern of breathing, for example mouth breathing, when a patient tries to gulp air in. This happens because there is less resistance to air flow through the mouth than the nose: noses can often block, as with a common cold, but this can cause the mouth to become dry and so oral hygiene is essential to help keep the mouth moist.
People with asthma, caused by narrowing of the airways, cannot 'shift' air and in some cases you might observe minimal movement of breathing, that is little rise or fall in the chest, which is serious and must be reported promptly. In general, you would observe the chest rise and fall to measure the respiratory rate and, to prevent a patient altering the respiratory rate, you can continue to hold the wrist as though still counting the radial pulse rate. This ensures that the respiratory rate is not altered consciously.
#### Sound
As noted earlier, breathing should be quiet, so, if it can be heard, there may be a problem (Maddex 2009).
A loud harsh, almost rasping sound (stridor), usually heard on inspiration, is frequently due to a partial or blocked larynx (airway) from injury, foreign body or illness, for example a tumour, and must be reported immediately (Wild and Peate 2012).
A wheeze, characterised by a noisy, high-pitched sound (Maddex 2009), usually on expiration, is usually found in people with asthma (during an asthmatic attack) and is caused by swelling, which leads to narrowing of the airways. Patients with chronic bronchitis and emphysema may also have a wheeze.
A 'rattly' chest is caused by the presence of fluid (e.g. sputum, blood) in the upper airway. Snoring, especially in the unconscious patient, may be due to a partial obstruction of the airway by the tongue airway (Wild and Peate 2012). Prompt checking and action are required here. Finally whooping cough causes a distinctive whoop sound, usually when coughing, and is most commonly found in children.
#### Regularity/rhythm
This might be considered similar to pattern, so breathing should be regular and rhythmic and any period without breathing (apnoea) must be reported immediately. Massey and Meredith (2010) and Wild and Peate (2012) describe Cheyne–Stokes respirations as a 'pattern' of breathing where the patient has periods of apnoea alternating with periods of overbreathing (hyperpnoea); it is often associated with left ventricular failure (heart failure), brain injury or the latter stages of dying.
#### Colour
As well as assessing rate, depth, pattern, sound and regularity, you should also be observing the patient's colour, to identify any abnormality. If patients are not getting enough oxygen they become cyanosed, which manifests as a bluish dusky colour of the mucous membranes, and can be observed on the skin and nailbeds. It is often most noticeable around the lips, earlobes, mouth and fingertips. In dark-skinned patients it is most noticeable in the lips, the mucous membranes of the mouth and nailbeds, which become dusky in colour (Wild and Peate 2012). This is also why we ask patients to remove makeup, especially before procedures such as surgery. The patient's condition will probably be poor by the time that you observe cyanosis, but it is one aspect that you should always consider whenever checking a patient's pulse and respiratory rate.
## How to measure and record a respiratory rate accurately
Although gaining consent is an important part of any procedure, it is important not to let your patient know when you are actually counting their respirations. This can affect the accuracy of the rate that is recorded, as often breathing patterns alter when people are being watched (Smith and Roberts 2011; Nicol et al. 2012). In order to count a patient's respirations they should be comfortable and in a position that is easy to count the rise and fall of their chest. Respiratory rate should be counted over a full minute and the use of a watch with a second hand will improve the accuracy of this (Nicol et al. 2012). How often you record will depend on the patient's condition, treatment and monitoring requirements (NICE 2007). A patient with acute asthma might need the respiratory rate measured every 15 minutes, so always follow your local policies and practice. A patient who is stable will have measurements gradually reduced, maybe from 4-hourly to twice a day, which is a minimum amount in an acute area. Respiratory measurement in community settings is likely to be monitored less frequently and should be based on individual patient's needs. Any changes, however, would need to be quickly monitored, recorded and reported.
Respiratory rate is a measurement that simply records the number of times a person breathes in a minute. However, measuring and recording a peak expiratory flow rate (PEFR) can give valuable information about the patient's lung capacity.
## Measuring and recording a peak expiratory flow rate
This is achieved by use of a meter called a peak flow meter; this simple device can be a very useful tool to monitor a patient's maximum expiratory force, and is very commonly used for monitoring asthma. It provides a simple, measurable, repeatable and objective measurement of airway function (Dougherty and Lister 2011).
The peak flow measures, in litres per minute, the maximum flow rate on forced expiration that a patient can blow out when starting from full inhalation. This measure allows monitoring of a patient with any lung disease; it is easy, quick and cheap, but technique is crucial to ensure accuracy (Maddex and Valler-Jones 2009; Dougherty and Lister 2011). It allows monitoring of ongoing treatments and can be very useful for someone who has difficulty recognising that their condition is worsening, for example asthma. Peak flow is also used for children and, in the same way as adults, gender and height considerations will affect the readings (Ford et al. 2010; Lewis 2008). Due to age and understanding considerations, the nurse must always be certain that the child has understood the instructions to ensure a reliable reading.
To measure a peak flow, a meter is commonly used (Figure 9.3) and this comes with a disposable mouthpiece for each patient. Peak flow meters can be dispensed on prescription for home monitoring; in clinics or hospitals some may be used for multiple patients, but are always used with a disposable one-way mouthpiece. For infection control purposes, always follow your local policy regarding cleaning the device between patients (Dougherty and Lister 2011).
**Figure 9.3** Peak flow meter with disposable one-way mouthpiece. Source: Photograph by I Lavery.
The patient should be sitting or standing upright, to allow full chest expansion. An exploration of the differences in measurements of various seating arrangements (lying, sitting and standing) determined that patients were able to produce higher scores when standing. However it should be noted that in acute areas it is not always possible for patients to stand because of their general condition (Wallace et al. 2013). Dougherty and Lister (2011) state that the patient must first be given information about the procedure so they can give consent and understand it. This is important to encourage compliance and prevents misunderstanding to ensure an accurate reading is obtained. With children, Lewis (2008) suggests that the nurse can demonstrate the technique to the patient first, and this technique may also be useful with adults whose technique is poor. Booker (2007) proposes that the nurse demonstrate the technique first to help the patient understand the procedure. The nurse must ensure that their hands are washed and an apron is put on before assembling the meter to follow infection control procedures. Box 1 outlines the technical aspects.
The frequency will depend on each patient's condition. For maintenance (to monitor ongoing treatment), the patient may measure the peak flow once in the morning, or in some cases twice daily and so also record an evening peak flow.
# Box 9.1 Technique
* Patient holds the meter level, and ensures their fingers don't obstruct the scale.
* Flow indicator is set to zero/lowest reading on the scale.
* With the mouthpiece fitted securely, the patient should take a deep breath, clamp the lips tightly round the mouthpiece and then blow out as hard and fast as possible, like blowing out candles.
* Check the flow indicator position and record the score, for example 370 l/min.
* It is recommended to do the best of three, so a further two attempts are made, ensuring that indicator is zeroed each time, then recording the best score
Adapted from Dougherty and Lister (2011); Nicol et al. (2012); Maddex and Valler-Jones (2009).
During any acute episode of illness the frequency would increase, so that any treatments and their effectiveness, such as nebuliser therapy, would be monitored. In some cases measurements are taken pre-treatment, for example for asthma and nebuliser treatment, and then again 30 min after treatment (this monitors the effectiveness of any treatment). However it should also be noted that for any patient who cannot talk in full sentences or for whom use of the device will cause exacerbation of their condition, peak flow should not be recorded as this puts excessive strain on the respiratory system when already stressed (BTS/SIGN 2011; Dougherty and Lister 2011)
### Normal peak flow measure
A peak flow measurement will vary depending on gender, age and height (Dougherty and Lister 2011):
* Gender: adults usually achieve 400–700 l/min, but males achieve higher readings and elderly women may range from 300 l/min.
* Age: children would be lower, and height is a factor in normal ranges. The normal range in children is 100–400 l/min.
* Height: this increases the lung capacity and so increases the peak flow scoring.
Other variations are due to timings; morning readings tend to be lower, with highest readings usually in the early evening, hence the usual twice daily readings for people with asthma to monitor and compare scores. Scores are plotted and trends can be spotted early, as one lower score may not be meaningful. However, it is best to report this remembering that other recordings will be monitored as well, such as temperature, pulse and blood pressure, and these can support findings. In people with asthma the pulse rate will increase, and if due to an infection they may also have a raised temperature.
Other circumstances can affect readings, for example cold air, animal hair acting as a trigger (allergies); and again, by keeping a record, these trends can be observed and identified.
Regular monitoring can therefore allow the patient to manage their breathing/condition, such as asthma, and respond quickly to any deterioration:
* If the rate falls below 80% of individual's best level, then refer to doctor as they would likely increase preventative treatment, such as an inhaler.
* If the reading falls below 50% of their usual reading, alert medical staff immediately (BTS/SIGN 2011).
Again, if in doubt refer to a professional colleague. Ask yourself – was the patient relaxed and rested? If the patient has just got back from the toilet, with maybe more demands on their breathing, they may be tired resulting in a lower reading, so wait 5 minutes and repeat.
# Think about it
Jenny Wilkinson is a 15 year old with asthma; you are supervising her peak flow measurement and notice that her technique is poor.
Explain how this might affect her readings and what advice you might give her to help improve her technique.
## Performing suctioning
Suctioning techniques are now considered; depending on your local policy it may be an accepted role with supervised training _, so please check before undertaking any aspect of a suctioning role_.
Dixon (2010) and Nicol et al. (2012) discuss methods of suctioning relevant to this book: oropharyngeal and nasopharyngeal suctioning.
### Oropharyngeal
This is oral suction, which is used to help a patient clear the airway when too weak to cough (expectorate) sputum from the pharynx. Other indications include:
* Unconscious or semi-conscious patient, for example after surgery.
* No gag reflex, for example drug overdose, alcohol poisoning or stroke.
* Oral surgery or trauma.
### Nasopharyngeal
This may be indicated when the oral suction catheter cannot pass to the back of the pharynx, as a result of teeth clenching, dental/oral surgery or trauma, or if the patient cannot tolerate a 'sucker' at the back of the pharynx, because it can often induce gagging. It is particularly useful for patients with a lot of secretions at the back of the throat who are unable to cough and expectorate (Nicol et al. 2012; Dixon 2010; Carey and Kelsey 2008).
Suction requires skillful practice, because some patients may be at risk of hypoxia (low oxygen level), causing cardiac arrhythmias (irregularities) if suctioning occurs for more than 10 seconds (Dougherty and Lister 2011).
Dougherty and Lister (2011) and Maddex and Valler-Jones (2009) describe three assessment aspects for suctioning (Table 9.2).
**Table 9.2** Assessment for suctioning
**Assessment** | **Rationale**
---|---
Patient's airway | Check if obstructed? Any obvious secretions, e.g. vomit?
Patient's knowledge | Have they had this before? Offer explanations to reassure
Risk factors | Does the patient have:
| Impaired cough or swallowing?
| Impaired gag reflex?
| Decreased level of consciousness?
Adapted from Dougherty and Lister (2011); Maddex and Valler-Jones (2009).
Having confirmed the need for suction, the following procedure should be followed:
1. **1.** Assemble the necessary equipment, for example a Yankauer (suction catheter) and suction tubing of appropriate size, suction machine (if not wall mounted), gloves, apron, sterile water with container, and clinical waste bag.
2. **2.** Wash your hands and apply non-sterile gloves to minimise risk of transmitting infection.
3. **3.** Turn on suction to appropriate level for your patient (Table 9.3).
4. **4.** Connect one end of plastic suction tubing to the machine and the other to the suction piece, for example a Yankauer (rigid short plastic tube). Test working by applying the Yankauer to a container with water and ensure that it sucks water.
5. **5.** Remove any oxygen mask if present on patient.
6. **6.** Insert the Yankauer catheter into the mouth, along the gum line to the pharynx; move the catheter gently around the mouth until all the secretions are cleared. This may take several repeated attempts. Also, if possible, encourage the patient to cough and check if there are any more secretions. Remember to take only a few seconds, and as Dougherty and Lister (2011) advise no more than 10 seconds per attempt to ensure that oxygen levels do not drop too low (hypoxia).
7. **7.** Replace the patient's oxygen mask, if present, after each suctioning and allow the patient time to recover breath between suctions, if required.
8. **8.** Clear the tubing by sucking more water, until tubing is clear of secretions, for example, sputum.
9. **9.** Switch off the suction.
10. **10.** Dispose of the tubing and Yankauer as per local policy, and gloves and apron into clinical waste.
11. **11.** Wash your hands.
12. **12.** Ensure that patient is comfortable; check respiratory rate and colour to ensure that patient is stable before leaving.
13. **13.** Ensure that the procedure is documented in patient records as per local policy.
14. **14.** Ensure monitoring after the procedure to check that the patient does not develop any unexpected side-effects, such as increasing breathlessness (Dougherty and Lister 2011).
**Table 9.3** Suction pressures
**Wall-mounted suction (mmHg)**
---
Adult | Child | Infant
100–120 | 80–100 | 60–80
Adapted from Dixon (2010); Dougherty and Lister (2011); Carey and Kelsey (2008).
Care of suction equipment is also important to prevent cross-infection. Many practice areas use plastic disposable suction units, so the entire suctioning equipment is disposed of after each use to minimise the risk of cross-infection. However, in some areas glass bottles may still exist and you need to follow your local guidelines for changing and disinfecting these bottles, which usually occurs every 24 hours (Nicol et al. 2012). _Please check local equipment and guidance_.
You must be guided by your local policy and be assessed as competent to carry out both forms of suctioning. Please refer to your employer for guidance.
# Think about it
Miss Barbara Jones, 34 years old, has returned from knee surgery. You observe that she is still very drowsy and is sounding chesty. If you were considering suctioning as an option, how would you assess her? Is suctioning appropriate here?
## Related aspects and terminology
* _Apnoea_ : cessation (stopping) of breathing.
* _Cyanosis_ : due to low oxygen levels and presents as a dusky bluish colour of the mucous membranes, for example lips, nailbeds.
* _Tachypnoea_ : raised respiratory rate, usually if rate above 20 breaths/min.
* _Bradypnoea_ : decreased respiratory rate, if rate below 10 breaths/min.
* _Dyspnoea_ : difficulty breathing, patient struggles to get air in so they might open their mouth and gulp air in, and heave shoulders up in an effort to get more air.
* _Hyperventilation_ : deep rapid breaths.
* _Hypoventilation_ : slow shallow breaths, often associated with drugs, such as morphine, an opioid that acts on the respiratory centre.
* _Cheyne–Stoke respirations_ : often seen in patients with heart failure, in palliative patients before death or with brain injured patients, it leads to a gradual increase in the depth of respirations, in turn leading to hyperventilation, followed by a gradual decrease in depth, and then a period of apnoea of 15–20 seconds, before the cycle starts again.
## Common problems
### Respiratory rate measurement
Nicol et al. (2012) suggest that any activity before taking respiratory rates should be recorded and that the patient should be unaware of the measurement as they can alter their breathing patterns leading to an inaccurate reading. The position of the patient is also important as this can aid lung expansion, which can give a more accurate measurement.
### Peak flow measurement
Dougherty and Lister (2011) and Maddex and Valler-Jones (2009) suggest the following problems should be monitored as these can affect the accuracy of the reading:
* Poor seal between lips and mouthpiece, so air leaks out.
* Forgetting to zero indicator between peak flow measures, leading to an inaccurate reading.
* Obstructing indicator with fingers, so blocking the movement of indicator.
* Poor position for recording, for example lying down, so hindering breathing.
* Failure to take maximum inhalation.
* Holding the breath at maximum inhalation for longer than two seconds, thus delaying blowing into the meter.
* Blocking the mouthpiece with tongue or teeth.
BTS/SIGN (2011) suggests that for those who are acutely breathless and cannot speak in full sentences, peak flow measurement should be avoided because of the exertion required. Therefore, you will need to decide, using your observational skills, if the patient is fit physically and able mentally to undertake this procedure. As noted before, a peak flow measure is simple and quick, but a wrong reading may have a serious effect if any treatment is based on a peak flow result.
### Suctioning
Problems with suctioning might relate to faulty or poorly maintained equipment, or poor suctioning technique. The suction is part of the workplace emergency equipment and should be checked daily to ensure it is working correctly. When suctioning, observe the patient and time taken to suction, as each attempt should take no longer than 10 seconds with time taken to allow the patient to recover between each attempt (Dougherty and Lister 2011). If the patient is becoming distressed or tired, stop and, if they are on oxygen therapy, replace the mask or nasal cannula and allow the patient to rest, before considering further attempts.
Tables 9.4–9.6 are competency frameworks for recording a respiratory rate and PEFR and for suctioning.
**Table 9.4** Competency framework: recording a respiratory rate
| **First assessment/reassessment**
---|---
Steps | Demonstration/supervised practice | Date/competent signature
Recording a respiratory rate | Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
1. **1.** Identify need for respiratory check
2. **2.** Ensure that patient is in best position (e.g. upright)
3. **3.** Consider if patient is rested, so true baseline
4. **4.** Explain to patient, reassure, get consent
5. **5.** Have watch with second hand ready
6. **6.** Note time and start counting for appropriate time
7. **7.** Observe rise and fall of chest,
8. **8.** Note depth of breaths
9. **9.** Observe pattern of breathing
10. **10.** Note sounds of breathing
11. **11.** Consider how regular/rhythmic breathing is
12. **12.** Observe patient's colour
13. **13.** Record rate on appropriate chart, note any abnormalities, e.g. irregular, noisy breaths
14. **14.** Report any abnormalities promptly and appropriately
| | | | | |
Supervisors/Assessor(s):
**Table 9.5** Competency framework: recording a peak expiratory flow rate (PEFR)
| **First assessment/reassessment**
---|---
Steps | Demonstration/supervised practice | Date/competent signature
Recording a PEFR | Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
1. **1.** Patient is upright, sitting or standing
2. **2.** Patient is ready for procedure, so rested and consented
3. **3.** Ensure that patient is able to undertake procedure, check understanding
4. **4.** Peak flow assembled with clean mouthpiece secure
5. **5.** Ensure that patient holds device level and fingers (nurse/patient) don't obstruct scale
6. **6.** Flow indicator set to zero reading on scale
7. **7.** Ensure that patient follows correct technique
8. **8.** Check flow indicator position, record score
9. **9.** Ensure that patient performs three, and record best score
10. **10.** Check and compare with previous scores
11. **11.** Report score and any variances promptly
12. **12.** Store peak flow meter correctly, cleaning or disposing of mouthpiece as per local policy
| | | | | |
Supervisors/Assessor(s):
**Table 9.6** Competency framework: suctioning
| **First assessment/reassessment**
---|---
Steps | Demonstration/supervised practice | Date/competent signature
Suctioning | Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5
1. **1.** Undertake risk assessment pre-procedure
2. **2.** Assemble the necessary equipment
3. **3.** Wash hands and apply non-sterile gloves
4. **4.** Turn on suction to required level
5. **5.** Connect and test equipment, by ensuring that the catheter is sucking sterile water
6. **6.** Remove oxygen mask, if present on patient
7. **7.** Commence suctioning correctly, noting time and patient comfort
8. **8.** Replace patient's oxygen mask, if present, and allow time to recover breath between suctions, if required
9. **9.** Clear the tubing by sucking sterile water, until tubing is clear of secretions
10. **10.** Switch off the suction
11. **11.** Dispose of equipment as appropriate
12. **12.** Remove gloves and wash hands
13. **13.** Ensure patient comfort, and check respiratory rate and colour after procedure
14. **14.** Ensure that documented in patient records
15. **15.** Ensure that monitoring after procedure is in place, e.g. pulse and respiratory checks
16. **16.** Report outcome to appropriate person
| | | | | |
Supervisors/Assessor(s):
_Please ensure that you have undertaken supervised practice, in your clinical area and follow your local workplace policy_.
## Summary
In this chapter the skills of recording a respiratory rate, measuring a peak flow and suctioning technique were explored. Observation and communication are essential skills, as well as effective recording and reporting.
# Case study 9.1
Melanie Jones is a 14-year-old girl admitted with an acute asthmatic attack. This is her first admission to hospital and she is very frightened.
What factors should you consider when admitting her and recording her respiratory rate?
Discuss what you might expect, in terms of her rate, depth, pattern, sound, regularity and colour.
# Case study 9.2
Mr Adjit Singh, is a 24-year-old man and is 6 foot tall. He attends your clinic in the community as he has been using his reliever inhaler more regularly recently. You are asked to start monitoring his peak flow rate and educate him in self-monitoring at home; when you approach him, he tells you that he has never done this before.
Describe how you would explain the procedure to him and how he should carry out the procedure and document the results at home.
His best score is 245 l/min. Describe your actions.
# Case study 9.3
Jane Sackler is a 78-year-old woman admitted with dense stroke and has developed a chest infection. She is very frail and is finding it hard to spit the sputum from her mouth and you are worried about maintaining her airway. She becomes very distressed and you can see thick sputum in her mouth.
Discuss possible actions that may aid her breathing.
If you are asked to undertake oropharyngeal suctioning, consider whether you are trained and competent in this procedure.
If yes, describe your actions in undertaking suctioning on Miss Sackler.
# Self-assessment
**Assessment** | **Aspects** | **Achieved ✓**
---|---|---
**Respiration** | _Have you considered all aspects of this section?_ |
| Patient assessment: rate, depth, pattern, sound, regularity/rhythm and colour |
| Recording the results |
| Reporting concerns or results |
| Problem solving |
**Peak flow** | _Have you considered all aspects of this section?_ |
| Measuring a peak flow – technique aspects |
| Cleansing/disinfection of equipment |
| Recording the results |
| Reporting concerns or results |
| Problem solving |
**Suctioning** | _Have you considered all aspects of this section?_ |
| Assessment of patient – risk assessment |
| Procedure |
| Maintenance and cleansing of equipment |
| Recording the results |
| Reporting concerns or results |
| Problem solving |
## References
1. Booker R (2007) Peak expiratory flow measurement. _Nursing Standard_ **21** (39): 42–43.
2. BTS/SIGN (2011) _British Guidelines on the Management of Asthma_. London: BTS/SIGN.
3. Carey M and Kelsey J (2009) Suctioning. In: Kelsey J and McEwing G (eds) _Clinical Skills in Child Health Practice_. Edinburgh: Elsevier.
4. Cook K and Montomery H (2010) Assessment. In: Trigg E and Aslam Mohammed T (eds) _Practices in Children's Nursing: Guidelines for Hospital and Community_. Edinburgh: Elsevier Ltd.
5. Clancy J and McVicar A (2009) _Physiology and Anatomy for Nurses and Healthcare Practitioners: A Homeostatic Approach_ , 3rd edn. London: Hodder Arnold.
6. Dixon M (2010) Suctioning. In: Trigg E and Aslam Mohammed T (eds) _Practices in Children's Nursing: Guidelines for Hospital and Community_. Edinburgh: Elsevier Ltd.
7. Dougherty L and Lister S (eds) (2011) _The Royal Marsden Hospital Manual of Clinical Nursing Procedures_ , 8th edn. Oxford: Blackwell Publishing.
8. Lewis G (2008) Peak flow monitoring. In: Kelsey J and McEwing G (eds) _Clinical Skills in Child Health Practice_. Edinburgh: Elsevier.
9. Massey D and Meredith T. (2010) Respiratory assessment 1: why do it and how to do it? _British Journal of Cardiac Nursing_ **5** (11): 537–541.
10. Maddex S (2009) Measuring vital signs. In: Baille L (ed.) _Developing Practical Adult Nursing Skills_ , 3rd edn. London: Hodder Arnold.
11. Maddex S and Valler-Jones T (2009) Assessing physical health and responding to sudden deterioration. In: Baille L (ed.) _Developing Practical Adult Nursing Skills_ , 3rd edn. London: Hodder Arnold.
12. National Institute for Health and Clinical Excellence (NICE) (2007) CG50. Acutely Ill Patients in Hospital: _Recognition of and Response to Acute Illness in Adults in Hospital_. London: NICE.
13. Nicol M, Bavin C, Cronin P, et al. (2012) _Essential Nursing Skills_. London: Mosby.
14. Smith J and Roberts R (2011) _Vital Signs for Nurses: An Introduction to Clinical Observations_. Oxford: Wiley-Blackwell.
15. Syers S (2008) Interpretation of observations. In: Kelsey J and McEwing G (eds) _Clinical Skills in Child Health Practice_. Edinburgh: Elsevier
16. Tortora G J and Derrickson B (2011) _Principles of Anatomy and Physiology_ , 13th edn. Hoboken, NJ: John Wiley & Sons Inc.
17. Ford L, Maddox C, Moore E and Sales R (2010) The safe management of medicines in children. In: Trigg E and Aslam Mohammed T (eds) _Practices in Children's Nursing: Guidelines for Hospital and Community_. Edinburgh: Elsevier Ltd.
18. Wallace J, George C M, Tolley E, et al. (2013) Peak expiratory flow in bed? A comparison of 3 positions. _Respiratory Care_ **58** (3): 494–497.
19. Wild K and Peate I (2012) Clinical observations 5/6: breathing/respiratory rate. _British Journal of Healthcare Assistants_ **6** (9): 438–441.
## Addendum
### Wright meter cleaning information
Reproduced with kind permission from Clement Clarke International.
How to disinfect the Mini-Wright Standard Peak Flow Meter, the AFS Low Range Mini Peak Flow meter and the Mini-Wright Digital
The Mini-Wright Peak Flow Meter was designed as a portable device to help healthcare professionals monitor lung function; to minimise the risk of cross-infection, it has an integral one-way valve that prevents the patient from breathing in any of the previous patient's exhaled breath that could remain in the meter (the Mini-Wright Digital does not have a one-way valve).
The importance of peak flow monitoring results in many patients receiving their own personal meter for home monitoring of lung function, by prescription or recommended purchase. Doctor's surgeries and hospitals may also wish to issue peak flow meters on a loan basis and therefore need a means of reprocessing each device before reissue. The following instructions have been prepared to facilitate multiple-patient use.
Note that we would recommend that, if the last user was diagnosed or suspected of having a serious communicable disease, the meter should be disposed of.
Devices used for multiple patients may need to be replaced more often than those used by only one person.
#### Frequency of disinfecting the Mini-Wright range of peak flow meters
The following recommendations for disinfecting peak flow meter frequencies are presented as a guide only. In practice, the person responsible for the clinical well-being of the patient should consider the specific circumstances of the next patient and the risk posed by cross-infection.
Mouthpiece type | Disposable one-way cardboard mouthpieces (single use devicea) | Disposable bacterial filters (single-use devicea) | Disposable cardboard mouthpieces (single-use devicea) | Sterilisable plastic mouthpieces
---|---|---|---|---
Frequency | WEEKLY | WEEKLY | Between patients | Between patients
aSingle use device means 'do not reuse' (EN 980:2003). Clement Clarke International Ltd consider that multiple measurements being made by the same patient in one consultation can be considered as 'single use' as long as the mouthpiece/filter is not damaged between measurements. This interpretation cannot be applied to all devices marked as 'single use'.
#### Reprocessing: sterilisable plastic mouthpiece
* Clean using an automatic dishwasher (2 min pre-wash, 3 min detergent wash, dry).
* Autoclave in saturated steam (max. 134–137°C) for 3 minutes (refer to autoclave manufacturer's instructions for details of cycles available).
* Alternatively, the method below can be used to disinfect the mouthpiece.
#### Cleaning and disinfection
1. **1.** Inspect the unit for signs of damage or wear; if any is evident replace meter.
2. **2.** Prepare a solution of detergent in accordance with the manufacturer instructions in a container large enough for the peak flow meter(s) to be totally submerged.
3. **3.** Agitate the meter while in the solution to ensure that any trapped air is expelled. Do not use any mechanical aids such as brushes or cloths.
4. **4.** Rinse and dry as recommended.
5. **5.** Prepare a quantity of your chosen disinfectant in a suitable container.
6. **6.** Immerse the peak flow meter; again agitate the meter to ensure that air is expelled and leave it in the solution for the recommended time.
7. **7.** Rinse as stated, shake gently to remove any excess water and allow to dry naturally; do not use hot air or a drying cupboard.
#### Detergents
The following detergents have been tested for compatibility with Clement Clarke International Ltd's peak flow meters.
**Name** | **Solution strength** | **Comments**
---|---|---
Lancerzyme | 40 ml in 5 litres of water | Enzymatic cleaner
Cidezyme | | Enzymatic cleaner
Hospec | |
#### Disinfectants
The following disinfectants have been tested for compatibility with Clement Clarke International Ltd's peak flow meters.
**Chemical type** | **Examples** | **Solution strength** | **Comments**
---|---|---|---
Chlorine dioxide generator | Tristel one day | 20 ml in 1 litre water | Safety data sheet and further information available from www.tristel.com
_ortho_ -Phthalaldehyde | Cidex OPA | Undiluted |
Sodium hypochlorite (NaOCL) | Milton | 1000 p.p.m. | Ensure thorough rinsing, as corrosion of the metal parts will occur if exposed to chlorine for long periods.
Sodium dichloroisocyanurate (NaDCC) | Presept, Actichlor, Sanichlor, Haz-Tab | 1000 p.p.m. |
Hydrogen peroxide and peroxygen compounds | Pera Safe | 1.62% w/v |
Clement Clarke International Ltd accepts no liability for damage caused to products if the above procedure and recommended solutions are not used.
It is the user's responsibility to choose which of the recommended solutions are used within their establishment or hospital and we stress that the infection control nurse/department should be consulted when making the choice.
It is the responsibility of the user to keep up to date with the latest information from the relevant disinfectant manufacturer concerning instructions, effects, concentrations and immersion times.
If your preferred cleaner/disinfectant is not on the recommended list, please contact our customer service advisers on 01279 414969 or fax 01279 456 304 or email resp@clement-clarke.com.
## Reference
1. Medical Healthcare product Regulatory Agency (MHRA). _Chemical disinfection in hospitals – PHLS, Sterilization, disinfection and cleaning of medical device equipment (MAC Manual)_. London: MHRA.
# Chapter 10
Urinalysis and faecal occult blood testing
# Learning objectives
* Identify the importance of urinalysis in practice
* Describe how to undertake urinalysis testing
* Discuss the importance of faecal occult blood testing and how this is performed
## Aim of this chapter
The aim of this chapter is to describe how to undertake urinalysis and faecal occult blood tests (FOBt) and to discuss why these are performed within the clinical environment.
## Reasons for performing urinalysis and FOB tests
Urinalysis is a simple non-invasive clinical procedure. It is quick, cost-effective and easy method of screening that can give clues as to the health status of the person and can be carried out by the healthcare worker or the patient at home (Foxley 2010). For this reason it is suggested that healthcare practitioners should not only be able to perform the task but interpret the results as well (Mulryan 2011).
Faecal occult (hidden) blood tests (FOBt) involve the testing of a specimen of faeces to identify whether there is any blood present that is not visible to the naked eye, which is referred to as malaena. It is useful in helping to diagnose many gastrointestinal conditions that may cause bleeding, for example colorectal (bowel) cancer or peptic ulcers (Baillie and Busuttil Leaver 2009). The procedure is simple and non-invasive and requires a small sample of uncontaminated faeces to smear onto a specimen card or place into a pot for the lab; it is also quick and easy for patients and healthcare workers to carry out. FOBt is a key part of the NHS National Bowel Cancer Screening Programme (Public Health England 2013). This national programme focuses on adults aged 60–69 and encourages self-collection of FOBt samples; it is thought to have reduced bowel cancer deaths by 16% since the programme commenced in 2006 (Moss et al. 2012).
## Relevant anatomy and physiology
In normal health, the urinary system has two kidneys, two ureters, one urinary bladder and one urethra (Tortora and Derrickson 2011) (Figure 10.1). The kidneys are located in the lumbar area and are described as bean-shaped organs. The kidneys are highly vascular and receive approximately 180 litres of blood per day via the renal arteries, and their main purpose is to filter the blood, reabsorb the required solutes and remove waste products and water for excretion via the formed urine (Clancy and McVicar 2009).
**Figure 10.1** Urinary system.
The kidneys are connected to the bladder by the ureters and are hollow tubes of length approximately 25–30 cm (10–12 inches). The formed urine passes through the ureters for storage in the bladder.
The urinary bladder is a hollow muscular organ lying in the pelvic cavity; in males directly anterior (in front) to the rectum, and in females anterior to the vagina and inferior to (below) the uterus (Tortora and Derrickson 2011).
The urethra is a hollow muscular tube that transfers the urine from the bladder to the external sphincter and is approximately 4 cm in females and 20 cm in males. The short length of the female urethra can predispose women to urinary tract infections (Clancy and McVicar 2009; Tortora and Derrickson 2011).
It is worth briefly reviewing the process of digestion, because from this we get the formation of faeces. Food is consumed via the mouth and transported to the stomach via the oesophagus. It is in the stomach that the first digestion of food begins that will enable the nutrients to be absorbed within the small intestine (Tortora and Derrickson 2011)) (Figure 10.2).
**Figure 10.2** Digestive system.
The small intestine begins at the pyloric sphincter (circular muscle that constricts an opening) at the exit of the stomach and coils round the abdominal cavity, before opening into the large intestine. The small intestine is 2.5 cm in diameter and can vary from around 3 m to 6.5 m long (Tortora and Derrickson 2011; Clancy and McVicar 2009). The small intestine is divided into three sections: duodenum, jejunum and ileum; most digestion occurs within these three sections while absorption of nutrients occurs at the end of the ileum.
The large intestine is 1.5–2 m long and 6.5 cm wide (Tortora and Derrickson 2011; Clancy and McVicar 2009). The function of the large intestine is to complete the absorption process (water, electrolytes and vitamins), manufacture certain vitamins such as vitamin K and vitamin B, form faeces, produce gases as a by-product of carbohydrate metabolism and aid the expulsion of faeces from the body (Tortora and Derrickson 2011; Clancy and McVicar 2009).
## Urinalysis testing
Elimination of urine is an essential normal bodily function and urinalysis is a useful tool to assess the presence of infection and for disease monitoring (Foxley 2010). Timing of urine testing is important, and the first voided sample (early morning urine) that has been stored in the bladder for at least 4 hours provides the most accurate results, because it is the most concentrated (Baillie and Busuttil Leaver 2009; Foxley 2010; Siemens Diagnostics 2009).
Siemens Diagnostics (2009) state that specimen collection must be in a clean, dry and preservative-free container. There are several methods of specimen collection depending upon the reason for the test and the individual patient:
1. **1.** A random (clean) sample at any time of day, for example on admission, although in women it may contain vaginal contamination during menstruation (monthly bleeding).
2. **2.** An early morning sample – first sample after sleep (as above).
3. **3.** A midstream urine (MSU) sample, usually taken for laboratory sampling so needs careful collection.
4. **4.** A catheter specimen of urine (CSU) sample, used when the patient has a catheter in situ.
5. **5.** A suprapubic catheter sample provides the purest sample, but is rarely used.
6. **6.** A urostomy specimen of urine, taken from patients who have urinary diversions and wear stoma bags to collect their urine.
(Baillie and Busuttil Leaver 2009; Williams 2012)
A urine sample must be tested within 4 hours of collection or bacteria can multiply affecting the accuracy test results. Where this testing period cannot be adhered to urine should be refrigerated and allowed to return to room temperature before testing. For the most accurate results, always test urine immediately after collection (Baillie and Busuttil Leaver 2009; Williams 2012; Foxley 2010).
# Think about it
How are you going to collect a specimen of urine from a patient on admission?
Before testing the urine using reagent test strips, there are useful observations that you can undertake, including the colour of the urine, the smell (odour) and the clarity (Baillie and Busuttil Leaver 2009; Siemens Diagnostics 2009).
Baillie and Busuttil Leaver (2009) and Dougherty and Lister (2011) describe urine as typically clear, pale to deep yellow in colour and slightly acidic (pH 6), although they add that the pH can change as a result of metabolic processes or diet (e.g. beetroot). Foxley (2010) suggested that some laxatives could change urine to an orange bright yellow, whereas diet and medications, for example rhubarb and antibiotics, can change urine to a red/orange colour.
The composition of urine can change dramatically as a result of disease and may contain red blood cells, proteins, glucose, bile or white blood cells. The presence of these abnormalities in the urine can be an indicator of illness (Dougherty and Lister 2011).
Dougherty and Lister (2011) state that freshly voided urine smells faintly aromatic, and Foxley (2010) suggests that urine can develop an ammonia smell if it is left standing. There should not be a strong odour to urine, which can signify the presence of bacteria (Baillie and Busuttil Leaver 2009). Foxley (2010) suggests the smell and clarity of the urine should be observed as this can also indicate illness. Infected urine can be described as having a 'fishy' smell, whereas acetone excreted by patients with diabetic ketoacidosis gives urine a sweet smell. Clancy and McVicar (2009) also state that certain foods in the diet can affect the odour of urine, such as asparagus and sugar-puffs.
Urine that is cloudy or has sediment (debris) can indicate the presence of infection, therefore observation is important (Foxley 2010). Cloudy urine is caused by suspended particles, such as white and red cells, which will settle on standing to leave a deposit, while frothy urine contains protein (Mulryan 2011).
Baillie and Busuttil Leaver (2009) identify the importance of ensuring that any patient providing a sample of urine for testing gets the following information. The procedure for catheter samples can be found in Chapter 11:
* An explanation of the reason for testing.
* Instruction in the method of collection.
* Provision of suitable equipment, for example a container for the specimen.
* An appropriate environment, for example privacy and space.
There is a lack of agreement in the literature as to best practice concerning cleaning around the urethral meatus. In two studies (Lifschitz and Kramer 2000; Unlu et al. 2007) there was found to be little difference in cleansing with soap and water, not cleansing or cleansing with a chlorhexidine solution. Therefore the individual nurse must look towards their own workplace policies for guidance. When obtaining a MSU from a male, patients should first wash their hands, then retract the foreskin and cleanse the meatus with soap and water, or as per local policy. To collect the sample the patient passes the first part of the urine stream (15–30 ml) into the toilet, and then collects the next part (50–100 ml) in a clean dry container, and finally finishes emptying the bladder into the toilet. The container cap must be replaced immediately and the hands washed.
For females, again patients wash their hands, then clean the vulval and urethral meatus with soap and water, or as per local policy, then separate the labia (this might be difficult for some patients, e.g. a patient with arthritis) and continue as above.
Jasper (2008) and Maddox and Pearson (2010) suggest there are several methods to collect samples from children or infants:
1. **1.** Adhesive urine bags, which attach to the perineal area; however, this is the least favoured method because it carries a risk of contamination from the perineum and rectum.
2. **2.** Urine collection pads: these need to be checked every 10 minutes for the sample or replaced after 30 minutes if the infant has not voided to prevent contamination of the sample.
3. **3.** 'Clean catch' where the child or infant is sat over a sterile container and urine collected as they pass urine.
4. **4.** MSU sample: most reliable for testing; however, not always possible in young children. Females should be encouraged to part the labia and males should retract the foreskin and then pass urine into a sterile container.
5. **5.** Catherter specimen of urine: used if the child has a catheter in situ. The sample is always taken from the specimen collection port to avoid contamination.
6. **6.** Suprapubic bladder aspiration would be performed only in urgent situations because it carries the risk of bladder puncture and is not suitable in children aged under 2 years.
Once the sample has been collected and you have observed, and recorded, the colour and noted the presence, if any, of odour, or if the urine is cloudy, you proceed to test the urine. Reagent test strips allow testing of a range of factors: leucocytes (white cells), nitrites, urobilinogen, protein, pH, blood, specific gravity, ketones, bilirubin and glucose (Baillie and Busuttil Leaver 2009). Check the strips in your area and check which substances are tested (Table 10.1). (Figure 10.3 is an example of a recording slip.)
**Table 10.1** Significance of substances in the urine
**Substance** | **Causes**
---|---
Glucose: not normally detected in urine | Diabetes mellitus, acute pancreatitis, pregnancy, glycosuria
Bilirubin (stale urine may give a false positive) | Liver cell damage: viral/drug induced, hepatitis, paracetamol overdose, cirrhosis;
Biliary tract obstruction – gallstones, cancer of pancreas
Ketones | Due to excessive breakdown of body fat – fasting, specially with fever/vomiting, some high protein diets, diabetic ketoacidosis, starvation/excessive dieting
Specific gravity: normal 1.001–1.035 | High: concentrated urine due to dehydration or chronic renal failure
Low: high fluid intake, renal disease
Blood: haematuria | Kidney disorders: urinary tract infection (UTI), stones, tumour, severe burns, transfusion reaction, trauma
pH: normal 4.5–8.00 | High: stale urine, UTI,
Low diabetic ketoacidosis, starvation
Protein: test may not be sensitive to presence of all proteins | UTI, fever, pre-eclampsia, heart failure, high-protein diet, severe hypertension, glomerulonephritis, diabetes and contamination of the sample
In men may be due to sperm after sex
Urobilinogen: normally present in urine, stale samples can give false positives | Increased secretion: viral hepatitis, cirrhosis, blood disorders such as sickle cell anemia or thalassemia
Decreased secretion – biliary tract obstruction caused by gallstones, pancreas cancer, medicines, e.g. neomycin
Nitrite: not usually found in urine | UTI
Leucocytes | Renal or bladder infection
UTI, urinary tract infection.
Adapted from Baillie and Busittil Leaver (2009), Foxley (2010).
**Figure 10.3** Example of a test recording slip. Source: Photograph by I Lavery.
### Procedure for testing
1. **1.** Check that reagent strips are correctly stored and have not expired (discussed later).
2. **2.** Explain and discuss the procedure with the patient (discussed earlier).
3. **3.** Wash hands using the Ayliffe technique and put gloves on.
4. **4.** Obtain fresh sample of urine from the patient.
5. **5.** Dip reagent strip fully into the urine, remove immediately and allow any excess urine to drain away ensuring the chemicals are not mixed.
6. **6.** Wait the specified time interval for each square as noted per bottle.
7. **7.** Read and record your findings as per local policy.
8. **8.** Dispose of urine in sluice or toilet and test strip and gloves into the clinical waste.
9. **9.** Wash your hands.
10. **10.** Report findings and results as per local policy.
11. **11.** Ensure that the patient is comfortable, and where appropriate given results; please discuss this role locally before proceeding. Rigby and Gray (2005) noted the debate over the reliability of urinalysis, and suggest that reports are only 85% reliable, so its use in screening is questionable. However NICE (2006) suggest that urinalysis should be completed on all women with incontinence to identify potential urinary tract infections. Therefore, it is important that the test is completed correctly to ensure that it is as accurate as possible.
# Think about it
Emily Boyd, aged 54 years, has type 2 diabetes and is frequently treated for UTIs and fungal infections. She requires a urine test while she is in clinic. What aspects will you observe and test for?
From the test results, any action taken may depend on other results (e.g. blood tests); however, your action must be to report any abnormalities immediately. If the specimen is old and has been lying for a while, a fresh sample of urine should be obtained. Depending upon the results obtained further laboratory tests may follow, for example urine for microscopy, culture and sensitivity (Baillie and Busuttil Leaver 2009). Therefore accurate testing, recording and prompt reporting is essential. If in doubt, report.
Accurate testing leads us to consider storage of the reagent strips. Baillie and Busuttil Leaver (2009) suggest that healthcare workers should check that strips are in date, stored and used correctly. Incorrect handling of the test strips can affect the results. Mulryan (2011) and Siemens Diagnostics (2009) advise the following to increase reliability of the test results:
* Store reagent strips out of direct sunlight.
* Keep strips at a constant temperature, usually cool and dark, not in the fridge.
* Use strips according to manufacturer's guidance.
* Strips should be stored in the bottle supplied.
* Replace cap on the bottle as quickly as possible after each test.
* Never remove desiccant (some manufacturers place this in the lid).
## Faecal occult blood testing
Faeces consist of the unabsorbed end products of digestion and contain fibre, some electrolytes, water and bile pigments, which give faeces their colour (Clancy and McVicar 2009). Nicol et al. (2012) states that normal stools are brown, soft and formed but should not have an offensive smell. Therefore when collecting a specimen for FOB testing, or any other stool specimen test, the colour, smell and consistency should be noted and recorded as part of the bowel assessment. The majority of clinical areas use the Bristol Stool Form Scale to classify faeces (see Addendum at end of chapter).
Baillie and Busuttil Leaver (2009) discussed smell as part of a bowel assessment. Fatty, offensive-smelling stools can indicate bowel disease, for example gallbladder disease. Stools that are covered with mucous and/or blood indicate disease such as ulcerative colitis. Black tarry stools can indicate digested blood and have a distinctive smell, often due to upper tract disorders, for example stomach ulcer. Finally, stools with fresh blood often indicate haemorrhoids. All these require prompt reporting.
There are different methods of FOBt sample collection. In many acute hospital settings the use of specimen pots with integral spatulas are used to send the sample to the lab. However in some areas sample cards may be used (Figure 10.4). There are two kinds of cards for FOBt collection, one aimed at healthcare workers with chemical additives and another aimed at patients as part of the National Bowel Cancer Screening Programme (Public Health England 2013). Ouyang et al. (2005) suggest that for 4 days before the first sample is taken and during the test period patients' diets should be modified as outlined below. However, in acute hospital settings, this may not be possible if specimens are urgently required. As gastrointestinal bleeding may be intermittent, three FOBts should be carried out on three different separate samples of faeces from the patient on different days, but do not need to be from consecutive samples (NHS Bowel Cancer Screening Programme 2013).
**Figure 10.4** A faecal occult blood (FOB) specimen card. Source: Photograph by I Lavery.
Kyle and Prynn (2004) offered advice for patients before having an FOBt; this may be a useful guide for staff to discuss with each patient, and suggests that patients:
* eat a diet rich in roughage (helps stimulate bleeding if any lesions present);
* avoid alcohol and aspirin or other non-steroidal anti-inflammatory drugs, and vitamin C or iron tablets (could worsen bleeding or affect results);
* avoid fish with dark meat, for example salmon, tuna, sardines, mackerel;
* avoid red meat and blood products, for example black pudding, kidneys or liver;
* avoid tomatoes, cauliflower, horseradish, turnip, melon, bananas and soybeans;
* are asked if menstruating (if female), have diarrhoea or had a recent nose or throat bleed (as could affect result); if yes postpone the test;
* ask staff if they have any concerns or queries.
Ouyang et al. (2005) note that, with guaiac FOBt (cards for healthcare workers use and for patient self collection), false positives can occur with red meats and some fruits and vegetables, such as turnip, and also false negatives can occur with high doses of vitamin C. However, research by Bapuji et al. (2012) states that there is a difference between the advice given by health professional in relation to FOBt, which can affect patients' compliance with the test and preparation for it. This potentially can lead to incorrect results, which makes the advice of healthcare workers essential in the accurate diagnosis of bowel cancer.
# Think about it
Wendy Williamson is to have FOB tests, and you have been asked to give her advice about the procedure and preparation. What advice might you offer?
### Equipment for the FOB test using a guiac impregnated card
* Sample card (see Figure 10.4) and wooden stick.
* Chemical solution.
* Non-sterile gloves and apron.
* Container.
Once the patient has opened their bowels, take the container to the sluice and collect two samples from different parts of the faeces (in case of false readings); smear a small amount from each on the two sample windows indicated on the card by the foldaway section. Once smeared on, close the cover and turn the card over, and then follow the instructions for administering the chemical, taking care not to spill the chemical because this can cause some hazards, for example a chemical might cause a skin reaction (Control of Substances Hazardous to Health (COSHH) – HMSO 1999).
The test area should be observed for a change in colour. Ouyang et al. (2005) indicate that this is a blue colour change depending on whether blood is in the stool, and usually occurring within 1 minute. This can be further classified, so if pale blue it could indicate weakly positive, whereas strong blue indicates strongly positive.
### Equipment needed for an FOB test using a specimen pot
* Gloves and apron.
* Labelled sterile specimen container with integral spatula (if not available then use a wooden tongue depressor).
* Labelled specimen bag.
Once the sample has been obtained from the patient (this should not be contaminated with urine), don gloves and apron and take a sample from the stool with the spatula or tongue depressor filling the pot around a third full. Close the lid tightly and remove your apron and gloves and wash your hands thoroughly. Ensure the specimen is labelled correctly and put it into a labelled laboratory bag. The sample should then be refrigerated if it is not being sent to the lab immediately (Nicol et al. 2012; Baillie and Busuttil Leaver 2009).
# Think about it
What hazards might you encounter with an FOB test?
## Related aspects and terminology
* _Jaundice_ : yellow pigmentation of the whites of the eyes, skin or mucous membranes due to build-up of bilirubin.
* _Cirrhosis_ : scarred liver, often due to chronic inflammation.
* _Diabetes mellitus_ : a group of disorders that lead to an elevation of glucose in the blood; as glucose (sugar) levels increase, glucose appears in the urine.
* _Glycosuria_ : presence of sugar in the urine.
* _Renal function_ : function of the kidneys.
* _Haematuria_ : presence of intact red blood cells in the urine.
* _Pre-eclampsia_ : abnormal condition of pregnancy associated with high blood pressure and protein in the urine.
* _Suprapubic_ : above the pubic bone.
* _Meatus_ : passageway or opening at the external point of the canal.
* _Labia_ : liplike structure.
* _Hypertension_ : high blood pressure.
* _Acute pancreatitis_ : inflammation of the pancreas.
(Tortora and Derrickson 2011.)
## Common problems
_Urinalysis_ , if not tested on a fresh sample, as noted before, can lead to false results, so always ensure that freshly passed urine is tested or that refrigerated urine has been allowed to return to room temperature before testing.
In females, take care if the patient is menstruating, because this can lead to a false reading of haematuria.
Ensure that you handle the strips correctly, when in storage and when undertaking the test, otherwise this can also affect results.
_FOB testing_ problems may be due to poor sampling (contaminated with urine or incorrect storage), in the case of guiaic test cards not smearing sufficient faeces on the test areas, insufficient chemical or reading the result too quickly (before it has time to change). Please check the type of test in your area and follow the manufacturer's instructions or hospital procedure concerning sample collection fully.
## Summary
Urinalysis and FOB testing are quick and simple tests and allow for prompt results; however, they require safe and competent practice to ensure their accuracy. As discussed, there are risks with these procedures and the healthcare assistant should follow universal precautions to prevent the risk of cross infection. Tables 10.2 and 10.3 are competency frameworks for urinalysis and FOB testing.
**Table 10.2** Competency framework: urinalysis testing
| **First assessment/reassessment**
---|---
Steps | Demonstration/Supervised practice | Date/competent signature
Urinalysis testing | Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
1. **1.** Checked reagent strips are correctly stored and in date
2. **2.** Explained procedure to the patient
3. **3.** Washes hands, applied disposable gloves and apron
4. **4.** Obtained fresh urine sample in clean container
5. **5.** Dipped reagent strip fully into the urine, removed immediately, excess urine removed
6. **6.** Held stick at an angle, to ensure no mixing
7. **7.** Waited specified time interval for each square as noted per bottle
8. **8.** Read and recorded findings
9. **9.** Disposed of urine in sluice or toilet and test strip into clinical waste
10. **10.** Disposed of gloves and apron, washes hands
11. **11.** Reported findings and results
12. **12.** Ensured patient is comfortable, where appropriate given results
| | | | | |
Supervisors/Assessor(s):
**Table 10.3** Competency framework: faecal occult blood (FOB) testing
| **First assessment/reassessment**
---|---
Steps | Demonstration/Supervised practice | Date/competent signature
FOB testing (Guiaic cards) | Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
1. **1.** Washes hands, dons disposable apron and gloves
2. **2.** Collected sample from the faeces
3. **3.** Smeared a small amount on the test card
4. **4.** Closed test area
5. **5.** Administered the chemical, carefully
6. **6.** Observed the test area for change of colour
7. **7.** Disposed of gloves and apron, washes hands
8. **8.** Disposed of card and protective clothing
9. **9.** Recorded and reported results
| | | | | |
1. **1.** Washes hands, dons disposable apron and gloves
2. **2.** Collected sample from the faeces
3. **3.** Fills sample pot using spatula or wooden tongue depressor to around a third full
4. **4.** Tightly seals pot
5. **5.** Disposes of gloves and apron, washes hands
6. **6.** Ensures specimen pot and laboratory form is labeled correctly
7. **7.** Stores specimen in refrigerator for collection or sends to laboratory immediately
8. **8.** Records and reports completion of specimen collection
| | | | | |
Supervisors/Assessor(s):
# Case study 10.1 Urinalysis
Julie Forth is 68 years old and lives in a nursing home; over the past few days she has had a couple of episodes of incontinence and is complaining of abdominal discomfort and pain on passing urine. Her temperature is 38 and the Nursing Home staff tell you she is confused. She has been admitted with a suspected UTI.
What might you expect to find present in her urine?
# Case study 10.2 FOB test
John Armour is 73 years old and has been admitted with weight loss and altered bowel habits.
Discuss why FOB will be requested, and outline how you will collect a sample of stool and test for the presence of occult blood.
# Self-assessment
**Assessment** | **Aspects** | **Achieved ✓**
---|---|---
Urinalysis | _Have you considered all aspects of this section?_ |
| Timing of collecting |
| Specimen collection procedure |
| Observation, e.g. colour, smell |
| Performing the test |
| Recording the results |
| Reporting concerns or results |
| Problem solving |
FOB testing | _Have you considered all aspects of this section?_ |
| Assessment, e.g. colour, smell and consistency |
| FOB test procedure |
| Storage and handling of equipment |
| Patient education |
| Recording the results |
| Reporting concerns or results |
| Problem solving |
## References
1. Baillie L and Busuttil Leaver R (2009) Meeting elimination needs. In: Baillie L (ed.) _Developing Practical Nursing Skills_ , 3rd edn. London: Hodder Education, pp. 321–393.
2. Bapuji, S. Lobchuk M M, McClement S E, et al. (2012) Fecal occult blood testing instructions and impact on patient adherence. _Cancer Epidemiology_ **36** : 258–264.
3. Clancy J and McVicar A (2009) _Physiology and Anatomy: A Homeostatic Approach_ , 3rd edn. London: Hodder Arnold.
4. Dougherty L and Lister S (eds) (2011) _The Royal Marsden Hospital Manual of Clinical Nursing Procedures_ , 8th edn. Oxford: Blackwell Publishing.
5. Foxley S (2010) Urinalysis: analysing urine and interpreting the results. _Journal of Renal Nursing_ **2** (3): 137–140.
6. HMSO (1999) Control of Substances Hazardous to Health (COSHH). No 437. Available at: www.hmso.gov.uk/is/si1999/19990437.htm (accessed 27 January 2007).
7. Jasper E (2008) Specimen collection. In: Kelsey J and McEwing G (eds) _Clinical Skills in Child Health Practice_. Edinburgh: Elsevier.
8. Kyle G and Prynn P (2004) Guidelines for patients undergoing faecal occult blood testing. _Nursing Times_ **100** (48): 62, 64.
9. Lifschitz E and Kramer L (2000) Outpatient urine culture. _Archives of Internal Medicine_ **160** : 2537–2340.
10. Maddox C and Pearson B (2010) Specimen collection. In: Trigg E and Mohammed T (eds) _Practices in Childrens Nursing: Guidelines for Hospital and Community_ , 3rd edn. Edinburgh: Elsevier.
11. Moss S M, Campbell C, Melia J, et al. (2012) Performance measures in three rounds of the English bowel cancer screening pilot. _Gut_ **61** : 101–107.
12. Mulryan C (2011) Urine testing through the use of dipstick analysis. _British Journal of Healthcare Assistants_ **5** (5): 234–239.
13. Bowel Cancer Screening Programme (2013) _NHS Bowel Cancer Screening Programme: Information Leaflet_. London: NHS.
14. NICE (2006) CG40. _Urinary Incontinence_. London: NICE.
15. Nicol M, Bavin C, Kronin P, et al. (2012) _Essential Nursing Skills: Clinical Skills for Caring_. Edinburgh: Mosby.
16. Ouyang D L, Chen J, Getzenberg R H and Schoen R E (2005) Noninvasive testing for colorectal cancer: a review. _American Journal of Gastroenterology_ **100** : 1393–1403.
17. Public Health England (2013) National Bowel Cancer Screening Programme. Available at: <http://www.cancerscreening.nhs.uk/bowel/index.html> (last accessed 15 May 2013).
18. Rigby D and Gray K (2005) Understanding urine testing. _Nursing Times_ **101** (12): 60–62.
19. Siemens Diagnostics (2009) _Your Practical Guide to Urine Analysis_. Camberley: Siemens Healthcare Diagnostics.
20. Tortora G J and Derrickson B (2011) _Principles of Anatomy and Physiology_ , 12th edn. Hoboken, NJ: John Wiley & Sons Inc.
21. Unlu H, Çetinkaya Şardan Y and Ülker S (2007) Comparison of sampling methods for urine cultures. _Journal of Nursing Scholarship_ **39** (4): 325–329.
22. Williams J (2012) Stoma care: obtaining a urine specimen from a urostomy. _Gastrointestinal Nursing_ **10** (5): 11–12.
## Addendum
### Bristol Scoring Chart
Permission granted via Wikipedia site: <http://en.wikipedia.org/wiki/Bristol_Stool_Scale> (accessed 3 March 2008).
Figure A10.1 The Bristol Stool Chart or Scale is an aid for healthcare staff that classifies faeces into seven categories. It was developed by Dr S J Lewis and Dr K W Heaton at the University of Bristol, and was first published in 1997 in the _Scandinavian Journal of Gastroenterology_ 32: 920–924.
**Figure A10.1** The Bristol Stool Form Scale. Source: Used under CC-BY-SA 3.0 Unported <https://creativecommons.org/licenses/by-sa/3.0/deed.en>.
# Chapter 11
Urinary catheterisation and catheter care
# Learning objectives
* List the reasons for inserting a urinary catheter
* Discuss common catheters and the equipment associated with catheterisation
* Outline the procedure of urinary catheterisation
* Discuss the importance of catheter care and how to prevent and manage common problems associated with catheterisation
## Aim of this chapter
The aim of this chapter is to discuss urinary catheterisation and catheter care in adults and children, and to review potential complications and their prevention or management. This chapter is aimed at supporting local training and supervision and focuses primarily on urinary catheterisation. Intermittent self-catheterisation is also discussed, because the healthcare assistant may need to assist a patient in this process or carry out this procedure.
## Urinary catheterisation
A urinary (or urethral) catheter is a hollow tube that is inserted from the urethral orifice into the bladder. NHS Quality Improvement Scotland (NHS QIS 2004) described urinary catheterisation as a procedure to enable emptying of the bladder by insertion of a catheter, and ongoing care and maintenance are considered as catheter care. The Department of Health (DH 2001) stated that the use of indwelling catheters should be considered only after alternative methods have been explored, and these include intermittent catheterisation, use of medications, voiding programmes or incontinence pads with children (NICE 2012).
Mangnall and Watterson (2006) indicated that urinary catheterisation is one of the most common healthcare interventions, with around 25% of patients in hospital requiring this procedure, so attention to infection control aspects is critical. Currently catheter-associated urinary tract infections (CAUTI) account for approximately 80% of all hospital acquired infections, which has ensured that the Department of Health has made this one of their focal points in their Harm Free Care agenda with the NHS Safety Thermometer by aiming to reduce the rates of infection by 50% (DH 2012; Foxley 2011). Leaver (2007) also noted that nurses insert at least 50% of all catheters and subsequently perform the majority of catheter care, so there is a need to ensure that they are at the forefront of good practice. This is supported by the RCN (2012), NICE (2012) and NHS QIS (2004) who discuss the importance of best practice in catheterisation and infection control.
## Relevant anatomy and physiology
Chapter 10 should be referred to for details of the urinary system; however, a review of the relevant parts of the urinary system may be useful.
The bladder is a hollow muscular structure lying in the pelvic cavity; in males directly anterior (in front) of the rectum, whereas in females it is anterior to the vagina and inferior (below) to the uterus (Tortora and Derrickson 2011). The urethra is an opening leading from the bladder to the exterior of the body, made of epithelial cells, which is often described as a tube; in females it is about 4 cm (1.5 inches) long, and in males about 15–20 cm (6–8 inches) long (Tortora and Derrickson 2011) (Figures 11.1 and 11.2). For this reason catheters come in different lengths and are often referred to as male and female lengths.
**Figure 11.1** Male bladder and urethra.
**Figure 11.2** Female bladder and urethra.
Elimination of urine is an essential bodily function and, normally, day- and night-time bladder control is developed by age 6 years (Pellatt 2007). Bray and Saunders (2006) suggest that children are usually toilet trained between 2 and 4½ years, and girls generally achieve dryness before boys.
In the adult, the kidneys filter about 150 l/day, and concentrate this into urine producing a minimum of 0.5 ml/kg/hr (Hughes 2004), while in children the output is usually 1 ml/kg body weight per hour (Bray and Saunders 2006).
### Reasons for urinary catheterisation and catheter care
Bray and Saunders (2006) suggest that the reasons for inserting a catheter in children are usually:
* Acute retention: with sudden onset often after surgery (after 12 hours), medication related, or after spinal or epidural anaesthesia; it can be an associated secondary complication due to acute constipation, spinal injury or obstruction at the urethral outflow.
* Post-operative urine monitoring: where a child is unwell after emergency surgery, trauma or injury, a catheter would be inserted to monitor fluid balance and measure specific gravity (see Chapter 10).
* Skin and wound integrity: a catheter is inserted after surgery to allow a wound to heal, and a catheter minimises the risk of infection, pain and discomfort for the child.
There are several reasons for catheterisation in adults that have been outlined by Dougherty and Lister (2011), Baillie and Busuttil Leaver (2009) and Foxley (2011), and which are outlined below:
* to empty bladder contents, for example before surgery, childbirth and some investigations;
* to accurately measure urinary output, especially if the patient is acutely ill;
* to determine residual urine;
* to allow bladder irrigation;
* to bypass an obstruction;
* to relieve urinary retention;
* to instil drugs into the bladder, for example cytotoxic drugs for bladder cancer or drugs for hyperactive bladders);
* to allow bladder function tests (e.g. urodynamics);
* to help bladder healing, for example after bladder, pelvic or urethral surgery;
* to maintain skin integrity in intractable incontinence where patients are at high risk;
* to avoid complications from insertion of radiotherapy (e.g. in gynaecological or prostate cancer).
## Types of catheterisation
This chapter focuses on indwelling catheterisation, and also discusses intermittent catheterisation by both the healthcare assistant and the patient. The other option for draining urine from the bladder is via a suprapubic catheter, where a catheter is inserted above the pubic bone; as this would be carried out by trained personnel it is not outlined in this book.
### Assessment considerations
NHS QIS (2004) suggested that intermittent catheterisation should be considered a first option, rather than inserting an indwelling catheter, and this would be done after a full patient assessment. Initial assessment would be to identify the reason for the bladder-emptying problem, which would include consideration of the holistic effects a catheter may have on the individual, such as impact on the patient's body image or sexuality. NHS QIS (2004) also indicated that catheterisation can be a challenge with children; older, frail, confused patients; or patients with a learning disability, and they will need additional consideration, especially around communication and consent.
The decision as to the type of catheter technique can then be made in consultation with the patient and carers or family if necessary. With older confused people or patients with a learning disability, consideration is also needed about their capacity to consent, briefly discussed in Chapters 1 and , as well as later in this chapter.
The materials, gauges, balloon sizes, tip design and lengths of catheters, and drainage systems, will now be discussed to assist in catheter selection.
#### Length of time the catheter is in place
Dougherty and Lister (2011) suggested the need to consider how long a catheter will be in situ, because this will affect the choice of material (Table 11.1). Therefore, Dougherty and Lister (2011) used the following time frames:
* Short term: 1–7 days.
* Short to medium term: 28 days.
* Medium to long term: 6 weeks–12 weeks.
**Table 11.1** Catheter selection
**Length in situ** | **Type of material** | **Discussion**
---|---|---
Short term | PVC with or without balloons | Rigid catheter with wide lumen, so allows rapid flow rate, used mainly for intermittent catheter or postoperatively. Due to rigidity it can cause some patients discomfort or pain, or bladder spasm
| Latex | Softest material, but causes surface friction which tends to allow encrustation formation. Also risk of patient allergy with latex, so ensure that this is checked with patient. Avoided where possible
| Teflon (PTFE) | Teflon is applied to latex to prevent the risk of latex allergy and reduce urethral irritation
Short to medium term | Silver alloy coating | Silver alloy coated latex. Evidence suggests that this material reduces bacterial growth in catheters in situ <7 days
Long term | 100% silicone | Less likely to cause urethral irritation. Has a large inner lumen with reduced tendency to develop encrustations. Silicone can also allow balloon to deflate (water leaks out) and so catheter can fall out prematurely
| Hydrogel coated latex | These coat the catheter and cause the least irritation and as they become rehydrated they become smoother, and so reduce friction in the urethra. This reduces the risk of becoming contaminated with bacteria or encrusted
| | NHS Quality Improvement Scotland (2004) note this type of material is unsuitable for patients with a latex allergy
| Hydrogel-coated silicone | Suitable for patients with latex allergy, however are rigid so can be uncomfortable for some patients
| Silicone elastomer coating | Latex catheters coated with silicone inside and out. Acts in a similar way to pure silicone with less incidence of encrustations
| Nitrofurazone coating | Bactericidal coating which reduces the frequency of asymptomatic bacteria in the urine within a week. Not for routine use
PVC, polyvinylchloride.
Adapted from Dougherty and Lister (2011) and NHS QIS (2004), and EAUN (2012)
#### Gauges (sizes)
Choose the smallest size suitable, because larger sizes can cause pain, discomfort, bypassing (urine leaks past catheter) and lead to abscess and stricture formation (Dougherty and Lister 2011; Bray and Saunders 2006).
Catheters are measured in Charrière (Ch) or French gauge (FG) which refers to the external circumference of the catheter. Each Ch is 0.3 mm and comes in a range of sizes for use with adults and pediatrics in varying lengths (Bailie and Busuttil Leaver 2009) (see Table 11.2 for paediatric sizes).
**Table 11.2** Paediatric catheter sizes
**Age (years)** | **Charrière (Ch) size**
---|---
0–2 | 6
2–5 | 6–8
5–10 | 8–10
10–16 | 10–12
Reproduced from Bray and Saunders (2006) with permission.
NHS QIS (2004), Dougherty and Lister (2011) and Nazarko (2010) all suggest that the smallest size catheter possible should be used to prevent trauma and complications. For both males and females a size 12 is usually suitable but the individual and the risk of encrustation leading to a blocked catheter in long-term use also need to be considered. The European Association of Urological Nurses (2012) suggests the following as a guide to catheter sizes in adults:
* size 10: clear urine, no debris, no grit (encrustation);
* size 12–14: clear urine, no debris, no grit, no haematuria;
* size 16: slightly cloudy urine, light haematuria with or without small clots, none or mild grit, none or mild debris;
* size 18: moderate to heavy grit, moderate to heavy debris; haematuria with moderate clots;
* size 20–24: used for heavy haematuria, need for flushing.
#### Materials
Catheters are manufactured from many different materials and selection of the material is based upon the purpose and length of time the catheter is likely to be in place. It is important to also consider patient comfort when choosing a catheter, the potential for the build up of encrustations in long-term catheterised patients and the potential of allergic reaction to the material (EAUN 2012). An outline of these materials can be found in Table 11.1.
#### Balloon sizes
Balloons are used to hold the indwelling catheter in place and are inflated once the catheter has been correctly inserted into the bladder (Baillie and Busuttil Leaver 2009). The volume in the balloon varies; in children the balloons are commonly filled with 3–5 ml of sterile water, and 5–10 ml for adults; however, some balloons inflate to 30 ml, but these are used mainly after urological procedures. Dougherty and Lister (2011) noted that as the balloon sits at the base of the bladder neck in a sensitive area called the trigone this can cause irritation to the bladder wall, often causing bypassing and bladder spasms, while an overfilled balloon can cause damage to the neck of the bladder and too little fluid can also cause irritation. It is important that balloons are not repeatedly inflated and deflated as this can create asymmetry of the balloon causing the tip of the catheter to irritate the trigone. If a Foley-type catheter (catheter with a balloon) is inserted, always make sure that it is draining before inflating the balloon with sterile water as per manufacturer's guidelines. Water is used in case the balloon leaks, and therefore prevents irritation of the bladder (NHS QIS 2004).
#### Design of catheter tip
Dougherty and Lister (2011) describe tip designs; these can affect drainage:
* the Tiemann-tip is curved with one to three drainage eyes;
* the Whistle-tip has a lateral eye in the tip and eyes above the balloon to provide a large drainage area; helpful in drainage of debris or blood clots;
* the Roberts tip has an eye above and below the catheter to help drain residual urine.
#### Length of catheter
Authors note a variance, but all agree on three lengths (Dougherty and Lister 2011; NHS QIS 2004; Baillie and Busuttil Leaver 2009; Bray and Saunders 2006):
1. **1.** Paediatric: 30–31 cm
2. **2.** Female: 20–40 cm
3. **3.** Male or standard: 40–45 cm.
However, Baillie and Busuttil Leaver (2009) suggested that standard length is often used for women, particularly if the patient is obese or chair bound, because it allows easier access to the connector end and the drainage bag (NHS QIS 2004). The use of standard length catheters in females is now much more common since their withdrawal from some areas following a patient safety issue where female catheters had been incorrectly used for male catheterisation. Where female catheters are available these must be clearly labelled to ensure patient safety (NPSA 2009).
# Think about it
Why are there different lengths of catheters (male and female)?
#### Drainage systems
A drainage bag allows periodic emptying, and so eliminates the need to disconnect it from the catheter, reducing the risk of catheter associated urinary tract infections (CAUTIs) (Baillie and Busuttil Leaver 2009). Dougherty and Lister (2011) noted that the highest risk of infection is when emptying or changing the bag, hence NHS QIS (2004) suggested changing bags every 5–7 days.
Most drainage bags attach either to a stand on the floor or bed side, or to a patient's leg, and depend on the patient's condition and mobility and also their preference. Bags also vary in capacity and length of inlet tube and type of outlet tap, and this will also influence choice. Baillie and Busuttil Leaver (2009) suggest that outlet taps are usually of a lever type or push-across design; therefore, when assessing the patient for the right product for them the cognitive and physical capability of patients or carers should be considered. Bags can vary from 180 ml capacity in leg bags to 2 litres for overnight bags, while for some people the choice of a valve rather than a bag provides greater freedom (Baillie and Busuttil Leaver 2009; Gibney 2010; EAUN 2012). See Figure 11.3 for bag and outlet tap.
# Think about it
When choosing a drainage bag, what could be some factors that you should consider?
**Figure 11.3** Catheter bag and outlet valve.
When considering the use of catheter valves as an alternative to a closed drainage system, EAUN (2012) suggests that this is a good alternative for patients who have good manual dexterity and no cognitive impairment. However it should be contraindicated in those who have physiological problems, such as urinary tract infections, overactive bladder syndrome or renal impairment. Gibney (2010) provides a good algorithm to determine the suitability of patients for valve use. Bray and Saunders (2006) calculated the bladder volume in children using the formula: 30 × child's age + 30, so, for example, a 6 year old would have a calculated bladder volume of 210 ml. This formula is applicable until a child reaches age 12 years, and then one would expect the bladder volume to be that of an adult, which ranges from 300 ml to 500 ml (Bray and Saunders 2006). Therefore, for some patients a valve may offer more privacy and fewer restrictions to their mobility and lifestyle. Dougherty and Lister (2011) and Gibney (2010) also add that the use of a valve largely eliminates the need for bags and can be cost effective in long-term indwelling catheters, as the valve can be in place for 5–7 days.
The use of closed drainage systems are commonplace, but to prevent CAUTI it is essential that effective aseptic non-touch techniques occur on insertion, emptying or removal, so care must be exercised at all times.
It is important that there is no tension on the catheter, so ensure that the bag, if attached to a stand, is in a good position, below the level of the waist and not caught in clothing or bedclothes. The same applies to a leg bag; here the use of adjustable straps or a 'sleeve or holster' is essential to secure the bag in a suitable position, remembering patient comfort, drainage and privacy (Baillie and Busuttil Leaver 2009; EAUN 2012; Fisher 2010).
## Patient preparation for catheterisation
Dougherty and Lister (2011) discuss the importance of explaining the procedure to the patient and gaining their consent. It is essential that the patient is educated regarding their catheter and how to care for it before the procedure with regards to cleansing around the catheter and fluid consumption to reduce the risk of infection.
If possible, patients should be advised to wash their genital area first with unperfumed soap and water, and then men need to retract the foreskin (where present) and clean the area thoroughly and then replace the foreskin, whereas women need to wash from front to back to prevent contamination from the rectal area.
Lubricating gel should be used in both male and female catheterisation (Dougherty and Lister 2011; NICE 2012). Workplace policy should be followed with regards to the type of lubricant used, that is anaesthetic or aqueous, as there is debate over which is the best to use (Patel 2008); EAUN (2012) suggest that anesthetic gel should be used. However, it is important to note that when using anaesthetic gel the manufacturer's instructions should be adhered to with regards to the amount of time to wait before the gel takes full effect. Bray and Saunders (2006) suggested that local anaesthetic gel (e.g. 2% lidocaine) should be used with children because this also acts as a lubricant and ideally is applied 3–5 min before catheterisation. This may not, however, be achievable with younger children due to their anxiety.
## Insertion technique
The catheterisation equipment required is: a sterile catheter pack preferably or sterile dressing pack with gallipot; two pairs of sterile gloves; catheter (recommend one of assessed size and one spare plus a smaller size); sterile sodium chloride or antiseptic solution as per local policy; sterile water and syringe as per age and balloon size; sterile single patient anaesthetic gel or lubricating gel; holder or leg straps; drainage bag (as appropriate); sterile receiver and waterproof protective sheet/pad (if not in catheter pack); sterile specimen container (often a sterile sample is sent to laboratory, depends on the reason for catheter insertion); apron; screens; and good lighting (may require portable or angled light).
The whole procedure must follow an aspetic non-touch technique, equipment used must be sterile and single use (Figures 11.4 and 11.5), and all packaging should be checked and verified intact and in date.
**Figure 11.4** Catheter.
**Figure 11.5** Sterile pack. Source: Photograph by I Lavery.
Table 11.3 describes the procedure for male or female catheterisation; however, in some clinical areas healthcare assistants may require additional training for male catheterisation because of technical aspects and the use of anaesthetic gel and, as this is an administration of a medicine, some clinical areas may not cover this role for healthcare assistants; as usual, _please check your local policy_. (See Figures 11.1 and 11.2 re male and female anatomy for catheterisation.)
**Table 11.3** Catheterisation procedure
**Step** | **Procedure**
---|---
1 | Approach the patient, explain procedure, and gain consent and cooperation
2 | Help patient into a safe position, preferably flat on back, covered and screened for privacy
3 | Wash hands, put on plastic apron, assemble equipment on clean trolley, take to the screened bedside/area
4 | Place waterproof sheet under patient's buttocks – to protect the bed
5 | Open catheter pack taking care not to touch inside – to protect sterile field
6 | Open the catheter but leave in internal packing and drop onto sterile field
7 | Draw up the required amount of sterile water with a sterile syringe
8 | Pour sterile sodium chloride into sterile gallipot in pack, and open single use gel (lubricating or anaesthetic), set up drainage bag (on stand if being used)
9 | The assistant now uncovers the patient and supports the legs, and knees bent up and apart
10 | Open sterile gloves and wash hands or use alcohol rub to cleanse hands
11 | Sterile gloves on, place sterile towels over patient's thighs and under buttocks
12 | Males: wrap a sterile towel around the penis, and retract the foreskin to clean round the top of urethra with the sodium chloride or antiseptic solution as per workplace policy
| Females: cleanse the perineal area with sodium chloride, then, using non-dominant hand, separate the inner labia (lips) and cleanse the meatus (opening). Change sterile gloves ready for the clean part of the procedure
13 | Males: insert the nozzle of the anaesthetic gel into the urethra, and squeeze the gel in, remove the nozzle and discard the tube, massage the gel along the urethra (penis) and wait 5 min
Females: carefully locate the urethra and insert either lubricant or anaesthetic gel and wait 5 min
14 | Males: grasp the penis behind the glans (acorn-shaped rim) and raise penis until extended and maintain this grasp till procedure finished – see below
Females: expose the tip of the catheter by pulling off serrated end of internal wrapper (also for male catheterisation)
15 | Males: place sterile receiver between patient's legs and insert selected catheter for 15–25 cm (6–9 inches) until urine flows, pulling back internal wrapper and ensuring that catheter end is in receiver
Females: place sterile receiver between patient's legs and insert selected catheter for 5–7 cm (2–3 inches) until urine flows, pulling back internal wrapper and ensuring that catheter end is in receiver
16 | Males: if resistance is felt, increase the traction on the penis slightly and ask the patient to strain gently as though passing urine and apply steady gentle pressure on the catheter; this may help insertion past bladder sphincter; if not, stop and seek advice
Females: Bray and Saunders (2006) noted that occasionally a catheter may enter the vagina and so no urine drains. If this happens, leave this catheter in place as a marker, and recommence with new catheter, then remove the first one once the second catheter is correctly in situ
17 | Males: advance catheter forward to ensure safely within the bladder to bifurcation (Y section) (Figure 11.4)
Females: advance the catheter a further 5 cm; never force the catheter. If resistance is met stop and seek medical advice
18 | Inflate balloon with sterile water as per manufacturer's instructions, and ensure that urine is still draining
19 | Withdraw catheter slightly – balloon will hold in place
20 | Attach free end to drainage system and ensure secured and no drag on catheter
21 | Males: ensure that penis is clean and foreskin is retracted
Females: ensure that genital area is clean
22 | Dispose of equipment, per local policy
23 | Check that patient is comfortable and has understood catheter education
24 | Document procedure, noting catheter type, size and balloon volume inserted, along with date, time and drainage, and if any specimen sent or tested
Adapted from Dougherty and Lister (2011), Baillie and Busuttil Leaver (2009) and EAUN (2012).
Men, particularly the older age population, may suffer from an enlarged prostate gland. Tortora and Derrickson (2011) describe this as a single doughnut-shaped gland, which surrounds the urethra, so if it enlarges this can affect the flow of urine and also the ease with which the catheter is inserted. If a male patient reports pain or discomfort during the procedure, stop and always seek advice.
Bray and Saunders (2006) note that in children's insertion the usual aspects should be documented as for point 24 in Table 11.3, plus the catheter batch number, the inserter's name, the type of analgesia used, if any, and consent.
### Intermittent catheterisation
Intermittent catheterisation can be undertaken by the patient, carer or healthcare professional, and the bladder must have sufficient capacity to store urine between catheterisations (NHS QIS 2004). Dougherty and Lister (2011) describe the procedure as the periodic removal of urine and, after the procedure, the catheter is removed, leaving the patient catheter free. The procedure is carried out (see Table 11.4 for the procedure) as often as the patient requires, usually four to five times a day.
**Table 11.4** Intermittent self-catheterisation procedure
**Step** | **Procedure in males** | **Procedure in females**
---|---|---
1 | Wash hands using bactericidal soap and water, or bactericidal alcohol hand rub and dry thoroughly | Take up a comfortable position, dependent on mobility, e.g. sitting on toilet or standing with one foot up on toilet rim (see Step 10)
2 | Stand in front of toilet, or low bench with a container if easier (see Step 10) | Spread the labia (lips) and wash the genitalia from front to back with soap and water, then dry
3 | Clean the glans of the penis (head) with plain water, retract foreskin, if applicable, during the procedure |
4 | Hold penis with left hand (if right handed) three fingers underneath and thumb on top, holding the penis straight out. Coat the end of the catheter with the lubricating gel | Insert the catheter, use lubricant gel if wish for comfort, and a mirror to help see genitalia
5 | Pass the catheter gently with the right hand (or left if left handed); it can be felt as it passes the fingers holding the penis. There will be a change in feeling as catheter passes through the prostate gland into the bladder. It may be a little painful on the first few occasions only; if any resistance is felt, stop and seek medical advice immediately | Urine will drain as soon as the catheter reaches the bladder, so have the end positioned over the toilet or the container
6 | Urine will drain as soon as the catheter enters the bladder, so have end positioned over toilet or container |
7 | Withdraw the catheter slowly so that all the urine is drained and it should slide out easily | Remove the catheter slowly when urine has stopped draining; it should slide out easily
8 | Wash catheter through if reusable and store in dry, clean container |
9 | Wash hands again as Step 1 |
10 | If patient has a large abdomen, a mirror standing in front can assist observation and insertion |
Source: Adapted from Dougherty (2011). Reproduced with permission of Wiley Blackwell.
When patients, commonly at home, carry out this procedure it is a clean procedure, whereas any healthcare assistant would carry it out as an aseptic procedure. At certain times, such as during acute illness, the patient may not have the usual physical and manual dexterity to carry out the procedure themselves. Therefore the healthcare assistant may carry out the procedure for the patient, or may even teach a carer to undertake this for the patient if they prefer it (NHS QIS 2004).
Dougherty and Lister (2011) suggest patients who are suitable for intermittent self-catheterisation as the following:
* Those who can comprehend (understand) the technique.
* Those with a reasonable degree of manual dexterity (able to use hands).
* Those who are highly motivated.
* Those who have a willing partner (if suitable for both to participate).
* Those who can position themselves to attain reasonable access to the urethra, especially in females.
The benefits of intermittent catheterisation can include an improved quality of life, greater patient satisfaction, greater freedom to express sexuality and minimisation of urinary complications (Dougherty and Lister 2011).
There are two types of catheters used for intermittent self-catheterisation. One is a single use pre-lubricated catheter where the lubrication is activated in water; the other type is PVC and requires lubrication. This latter catheter can be used for up to 1 week before being discarded. NHS Quality Improvement Scotland (NHS QIS 2004) suggest intermittent catheter cleaning (PVC reusable catheters) should involve washing in warm soapy water, rinsing thoroughly and then leaving in a clean dry area to air dry, before storing in a clean dry container.
## Catheter care
NHS QIS (2004) outlined the following aspects:
* Maintain a closed system, as much as possible.
* Empty drainage bags regularly (when bag two-thirds full); always ensure they are positioned below level of bladder (exception: a 'belly bag', see Figure 11.6) and change every 5–7 days.
* Body-worn bags, for example a 'belly bag' (Figure 11.6): change weekly (a 'belly bag' is worn round the waist and has 1000 cm3 capacity and can be used with Foley-type catheters).
* Bedside-type drainage bags must be supported off the floor to reduce the risk of infection.
* A separate clean container is used for each individual when emptying the catheter; avoid contact with the drainage tap and container.
* Wear gloves to empty drainage bags and ensure new gloves and hands washed between patients – strict aseptic technique.
* Leg bags can be emptied directly into toilets.
* When overnight bag is required, a new single-use 2-litre bedside bag is used and emptied and discarded in the morning.
* Encourage the patient to have a daily bath or shower and wash around the catheter with warm soapy water.
* Frequent vigorous meatal (genital area) cleansing with antiseptic solutions is not needed, and may even increase the risk of infection.
* Clean the outlet valve with a 70% isopropyl alcohol-impregnated swab and allow to dry thoroughly.
* Once urine is drained, re-clean as above.
* Record volume and document if necessary.
(Adapted from Dougherty and Lister 2011; NHS QIS 2004; EAUN 2012)
**Figure 11.6** Belly bag. Source: Photograph by I Lavery.
## Sampling
Breaking the closed system to obtain a sample increases the risk of catheter-related infection, so use of a drainage bag with a sample port (Figure 11.7) incorporated removes the need to break the closed system (NHS QIS 2004).
**Figure 11.7** Sampling ports.
Dougherty and Lister (2011) and NHS QIS (2004) described the steps in sampling as follows:
* Only take a sample for a valid reason, such as a suspected urinary infection.
* Wash hands, put on gloves and apron.
* Cleanse port with a 70% isopropyl alcohol-impregnated swab and allow to dry thoroughly.
* Take the sample from the bag sample port.
* Using a sterile syringe (and needle if necessary), aspirate the required amount of urine taking care not to touch the far side of the catheter tube to prevent contamination of the sample. Dougherty and Lister (2011) noted that, if there is no urine in tubing, it is possible to clamp the tubing below the sample port/cuff only until sufficient volume collects.
* Re-clean sample port with a 70% isopropyl alcohol-impregnated swab and allow to dry thoroughly.
* Place specimen into sterile container and label correctly.
* Dispose of needle and syringe.
* Wash hands again with bactericidal soap and water, and dry thoroughly.
* Unclamp tubing, if necessary.
* Consider recording volume, where applicable, for example if the patient is on a fluid balance chart.
* Send specimen and form promptly to laboratory, as per local policy.
Trigg and Mohammed (2010) suggest that the same procedure should be used for catheterised children. Tables 11.6–11.9 are competency frameworks for catheterisation procedures and sampling.
## Removal of catheter
NHS QIS (2004) indicate removal of the catheter as soon as possible to reduce the risk of infection, depending on the patient's condition and the judgement of healthcare staff. Assessment of patients should consider whether they are physically and mentally able to cope with normal micturition (passing urine).
Kelleher (2002) suggested removal at 12 midnight, increasing the time before the patient would pass urine, leading to a greater initial volume and faster return to normal voiding (passing) of urine, which can decrease levels of anxiety. A Best Practice Statement from the Joanna Briggs Institute (JBI 2006) discussed the time of removal and noted that this is a balance between avoiding infection (early removal) and voiding (passing urine) problems (by later removal), and midnight removal may lead to shorter hospital stays.
The urine output must be monitored after removal, to ensure that the patient is passing urine and in adequate volumes (Baillie and Busuttil Leaver 2009). It may be recommended that a portable bladder scan be used to measure residual volumes in the first few days, because retention can often be a problem after a catheter is removed in patients who have had their catheter for some time (NHS QIS 2004). Bray and Saunders (2006) and EAUN (2012) noted that careful gentle removal must be ensured in case a catheter has become encrusted (possible in medium- to long-term catheters), while EAUN (2012) suggest that letting the balloon deflate naturally and not applying suction to it can reduce the ridge that can be left around the balloon and therefore decrease discomfort on removal.
Dougherty and Lister (2011), EAUN (2012) and Baillie and Busuttil Leaver (2009) outlined the procedure as follows:
* Explain the procedure to the patient and any possible after effects, for example urgency or discomfort as well as the need for a good fluid intake of around 2–3 litres a day where physically allowed.
* Wash hands and, wearing gloves, clean the meatal/urethral area with sodium chloride, females from front to back, males around urethral opening.
* Clean/change gloves, having previously checked volume of water in the balloon, use a syringe to withdraw the water and deflate the balloon.
* Ask the patient to breathe in and out and, on an exhalation, gently but quickly remove the catheter. Advise males that they may note some discomfort as the deflated balloon passes the prostate gland.
* Cleanse area; dry, remove and dispose of equipment as per local policy. If urine is present in drainage bag, empty before disposal in clinical waste and wash and dry hands.
* Document removal, volume in bag, and date and time; also whether any problems reported, for example patient discomfort.
## Related aspects and terminology
### Communication, consent and clinical holding
In adults this includes consideration of communication, consent and education and in children one may also need to consider the issue of holding (see Chapters 3 and for more information on consent).
NHS QIS (2004) discussed patient consent and gender issues, and indicated key aspects in relation to catheterisation:
* Informed consent must be obtained first and is ongoing, so the patient may/can withdraw consent at any time.
* Patient's capacity is crucial (e.g. in Scotland, the Adults with Incapacity Act 2000 protects the interests of adults who are not capable of making a decision, e.g. learning difficulty or mental health problem).
* Ensure accurate documentation, which includes the process for consent, and indicates that the patient has understood and verbally consented to the procedure.
* Patients are entitled to request the procedure be carried out by a specific gender of healthcare worker, for example a male patient may wish a male nurse, to fit with their cultural/personal preferences.
Dingwall and McLafferty (2006) also considered patient preferences in relation to catheterisation because the patient may be embarrassed; in addition they considered the effect that a catheter may have on body image and sexuality, and found that this was noted more in males. However, as Rees and Mawson (2007) indicated, if the reason for an indwelling catheter is because of incontinence, this in itself can cause social embarrassment and isolation and so affect their quality of life. Thus, the option of a catheter may be seen here as advantageous. Incontinence affects 6 million people worldwide and in the UK 40 in 1000 people are affected (Rees and Mawson 2007).
Bray and Saunders (2006) stated that catheterisation in children is a sensitive issue that requires effective communication, sensitivity and diplomatic skills. They further noted that a child's rights can be ambiguous where procedures such as catheterisation are to be carried out, as a parent or healthcare professional can override a child's wishes. Bray and Saunders (2006) therefore discussed the need for healthcare workers to understand the child's level of understanding and, as catheterisation is an unpleasant procedure, ensure that the child is involved, so that they feel they have some control over the situation.
Parents should be encouraged to be present, because they can act as chaperones and relieve their child's anxiety by being there (Bray and Saunders 2006). If the child is strongly opposed, Bray and Saunders (2006) stated that this must be fully explored with the child before the procedure is undertaken. Therefore discussions must take place with the child and their parent(s) or carer(s), including the reason for catheterisation versus other options, such as a voiding programme or incontinence pad.
Education would include the reason for the initial catheterisation, how long the catheter might remain in place and how it will be secured and emptied, and patients can be encouraged to self-cleanse the genital area and catheter: a daily bath or shower with soap and water is adequate (NHS QIS 2004; Baillie and Busuttil Leaver 2009). Further education would include asking the patient to drink adequate fluids; this is good practice (maintaining healthy fluid levels), and would ensure good urine drainage and output and reduce the risk of urinary infections. Other aspects: advise the patient to ensure that the drainage bag (if used) is always kept below bladder level to achieve drainage and to observe that urine is draining (Baillie and Busuttil Leaver 2009), the exception to this would be if a patient was to use a belly bag which allows for discrete draining of urine.
Bray and Saunders (2006) talked about clinical holding – positioning a child for a medical procedure, so that it can be carried out in a safe and controlled manner and, where possible, with the consent of the child and the parent/carer. Holding must be seen as a last resort, so other options that should be considered first are use of a play specialist to help distract or guided imagery. Preparation can include acting out the procedure with a doll and playing with products that may be used (Bray and Saunders 2006). Finally, Bray and Saunders (2006) noted the use of pharmacological interventions (drugs) that may aid with relaxation and minimise discomfort, for example Entonox (this gas would be administered only under prescription by a registered children's nurse and/or doctor).
## Terminology
* _Intermittent catheterisation_ : catheter inserted routinely and not left in place.
* _Suprapubic_ : above the pubic bone.
* _Acute retention_ : sudden inability to pass urine (micturate).
* _Epidural anaesthesia_ : anaesthetic drug is injected into spine to 'numb' lower body, often used in childbirth and if a patient is unable to tolerate a general anaesthetic, for example a patient with chronic bronchitis.
* _Residual urine_ : volume left in bladder after voiding (passing urine).
* _Cytotoxic_ : medicine therapy to destroy 'cancer' cells.
* _Bladder irrigation or instillation_ : drug therapy inserted directly into the bladder.
## Common problems
The most common problem is urinary infection, hence thorough asepsis at all times is necessary (Bray and Saunders 2006). EAUN (2012) suggest that for each day a catheter is in place then the risk of CAUTI is increased by 3–10%.
Another patient problem associated with catheterisation is bladder spasms, which often cause the urine to flow around the catheter. In instances such as this medication may be prescribed, and can include anticholinergic drugs (NHS QIS 2004). However Bray and Saunders (2006) noted that, in children, the use of oxybutynin or tolterodine has been found to be successful, but care is needed because these can cause side-effects and some may not be licensed for certain ages. _The administration of these to children would not necessarily be part of a healthcare assistant's role; please check your local policy_.
However, NHS QIS (2004), EAUN (2012) and Bray and Saunders (2006) identified other problems and these are shown in Table 11.5.
**Table 11.5** Problem solving
**Catheter problem** | **Possible reason** | **Possible solution**
---|---|---
Urine not draining/blockage | Catheter in wrong position – not in bladder, maybe in vagina | Deflate balloon and gently reposition catheter forward
| Drainage bag in wrong position – above the level of the bladder | Check bag position – move to below bladder level
| Drainage tubing may be kinked | Check tubing and unkink
| Catheter blocked by debris | Prescribed flush, gently with saline preferably or sterile water
| Bladder spasm | Consider use of medication
Haematuria (presence of blood in urine) | Trauma post-catheterisation
Infection
Calculi (stones)
Cancer
Prostatic enlargement | Observe output and document
severity of haematuria, report to
nurse in charge and/or doctor
Observe and report as above
Encourage fluid intake and observe and report as above
Bypassing of urine around catheter | May indicate infection | Send sterile urine specimen if indicated.
| Bladder spasm/instability | Consider use of medication
| Constipation | Increase fluid and dietary fibre intake: 2–3 l in adults, 1500 ml for children over 5 years and 2000 ml for teenagers where clinically indicated
| Incorrect positioning of drainage system | Check drainage bag position
| Balloon volume incorrect | Check volume in balloon, remove if overinflated or add if less than specified volume
| Drainage bag more than two-thirds full | Regular emptying
Pain or discomfort | The eyes of the catheter may be blocked | Raise the drainage bag above the level of the bladder for 10–15 s only
| Maybe a sign of infection | Obtain sterile specimen of urine
| On removal, may indicate crusting | Ensure correct catheter size inserted in first place and the patient maintains daily cleaning of genital area and catheter
Catheter retaining balloon will not deflate | Valve port and balloon inflation channel may be compressed | Check no compression on tubing
| Faulty valve mechanism. | Aspirate balloon port slowly; if too fast can cause valve mechanism to collapse
| | Can inject a small additional amount of sterile water in and then slowly aspirate again
| | Do NOT cut catheter, if all fails, seek medical advice
Adapted from NHS Quality Improvement Scotland (QIS 2004), EAUN (2012) and Bray and Saunders (2006).
**Table 11.6** Competency framework: indwelling catheterisation
| **First assessment/reassessment**
---|---
**Steps** | **Demonstration/supervised practice** | **Date/competent signature**
**Indwelling catheterisation** | Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
**Procedure stages: male and female** | 1 | 2 | 3 | 4 | 5 |
1. **1.** Patient approached, procedure explained, consent/cooperation gained
2. **2.** Helped patient into safe position, covered and screened
3. **3.** Washed hands, equipment assembled on clean trolley
4. **4.** Placed waterproof sheet/pad under patient's buttocks
5. **5.** Catheter pack opened protecting sterile field
6. **6.** Catheter opened onto sterile field
7. **7.** Appropriate volume of sterile water drawn up with sterile syringe
8. **8.** Sterile sodium chloride prepared and single use gel opened
9. **9.** Patient uncovered and legs supported in appropriate position
10. **10.** Sterile gloves opened and hands washed as per policy
11. **11.** Sterile gloves on, sterile towels placed over patient's thighs and under buttocks
| | | | | |
**Male-specific aspects** | Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
1. **12.** Sterile towel wrapped around penis, foreskin retracted, and top of urethra cleaned with sodium chloride or antiseptic solution, wash hands and change gloves
2. **13.** Anaesthetic gel nozzle inserted into urethra, gel squeezed in, nozzle removed, discarded, massaged gel along penis, waited 5 min
3. **14.** Penis grasped safely and raised until fully extended, for all procedure
4. **15.** Sterile receiver placed between patient's legs, catheter tip exposed, then inserted smoothly and gently for 15–25 cm until urine flows
5. **16.** Catheter advanced forward so safely within bladder, and urine is draining into receiver
6. **17.** Balloon inflated with sterile water and ensured urine still draining
7. **18.** Catheter withdrawn slightly to ensure secure in bladder
8. **19.** Free end attached correctly and securely to selected drainage system
9. **20.** Ensured penis clean and foreskin retracted at finish
| | | | | |
**Indwelling catheterisation: female-specific aspects** | Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
1. **12.** Perineal area cleansed with sodium chloride, inner labia separated and meatus cleansed too. Wash hands and change gloves
2. **13.** Urethra located, lubricant or anaesthetic gel inserted, waited 5 min
| | | | |
1. **14.** Tip of catheter exposed by pulling off serrated end of internal wrapper
2. **15.** Sterile receiver placed between patient's legs, catheter inserted smoothly and gently for 5–7 cm until urine flows
3. **16.** If no urine drained, checked if catheter in vagina, so left in place, recommenced with new catheter, then removed first once second is correctly in situ
4. **17.** Advanced catheter a further 5 cm to ensure safely within the bladder and urine still draining into receiver
5. **18.** Balloon inflated with sterile water and ensured urine still draining
6. **19.** Catheter withdrawn slightly – to test secured in bladder
7. **20.** Free end attached correctly and securely to drainage system and genital area is clean
**Male and female aspects** | Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
1. **21.** Disposed of equipment, per local policy, gloves removed and hands washed
2. **22.** Checked patient is comfortable, has understood catheter education, allowed questions
3. **23.** Procedure documented, noting catheter type, size and balloon volume inserted, along with date, time and drainage, and if any specimen sent or tested
| | | | | |
Supervisors/Assessor(s):
**Table 11.7** Competency framework: intermittent catheterisation competency – patient/carer
| **First assessment/reassessment**
---|---
Steps | Demonstration/supervised practice | Date/competent signature
**Supervised aspects for _learner_ patient/carer self-catheterisation** | Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
1. **1.** Patient/carer washed hands using bactericidal soap and water, or bactericidal alcohol hand rub and dried thoroughly
2. **2.** Took up a comfortable position, e.g. sat on toilet or stood with one foot up on toilet rim (female); or stood at toilet or low bench with a container (male)
3. **3.** Genital area cleaned correctly:
**Female:** spread labia and washed from front to back with soap and water, then dried
**Male:** cleaned the head of penis with water, foreskin retracted during procedure
4. **4.** **Male:** held penis with three fingers underneath and thumb on top, straight out, coated the end of the catheter with the lubricating/anaesthetic gel
**Female:** inserted catheter, used lubricant or anaesthetic gel if wished, and a mirror to help see genitalia
5. **5.** Passed catheter gently with one hand; in males it can be felt as it passes the fingers holding the penis. Urine drained and catheter end positioned over toilet or container
6. **6.** Withdrawn catheter slowly once all the urine is drained
7. **7.** If container, urine disposed in toilet and container cleaned/disposed
8. **8.** Catheter washed correctly if re-usable and stored in clean container
9. **9.** Hands washed again post procedure
| | | | |
Supervisors/Assessor(s)
**Table 11.8** Competency framework: intermittent catheterisation by healthcare assistant
| **First assessment/reassessment**
---|---
Steps | Demonstration/supervised practice | Date/competent signature
Intermittent catheterisation by healthcare assistant | Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
1. **1.** Hands washed using bactericidal soap and water, or bactericidal alcohol hand rub and dried thoroughly
2. **2.** Patient assisted into a comfortable position
3. **3.** **Females:** perineal area cleansed with sodium chloride then inner labia separated and meatus cleansed too
**Males:** sterile towel wrapped around penis, foreskin retracted and top of urethra cleaned with sodium chloride or antiseptic solution
4. **4.** Urethra located, lubricant or anaesthetic gel inserted, waited 5 min
5. **5.** Sterile receiver placed between patient's legs, catheter inserted smoothly and gently for required distance; Males 15–25 cm and females 5–7 cm, until urine flows
6. **6.** Catheter withdrawn slowly once all the urine is drained
7. **7.** Catheter washed correctly if reusable and stored in dry clean container or if single use disposed of correctly as per local policy
8. **8.** Procedure documented and volume recorded
9. **9.** Patient left clean and comfortable
| | | | |
Supervisors/Assessor(s):
**Table 11.9** Competency framework: sampling competency
| **First assessment/reassessment**
---|---
Steps | Demonstration/supervised practice | Date/competent signature
Sampling competency | Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
1. **1.** Checked reason for sampling valid, e.g. suspected urinary infection
2. **2.** Washed hands, put on gloves and apron
3. **3.** Cleansed port with isopropyl alcohol 70% swab and allowed to dry thoroughly
4. **4.** Used sterile syringe (and needle if necessary) aspirated the required amount of urine
5. **5.** If no urine in tubing, clamped the tubing below the sample port/cuff until sufficient volume collected
6. **6.** Re-cleaned sample port with isopropyl alcohol 70% impregnated swab and allowed to dry thoroughly
7. **7.** Placed specimen into sterile container and labelled correctly
8. **8.** Washed hands again with bactericidal soap and water and dried thoroughly
9. **9.** Unclamped tubing, if necessary
10. **10.** Recorded volume, if patient is on fluid balance chart
11. **11.** Sent specimen and form promptly to laboratory, per local policy
| | | | |
Supervisors/Assessor(s):
## Summary
This chapter has outlined the skills necessary for inserting and removing urinary catheters, discussed intermittent catheterization and sampling, as well as ongoing catheter care. All require strict aseptic technique and competent practice. Also required are effective communication and documentation.
# Case study 11.1
Mrs Fiona Wilson is 82 years old and lives in a nursing home; she was diagnosed with terminal cancer two years ago and her condition has steadily deteriorated and she now requires full assistance with her activities of daily living and spends most of her time sleeping in bed. She is now incontinent of urine and her skin is becoming excoriated.
What actions would you recommend and why?
# Case study 11.2
Brian Fredericks, aged 32 years and wheelchair bound after a road traffic accident, is being discharged home in a few days. You are part of a team caring from him and he is being considered for intermittent self-catheterisation.
What might be the benefits for this young male?
How would you explain the technique?
Below there is a self-assessment checklist; however, you may also wish to review Skills for Health (2010) guidelines regarding the insertion of urethral catheters.
# Self-assessment
**Assessment** | **Aspects** | **Achieved ✓**
---|---|---
**Indwelling catheterisation** | _Have you considered all aspects of this section?_ |
| Reasons for insertion or other options explored |
| Catheter material, gauge and length considered |
| Patient assessment carried out |
| Consent, communication and patient education |
| Procedure and infection control aspects |
| Recording the procedure |
| Reporting concerns or outcome |
| Problem solving |
| Disposal of equipment |
**Sampling** | _Have you considered all aspects of this section?_ | **Achieved ✓**
| Procedure and infection control aspects |
| Process for dealing with sample |
| _If for testing refer to Chapter_ 10 _If for laboratory purposes, is aware of local process for sending sample_ |
| Recording the results |
| Reporting concerns or results |
| Problem solving |
| Disposal of equipment |
**Catheter care** | _Have you considered all aspects of this section?_ | **Achieved ✓**
| Procedure and infection control |
| Reporting concerns or results |
| Problem solving |
| Disposal of equipment |
**Removal** | _Have you considered all aspects of this section?_ | **Achieved ✓**
| Procedure and infection control |
| Reporting concerns or results |
| Problem solving |
| Disposal of equipment |
**Intermittent catheterisation** | _Have you considered all aspects of this section?_ | **Achieved ✓**
| Assessment – nurse or patient procedure? |
| Procedure and infection control |
| Self-catheterisation: patient education and clean technique and storage and cleaning of catheter |
| Reporting concerns or results |
| Problem solving |
| Disposal of equipment |
| Ordering of equipment |
## References
1. Baillie L and Busuttil Leaver R (2009) Meeting elimination needs. In: Baillie L (ed.) _Developing Practical Nursing Skills_ , 3rd edn. London: Hodder Education, pp. 321–393.
2. Bray L and Saunders C (2006) Nursing management of paediatric urethral catheterisation. _Nursing Standard_ **20** (24): 51–60.
3. Department of Health (DH) (2001) Guidelines for preventing infections associated with the insertion and maintenance of short-term indwelling urethral catheters in acute care. _Journal of Hospital Infection_ **47** (suppl): S39–46.
4. Department of Health (DH) (2012) _The NHS Safety Thermometer Equality Analysis_. London: DH.
5. Dingwall L and McLafferty E (2006) Nurses' perceptions of indwelling urinary catheters in older people. _Nursing Standard_ **21** (14–16): 35–42.
6. Dougherty L and Lister S (eds) (2011) _The Royal Marsden Hospital Manual of Clinical Nursing Procedures_ , 8th edn. Oxford: Blackwell Publishing.
7. European Association of Urological Nurses (EAUN) (2012) _Evidence-based Guidelines for Best Practice in Urological Health Care: Catheterisation & Indwelling Catheters in Adults_. EAUN: Arnhem.
8. Fisher J (2010) The importance of effective catheter securement. _British Journal of Nursing (Continence Care Supplement)_ **19** (18): S14–S18.
9. Foxley S (2011) Indwelling urinary catheters: accurate monitoring of urine output. _British Journal of Nursing_ **20** (9): 564–569.
10. Gibney L (2010) Offering patients a choice of urinary catheter drainage system. _British Journal of Nursing_ **19** (15): 954–958.
11. Hughes E (2004) Principles of post-operative care. _Nursing Standard_ **19** (5): 43–51.
12. Joanna Briggs Institute (JBI) (2006) _Best Practice: Removal of Short Term Indwelling Urethral Catheters_ , vol **10**. Adelaide: Blackwell Publishing.
13. Kelleher M (2002) Removal of urinary catheters: midnight vs 0600 hours. _British Journal of Nursing_ **11** (2): 84–90.
14. Leaver R B (2007) The evidence for urethral meatal cleansing. _Nursing Standard_ **21** (41): 39–42.
15. Mangnall J and Watterson L (2006) Principles of aseptic technique in urinary catheterisation. _Nursing Standard_ **21** (8): 49–56.
16. Nazarko L (2010) Effective evidence-based catheter management: an update. _British Journal of Nursing_ **19** (15): 948–953
17. NHS Quality Improvement Scotland (NHS QIS) (2004) _Best Practice Statement: Urinary Catheterisation and Catheter Care_. Edinburgh: NHS Quality Improvement Scotland.
18. National Institute for Health and Clinical Excellence (NICE) (2012) _Infection Control, Prevention of Healthcare-associated Infection in Primary and Community Care_. Clinical Guideline 139. London: NICE.
19. NPSA (2009) Female urinary catheters causing trauma to adult males: Rapid Response Report RRR02 Available at: <http://www.nrls.npsa.nhs.uk/alerts/?entryid45=59897> (accessed December 2015).
20. Pellatt G C (2007) Anatomy and physiology of urinary elimination. Part 1. _British Journal of Nursing_ **16** : 406–410.
21. Patel A R, Jones J S and Babineau D (2008) Lidocaine 2% gel versus plain lubricating gel for pain reduction during flexible cystoscopy: a meta-analysis of prospective, randomised, controlled trials. _The Journal of Urology_ **179** (3): 986–990.
22. RCN (2012) Catheter Care: _RCN Guidance for Nurses_. RCN: London.
23. Rees J and Mawson T (2007) Guidelines on catheter use in patients with a hip fracture. _Nursing Times_ **103** (16): 30–31.
24. Skills for Health (2010) CC02 Insert and secure urethral catheters. Available at: <https://tools.skillsforhealth.org.uk/competence/show/html/id/1008/> (accessed 9 December 2015).
25. Tortora G J and Derrickson B (2011) _Principles of Anatomy and Physiology_ , 12th edn. Hoboken, NJ: John Wiley & Sons Inc.
26. Trigg E and Mohammed T (2010) _Practices in Children's Nursing_ , 3rd edn. Churchill Livingston: Edinburgh.
# Chapter 12
Venepuncture
# Learning objectives
* Discuss the anatomy and physiology relating to venepuncture
* Review skills and competence with regard to undertaking venepuncture
* Describe possible complications of venepuncture and how to manage them
## Aim of this chapter
The aim of this chapter is to review the reasons for undertaking peripheral venepuncture (blood sampling) and the associated complications and risk prevention. _This may not, however, be a role that is expected of all healthcare assistants, so please check your local policy and access any approved training_.
## Reasons for performing venepuncture
The term 'venepuncture' is used to describe the introduction of a needle into a vein to obtain a representative sample of the circulating blood for laboratory (haematological, biochemical or bacteriological) analysis, and is usually requested by a medical practitioner/doctor to diagnose or monitor a patient's condition and/or treatment.
## Relevant anatomy and physiology
It is essential that healthcare assistants and assistant practitioners undertaking the technique have a good understanding of the anatomy and physiology of arteries, veins and associated nerves.
Blood vessels comprise a network of channels through which blood flows and they are active organs that, when functioning properly, assist the heart in circulating the blood and influence the blood's constitution. The vessels that take blood away from the heart are arteries. The vessels that bring blood toward the heart are veins. Veins carry deoxygenated blood back to the heart and their pressure is significantly lower than in arteries. Arteries transport blood away from the heart under pressure and are larger vessels with more elastic tissue and muscle, although this does vary depending on the size of the vessel. Generally, arteries have veins of the same size running right alongside or near them, and they often have similar names (Norris and Siegfried 2011). Veins and arteries are different; both have three layers of tissue but vein walls are thinner, having less muscle and elastic tissue in the middle layer (tunica media) (Tortora and Derrickson 2014). Veins also have valves (which help blood return to the heart) that are common especially where blood return is against gravity, for example lower limbs. Care must be taken to avoid sites where veins meet (bifurcation) due to the presence of these valves, because these can be damaged.
For successful venepuncture, blood is sampled from a vein in the patient's arm. As arteries, veins and nerves can be in similar locations, care must be taken during the assessment and procedure to avoid arteries and nerves.
## Common sites for venepuncture
The site most commonly chosen for taking a sample of venous blood is the area in the bend of the elbow, the antecubital fossa, where superficial veins (the median cubital vein, the basilica vein, the cephalic vein) are readily accessible (Bishop 2009). Preferred or first choice should be the median cubital vein (Figure 12.1).
**Figure 12.1** Common sites (upper arm).
The healthcare assistant and assistant practitioner needs to consider many aspects when selecting a vein and Table 12.1 gives some reasons for choice.
# Think about it
What are two differences between a vein and an artery?
**Table 12.1** Summarising possible considerations for vein choice
**Consideration** | **Explanation**
---|---
Patient knowledge | Discussing past experience with the patient is always advisable. Patients can tell you of any previous difficulties and preferred sites (Bishop 2009) which may result in less discomfort for the patient (Ingram and Lavery 2009). You may also take consideration as to whether the patient is left or right handed.
Belonephobia – fear of needles | Patient anxiety is well documented; for some, fear of needles, however, goes beyond anxiety to phobia. Physical symptoms range from sweating to fainting and even death (Ellson 2008). It is important to use good communication skills and distraction therapy to help to relax your patient. Check with local policy for recommendations regarding use of a local anaesthetic cream to. Refer to a more experienced member of staff.
Feeling/palpate the vein | This helps to distinguish veins from arteries or tendons. To palpate a vein, place one or two fingertips over it and press lightly. Release the pressure to assess the veins elasticity and rebound filling (Bishop 2009). A vein suitable for venepuncture should feel round, bouncy and engorged as opposed to hard (tendon), bumpy and flat. Nerves are not palpatable and the patient will complain of a shooting 'electric shock' type of pain if a nerve is touched (Witt 2011).
Vein choice | Veins to avoid are those that appear sclerosed, fibrosed, oedematous, small, non-palpable, inflamed, bruised, sore and close to arteries, valves or nerves (Hobson 2015).
Visual appearance of skin | Skin should be assessed for dermatological conditions (e.g. psoriases); signs of infection; haematoma; oedema; injury/damage (e.g. burns, wounds) which could result in increased complications and/or discomfort for the patient.
Health factors – existing conditions may result in complications for example:
Rheumatiod arthritis
Parkinson's disease
Cerebrovascular accident
Arterioveous fistula for dialysis
Intravenous infusion in place | The joint capsule, for example the elbow, may be inflamed and the tourniquet position may cause pain (Ingram and Lavery 2009).
Tremors and movement may make venepuncture difficult, additional help maybe required (Witt 2011).
Do not use the affected arm because sensation and circulation may be altered, and thus, if pain or injury occurs, may not be identified at an early stage (Ingram and Lavery 2009).
An arteriovenous fistula is an artificial shunt, which is permanent fusion of a vein of artery for patients undergoing dialysis. This site must **not** be used – seek advice. Check local policy.
Any samples of blood taken above an IV infusion may be contaminated (Witt 2011), otherwise this may alter blood results (Ingram and Lavery 2009). Devices may be turned off prior to blood tests, however, _remember to check your policy and always seek advice on any action taken._
In summary, the healthcare assistant must, as part of good assessment practice, be able to see and feel (palpate) the vein.
## Infection
Understanding infection control issues in venepuncture is essential to prevent complications due to poor practice (Hobson 2008). Venepuncture is the most common clinical practice that breaches the circulatory system, so healthcare assistants and assistant practitioners should consider their role in the prevention of infection (Box 12.1).
# Box 12.1 Predisposing infection risk factors and management
* Skin colonisation (surface bacterial spread) can allow bacteria to enter the circulatory system through the insertion of a needle, so ensure careful site selection and cleansing if there is evidence or concern of contamination.
* Remote infection (e.g. urinary tract infection) can also lead to a risk; the patient should be educated about not tampering with the site or sterile dressing, if used, and this should reduce the risk.
* Multi-use disinfectants can become colonised with bacteria very quickly, so use only single-use sachets when cleansing the site.
* Expired or damaged stock can be a source of infection; ensure that stock is in date and has been stored correctly, and is used for its intended purpose; single-use devices must be used (Medicines and Healthcare Products Regulatory Agency (MHPRA) 2013).
* Practitioner hands are the single most common way that bacteria are transferred onto devices (equipment), so ensure correct hand cleansing.
Adapted with permission from NHS Lothian (2007).
# Box 12.2 Additional requirements (for vacuum system)
* Blood culture set (aerobic and anaerobic bottles).
* Three needles.
* Two alcohol wipes.
* 20 ml syringe and adaptor (Figure 12.7).
## Hand hygiene
Transmission of microorganisms by the hands of healthcare workers is the most likely method of contributing to the spread of infections in hospitals (Loveday et al. 2014). The Royal College of Nurses (RCN 2013a) emphasise the need to be vigilant about hand hygiene. Standard infection control precautions, formerly known as universal precautions, underpin routine safe practice, protecting both staff and clients from microorganisms that may cause infection. By applying standard precautions at all times and to all patients, best practice becomes second nature and the risks of infection are minimised (RCN 2012). The WHO's Five Moments for Hand Hygiene (WHO 2014) defines the crucial times when healthcare workers should perform hand hygiene and has been adapted by the National Patient Safety Agency (NPSA) for application in the UK context to include:
1. **1.** Before contact.
2. **2.** Before aseptic task.
3. **3.** After body fluid exposure risk.
4. **4.** After patient contact.
5. **5.** After contact with patient surroundings.
The Five Moments approach to hand hygiene applies the most comprehensive evidence that aims to improve hand hygiene across the NHS. The approach supports coordinators in ensuring hand hygiene is performed at the right time (the Five Moments) in the right place (the point of care) using the appropriate method (soap and water hand washing or alcohol hand rub) using the correct technique. The RCN (2015) highlights the importance of reducing Healthcare Associated Infections (HCAIs), which is an essential part of the role of the HCA and AP when performing venepuncture. Please check your local policies and procedures.
An effective handwashing technique involves three stages: preparation, washing and rinsing, and drying. Preparation requires wetting hands under tepid running water before applying liquid soap or an antimicrobial preparation. The handwash solution must come into contact with all of the surfaces of the hand. The hands must be rubbed together vigorously for a minimum of 10–15 seconds, paying particular attention to the tips of the fingers, the thumbs and the areas between the fingers. Hands should be rinsed thoroughly before drying with good quality paper towels.
# Think about it
Read the WHO's Five Moments for Hand Hygiene, thinking about your own actions. Think about the effects that not washing your hands can have on a single patient in one shift.
## Aseptic (sterile) technique
Aseptic technique is a term used to describe a sterile process within nursing practice to minimise infections associated with invasive procedures (Hobson 2008). The National Institute for Health and Care Excellence (2012) assert that aseptic technique ensures only uncontaminated equipment and fluids come into contact with susceptible body sites. Using the principles of asepsis minimises the spread of organisms from one person to another and should therefore be used during any clinical procedure that bypasses the body's natural defences.
The use of aseptic technique should be used in line with local policy. The venepuncture site should be cleansed thoroughly with a cleaning agent, such as with a 70% isopropyl alcohol/2% chlorhexadine wipe (e.g. Clinell swab) or a 70% isopropyl alcohol wipe (e.g. street). It must then be left to dry. Povidine iodine must be used as an alternative if the patient is sensitive to chlorhexadine. It is recommended that the site is not re-palpated after cleansing, although this may be necessary if the patient's vein is difficult to find (Boyd 2013). Skills for Health (2015) have identified the importance of infection control in Standard 15 of the Care Certificate.
## Health and safety
All staff who undertake venepuncture should be up to date with their hepatitis B vaccination and, as Bishop (2009) points out, should be aware of local policy and practice in order to protect themselves and others. Appropriate protective clothing such as gloves and aprons should be worn to minimise the risk of infection when undertaking the procedure (Hobson 2008). It is important to check if the patient has an allergy to latex in order to avoid wearing gloves that may cause a reaction. The Health and Safety Executive (HSE) report that natural rubber latex (NRL) proteins have the potential to cause asthma and urticaria. More serious allergic reactions, such as anaphylaxis, are also possible. NRL proteins are substances hazardous to health under COSHH (Control of Substances Hazardous to Health Regulations). Therefore, careful patient history must be taken into account when selecting gloves to avoid impacting patients who suffer with allergies and sensitivity to latex.
## Environment
The environment must be visibly clean, free from dust and soilage. Hart (2011) maintains cleaning and disinfection programmes and protocols for environmental surfaces in patient care areas must be defined and areas fully monitored to ensure high standards of cleanliness are achieved. The trolley and equipment must be prepared in line with local policy to ensure good practice with adequate lighting to enable careful assessment of the patient and veins.
The patient needs to be prepared and made as comfortable as possible, which will go some way to reducing the level of anxiety experienced. If the patient is relaxed, effective interpersonal skills used and the arm supported, veins are likely to be dilated and access less painful and so there is greater likelihood of a positive patient experience (Dougherty 2011) (Table 12.2).
# Think about it
Identify the common predisposing infection risk factors and describe how to prevent these risks in venepuncture practice.
**Table 12.2** Guide to good venepuncture practice: vacuum system
**Action** | **Reason**
---|---
1. Wash hands with liquid soap, and dry hands thoroughly followed by an alcohol hand rub, or wash with an approved antiseptic solution | To minimise the risk of healthcare-associated infection
2. Assemble the equipment required for the procedure on a trolley or a tray. Ensure that all equipment and disposables used are intact and within their expiry dates | Procedure is carried out safely, efficiently and without interruptions
To maintain asepsis during the procedure
3. Identify the tests on the requisition form and select the appropriate blood collection tubes | To ensure correct sampling
4. Allow the patient time to ask questions and express concerns about the procedure | To obtain patient consent and cooperation
5. Identify the patient, check the addressograph label or written details on the requisition form and ensure that it corresponds with the details on the patient's identity wristband
Check all details verbally by actively asking the patient to state their name and date of birth (DOB)
Where a patient is unable to verbally state their name and DOB, good practice suggests that two staff check the identity bracelet against health records and requisition form(s) | To ensure the blood specimen is taken from the patient indicated on the request form
To ensure all details are correct
6. Help the patient into a comfortable position either sitting in a chair or lying on the bed. The arm must be supported in an extended (straight) position | To enable the healthcare assistant to carry out the procedure with ease and maintain the patient's comfort
7. Prepare the area, e.g. provide adequate lighting, and heighten the bed, lower cot sides | To ensure a safe working environment
Source: Adapted from NHS Lothian 2007. Reproduced with permission of NHS Lothian.
## Performing the skill: requirements and technique
### Venepuncture equipment
For equipment using a vacuum system, see Figure 12.2 and examples below.
**Figure 12.2** Vacuum tubes.
#### Examples of venepuncture equipment
* Tourniquet: consider the quick-release type.
* Non-sterile gloves.
* Apron.
* Alcohol wipe, for example 70% isopropyl alcohol.
* Bactericidal alcohol hand rub, for example Hibisol.
* Requisition forms and blood specimen bags.
* Blood specimen tubes: system as used by local organisation.
* Sterile needle: size (gauge) appropriate to the vein and sampling needs, using smallest where possible (RCN 2013b).
* Cotton-wool ball: non-sterile.
* Tray or trolley.
* Sterile hypoallergenic plaster.
* Sharps disposal bin.
Patient safety must be considered in relation to the patient's position when this procedure is being performed, so ensure that the arm is supported (Figure 12.3). Morris (2011) advocates that the practitioner anticipates if the patient may faint; in which case, lie them flat on a couch or the bed prior to commencing the procedure to ensure patient safety. When performing venepuncture it is essential that the HCA or AP remains calm and talks to the patient in a supportive manner. The ability to perform this task confidently and competently not only reassures the patient but also helps to reduce the risk of avoidable complications occurring (Table 12.3).
**Figure 12.3** Insertion technique example.
**Table 12.3** Specific actions and observations during the procedure
**Action** | **Reason**
---|---
1. Wash hands with liquid soap, and dry hands thoroughly followed by an alcohol hand rub, or wash with an approved antiseptic solution | To minimise the risk of healthcare-associated infection
2. Identify the patient's own preferred site for the procedure based on their previous experience | To actively involve the patient in their treatment. To familiarise the healthcare assistant with the patient's medical history and factors that may influence choice of vein
3. Apply a tourniquet to the upper arm on the chosen side approx 7–10 cm (3–4 inches) above the puncture site | Increases venous pressure to help vein identification and entry. Careful attention is paid to length of time tourniquet is left on (No more than 1½ min or can cause an adverse effect, as below)
4. Apply enough pressure to impede (slow) venous circulation but not arterial blood flow, check for arterial pulse | Prolonged pressure may lead to vein spasm, pain and haematoma (blood in the tissues)
5. To further encourage venous filling consider:
* Allow their arm to hang at the patient's side.
* Stroke vein lightly.
* Ask the patient to wash their hands or place in warm/hot water.
* Ask patient to assist by clenching and unclenching their hand.
| Aid vein filling and make procedure easier
_Take care because this may affect some results, so may not be recommended_
6. Observe and palpate (feel) the selected vein | To identify its course, depth and distinguish structures such as tendons, and to avoid nearby arteries
7. Release the tourniquet. Check that the vein has decompressed (a thrombosed vein will remain firm and palpable) | Reduce the length of time that tourniquet is in situ (see 3)
Check for a thrombosed (clotted) vein.
8. Push the tube into the needle adaptor by twisting clockwise | Opens the system
9. Wash hands with liquid soap, and dry hands thoroughly followed by an alcohol hand rub, or wash with an approved antiseptic solution
Put on gloves | To minimise the risk of healthcare associated infection. Gloves are worn for the protection of staff against blood spillage. They will not protect against needlestick injuries
10. Ensure the patient's skin is clean. Wash with soap and water and dry thoroughly if visibly dirty
Use alcohol wipe if deemed appropriate, but essential for blood cultures. _Check local policy_
If using alcohol wipe, cleanse the site in a circular movement from the proposed puncture site for 30 s, then allow to air dry for 30 s | To minimise the risk of infection from the patient's own skin during this invasive procedure
Recommended in hospital patients, but may not be required in a community setting
11. Reapply the tourniquet to the identified site | Encourage venous filling
12. Inspect the needle | To ensure needle is sharp with no barbs (hooks)
13. With the patient's arm in a downward position, line up the needle and collection tube with the vein from which the blood will be drawn. Using the thumb or first finger of free hand anchor the vein by applying manual traction of the skin 2–5 cm below the proposed insertion site. With the bevel of the needle upward insert the needle into the vein. A sensation of resistance will be felt followed by the needle entering the vein | To hold the vein steady and provide countertension, which will facilitate a smooth needle entry
14. Advance the needle a further
1–2 mm into the vein | To stabilise the needle within the vein and prevent it becoming dislodged
15. Secure the needle by holding the guide sheath firmly | To prevent movement of the needle in or out of the vein
16. Using the syringe technique for the initial specimen, fill the blood collection tube by slowly pulling back the plunger, keeping the needle in centre of the vein | To ensure appropriate filling of blood sample tube
17. Remove the tube from the needle by twisting anticlockwise (grip the needle guide sleeve firmly). The needle remains in the vein. Secure next prepared tube onto the needle by twisting clockwise | To minimise the movement of needle and prevent mechanical phlebitis (infection due to friction)
18. The second and subsequent samples may be taken either by the syringe technique or alternatively by the vacuum principle where there is good venous supply
Remove the final tube from the needle | To aid blood sampling procedure
To ensure the system is 'closed'
19. Release the tourniquet | To release venous congestion
Ensure it is not left on
20. Then slip the cotton wool ball down over the puncture site and do not apply pressure until needle has been fully removed
Once removed, apply firm finger pressure until bleeding stops (approximately 2 minutes).
Do not allow the patient to bend the arm | Prevent bleeding and haematoma formation
To prevent pain on removal
Prolonged finger (digital) pressure may be required if treatment and/or medical condition interferes with clotting mechanisms
Prevent shearing to vein, which causes more bleeding/bruising
21. Once venepuncture site has stopped bleeding, if required, cover site with an Elastoplast dressing, or hypoallergenic dressing if patient has an allergy | To prevent leakage of blood until healing is complete
22. Make no more than two attempts to obtain blood sample/s. If unsuccessful, obtain assistance from more experienced staff | Patient comfort
Prevent trauma to vein
23. Ensure the patient is comfortable.
Advise the patient to inform staff if venepuncture site starts to bleed or is tender or painful, and when to remove any dressing applied
Explain to the patient that results may take some time to come back and that they will be informed when they are available | Reduce anxieties
24. Complete the labels on the blood samples you have taken prior to leaving the patient/bedside, checking details with the patient and the blood forms | Ensure that blood samples are correctly labelled
Source: Adapted from NHS Lothian 2007. Reproduced with permission of NHS Lothian.
### Winged infusion device, for example the butterfly option
The option of using a winged infusion device may not be open to all healthcare assistants; _please check local policy and confirm if this practice is taught, supported and supervised before undertaking_. Refer to Table 12.4 for specific guidance on inserting a winged device.
**Table 12.4** Guide to good practice and winged device (butterfly) insertion
**Action** | **Reason**
---|---
1. Assess and prepare patient as 1–12 in Table 12.3 |
2. Attach adaptor to the tail of the butterfly before attaching the first tube. Fold up wings of butterfly and insert needle into vein as detailed in 13–14 in Table 12.3 (Figure 12.5); bring the device level with skin and then advance along length of the needle, keeping it level and in line with the vein | To prevent blood spillage or leakage
3. Flatten the wings of the butterfly to the skin and secure with Micropore tape | To prevent dislodgement of the butterfly during specimen collection
4. Collect the first specimen using the syringe technique |
5. Complete procedure as 16–24 in Table 12.3 |
#### Additional requirements for winged infusion device
* Butterfly 21 or 23 gauge, size depending on patient's vein, for example a 23 gauge for a frail elderly patient with small veins.
* Adaptor: see Figure 12.4.
* Tape for securing butterfly.
**Figure 12.4** Winged device and adaptor.
**Figure 12.5** Insertion technique.
Some practice areas only use senior and experienced healthcare staff in blood culture sampling, _so again please check local policy and practice prior to undertaking this procedure, if an accepted role_.
According to Gilligan (2012), low contamination rates are because of training, practice, resources and professionalism. Ernst (2001) said that the most common cause of contamination occurred when a practitioner touched the prepared site, and suggested the use of mental markers, such as freckles, to reduce this urge.
The ideal volume for an adult is 20 ml evenly distributed between both collection bottles, and not exceeding 12 ml (Ernst 2001). Ernst (2001) also proposed that, if the yield is less than 20 ml, it is better to load (fill) 10 ml into the aerobic bottle (e.g. blue), because 98% of septicaemias are caused by aerobic (need oxygen) organisms, and most of the causative organisms can still be detected, even if the anaerobic (e.g. pink) bottle has less than the optimum volume. Overfilling can lead to false positives, so take care when filling. However, fill the anaerobic (e.g. pink) bottle first, to minimise the risk of air in the syringe getting in and altering the anaerobic (oxygen not needed) environment (Ernst 2001).
If a blood culture sample is falsely positive, due to incorrect skin cleansing or contamination from the healthcare assistant's hands, then a patient could have an increased length of hospital stay, which increases costs, with the associated risk of infection. The patient may require transfer if thought to be septicaemic (bacteria in the blood), suffer the unnecessary use of antibiotics and the increased risks associated with this (Figure 12.6). The intravenous (IV) route would be preferred to treat septicaemia, and so would also incur increased costs and pressure on staff time. Thus the longer a patient is in hospital, the more admissions will be restricted, putting more pressure on to limited beds. Therefore extra care is needed when sampling for blood cultures (Table 12.5) (Lavery and Ingram 2005).
**Figure 12.6** Example of blood culture set.
**Table 12.5** Blood cultures: good practice guide
**Action** | **Reason**
---|---
1. Cleanse the proposed venepuncture site as per Table 12.3, Step 10 | To prevent contamination of blood sample from microorganisms on the skin
2. Do not re-palpate the vein after the site has been cleansed | As above
3. Remove flip top cap from bottles, wipe the tops with fresh alcohol wipe, allow to dry, then insert clean needle into each | Preventing contamination of the sample
4. Withdraw 20 ml of blood (1–3 ml in neonates) from the adult patient using technique described in Table 12.3 | Adequate sample for laboratory testing
5. Fill both bottles and divide blood equally, 10 ml in each | Ensure adequate sample size
6. Dispose of sharps immediately into sharps container | Reducing the possibility of a needlestick injury
7. Decontaminate (cleanse) hands | Preventing infection
8. Minimum data required on samples are surname, forename, date of birth, gender, date and time of sample, type and site of sample, location of patient | Ensuring that laboratory has correct information
9. Minimum data are also required on request form, addressographs can be used including the time and date of sampling; if high risk (e.g. HIV), any antibiotic therapy and relevant clinical details | Ensuring that laboratory has the correct and appropriate information
10. Arrange for transport to the laboratory, if not available immediately, e.g. night-time, leave cultures at room temperature | Appropriate storage of blood cultures
Source: Adapted from NHS Lothian 2007. Reproduced with permission of NHS Lothian.
# Think about it
Consider if skin surface bacteria contaminate a sample for blood culture. What might be the outcome for the patient and the service?
## Related aspects and terminology
### Consent
NHS Choices (2014) reports that, for consent to be valid, it must be voluntary and informed and the person consenting must have the capacity to make the decision. For consent to be voluntary, the decision to either consent or not to consent to treatment must be made by the person themselves, and must not be influenced by pressure from medical staff, friends or family. The person/patient must be given all of the information in terms of what the treatment involves, including the benefits and risks, whether there are reasonable alternative treatments and what will happen if treatment does not go ahead: this is informed consent. With venepuncture it is sometimes thought that patients have voluntarily consented when their actions support this idea, for example turning up for an appointment or simply rolling up a sleeve and presenting an arm to have the sample of blood taken. For more discussion on consent, refer to Chapters 1 and .
### Anxiety
In an effort to reduce anxiety, patients should be asked whether they have had venepuncture performed previously. Attention should be paid particularly where there were any adverse (poor) outcomes or experiences, so that reassurance or further action can be taken.
With regard to the actual procedure, anxiety can be caused by a previous bad experience, a degree of 'needle phobia' (fear of a needle) or just a dislike of medical procedures. The RCN (2010) noted the need for skilled practice that minimised pain and anxiety in relation to children or young people, but can be seen as good practice for all. Dougherty (2011) reports a number of approaches have been successful in reducing patient anxiety, including the use of guided imagery (imagining a place where they can feel comfortable and relaxed), music and distraction techniques (RCN 2013b). Distraction therapy is simply a means of taking the mind off a procedure by concentrating on something else, for example there may be a television programme on or a conversation about a subject of interest or even asking the patient to focus on their breathing to relax.
**Figure 12.7** Adaptor.
There are a number of local anaesthetic creams that can be applied to the skin to help reduce pain, such as EMLA and Amatop. These are medicines and will need to be prescribed and administered. Dougherty (2011), however, warns us that although less painful, these creams can cause vasoconstriction making venepuncture more difficult. _Please check your local policy to see if this is within the boundaries of your role otherwise you may be breaking vicarious liability_ (Boyd 2013).
## Common problems
### Unsuccessful sampling
This may be due to poor vein assessment, incorrect choice of sampling device or poor technique. Careful review of veins and technique before starting the procedure, as well as consideration of patient comfort and position, is necessary to prevent this. Table 12.6 is a competency framework for venepuncture.
**Table 12.6** Competency framework: venepuncture
| **First assessment/reassessment**
---|---
Steps | Demonstration/supervised practice
Venepuncture | Date/sign | Date/sign | Date/sign | Date/sign | Date/competent signature
| 1 | 2 | 3 | 4 | 5
1. **1.** Gives explanation of procedure and obtains patient's verbal consent
2. **2.** Selects appropriate equipment and sample tubes
3. **3.** Correctly identifies the patient against the request form
4. **4.** Ensures patient comfort and privacy
5. **5.** Reassures patient, and uses anxiety relieving measures (if appropriate)
6. **6.** Hands washed, gloves and apron worn
7. **7.** Uses appropriate methods to encourage good venous filling
8. **8.** Identifies appropriate vein for venepuncture
9. **9.** Prepares patient's skin as per local policy
10. **10.** Carries out procedure successfully
11. **11.** Removes last sample tube and tourniquet before removing needle
12. **12.** Disposes of sharps immediately
13. **13.** Applies pressure and seals puncture site
14. **14.** Labels and packages samples correctly for transport
15. **15.** Records information in patient's notes
| | | | |
Supervisor/assessor(s):
### Potential complications of venepuncture
#### Bruising/ecchymosis
Hobson (2008) and Morris (2011) report that bruising is caused by blood seeping into surrounding tissues. Older people, especially if they have fragile skin or are on anticoagulation therapy such as warfarin, are likely to bleed or bruise easily. Good technique is of paramount importance.
Bruising is preventable by the following:
* Accurate identification of a suitable vein.
* The correct insertion technique and angle.
* Ensuring that the tourniquet is not applied with excessive pressure or below previous puncture sites.
* 'Fixing' the vein position by skin traction during the insertion of the needle.
* Ensuring adequate pressure to the puncture site after needle removal, which will prevent further damage (Morris 2011).
Accurate monitoring of the site and documentation of the bruise is also necessary.
#### Haematoma
A haematoma is described by Hobson (2008) as a complication that results in blood leaking from the vein into surrounding tissue, which is caused by poor technique and failure to select the appropriate vein.
Other causes identified by Morris (2013) are inadequate pressure to the puncture site or failure to remove the tourniquet before removing the needle; poor vein selection; vulnerable patient such as those on anticoagulant therapy; incorrect use of the tourniquet; multiple attempts to access the vein and failure to insert the needle correctly into the vein. In order to manage a haematoma that occurs during the procedure, remove the tube, release the tourniquet and then remove the needle using a sterile swab according to local policy (Dougherty and Lister 2011). The patient should be taken care of and the haematoma monitored and documented (NMC 2015).
#### Excessive pain
This can be caused by the frequent use of a vein, or poor technique, such as blind plunging manoeuvres (without feeling/assessing for vein); where a nerve or valve is touched; or if the patient is anxious, fearful or has a low pain threshold.
This is prevented by:
* ensuring that the patient is comfortable and the arm supported;
* allowing the alcohol to dry at the skin site;
* carrying out the procedure in a confident unhurried manner.
Consider the use of local anaesthetic cream as previously discussed. _Please check your local practice and policy, because it may not be within the HCA or AP role to apply local anaesthetic cream/gel_.
#### Arterial puncture
Arterial puncture is characterised by pain and spurting of bright red blood. This is caused by poor technique or inadequate assessment and the healthcare assistant would see bright red blood pulsating into the tube and needle. Prevention is by:
* thorough assessment of the site;
* the use of the correct insertion technique and angle.
Management is to immediately remove the needle and apply prolonged finger pressure for 5 minutes and then a pressure bandage for at least a further 5 minutes. The patient should be under observation, assessment and medical supervision, and the incident should be recorded in the patient's case notes and the local adverse incident reporting mechanisms followed and reported to the nurse in charge (RCN 2013b).
#### Fibrosis
This is where the vein becomes hard or cord-like and may occur with prolonged use of one site. It is prevented by:
* careful assessment
* rotation of sites.
#### Phlebitis
This is an infection caused by mechanical irritation (needle rubbing inside the vein) or poor aseptic technique, and is considered a rare complication in venepuncture. The symptoms of phlebitis are pain, oedema, and erythema – often presenting as a red streak along the length of the vein. Prevention is by:
* following sound infection control practice (Morris 2011; RCN 2013b);
* not re-palpating the vein after cleansing the site with alcohol.
Ongoing site monitoring and documentation are critical, as is investigation to identify the cause and plan the steps for future prevention.
# Think about it
What action should be taken if an artery is punctured?
What preventive measures should have been considered?
## Summary
Venepuncture is a common procedure and is carried out by many members of the multidisciplinary team both in hospitals and in the community. Thus effective communication and prompt recording are critical for safe patient care. Venepuncture is invasive and is a diagnostic requirement; therefore, it is important practitioners have a theoretical knowledge to underpin the competent performance of this skill.
# Case study 12.1
Mr Robert Walls is an older man aged 90 years and requires samples for full blood count (FBC) and urea and electrolytes (U&Es).
He is frail and dehydrated after a fall, and has an intravenous infusion running into his left median cubital vein. He has a residual weakness in his right arm from a previous stroke (cerebral vascular accident). He is restless and upset at being in hospital, and slightly confused.
_Outline the assessment process here and discuss the choice of venepuncture device and describe why you would choose it_.
Below is a self-assessment checklist; however, you may also wish to review some of the skills involved in venepuncture, for example infection control is a part of the Skills for Health Care Passport. You might wish to discuss this with your manager.
# Self-assessment
**Assessment** | **Aspects** | **Achieved ✓**
---|---|---
Patient | _Have you considered all aspects of this section?_
Patient assessment: veins and general condition
Infection control and asepsis aspects
Consent, communication and education
Problem solving |
Procedure | _Have you considered all aspects of this section?_
Equipment selection and insertion technique
Recording and labelling
Reporting concerns
Problem solving
Disposal of equipment | **Achieved ✓**
Winged device | _Have you considered all aspects of this section?_
Selection and insertion of butterfly
Recording and labelling
Reporting concerns
Problem solving
Disposal of equipment | **Achieved ✓**
Blood cultures | _Have you considered all aspects of this section?_ | **Achieved ✓**
| Infection control and procedure |
| Disposal of equipment |
## References
1. Bishop T (2009) Venepuncture. _Practice Nurse_ **37** (12): 18–21.
2. Boyd C (2013) _Student Survival Skills: Clinical Skills for Nurses_. London: John Wiley & Sons.
3. Dougherty L (2011) Patient's perspective. In: Phillips S, Collins M and Dougherty L (eds) _Venepuncture and Cannulation_. Oxford: Wiley Blackwell, pp. 281–296.
4. Dougherty L and Lister S (eds) (2011) _The Royal Marsden Manual of Clinical Nursing Procedures_ , 8th edn. Oxford: Blackwell Wiley.
5. Ellson R (2008) Venepuncture and cannulation: In: Richardson R (ed.) _Clinical Skills for Student Nurses: Theory, Practice and Reflection_. Devon: Reflect Press.
6. Ernst D J (2001) The right way to do blood cultures. _Nursing Journal for Registered Nurses_ **64** (3): 28–32.
7. Gilligan P (2012) Blood culture contamination: a clinical and financial burden. _Infection Control and Hospital Epidemiology_ **34** (10): 22–23.
8. Hart T (2013) Promoting hand hygiene in clinical practice. _Nursing Times_ **109** (38): 14–15.
9. Hobson P (2008) Venepuncture and cannulation: theoretical aspects. _British Journal of Healthcare Assistants_ **9** (3): 75–78.
10. Ingram P and Lavery I (2009) _Clinical Skills for Healthcare Assistants_. Oxford: Wiley-Blackwell.
11. Lavery I and Ingram P (2005) Venepuncture: Best practice. _Nursing Standard_ **19** (49): 55–65.
12. Loveday H P, Wilson J A, Pratt R, et al. (2014) epic3: national evidence based guidelines for preventing health care associated infections in NHS hospitals in England. _Journal of Hospital Infection_ **86** Suppl 1: S1–S70.
13. Medicines and Healthcare Products Regulatory Agency (MHPRA) (2013) _Single-Use Medical Devices: Implications and Consequences of Reuse_. London: Medicines and Healthcare Products Regulatory Agency.
14. Morris W (2011) Complications. In: Phillips S, Collins M and Dougherty L (eds) _Venepuncture and Cannulation_. Oxford: Wiley Blackwell, pp. 281–296.
15. National Institute for Health Care Excellence (NICE) (2012) Infection Prevention and Control of Healthcare-associated Infections in Primary and Community Care. NICE Clinical Guideline 139 Available at: <https://www.nice.org.uk/guidance/cg139/evidence/control-full-guideline-185186701> (accessed December 2015).
16. NHS Choices (2014) Consent to Treatment. Available at: <http://www.nhs.uk/conditions/consent-to-treatment/pages/introduction.aspx> (accessed December 2015).
17. NHS Lothian (2007) _Adult Venepuncture and/or Peripheral IV Cannulation: Clinical Skills Education Package_. Edinburgh: NHS Lothian.
18. Norris M and Siegfried D (2011) _Anatomy and Physiology for Dummies_ , 2nd edn. London: Wiley Publishing Inc.
19. Nursing and Midwifery Council (NMC) (2015) _The Code: Professional Standards of Practice and Behaviour for Nurses and Nidwives_. London: NMC.
20. Royal College of Nursing (2010) _Standards for Infusion Therapy_ , 3rd edn. London: RCN.
21. Royal College of Nursing (2012) _Essential Practice for Infection Prevention and Control: Guidance for Nursing Staff_. London: RCN.
22. Royal College of Nursing (2013a) Wipe It Out: One Chance to Get it Right. _Infection Prevention and Control Information and Learning Resources for Health Care Staff_. London: RCN.
23. Royal College of Nursing (2013b) _Competencies: An Education and Training Competency Framework for Capillary Blood Sampling and Venepuncture in Children and Young People_. London: RCN.
24. Royal College of Nursing (2015) _Infection Prevention and Control within Health and Social Care_. London: RCN.
25. Skills for Health (2015) The Care Certificate Framework (Assessor) Health Education England, Skills for Care and Skills for Health.
26. Tortora G J and Derrickson B (2014) _Principles of Anatomy and Physiology_ , EMEA edn. Hoboken, NJ: John Wiley & Sons Inc.
27. Witt B (2011) Patient's perspective. In: Phillips S, Collins M and Dougherty L (eds) _Venepuncture and Cannulation_. Oxford: Wiley Blackwell, pp. 108–130.
28. World Health Organization (2014) Your Five Moments for Hand Hygiene. tinyurl.com/WHO5Moments.
# Chapter 13
Blood glucose monitoring
# Learning objectives
* Explain what causes diabetes
* Define the different types of diabetes
* List the common symptoms and risk factors
* Describe complications associated with diabetes
* Describe how to measure and record accurate blood sugar levels using appropriate equipment
## Aim of this chapter
The aim of this chapter is to understand the fundamental principles of diabetes and apply this to the skill of measuring blood glucose.
## What causes diabetes?
The World Health Organisation (2015) describes diabetes as a chronic disease that occurs either when the pancreas does not produce enough insulin or when the body cannot effectively use the insulin it produces. Insulin is a hormone that regulates blood sugar. Hyperglycaemia, or raised blood sugar, is a common effect of uncontrolled diabetes and over time leads to serious damage to many of the body's systems, especially the nerves and blood vessels. The main two types of diabetes are type 1 and type 2, both of which are described later.
## Reasons for performing blood glucose measurement
Monitoring and self-monitoring of blood glucose is recognised as an important tool in diabetes management (Wallymahmed 2013). Glucose monitoring is done to obtain information on blood glucose levels at various times to allow a therapeutic regime to be adjusted, facilitating optimal control avoiding hypoglycaemia and hyerglycaemia (Whitmore 2012).
Blood glucose monitoring is widely undertaken in a number of settings and situations, for example in hospital or at home (Dunning 2014). Point of care testing or near patient testing (where samples are not sent to the laboratory) is a convenient and quick way to obtain blood glucose measurements. Whitmore (2012) identified the need to use equipment correctly and ensuring the readings are accurate. There is a clear link between good blood glucose or glycaemic control and the prevention of long-term complications. It important for staff to work within the boundaries of their role; please check local policy and ensure you have had the required training in order to undertake this procedure. Blood glucose levels are carried out for a variety of reasons, and these are shown in Box 13.1.
# Box 13.1 Reasons for taking blood glucose monitoring
* Frequent hypoglycaemic episodes and hypoglycaemic unawareness.
* Unstable or diabetic.
* Managing illnesses at home when recovering from an illness.
* Gestational diabetes mellitus (GDM) pregnancy and in neonates born to women with GDM and diabetes.
* Stabling a new treatment regimen.
* Stabilising Oral Hypoglycaemic Agents (OHA) and/or insulin doses: for example patients with renal failure and/or CVD where signs of hypoglycaemia can be masked; during investigations; during travel and/or to monitor medicine interactions.
There are benefits to patients in keeping their blood glucose levels within acceptable limits, and these include the patient:
* running a smaller risk of developing complications (Wallymahmed 2013) (see later);
* feeling more active and healthy;
* having better clinical outcomes if they have an acute cardiovascular event, for example myocardial infarction (heart attack) or stroke (Ritsinger et al. 2014; Laird 2014).
In order to fully understand diabetes, and the importance of blood glucose monitoring, revision of the anatomy and physiology of the pancreas is necessary.
## Relevant anatomy and physiology
### The pancreas
The pancreas is situated in the abdominal cavity with the head nesting in the curve of the duodenum (part of the small intestine). It is a pale grey/pink gland that consists of a broad head, body and narrow tail (Tortora and Derrickson 2014). It is the size of an apple and weighs between 70–100 g (Tan 2011). Figure 13.1 shows the position of the pancreas in relation to other organs. The adrenal glands produce steroid hormones, which are essential for well-being and maintenance of life (Tortora and Derrickson 2014).
**Figure 13.1** Pancreas shown in relation to the kidneys, duodenum and adrenal glands.
The pancreas has both an endocrine and an exocrine function: endocrine means excretion of substances directly into the bloodstream – in this case insulin – and exocrine means excretion via ducts and refers to digestive juices.
Only 2% of the pancreas fulfils the endocrine function and this is performed by collections of cells found in clusters irregularly distributed throughout the pancreas, known as the islets of Langerhans. Within the islets of Langerhans there are two types of cells: _α_ (alpha) cells that produce glucagon and _β_ (beta) cells that produce insulin. The body balances these two hormones to maintain a healthy blood glucose level; Figure 13.2 illustrates the variance in their roles.
**Figure 13.2** Maintenance of blood glucose. Adapted from Tortora and Derrickson (2006), Marieb and Hoehn (2007) and Thibodeau and Patton (2007).
## Related aspects and terminology
### Effects of diabetes
Figure 13.2 demonstrates how the body maintains normal blood glucose levels despite periods of fasting or eating. In diabetes, the blood glucose level remains high after the intake of a carbohydrate meal due to defective glucose metabolism by body cells, thus glucose cannot cross the cell membrane and be absorbed by the body. Conversion of glucose to glycogen in the liver and muscles is diminished, leading to protein being broken down instead.
# Think about it
List some signs or symptoms of diabetes.
### Common terminology
* _Blood glucose_ : the amount of glucose (sometimes also called 'sugar') in the circulating blood.
* _Hypoglycaemia_ : low blood glucose. This is sometimes referred to as a 'hypo'.
* _Hyperglycaemia_ : high blood glucose.
* _DKA (diabetic ketoacidosis)_ : dangerously high blood glucose levels. This can result in the patient being in a coma, and may well be the first symptom to be noticed prior to a diagnosis of diabetes.
* _Polydipsia_ : increased thirst/appetite (Tortora and Derrickson 2014).
* _Polyphagia_ : excess eating (Tortora and Derrickson 2014).
* _Polyuria_ : frequently needing to pass urine (micturition) due to excessive urine production and the kidneys being unable to reabsorb excess water (Tortora and Derrickson 2014).
* _Ketonuria_ : ketones (a byproduct of red blood cells) present in the patient's urine. This is why people with diabetes often test their urine for both ketones and glucose.
* _HbA1c (glycated haemoglobin)_ : percentage of haemoglobin bound to glucose. This is shown in a blood sample that is taken to monitor how well controlled the patient's diabetes is.
### Type 1 diabetes
This usually occurs as a result of the progressive destruction of _β_ cells within the islets of Langerhans, which leads to insulin deficiency (Thrower and Bingley 2014). Type 1 diabetes is thought to be triggered by a variety of environmental factors, for example a prolonged period of ill-health, ingestion of certain toxins, dramatic change in life circumstances and perhaps a genetic predisposition (Dunning 2014). The presence of infection can also result in damage to some cells and the subsequent production of antibodies as part of the autoimmune response. Despite these antibodies being detectable before the symptoms of type 1 diabetes become apparent, the antibodies usually disappear within months of the diagnosis (Knipp and Simell 2012). Other symptoms of diabetes usually only appear once 80–85% of all the _β_ cells have been destroyed. The disease is usually of sudden onset in young adults or children, with the cause being generally unknown. The only treatment option for a patient with type 1 diabetes is subcutaneous insulin replacement therapy and the condition cannot be cured, only managed.
#### Symptoms of type 1 diabetes
* Polydipsia.
* Polyuria.
* Polyphagia.
* Weight loss, due to the body not being able to release insulin, which prevents glucose being released (Tortora and Derrickson 2014).
* Increased incidence of infection.
* Lethargy (extreme tiredness).
* Symptoms of ketoacidosis (see below): collapse, reduced consciousness, restlessness, leading to coma and death if undetected.
#### Ketoacidosis
Diabetic ketoacidosis (DKA) is the result of very low or zero insulin levels, and generally only occurs in type 1 diabetes, because patients with type 2 diabetes have sufficient reserves to prevent this occurring (Noble-Bell and Cox 2014). If it does occur in type 2 diabetes, this is provoked by severe illness and is more likely to develop in people from non-Caucasian ethnic groups (Noble-Bell and Cox 2014). The signs and symptoms Dunning (2014) identifies include polyuria, polydipsia, weakness, fatigue and weight loss and patients tend to present with abdominal pain and vomiting. In severe ketoacidosis there may be tachycardia, hypotension, skin turgour, the smell of acetone (pear drops) on their breath plus deep and/or laboured breathing.
### Type 2 diabetes
Type 2 diabetes is related to both reduced insulin sensitivity (insulin resistance) and impaired _β_ cell function (Meier and Bonadonna 2013). It is the most common form of diabetes and occurs in around 90% of cases of diabetes in the developed world and, according to the WHO (2015), is largely the result of excess body weight and physical inactivity. Other causes are thought to include genetic disposition, age and ethnicity. Until recently, this type of diabetes was seen only in adults, but it is now also occurring in children. Whilst the exact cause is unknown, it is thought to relate to lack of physical activity and obesity. The disease is usually late onset and can often be undiagnosed for many years, so in some instances the complications of diabetes will present rather than the disease. Insulin secretion may be below or above normal, but deficiency of glucose inside body cells leads to hyperglycaemia and a high insulin level. This may be due to changes in cell membranes, which block the insulin-assisted movement of glucose into cells.
#### Symptoms of type 2 diabetes
* Tiredness.
* Blurred vision, this may be due to complications (see below) (Rubin 2008).
* Dry skin.
* Increased appetite and thirst.
* Needing to pass urine more frequently (micturition).
#### Managing childhood type 2 diabetes (MODY)
This is a form of type 2 diabetes and is due to a _β_ cell defect that reduces the insulin secretion in response to specific blood glucose levels, rather than insulin resistance. Dunning (2014) reports that it requires strict diagnostic criteria, including: diagnosis before the age of 25 years, no requirement for insulin therapy 5 years after diagnosis and a previous familial history spanning several generations.
#### Gestational diabetes (during pregnancy)
Diabetes can occur for the first time during pregnancy and, after delivery of the baby, glucose tolerance returns to normal. However, it is thought that if gestational diabetes is experienced, the development of type 2 diabetes later in life is more common (Wallymahmed 2007). Treatment involves dietary control and insulin, if required, because the use of oral diabetic medication during pregnancy is not recommended (Dunning 2014).
## Blood glucose levels
The two main methods used to monitor blood glucose in people with diabetes are HbA1c and monitoring of blood glucose levels. HbA1c is the gold standard in monitoring and provides information on a person's long-term glycaemic control. To test HbA1c, a venous sample of blood is taken and analysed to determine the amount of glucose attached to red blood cells. This is known as glycated haemoglobin and is recorded as mmol/mol (previously a percentage) with 48 mmol/mol or below being the optimum to achieve (Holt 2014).
Blood glucose level monitoring should be performed to complement HbA1c and provide real time measurement of blood glucose, which is measured in millimoles of glucose per litre of blood and is abbreviated to mmol/l (Dunning 2014). NICE also advises that self-monitoring of blood glucose levels should be used as part of an integrated approach, with pre-meal target levels of 4.0–7.0 mmols/l and post-meal targets of <9 mmol/l for people with type 1 diabetes and <8.5mmol/l for those with type 2 diabetes. The desired range for patients with diabetes is shown in Box 13.2.
# Box 13.2 Desired blood glucose levels for patients with diabetes
| **Before meals** | **2 hours after meals**
---|---|---
| **(preprandial)** | **(postprandial)**
**Non-Diabetes** | 4.0 to 5.9 mmol/l | under 7.8 mmol/l
**Type 1 Diabetes** | 4.0 to 7.0 mmol/l | under 8.5 mmol/l
**Type 2 Diabetes** | 4.0 to 7.0 mmol/l | under 9.0 mmol/l
**Children w/ type 1 diabetes** | 4.0 to 8.0 mmol/l | under 10 mmol/l
**NICE recommended target blood glucose level ranges**
### Sites for blood glucose testing
The most commonly used site to take a blood sample from is the side of the finger using a single-use lancet. It is important to ensure the site of piercing is rotated and overuse of the thumb and index finger is avoided otherwise these areas become very painful (Dougherty and Lister 2011). Alternative site testing is available, which can cause less discomfort but only yields a small quality of blood, and glucose levels vary among sites which may have implications for treatment (Dunning 2014). All readings and sites of piercing should be documented accurately. Diabetes UK advise patients that there are ways to make blood glucose testing easier, such as washing the hand in warm water and shaking them to increase blood flow before you test, and that you should always use the sides of the fingers rather than the more sensitive fleshy pulp at the tips. Many Trusts allow patients to self-test, but patients may need some education if their device is different from that at home. _Check local policies and procedures for further advice on using this site_.
### Equipment
There are a variety of blood glucose meters available with varying degrees of technicality and different features (Whitmore 2012; Holt 2014) (Figure 13.3). Competency based training and comprehensive reading of the manufacturer's instructions regarding both the meter and the associated test strips are essential to ensure safe and accurate measurement. Many meters require daily quality assurance checks to guarantee accuracy of the readings and safety of the patients (Dougherty and Lister 2011) which should be accurately documented. Whitmore (2012), Wallymahmed (2013) and Dunning (2014) emphasise the need for education, training and quality control measures to ensure safe blood glucose monitoring and avoiding errors which can be fatal.
# Think about it
Imagine that you are going to take your own blood sugar level. What anxieties would you have? If you can get permission to perform a blood glucose reading on yourself, how did it feel? Consider physical, emotional and psychological aspects.
**Figure 13.3** Advantage blood glucose meter by Roche. Source:
Reproduced with permission of Roche Diagnostics.
### Taking a blood glucose sample
When considering taking a blood glucose level there are certain contraindications that have been identified and these are listed in Box 13.3.
# Box 13.3 Contraindications to blood glucose levels
* Peripheral circulatory failure and severe dehydration, for example, diabetic ketoacidosis, non-ketotic coma, shock and hypotension (low blood pressure). In these situations capillary blood glucose readings can be artificially low due to peripheral shut down (reduced blood to peripheral areas).
* Haematocrit (red blood cells) values: >55% may lead to inaccurate results if the blood glucose level is >11 mmol/l.
* Intravenous infusion of ascorbic acid.
* Some treatments for renal dialysis.
* Hyperlipidaemia (increased fat levels): cholesterol levels >13 mmol/l may lead to artificially raised capillary blood glucose readings.
It would not be expected that a healthcare assistant would identify these contraindications, but it may assist in explaining the treatment plans for some patients. Blood samples for glucose measurement can be capillary, venous or arterial (Dougherty and Lister 2011). Capillary blood is the blood obtained by using a lancing device and is described later. To obtain venous blood the patient would require blood to be taken from their veins (see Chapter 12), which would involve an invasive procedure. An arterial sample would be obtained if the patient has either a central line or similar in place, such as in an intensive care unit (ICU). Table 13.1 describes the procedure for taking a capillary blood sample to measure blood glucose.
**Table 13.1** Procedure for taking blood glucose measurements using a capillary blood sample
**Action** | **Rationale**
---|---
**Before the procedure** |
Collect the required equipment: |
* Blood glucose monitor – check that it is clean, has been calibrated for use with the test strips and has had the quality control test performed and documented (Dougherty and Lister 2011)
| A clean meter will prevent cross-infection; follow local policy if it requires cleaning
Calibration will ensure the meter is fit for purpose and gives accurate readings
* Test strips, ensure that they are in date and have not been exposed to air (Dougherty and Lister 2011)
| To ensure accurate readings
* Single-use disposable finger-pricking device or lancets (MHPRA 2013; Dougherty and Lister 2011)
| To prevent cross-infection
* Cotton wool or sterile gauze (Duning 2014)
| To stop bleeding at site
* Sharps container
| To prevent needlestick injury
**The procedure** |
1. Describe the procedure to the patient and gain consent Explain that some patients want to look away at the sight of a lancing device (Dougherty and Lister 2011) | To get cooperation from the patient, ensure that they understand the procedure fully
Patient comfort and safety; some patients may faint when blood is taken (Dougherty and Lister 2011)
2. Ask the patient to wash and dry their hands with soap and water (Dougherty and Lister 2011) | Prevention of cross-infection (Dougherty and Lister 2011)
3. Position the patient comfortably – either lying down or sitting up | For patient comfort
4. Wash own hands and put on protective gloves and an apron (Wallymahmed 2007) | Prevention of infection
5. Massage the finger from its base to its tip to increase its perfusion (blood flow (Dunning 2014). |
6. Take blood from the side of the finger, using a site that has not been used recently, if possible (Figure 13.4) | As there are comparatively fewer nerve endings in the side rather than the tip of a finger it is less painful (Dunning 2014)
The finger may bleed without assistance (Figure 13.5) or may need to be milked to form a droplet of blood large enough to cover the test pad (Dougherty and Lister 2011) |
7. Some strips 'suck' blood up automatically, stopping when the correct volume is obtained whilst others may still require blood to be dropped onto the strip (Whitmore 2012) |
8. Read the blood glucose level from the machine, using it as per manufacturer's recommendation. | To provide an accurate reading
9. If there is not enough blood, prick the finger again with a new lancet ensuring the patient is fully informed and offer sympathy to the patient | To ensure accurate results by using disposables as intended by the manufacturer
**After the procedure** |
Immediately dispose of the lancet in the sharps box (Dougherty and Lister 2011) | To prevent sharps injury and cross-infection
Apply cotton wool or gauze, with pressure applied | To stop bleeding at the site
When the result is available document into patient's notes/blood glucose chart or patient records, informing the patient | Accurate recording of the results
The patient may self-manage their condition and make adjustments themselves to the regimen (Holt 2014)
Inform the nurse in charge of any abnormal or unusual results (Holt 2014) | To allow further intervention if required
Assess the patient clinically, repeating the procedure if they do not appear to correlate (agree) with the results and report to nurse in charge | Incorrect reading, could result in inappropriate management
Dispose of waste as per local policy. | Prevent cross-infection
Observe site for further bleeding, applying further pressure to stop bleeding if necessary | To allow management of any further bleeding
Ensure the patient is comfortable and reassure if necessary | Patient comfort
Wash and dry hands | Prevent cross-infection
**Figure 13.4** Site for blood glucose sampling.
**Figure 13.5** Blood specimen for blood glucose testing.
Usually the role of the healthcare assistant and/or AP will be to carry out the procedure following guidance from either nursing or medical staff. This will be based on many factors, some of which are detailed in Box 13.4.
# Think about it
A patient with type 1 diabetes is having hip replacement surgery tomorrow. What factors do you think should be considered for this patient with regard to their diabetic control?
# Box 13.4 Factors that influence how often blood glucose should be tested
* Patients with type 1 diabetes and people with type 2 diabetes using insulin need to test. Due to financial pressures in the NHS and conflicting research on the usefulness of self-monitoring in non-insulin treated type 2 diabetes, some Trusts have restricted the blood glucose strips to people using insulin (Whitmore 2012).
* The quantity and frequency of the patient's medication.
* The variance of the blood glucose level during the day, increasing if the variance is abnormal.
* If the patient is ill or under stress; this often results in patients who are in hospital requiring more frequent testing (Wallymahmed 2007).
* If dietary intake is altered or eating is prevented, for example fasting before a surgical procedure.
* If more exercise is taken than is normal for the patient.
* If medication has been altered.
### Documentation
Results may be recorded in the patient's case notes, care pathway, the patient's own documents or, if an inpatient, on a specific blood glucose chart.
## Hypoglycaemia
This is when the blood glucose level is <4.0 mmol/l, occurring with or without symptoms (Table 13.2). If it is not possible to test the blood glucose, but symptoms are experienced, immediate action (treatment) should be considered. It is sometimes abbreviated to 'hypo'.
**Table 13.2** Symptoms of hypoglycaemia
**Early onset** | **Severe symptoms**
---|---
Tremor (Tortora and Derrickson 2011) | Mental disorientation/confusion
Nervousness/shaking (Tortora and Derrickson 2011) | Convulsions
Sweating (Tortora and Derrickson 2011) | Unconsciousness
Increased heart rate (tachycardia) (Tortora and Derrickson 2011) | Shock
Hunger (Tortora and Derrickson 2011) |
Drowsiness |
Abnormal speech (Dunning 2014) |
### Symptoms
The symptoms of hypoglycaemia occur when glucose levels drop, which triggers hormones that result in early onset symptoms; if left untreated it leads to severe symptoms (see Table 13.2).
The causes of hypoglycaemia can be varied and are shown in Box 13.5. These causes should be taught to patients because taking preventive steps could prevent hypoglycaemia occurring.
# Box 13.5 Causes of hypoglycaemia
* Too much insulin or oral medication.
* More than the usual amount of exercise or activity.
* Changing the patient's insulin injection site (it is important to rotate sites regularly as overuse of an area may result in the site losing the ability to absorb insulin effectively). Increased uptake of glucose can also occur at a new site.
* Change of insulin schedule.
* Missing or postponing regular meals or eating less than normal.
* Liver failure (Dougherty and Lister 2011).
* Infection (Dougherty and Lister 2011).
* Insulin-secreting tumours (Dougherty and Lister 2011).
* Consuming alcohol.
To ensure patient safety and prevention of late symptoms, where possible treatment should be prompt. Table 13.3 gives the series of actions that should be undertaken, _but check local policy for any variations_.
# Think about it
If a patient is hypoglycaemic, explain what action you would take and why.
**Table 13.3** Treatment for hypoglycaemia
**Action** | **Rationale**
---|---
1. Report to registered staff and/or medical staff | To alert other personnel of patient's condition
2. Assist in giving the patient fast acting glucose, or give on instruction from a registered nurse, without delay. Possible examples include three to six dextrose tables, a sweet soft drink (not diet), or three to five sugar lumps. Glucose gels may also be used | To increase patient's blood glucose
3. Test the patient's blood glucose level both immediately, and after 15 min
If the patient's blood glucose has increased, and it is over an hour and a half until the patient's next meal, a sandwich, some fruit or biscuits, etc. may be given | To assess if the glucose has entered the patient's bloodstream
If the patient eats too soon after the first dose of glucose it will delay the absorption of glucose into the bloodstream
4. If the level has not increased seek further advice | To decide on patient management that may include further glucose
5. Monitor the patient as directed | To ensure that the patient makes a full recovery
## Hyperglycaemia
Hyperglycaemia is when blood glucose level is too high, usually >10 mmol/l of glucose. The symptoms are shown in Box 13.6.
# Box 13.6 Symptoms of hyperglycaemia
* Increased urination.
* Ketones in urine.
* Increased thirst.
* Lethargy.
* Dehydration.
* Weight loss.
* Blurred vision.
* Cramps/weakness caused by excessive urination.
* Increased likelihood of infection.
As with hypoglycaemia the symptoms and causes of hyperglycaemia should be taught to the patient with a view to the patient taking preventive action. The possible causes of hyperglycaemia are shown in Box 13.7. Hyperglycaemia can affect the patient's well-being and should be treated promptly. Table 13.4 gives the actions required for patients who are hyperglycaemic. _Please check with your local policy_.
# Think about it
Go through the possible causes of hypo- and hyperglycaemia and give examples of how they may apply to patients in hospital.
**Table 13.4** Treatment for hyperglycaemia
**Action** | **Rationale**
---|---
1. Report to registered staff and/or medical staff | To alert other personnel of patient's condition
2. Insulin will be reviewed by medical staff and if prescribed will be administered. The healthcare assistant may assist with this | To reduce blood glucose levels
3. Test the patient's blood glucose level both immediately, and after 15 min | To determine blood glucose level
4. Encourage the patient to drink fluids | Prevent dehydration
5. Monitor the patient as directed | To ensure the patient makes a full recovery
# Box 13.7 Possible causes of hyperglycaemia
* Untreated diabetes.
* Decreased mobility/reduction of physical activity.
* Infections/illness.
* Stress.
* Too much food.
* Insufficient medication.
* Overuse of injection sites/poor injection technique.
* Increase in weight.
* Insufficient insulin.
* The wrong type of food.
## Common problems
### Complications of diabetes
It is of vital importance for the patient with diabetes to have well-controlled blood glucose, because uncontrolled diabetes can lead to either short- or long-term complications. The physical long-term complications of diabetes are generally classified as: macrovascular disease; microvascular disease and neuropathy (Dunning 2014). Table 13.5 summarises some of the common complications.
**Table 13.5** Complications of diabetes
**Complication** | **Type of disease**
---|---
Macrovascular complications include: | Cardiovascular disease (e.g. heart attack), cerebrovascular disease (e.g. stroke) and peripheral vascular disease (disorders that affect blood vessels outside of the heart and brain known as 'hardening of the arteries') (Dunning 2014)
Microvascular disease includes: | Nephropathy (reduced renal function) damage to the small blood vessels cause damage to the kidneys, one of the main reasons for dialysis
| Retinopathy (ophthalmic (eye) problems) damage to small vessels that can lead to cataract formation and blindness
Neuropathy (nerve damage) | This can cause sensory deficits, particularly in the feet (Currie 2007b; Sewell 2007) and can increase the incidence of injury, ulcers and infections, resulting in poor circulation
Peripheral damage mainly affects the feet and legs and autonomic which can lead to erectile dysfunction, delayed gastric emptying and hypoglycaemic unawareness
| (Dunning 2014)
### Common problems in obtaining a blood glucose measurement
The problems associated with taking a blood glucose measurement can be divided into three areas: the patient, the equipment and technique.
#### The patient
If the patient has poor circulation, obtaining a sample can be more challenging. Keeping the hand warm can improve circulation and, if the fingers are massaged, this can increase blood flow (perfusion) to the site, allowing the capillaries to bleed more easily (Dougherty and Lister 2011; Dunning 2014). Where the skin has become hardened the patient should be discouraged from using alcohol gel to wash hands (this can also affect the blood glucose reading) (Dougherty and Lister 2011). If the patient is uncooperative with regard to the procedure, despite a full explanation, seek assistance because this may be the first sign of hypoglycaemia.
#### The equipment
It is essential that the machine be serviced and calibrated as per local policy to ensure that accurate results are obtained. If the machine displays an error code or is malfunctioning another machine should be used. Regular quality control checks are required of both the machine and the strips and these need to be documented (Dougherty and Lister 2011). The strips should be in date, have not been exposed to the air and calibrated for use with the specific machine being used (Dougherty and Lister 2011; Whitmore 2012). The lancets (finger-pricking devices) should be for single-patient use to prevent infection (MHPRA 2013; Dougherty and Lister 2011). Competency based training with the machine should have been completed as per local policy (Whitmore 2014).
#### Technique
The site for obtaining a sample (as mentioned earlier) should be the side of the finger and, where possible, a site that has not been used recently to prevent damage. Due to the fact that there are comparatively fewer nerve endings in the side than the tip of the finger, this site is less painful (Dunning 2014). If the finger does not bleed it should be milked but not squeezed because this can give inaccurate results (Dougherty and Lister 2011; Wallymahmed 2007). It is essential that all staff performing this procedure should have had competency based training on the specific machine and accessories being used. When recording the blood glucose level, best practice is also to assess the patient's other observations to ensure that the result appears correct, reporting any concerns immediately. This is highly significant because inaccurate results can lead to mismanagement of patients and can be potentially life threatening.
## Summary
Taking blood glucose levels provides important information that affects patient management. It is essential that quality control and good technique be mastered to ensure best practice. Care of the equipment should be followed in line with the manufacturer's guidelines, NICE (2004) and NICE (2009) guidelines, health and safety policy and local glucose monitoring policy and procedure. Where possible, if patients have previously been active in this procedure, they should be encouraged to continue self-care, especially for management of diabetes at home. As with all abnormal or unusual results, the healthcare assistant or assistant practitioner should report these immediately to the nurse in charge or medical staff and act according local policy. An example of competency framework for blood glucose measurement is shown in Table 13.6.
**Table 13.6** Competency – blood glucose monitoring
| **First assessment/reassessment** |
---|---|---
**Steps** | **Demonstration** | **Date/competent/signature**
| Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
Blood glucose monitoring | | | | | |
1. **1.** Define the types of diabetes
2. **2.** Describe the effect of insulin on the body
3. **3.** Discuss conditions where a patient's blood glucose may require careful monitoring
4. **4.** Identify the contraindications to blood glucose measurement
5. **5.** State the normal range for blood glucose readings
6. **6.** Identify signs and symptoms of hypoglycaemia
7. **7.** Identify signs and symptoms of hyperglycaemia
8. **8.** Discuss the equipment required to undertake this task
9. **9.** Demonstrate an understanding of using appropriate calibration and quality control techniques and what checks should be made on the monitor before use
10. **10.** Demonstrate the proper use of the equipment as laid down by the operating instructions and specifications and discuss the consequences of improper use
11. **11.** Demonstrate that, before taking device to patient, the monitor is checked for the following:
That one pack of strips is open and are in date, ensure that the monitor and the test strips have been calibrated together. Discuss the actions that would be taken if there was doubt about the quality of the strips
| | | | | |
1. **12.** Check that the quality control test has been carried out that day, when the batteries require changing, when opening new strips and any unusual, unpredicted result
2. **13.** Confirm that the quality control check has been recorded in the record book and signed
| | | | | |
**Blood glucose monitoring procedure** | **Demonstration** | **Date/competent/signature**
| 1 | 2 | 3 | 4 | 5 |
1. **1.** Demonstrate satisfactory explanations of the procedure to the patient
2. **2.** Show awareness of preparation of site before blood sampling
3. **3.** Demonstrate appropriate positioning of patient
4. **4.** Demonstrate safe hand washing according to infection control policy
5. **5.** Demonstrate procedure for safe practice in obtaining a blood sample from the patient to apply to the test pad
6. **6.** Demonstrate safe disposal of lancet
7. **7.** Demonstrate the proper use of the monitor as per individual manual and local policy
8. **8.** Demonstrate the procedure for recording and reporting the result
9. **9.** Show awareness of appropriate disposal of waste
10. **10.** Demonstrate knowledge of care for the patient following the procedure
| | | | | |
Supervisors/Assessors:
# Case study 13.1
The blood glucose level of an acutely ill patient is taken. Instead of taking the current reading, a value from the previous patient is retrieved from the history function of the machine.
What do you think are the implications of this error?
# Case study 13.2
Ben is a 17-year-old boy who has taken his own blood glucose level. The level recorded is very high but he appears asymptomatic (he has no symptoms). You notice a bag of sweets on his locker.
What explanation do you think may be applicable to this patient and what would be your planned actions?
# Self-assessment
**Assessment** | **Aspects** | **Achieved ✓**
---|---|---
Patient/Disease | _Have you considered all aspects of this section?_ |
| Types of diabetes and the role of the pancreas |
| Signs and symptoms of diabetes |
| Complications that can occur due to diabetes |
Procedure | _Have you considered all aspects of this section?_ | **Achieved ✓**
| Selecting equipment and reasons for blood glucose measurement |
| Technique required |
| Normal values |
| Recording and reporting concerns |
| Safe disposal of sharps |
## References
1. Currie J (2007) Diabetic complications. _Scottish Nurse_ **10** (11): 28–29.
2. Dougherty L and Lister S (2011) _The Royal Marsden Hospital Manual of Clinical Nursing Procedures_ , 8th edn. Oxford: Blackwell Publishing.
3. Dunning T (2014) _Care of People with Diabetes. A Manual of Nursing Practice_ , 4th edn. Oxford: Wiley Blackwell.
4. Holt P (2014) Blood glucose monitoring in diabetes. _Nursing Standard_ **28** (27): 52–57.
5. Knip M and Simell O (2014) Environmental triggers in Type 1 Diabetes. _Cold Spring Harbour Perspectives in Medicine_ **2** (7). Available at: <http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3385937>/ (accessed December 2015).
6. Laird E (2014) Blood glucose monitoring and management in acute stroke care. _Nursing Standard_ **28** (19): 52–56.
7. Marieb E N (2007) _Human Anatomy & Physiology. A Brief Atlas of the Human Body_. San Francisco; Harlow: Benjamin Cummings; Pearson.
8. Medicines and Healthcare Products Regulatory Agency (2013) _Single-Use Medical Devices: Implications and Consequences of Reuse_. London: Medicines and Healthcare Products Regulatory Agency.
9. Meier J and Bonadonna R (2013) Role of reduced b-cell mass versus impaired b-cell function in the pathogenesis of type 2 diabetes. _Diabetes Care_ **36** (2): S113–S116.
10. National Institute for Health and Clinical Excellence (NICE) (2004) _CG15. Diabetes: Type 1 Diabetes: Diagnosis and Management of Type 1 Diabetes in Children, Young people and Adults_. London: NICE. Available at: <http://publications.nice.org.uk/type-1-diabetes-cg15> (accessed 28 February 2015).
11. National Institute for Health and Clinical Excellence (NICE) (2009) _Type 2 Diabetes: The Management of Type 2 Diabetes_. London: NICE. Available at: <http://publications.nice.org.uk/type-1-diabetes-CG66> (accessed 28 February 2015).
12. Noble-Bell G and Cox A (2014) Management of diabetic ketoacidosis in adults. _Nursing Times_ **110** (10): 14–17.
13. Ritsinger V, Malmberg K, Mårtensson A, et al. (2014) Intensified insulin-based glycaemic control after myocardial infarction: mortality during 20 year follow-up of the randomised Diabetes Mellitus Insulin Glucose Infusion in Acute Myocardial Infarction (DIGAMI 1) trial. _The Lancet Diabetes & Endocrinology_ **2** (8): 627–633.
14. Rubin A (2008) _Diabetes for Dummies_ , 3rd edn. London: Wiley Publishing, Inc.
15. Sewell J (2007) Diabetes: causes, complications and management. _British Journal of Healthcare Assistants_ **1** (1): 6–9.
16. Tan G (2011) The pancreas. _Anaesthesia & Intensive Care Medicine_ **12** (10): 469–472.
17. Thibodeau G A and Patton K T (2007) _Anatomy and Physiology_ , 6th edn. Elsevier, MO: Mosby.
18. Thrower S L and Bingley P J (2014) What is type 1 diabetes? Diabetes basic facts. _Medicine_ **42** (12): 682–686.
19. Tortora G J and Derrickson B (2014) _Principles of Anatomy and Physiology_ , 13th edn. Hoboken, NJ: John Wiley & Sons Inc.
20. Wallymahmed M (2007) Capillary blood glucose monitoring. _Nursing Standard_ **21** (38): 35.
21. Wallymahmed M (2013) Encouraging people with diabetes to get the most from blood glucose monitoring: Observing and acting upon blood glucose patterns. _Journal of Diabetes Nursing_ **17** : 6–13
22. Whitmore C (2012) Blood glucose monitoring: an overview. _British Journal of Nursing_ **21** (10): 58–62.
23. World Health Organisation (WHO) (2015) Diabetes Fact Sheet No 31 (online). Available at: <http://www.who.int/mediacentre/factsheets/fs312/en/> (accessed 14 February 2015).
# Chapter 14
Fluid balance and intravenous maintenance
# Learning objectives
* Define fluid balance and its importance to nursing practice
* Discuss the body's response to changes in fluid balance
* List the instances when intravenous (IV) fluids are necessary
* Describe how to prime (run through) an IV line
* Describe how to discontinue an IV line
* Identify the common problems with IV administration via gravity infusion sets
## Aim of this chapter
This chapter will focus upon the importance of maintaining and monitoring a patient's fluid balance in the clinical environment and the potential need for intravenous (IV) fluids via a peripheral cannula.
To revise the anatomy and physiology of the placement of a cannula, please refer to Chapter 16. Fluids administered by the subcutaneous route are not covered.
## Reasons for monitoring fluid balance
Maintaining the balance within the volume and composition of body fluids is essential to health (Tortora and Derrickson 2011). An imbalance in fluid and electrolyte levels can cause changes to a patient's clinical condition and subsequently increase their MEWS score (Shepherd 2011).
## Related anatomy and physiology
The total body water for adults is about 60% of the body weight, with a higher percentage in young people and adults of below-average weight (Waugh and Grant 2010; Tortora and Derrickson 2011). Older people have a reduced amount of water, whereas in infants it is around 75%. Women also tend to have slightly lower water content than men (Thibodeau and Patton 2009). These differences in total body water volume account for the different percentages of lean body tissue. As water isn't stored in fat cells, men and people across the lifespan with greater lean body mass have a higher percentage of total body water compared to women who genetically have more fat cells.
Dougherty and Coote (2006) describe a number of regulators that work together to maintain fluid balance (Table 14.1).
**Table 14.1** Regulator of fluid balance
**Organ** | **Role in fluid balance**
---|---
Kidneys | If the kidneys reabsorb more water, fluid will remain in the body and prevent loss. This would result in the patient passing concentrated urine
Hypothalamus/Pituitary gland | If there is a reduction in blood volume, e.g. haemorrhage (blood loss) the body will respond by trying to restore normal fluid levels. It does this by releasing the hormone antidiuretic hormone (ADH), which, after being made in the hypothalamus, is released from the posterior pituitary gland. ADH increases the reabsorption of water and therefore increases the circulating blood volume
Adrenal cortex | Reabsorption of sodium is an important part of fluid balance and aldosterone is a hormone secreted to regulate both the reabsorption of sodium and water
Adapted from Dougherty and Coote (2006).
The body's required input can be provided by the patient drinking or eating (as some foods contain fluids) or, after medical intervention and insertion of a cannula, subcutaneous or IV fluids. Excretion is sustained through not only urine output but also insensible losses such as sweating, breathing and faeces, which contribute to small fluid losses (Tortora and Derrickson 2011).
The body is in balance when the required amounts of water and solutes (dissolved substances) are present and are correctly proportioned among the various compartments (Tortora and Derrickson 2011). The body keeps fluid levels constant when water loss equals water gain (Tortora and Derrickson 2011). This is termed homeostasis. Here the body is said to be maintaining its constant internal environment through its own controls, which allows it to return to normal parameters when there has been a change to its balance (Clancy and McVicar 2009). An imbalance in homeostasis can cause problems for some patients and is often associated with diseases, such as renal (kidney) or cardiac (heart) problems. Figure 14.1 shows how the body reacts to a stimulus that caused a decreased volume of fluid in the body. In some very unwell patients a central venous pressure (CVP) line may be inserted into a large vessel where the tip of the cannula sits in the right atrium (top chamber) of the heart to determine the amount of fluid contained within the body. Because of the dangers associated with CVP line insertion, these are always placed by medical staff and the monitoring of this observation is currently the role of a registered nurse (Cole 2007).
**Figure 14.1** Fluid regulation in the body. Source: Thibodeau 2009. Reproduced with permission of Elsevier.
Body fluids are distributed within two compartments in the body known as extracellular and intracellular. Extracellular fluid, also called interstitial fluid, can be found outside the cells, consisting of fluids in the blood, lymphatic system (a system that fights infection), spinal fluid (cerebrospinal (CSF)) and fluid that bathes body cells. Intracellular fluid is contained within cells (Waugh and Grant 2010) and both the intracellular and extracellular compartments are separated by a plasma membrane that allows the fluids to move through the compartments (Tortora and Derrickson 2011).
## Electrolytes
These are particles that have a positive or negative charge attached to them, and they play an essential role in the body because they control the movement of water between body fluid compartments (Thibodeau and Patton 2009). Patients who have an imbalance in the blood's electrolytes can develop fluid imbalance (Mooney 2007). Examples of some common electrolytes are shown in Box 14.1.
# Box 14.1 Common electrolytes in the body
1. Na+: sodium
2. Cl–: chloride
3. K+: potassium
4. Ca2+: calcium
5. Mg2+: magnesium
# Think about it
Ask to view a patient's blood results and look at the electrolytes contained in the blood. There will be a list of the 'normal' values to which you can compare the results. Identify if they are normal or abnormal. Can you think why this might be? Discuss your thoughts with a registered nurse or a doctor in your clinical area.
## Related aspects and terminology
* _Hypovolaemia_ : loss of fluid (Mooney 2007).
* _Hypervolaemia_ : fluid overload (Mooney 2007).
* _Electrolytes_ : negatively or positively charged particles within the body.
* _Extracellular_ : fluid outside cells.
* _Intracellular_ : fluid contained in or around cells.
### Hypovolaemia/dehydration
The term 'dehydration' is used to describe the condition that results from excessive loss of body water and electrolytes (Thibodeau and Patton 2009).
#### Causes of dehydration
* Gastrointestinal problems that cause fluid loss are commonly vomiting and diarrhoea (Tortora and Derrickson 2011). These can be sudden onset and have rapid effects on fluid loss, particularly in vulnerable patient groups such as babies and older people. Some chronic diseases can also cause these symptoms, for example ulcerative colitis (inflammation of the bowel) or irritable bowel syndrome. Patients with a high output ileostomy can also be vulnerable to fluid losses and need to replace lost fluids to prevent dehydration.
* Where there is a reduced oral input, this can be due to altered mental state, for example dementia, depression or where the patient may have a reduced consciousness level or is required to lie flat (Tortora and Derrickson 2011). In such instances the role of the healthcare assistant may be to ensure that the patient is assisted to take regular drinks. Where patients have poor or reduced mobility it is essential to ensure that fluids are within easy reach. Localised problems in the mouth may also affect the patient's desire to drink because it may cause further discomfort and this should be reported to the nurse in charge.
* Environment can also contribute to a reduced oral input, for example lack of water in a hot climate (Thibodeau and Patton 2009).
* Excessive urination (passing urine) may be due to diuretic medication (encourages increased urine output) with less absorption occurring in the kidneys (Mooney 2007). If fluid balance is being monitored, giving the patient a bed pan or bottle if they are in a care environment to measure urine output can be successful in recording an accurate output. If the patient has mobility problems, ensuring that they are near a toilet after the diuretic medication can reduce any anxiety and prevent incidents of incontinence.
* Any disease or condition that alters fluid loss can cause dehydration, such as haemorrhage, severe burns, diabetes, acute renal failure or gastroenteritis (Marieb and Hoehn 2007).
#### Signs and symptoms of dehydration
* Changes to cognitive function.
* Muscle weakness, headaches and fatigue.
* Skin that is less elastic, which is sometimes referred to as 'turgor'.
* Poor urine output, which will also be dark in colour.
* Thirst, leading to dry lips and tongue (Campbell 2011; Shepherd 2011).
* Severe dehydration can lead to clinical signs of low blood pressure (hypotension); fast pulse (tachycardia), which can become weak and thready; and cold hands and feet, as the circulating blood is diverted to the major organs (Shepherd 2011).
#### Treatment
Medical and nursing staff should treat the cause of dehydration; for example, if the patient is vomiting they can be give an anti-emetic (anti-sickness medication) to try to rectify the problem or if the patient is dehydrated following surgery it may be appropriate to supplement their oral intake with IV fluids.
Monitoring and recording the patient's intake and output may be essential to promote recovery for some patients and fluid balance charts can provide vital clues to the patient's level of hydration.
### Hypervolaemia (excess fluid)
This is an excess of fluid in the body.
#### Cause
* Over-infusion of intravenous fluids.
* Congestive cardiac failure, renal (kidney) failure, cirrhosis of the liver due to the kidneys retaining large amounts of sodium and water (Thibodeau and Patton 2009).
#### Signs and symptoms of excess fluid
* Weight gain.
* Oedema (excess fluid in tissues).
* Breathlessness, which is often made worse when lying flat.
* Increased pulse rate.
* Lung problems – congestion where breathing can sound crackly. (Adapted from McMillen and Pitcher 2011.)
#### Treatment
* Once medical and nursing staff identify the underlying cause, treat it; for example, if the patient has had too much IV fluid, the regimen should be reviewed by medical and nursing staff, and it is essential that any IV infusion is closely monitored.
* If prescribed, assist – if this is in line with your workplace policy – in giving diuretic medication that will promote excretion of fluid from the kidneys, resulting in an increased urine output. Accurate recording of the urine output on fluid balance charts is essential for monitoring the patient's condition
If a person steadily consumes more water than the kidneys can excrete, water intoxication can occur, which results in the cells within the body swelling dangerously; this can result in death (Tortora and Derrickson 2011).
## Fluid balance charts
Fluid balance charts are used to monitor the patient's input and output, and are an important aspect of care, particularly with ill patients. Failure to maintain fluid balance can cause dehydration and can seriously affect the health of patients (Begum and Johnson 2010). Figure 14.2 shows an example of a fluid balance chart. When calculating total losses or gains over a 24-hour period, insensible losses (fluid loss that cannot be directly measured, such as perspiration etc.) should also be considered. For patients with high temperatures or with lung conditions that cause rapid breathing, the increase in insensible losses can lead to dehydration if fluid is not replaced.
**Figure 14.2** Fluid balance chart. Source: NHS Lothian 2008. Reproduced with permission of NHS Lothian.
The role of the healthcare assistant involves completing the fluid balance chart accurately, therefore training should be undertaken to ensure that the correct information is recorded, given its importance in patient management. Reid et al. (2004) suggest that mandatory education for fluid balance should be incorporated within local training programmes for all staff, to overcome the problems of incomplete charts. Involving patients in completion can be very useful to promote accuracy and can reduce workload for the nursing team (Chung et al. 2002). Box 14.2 shows the potential problems in fluid balance chart completion.
# Box 14.2 Potential problems in fluid balance chart completion
* Chart not completed at all.
* Inaccurate volumes entered, e.g. sips/??? or wet pad/used toilet (Reid et al. 2004).
* Staff unaware of the volumes in cups/glasses, etc. and estimate wrongly.
* Patient forgets to measure output.
* Patient cannot remember input.
* Patient may be unable to give a history due to previous cerebrovascular accident (stroke) or dementia.
* Domestic staff remove cups without alerting staff to volume consumed.
In 2007, the NPSA highlighted the importance of hydration in preventing patients from becoming ill (NPSA 2007a). Because of the potential difficulties in monitoring and maintaining fluid balance, some NHS Trusts have implemented hydration care bundles (East of England NHS Trust 2011) to assist both staff and patients in understanding the importance of assessing, planning and monitoring fluid balance. This care bundle allows patients to have input in closely monitoring their hydration and also acts as an educational tool for both staff and patients, thus reducing the risks of dehydration whilst in hospital care. Although this is directed at the hospitalised patient, this has the ability to be adapted for care in other environments helping to reduce the risk of dehydration to all patients.
## The intravenous route
When IV fluids would be commenced:
* Patient is nil by mouth, for example before or after surgery.
* Medication is only available in this form.
* Where the patient is feeling nauseous and not taking oral fluids.
* Where the patient is vomiting, so medication cannot be absorbed in the gut.
* To assist in fluid balance maintenance or correct dehydration.
* To correct electrolyte imbalance.
IV fluids are delivered by a cannula inserted into a vein (Figure 14.3; see Chapter 16). Cannulation involves direct entry into the circulatory system and is a route for infection (Lavery and Ingram 2006). Great care must therefore be taken to prevent infection, and this would involve only touching the cannula/IV line when necessary. Preventing equipment coming into contact with potentially harmful organisms can be maximised by using the aseptic or non-touch technique (Rowley 2001). If the healthcare assistant's role involves dealing with IV lines, training and competency in this skill is required.
**Figure 14.3** Cannula with intravenous line attached.
### Priming an IV line
Before administering fluid via the intravenous route the nurse must first fill the line with fluid (primed) to prevent air entering the patient's circulatory system, which could lead to an air embolus (NPSA 2007b; Younger and Kahn 2008). This is important as air emboli, in large volumes, can lead to cardiac arrest. The line, sometimes also referred to as an IV set, comes packed in a sterile pack to prevent infection. Table 14.2 describes the procedure for priming an IV line.
**Table 14.2** The procedure for priming an intravenous (IV) line
**Action** | **Rationale**
---|---
1. Ensure that the registered nurse has checked that IV fluid has been prescribed, and not already given. Two practitioners should have checked this, because it is by the IV route
Check the IV fluid, ensuring that it is clear, so has no contamination or debris and that in date | Administration of medicines is the role of the registered nurse (Nursing and Midwifery Council (NMC) 2008)
IV fluid fit for purpose and within expiry date
2. Collect all other equipment: administration set, gloves/apron, receptacle for any discarded fluid, drip stand, air inlet if the container is glass or rigid, alcohol swab | To ensure that the process can be done timely
3. Wash hands, put on gloves and apron. Where possible undertake procedure in sterile environment, e.g. clinical treatment room in the hospital | Prevent cross-contamination
4. Read the instructions on the IV line packaging, including expiry date if applicable
Remove the line from outer packaging and close the roller clamp. Remove the IV fluid from outer bag if applicable | All outward packaging removed
5. Remove the seal on the IV bag where the trocar (spike) will be inserted
Insert the trocar into the bag taking care not to spike and puncture the bag (Figure 14.4) | Mis-spiking the bag will allow entry for microorganisms and potentially could cause sharps injury
6. Squeeze the drip chamber at the top to fill around half to two-thirds full (check manufacturer's recommendation) (Figure 14.5) | Some manufacturers' sets may have specific instructions
7. Slowly open the roller clamp allowing the fluid to flow down the IV line | Slow priming of the line will reduce the amount of air in the line
8. Close the roller clamp when the fluid has filled the line completely and come out the end (Figure 14.6) | To expel all air from the line
9. The line is now filled with fluid and ready for connection to the patient. Place a sterile cap over the end ready for connection to the patient | Sterile cap prevents contamination of the line before it is connected to the patient
**Figure 14.4** Spiking an IV bag.
**Figure 14.5** Filling the drip chamber.
**Figure 14.6** Priming the IV line.
Priming the line should be undertaken only if local policy allows, and when competency training in both aseptic technique and the actual task has been undertaken.
### Flushing an IV line
If an IV cannula is in place but is being used only intermittently, often fluid (e.g. sodium chloride or 'saline') will be introduced to keep the line patent (free from blockages). This is known as 'flushing the line'. The administration of IV medication is currently a post-registration role and therefore flushing before, between and after medicine – also seen as good practice – is performed by the registered nurse (National Institute for Health and Clinical Excellence (NICE) 2003; NPSA 2007b). However, it is anticipated that this may change in the future. Where this role is permitted in the future it should only be performed by healthcare assistants under local protocols and after competency based training, including aseptic technique.
As mentioned, the medicine used for flushing peripheral lines is usually 0.9% sodium chloride, provided that this does not react with other medications being administered via this route. The volume should be equal to twice the volume of the cannula plus any additional devices, such as needle-free connectors (Royal College of Nursing (RCN) 2010). The recognised technique is a pulsated push–pause (stop–start, stop–start), which creates turbulence with the cannula, removing debris from its internal wall (NHS Grampian 2010).
## Care of the cannula
Refer to Chapter 16; however, a summary of care is as follows:
* The cannula site should be inspected regularly to identify potential problems promptly. Phlebitis refers to inflammation of a vein and the use of Visual Infusion Phlebitis (VIP) scales are useful in assessing the need for the removal of the cannula (RCN 2010). Although a healthcare assistant would not necessarily be expected to complete this, having an awareness of its importance in clinical practice is useful in maintaining patient safety. An awareness of this will guide the healthcare assistant in observing the cannula site and reporting its appearance to a registered nurse as appropriate.
* Whenever dealing with an intravenous infusion or a cannula, good handwashing practices and the use of sterile gloves are essential to prevent infection. Always follow your employer's policies over the dressings used for cannulas in your area; and whenever dressings are used it is essential that these do not prevent observation of the cannula or prevent flow of the solution or occlude the vessel in any way (RCN 2010).
## Discontinuing an IV infusion
Discontinuing an infusion requires the line to be clamped off (by closing off the roller clamp and then removing it (Figure 14.7)). Disconnection at the cannula requires competency in aseptic technique (discussed earlier), and a sterile cap to be applied where the line previously entered the cannula. However, as the role of the healthcare assistant is to monitor fluid balance, it is essential that this is recorded on the fluid balance chart, especially if the infusion is discontinued while there is still fluid in the bag. Understanding the reason for the infusion is important as this can guide the care you provide after removal of the cannula. For example, if the infusion had been in place to keep the patient hydrated whilst nil by mouth, the patient may then need advice and assistance in drinking fluids to ensure hydration. Table 14.3 details the procedure for discontinuing an intravenous infusion (IVI).
**Figure 14.7** Discontinuing an IV line.
**Table 14.3** Procedure to discontinue an intravenous infusion
**Action** | **Rationale**
---|---
1. Explain the procedure to the patient and obtain verbal consent | To ensure that patient understands and cooperates. Consent for legal purposes
2. Gather all necessary equipment, which includes: gloves, sterile cap, clinical waste bag and sharps bin | To promote safe and efficient removal
3. Close roller clamp on IV line
Put on gloves and apron | To prevent spillage of fluid
Gloves prevent cross-infection
4. Open sterile cap and place carefully ensuring aseptic technique. Ensure that within easy reach | Prevents contamination
5. Remove IV line carefully (Figure 14.7) asking the patient to elevate the arm upwards if the cannula is in the back of the hand. Application of some light pressure over the cannula (where the cannula enters the vein) can also prevent bleeding (Figure 14.7) | To prevent blood spillage
6. Attach sterile cap | Ensures line is capped off securely
7. Wash hands, dispose of all equipment as per policy | Prevents infection
8. Observe site | To identify any problems with the site
9. Document removal in the patient's notes | Provides a legal record
## Common problems
Despite IV administration being a qualified nursing task, the role of the healthcare assistant may include ensuring that the infusion is running and there are no complications, if competent to do so. As mentioned earlier, patients may well report symptoms of pain, discomfort, swelling or leakage to the healthcare assistant first.
IV infusions can be delivered via infusion devices or by a gravity infusion set (as seen previously). Infusion devices should be used only by individuals who have had competency based training on their use, with local policy dictating which staff are permitted to be involved in this aspect of care. When an infusion device is being used, the role of the healthcare assistant may be to alert staff to infusion problems, which may have resulted from either the patient reporting problems or the alarm on the pump being activated.
A standard gravity set is used for fluid administration, with specialised blood sets for blood and blood products. Table 14.4 details the common problems, presentation and actions that should be taken in relation to gravity infusion sets.
**Table 14.4** Common problems with gravity infusion sets
**Problem** | **Presentation** | **Action**
---|---|---
**The infusion has stopped dripping**
**Causes:**
* Cannula may be blocked
* The infusion bag needs to be elevated
* The infusion is switched off
| No drips evident in the chamber | Inform nurse in charge
**The infusion is not running to time**
**Causes:**
* The patient may have interfered with the infusion
* The cannula may allow only intermittent flow depending on the position of the patient's arm
* The rate has been set incorrectly.
| The infusion bag appears to have a volume that is not consistent with the planned infusion duration | Inform nurse in charge
**The dressing is not clean, dry and secure**
**Causes:**
* The infusion may have leaked
* The patient has caused contamination of the dressing
* The patient may have interfered with the infusion
| Dressing visually contaminated or dislodged | Change dressing if competent to do so; report
**The patient reports pain or wetness at the cannula site (see also Chapter** 16 **)**
**Causes:**
* The IV may have leaked
* An acute inflammation of the vein has occurred due to the presence of the cannula, known as phlebitis (Jackson 1998)
* Infiltration or extravasation has occurred. This involves leakage of medication into the surrounding tissues.
* The classification is linked to the type of medication that has caused the leakage (Ingram and Lavery 2005)
| Dressing is wet. Site is painful | Report to nurse in charge. Stop infusion
In some instances, the registered nurse may delegate the task to close the roller clamp on the infusion line to a healthcare assistant, but this should only be done when instructed to do so and under local protocol or policy.
## Summary
Fluid balance is an important aspect of patient care, which can lead to serious clinical problems where there is an imbalance. The healthcare assistant's role may involve encouraging and recording oral fluids and reporting potential problems where the patient is receiving fluids by the IV route. The healthcare assistant can also assist in monitoring the output either by recording when the patient goes to the toilet or through care of indwelling catheters. The healthcare assistant is often the first person to witness or deal with problems regarding IV infusions, but any interaction must be underpinned by a strong knowledge base and competency based training in accordance with local policies and procedures.
Tables 14.5 and 14.6 are competency frameworks for recording fluid balance and IV maintenance.
**Table 14.5** Competency framework: record clinical observations (fluid balance)
| **First assessment/reassessment**
---|---
Steps | Demonstration | Date/competent/signature
| Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
Fluid balance
1. **1.** List the two fluid compartments in the body
2. **2.** Describe how the body controls fluid balance
3. **3.** Discuss the symptoms of dehydration/hypervolaemia (excess) fluid
4. **4.** Demonstrate how to complete a fluid balance chart
| | | | | |
**Table 14.6** Competency framework: record clinical observations (intravenous (IV) maintenance, including priming and discontinuing an infusion (IVI))
| **First assessment/reassessment**
---|---
Steps | Demonstration | Date/competent/signature
| Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
IV maintenance | | | | | |
1. **1.** Describe the instances where the IV route is required
2. **2.** Explain why aseptic technique is important when dealing with the IV route
3. **3.** Demonstrate the correct procedure for priming (running through) an IV line
4. **4.** Demonstrate the correct procedure for discontinuing an IV line
5. **5.** Discuss the common problems associated with the IV route, giving the actions expected from a healthcare assistant
| | | | | |
# Case study 14.1
Mrs Jones, who is 88 years old, has been admitted to correct dehydration. Her IV infusion has now been discontinued. What is the role of the healthcare assistant in ensuring that a correct fluid balance is both maintained and recorded?
# Case study 14.2
Mr Bob Mills is a 49 year old who has had prostate surgery. He has an intravenous infusion running and is complaining of pain at the site. Describe the actions that you would take.
# Self-assessment
**Assessment** | **Aspects** | **Achieved ✓**
---|---|---
Patient | _Have you considered all aspects of this section?_ |
| Describe the regulators that maintain fluid balance in the body |
| The role of electrolytes in the body |
| The symptoms of dehydration/over hydration |
**Procedure(s)** | _Have you considered all aspects of this section?_ | **Achieved ✓**
| Maintaining and recording on fluid balance charts |
| Priming an IV line |
| Common problems with gravity infusion lines |
| Discontinuing an IV line |
## References
1. Begum M and Johnson C S (2010) A review of the literature on dehydration in the institutionalized elderly. _The European e-Journal of Clinical Nutrition and Metabolism_ **5** (1): e47–e53.
2. Chung L H, Chong S and French P (2002) The efficiency of fluid balance charting: an evidence based management project. _Journal of Nursing Management_ **10** (2): 103–113.
3. Campbell N (2011) Dehydration: Why is it still a problem? _Nursing Times_ **107** (22): 12–15.
4. Clancy J and McVicar A (2009) _Physiology and Anatomy for Nurses and Healthcare Practitioners_ , 3rd edn. London: Hodder Arnold.
5. Cole E (2007) Measuring central venous pressure. _Nursing Standard_ **22** (7): 40–42.
6. Dougherty B and Coote S (2006) Fluid balance monitoring as part of track and trigger. _Nursing Times_ **102** (45): 28–29.
7. East of England NHS Trust (2011) _Adult Intelligent Fluid Management Bundle_. Cambridgeshire: NHS.
8. Ingram P and Lavery I (2005) Peripheral intravenous therapy: key risks and implications for practice. _Nursing Standard_ **19** (46): 55–64.
9. Jackson A (1998) Infection control: a battle in vein; infusion phlebitis. _Nursing Times_ **94** (4): 68–71.
10. Lavery I and Ingram, P (2006) Prevention of infection in peripheral intravenous devices. _Nursing Standard_ **20** (49): 49–58.
11. Marieb E N and Hoehn K (2007) _Human Anatomy and Physiology_ , 7th edn. San Francisco, CA: Pearson Benjamin Cummings.
12. Mooney G P (2007) Fluid balance. _Nursing Times_. Available at: www.nursingtimes.net/ntclinical/Fluid_balance.html (accessed 16 October 2008).
13. National Institute for Health and Clinical Excellence (NICE) (2003) _Infection Control: Prevention of Healthcare-associated Infection in Primary and Community Care. Clinical Guidelines 2_. London: NICE.
14. NHS Lothian (2008) _Fluid Balance Chart_. Edinburgh: NHS Lothian.
15. NHS Grampian (2010) _Patient Group Direction for the Administration of Sodium Chloride 0.9% injection for flushing intravenous catheters/cannulae by certified healthcare professionals working within NHS Grampian, Scotland_. Edinburgh: NHS Grampian.
16. NPSA (2007a) _Water for Health: Hydration Best Practice Toolkit for Hospitals and Healthcare_ , London: NPSA.
17. NPSA (2007b) _Promoting Safer Use of Injectable Medicines_ , Alert No. 2007/20, 28th March. NPSA, London.
18. Nursing and Midwifery Council (NMC) (2008) _Standards for Medicines Management_. London: NMC.
19. Royal College of Nursing (RCN) (2010) _Standards for Infusion Therapy_ , 3rd edn. London: RCN.
20. Reid J, Robb E, Stone D, et al. (2004) Improving the monitoring and assessment of fluid balance. _Nursing Times_ **100** (20): 36–39.
21. Rowley S (2001) Aseptic non-touch technique. _Nursing Times_ **97** (7): 6.
22. Sheppherd A (2011) Measuring and managing fluid balance. _Nursing Times_ **107** (28): 12–16.
23. Thibodeau G A and Patton K T (2009) _Anatomy and Physiology_ , 7th edn. St Louis, MO: Mosby.
24. Tortora G J and Derrickson B (2011) _Principles of Anatomy and Physiology_ , 13th edn. Hoboken, NJ: Wiley & Sons.
25. Waugh A and Grant A (2010) _Ross and Wilson Anatomy and Physiology in Health and Illness_ , 11th edn. Edinburgh: Churchill Livingstone.
26. Younger G and Khan M (2008) Setting up and priming an intravenous infusion. _Nursing Standard_ **22** (40): 40–44.
# Section III
## Complex clinical skills
# Chapter 15
Medicines
# Learning objectives
* Clearly identify the role and accountability of healthcare assistants and assistant practitioners in administration of medicines
* Identify the main components of the Medicine Act that have an impact on the role of the healthcare assistant and assistant practitioner
* Identify the circumstances where nurses can prescribe medication
* Identify the common routes and considerations for administration of medicines with which healthcare assistants and assistant practitioners may assist
* Discuss the circumstances where healthcare assistants and assistant practitioners may check medications
## Aim of this chapter
A medication is a substance administered for the diagnosis, cure, treatment or therapeutic relief of a symptom or for prevention of disease. In healthcare, the words medication and drug are used interchangeably (Dougherty and Lister 2011).
## The role of healthcare assistants and assistant practitioners in relation to medicine administration
The role of healthcare assistants and assistant practitioners in medicine administration is currently under the delegation of a registered nurse who will take accountability for this task (see Chapter 15). This is identified in the Nursing and Midwifery Council (NMC) (2010) Standards for Medicine Management, which set standards for safe practice in the management and administration of medicines by registered nurses, midwives and specialist community public health nurses. The NMC (2010) acknowledge the administration of medicine is not solely a mechanistic task but one that requires thought and the exercise of professional judgement.
The legal limitations and boundaries for medication administration by HCAs and APs is exacerbated by the lack of regulation and registration as well as the incredible diversity of the roles that often include tasks previously considered the domain of the registered professional.
O'Flannaghan (2014) expresses the notion that registration by an independent regulatory body would no doubt give more credibility, especially to the role of the AP, and win confidence from other staff in delegating certain tasks. It would also provide a framework for legal boundaries and possibly give scope for further future development of the role, especially in relation to medication.
This chapter focuses on some of the issues surrounding medicine administration, but local policies will dictate accepted local practice, especially as these roles continue to advance and develop.
## Types of medicines
Different classifications of medicines are defined by the Medicines Act 1968, including the following three classification categories provided here.
### Prescription-only medicines (POMs)
These are medicinal products that may be supplied, including sold, to a patient on the instruction of a doctor/dentist supplementary prescriber or nurse/pharmacist as an independent prescriber.
### Pharmacy-only medicines (Ps)
These are medications that do not require a prescription but can be purchased only from a registered pharmacy, with the sale being supervised by a pharmacist, for example cough medicines.
### General sales list medicines (GSLs)
These include all medications that can be bought by the public, for example in supermarkets, and do not require either supervision of a pharmacist or a prescription, for example paracetamol. However, in a hospital setting there is control over these medications and patients cannot take these without prior consultation with medical and nursing staff.
# Think about it
Consider the above categories of medicines and give an example of each. If you are unsure, you could take a trip to a supermarket with a pharmacy department and view what is out on the shelves (thus not requiring a pharmacist to be present), and the medications that are behind the counter (requiring a pharmacist to be present). For a prescription-only medication this needs to be prescribed by an approved person either in the community or hospital setting and could be medication for yourself, a family member or a patient.
## Medication prescribing and legal aspects
The Medicines Act of 1968 was prompted in part by the consequences of thalidomide in the 1960s. This Act states that only authorised healthcare practitioners can legally prescribe medicines in the UK.
With the evolution of healthcare and the findings of the Crown Reports (1989 and 1992), it was firmly established that there could be significant benefits to nurses having prescribing rights. These rights were extended, initially only to community nurses through the Medicinal Products: Prescription by Nurses Act (1992), then later to nurses and midwives in all aspects of care. More recently, it now includes pharmacists, physiotherapists, chiropodists, podiatrists, optometrists and radiographers; referred to as non-medical prescribers.
In order to enable nurses, midwives and allied health professionals to prescribe legally, this legislation has had to be extended several times. The Amendments to the Prescription Only Medicines (Human Use) Order (2005) is the most recent change enabling the further development of non-medical prescribing.
The Medicines Act (1968) also provides all prescribers with a framework for what medicines require a prescription, and what medicines are available to the public without a prescription and under what circumstances. It outlines the three different categories of medicine.
### A brief over view of prescribing legislation in Scotland
Following extensive consultation, nurse and midwifery prescribing was implemented in Scotland in 1996. In 2003 the Health and Social Care Act introduced a new category of prescriber – the supplementary prescriber. Since 2003, legislation has further been amended to extend the powers of supplementary prescribing for nurses, midwifes and pharmacists of all controlled drugs and unlicensed medications. In April 2005, supplementary prescribing was introduced for physiotherapists, chiropodists, podiatrists, radiographers and optometrists.
In May 2006, legislation was amended to extend the independent prescribing powers of nurses and midwives in Scotland to all licensed medication and some controlled drugs.
'Controlled drugs' are, as the name suggests, the most tightly controlled medicines available. The Misuse of Drugs Regulations (2001) set out the requirements for obtaining, storing, prescribing, record keeping and supply (NES 2015).
Any qualified and registered independent prescriber may prescribe all prescription-only medicines for all medical conditions, with some nurse independent prescribers also able to prescribe some controlled drugs (NMC 2010). Supplementary prescribers can prescribe where there is a management plan for the patient, provided that an arrangement with the doctor or dentist and the patient has been formulated (NMC 2010).
Nurses and midwives who have recorded their medication qualification on the NMC register fall into two categories (NMC 2010): practitioner nurse prescribers, where they can prescribe from the community _Practitioner Nurse Prescribers' Formulary_ , which includes dressings and some POMs; and independent or supplementary nurse and midwife prescribers, who are trained both to make a diagnosis and to prescribe (independent prescribing) (NMC 2010). These practitioners can also review and change medication as part of a clinical management plan; this is known as supplementary prescribing (NMC 2010).
It is essential to check local policies and procedures about both prescribing and administrating medicines because local policy will dictate current practice.
### The law
Legislations relating to medicines are complex and are designed to safeguard patients (Obrey and Caldwell 2013). The administration of medicines has been demonstrated to encompass many areas for potential error. Two pieces of legislation have been identified as important in medicines management: the Medicines Act 1968 and the Misuse of Drugs Act 1971 (Dougherty and Lister 2011).
#### Medicines Act 1968
This provides a legal framework for manufacture, licensing, prescription, supply and administration of medicines that must be adhered to (NMC 2010). POMs are covered by the Human use order 1997 (SI no. 1830), which gives information and legislation on medicines that require a prescription to be written by specific personnel (NMC 2010).
In the NHS, hospitals adhere to this act by ensuring that a pharmacist supervises the purchasing and supply of medicines, and that supply or administration to a patient is only by personnel authorised to prescribe (Dougherty and Lister 2011).
Within a community setting, doctors, dentists, pharmacists and nurses are exempt from this restriction, allowing them to supply and use medication in the practice of their respective professions without pharmacy supervision (Dougherty and Lister 2011).
#### Misuse of Drugs Act 1971
This prohibits the possession, supply and manufacture of medicinal and other products unless legal (NMC 2010). It is mostly concerned with 'controlled' drugs, which are medications that are potentially addictive or habit forming, such as morphine substances (Dougherty and Lister 2011).
The role of the healthcare assistant and assistant practitioner in controlled drug administration can exist in the community through local policy, but this is usually advised only where no other registered nurse is available. In this instance, the accountability of the preparation and administration of the medicine still lies with the registered nurse (NMC 2010; NMC 2015) (see the section 'Delegation').
# Think about it
You are asked to assist in the preparation and checking of diamorphine for use in an MS26 syringe driver. Do you think this is an appropriate task to be delegated to you? (Think about your knowledge, skills, training and competence.)
In relation to controlled drugs, healthcare assistants and assistant practitioners may be required, through local policy, to witness the preparation and administration of controlled medicines, including in a syringe driver. This is a portable device that is often used for palliative care and delivers medication via a syringe, which is placed in the syringe driver. Where controlled medicines are used, if the unregistered practitioner is assisting with the ingestion or application, the unregistered practitioner must remain under direct supervision at all times (NMC 2010). Competency based training should have been undertaken for all registered nurses undertaking this role to ensure patient safety. Local policies should be in place if a healthcare assistant or assistant practitioner is to assist with this method of administration, and education about palliative care (management of symptoms where there is no cure) and the device should be undertaken.
## Related aspects and terminology
### Registered nurses' role
The Nursing Midwifery Council's (NMC) (2010a) Standards for Pre-registration Nursing Education: Essential Skills Clusters state: 'People can trust the newly registered nurse to ensure safe and effective practice in medicines management through comprehensive knowledge of medicines, their actions, risks and benefits.'
The nurse's role is clearly defined by the NMC who have set out principles that must be considered by registered nurses before the administration of medicines; these are detailed in Box 15.1 (NMC 2010). Once the 'direction to supply or administer' principles above have been adhered to, the registered nurse must follow the principles for administration, detailed in Box 15.2. These principles aim to improve and standardise practice, which in turn can reduce errors. Furthermore, Standard 18 of the Code (NMC 2015) clearly states nurses:
> 18 Advise on, prescribe, supply, dispense or administer medicines within the limits of your training and competence, the law, our (NMC) guidance and other relevant policies, guidance and regulations.
# Box 15.1 Methods of supplying and/or administration of medicines (NMC 2010)
## Standard 1: Methods
Registrants must only supply and administer medicinal products in accordance with one or more of the following processes:
* Patient specific direction (PSD).
* Patient medicines administration chart (may be called medicines administration record MAR).
* Patient group direction (PGD).
* Medicines Act exemption.
* Standing order.
* Home remedy protocol.
* Prescription forms.
## Standard 2: Checking
Registrants must check any direction to administer a medicinal product.
## Standard 3: Transcribing
As a registrant you may transcribe medication from one 'direction to supply or administer' to another form of 'direction to supply or administer'.
# Box 15.2 Standards for practice of administration of medicines (NMC 2010)
## Standard 8
As a registrant, in exercising your professional accountability in the best interests of your patients:
* You must be certain of the identity of the patient to whom the medicine is to be administered.
* You must check that the patient is not allergic to the medicine before administering it.
* You must know the therapeutic uses of the medicine to be administered, its normal dosage, side-effects, precautions and contraindications.
* You must be aware of the patient's plan of care (care plan/pathway).
* You must check that the prescription or the label on the medicine dispensed is clearly written and unambiguous.
* You must check the expiry date (where it exists) of the medicine to be administered.
* You must have considered the dosage, weight where appropriate, method of administration, route and timing.
* You must administer or withhold in the context of the patient's condition, (for example, Digoxin is not usually to be given if pulse below 60) and co-existing therapies, for example, physiotherapy.
* You must contact the prescriber or another authorised prescriber without delay where contraindications to the prescribed medicine are discovered, where the patient develops a reaction to the medicine or where assessment of the patient indicates that the medicine is no longer suitable (see Standard 25).
* You must make a clear, accurate and immediate record of all medicine administered, intentionally withheld or refused by the patient, ensuring the signature is clear and legible; it is also your responsibility to ensure that a record is made when delegating the task of administering medicine.
## In addition:
* Where medication is not given the reason for not doing so must be recorded.
* You may administer with a single signature any prescription-only medicine (POM), general sales list (GSL) or pharmacy (P) medication.
In respect of controlled drugs:
* These should be administered in line with relevant legislation and local standard operating procedures.
* It is recommended that for the administration of controlled drugs a secondary signatory is required within secondary care and similar healthcare settings.
* In a patient's home, where a registrant is administering a controlled drug that has already been prescribed and dispensed to that patient, obtaining a secondary signatory should be based on local risk assessment.
* Although normally the second signatory should be another registered healthcare professional (for example doctor, pharmacist, dentist) or student nurse or midwife, in the interest of patient care, where this is not possible, a second suitable person who has been assessed as competent may sign. It is good practice that the second signatory witnesses the whole administration process. For guidance, go to www.dh.gov.uk and search for safer management of controlled drugs: guidance on standard operating procedures.
* In cases of direct patient administration of oral medication from stock in a substance misuse clinic, it must be a registered nurse who administers, signed by a second signatory (assessed as competent), who is then supervised by the registrant as the patient receives and consumes the medication.
* You must clearly countersign the signature of the student when supervising a student in the administration of medicines.
### Delegation
The NMC guidelines (2008) state that nurses who delegate the responsibility of administration must ensure that the patient, carer, healthcare assistant or assistant practitioner is competent to carry out the task. This requires education, training and assessment of the patient, carer, healthcare assistant or assistant practitioner, including further support if necessary. This is in the best interests of the registered nurse, the assistant practitioner, the healthcare assistant and patient, with the ultimate responsibility for ensuring the correct patient, dose, drug, time and route lying with the registered nurse who delegated the task (Boyd 2013).
The nurse is also accountable for decisions to delegate tasks and duties to other people (NMC 2015).
### Informed consent
All patients have rights, and before administering any medicine it is necessary to obtain informed consent from them (Obrey and Caldwell 2013). A patient who is asked to consent to treatment must be given all the relevant information that they need to make an informed decision. All questions must be answered honestly and fully. If you cannot answer, then find a member of staff who can. Boyd (2013) requires the following points to be worked through:
* Hygiene – do not forget that standard precautions are necessary. Infection control and contamination measures are essential.
* Medicines administration chart – ensure the chart is accurately completed with all the relevant information available.
* Medicine – check the label correctly, including expiry date and measure dose. It should be noted that once some medicines have been opened they have a limited shelf life or are ineffective.
* Patient – check the patient's identity and explain again what you are administering.
* Administer – in an appropriate manner.
* Record – sign record immediately and maintain up-to-date documentation.
There may be times when a patient is unable to take their medication as prescribed. Do not crush or cut tables using tablet cutters if there are swallowing difficulties. Inform the pharmacist that an alternative may need to be prescribed, such as administering the drug in a liquid form. When medication is refused and consent withheld, this must be clearly documented. In the case of children and those whose capacity is lacking, advice must be sought and local policies and procedures followed.
### Patient group directions or group protocols
A patient group direction is a specific written instruction for the supply and administration of a named medicine or vaccine in an identified clinical situation (NMC 2010). A pharmacist and a doctor or dentist should have been involved in the development, and then approval must be obtained from the appropriate Health Board, Trust or Division. The role of the healthcare assistant may well be in giving a medicine within specific guidelines, but further training and assessment is essential.
# Think about it
Does your clinical area have any patient group directions? If so, identify which medications and patients they cover.
### One-stop dispensing
Following the publication of A Spoonful of Sugar in England and Wales (Audit Commission 2002) and The Right Medicine (Scottish Executive 2002) in Scotland, one-stop dispensing has been encouraged within the hospital setting. This is a system of administering and dispensing medicinal products involving the use of patients' own medications while in hospital (NMC 2010). In some instances this may also involve patients administering their own medication via a locked locker at the bedside.
### Self-administration
Adult patients who have been screened by the multidisciplinary team may be permitted to self-medicate their medication whilst in hospital (Figure 15.1). The rationale for self-medication is to be proactive in improving compliance and concordance. Boyd (2013) identifies that this is not possible for all patients, for example:
* those patients who are thought of at risk of deliberate overdose;
* those patients being discharged to nursing homes;
* those patients with unstable mental health conditions;
* controlled drugs (patients must not self-administer these);
* those too ill or confused to be ultimately discharged home;
* if patients are identified as having difficulty in opening bottles or reading labels. (This should be brought to the pharmacists' attention so that arrangements can be made for their discharge.)
**Figure 15.1** Compliance aid for medication delivery.
Source: Reproduced with permission of PivoTell® Ltd.
### Record keeping
Accurate records detailing medication given or omitted are essential parts of medicine administration (see Chapter 15 for further information).
### Allergies
The need to be vigilant about allergies by asking patients and clearly documenting any allergies cannot be overstated. Please check your local policy and procedure and access anaphylaxis training.
## Common medications
The Consumer Protection Act (1987) and Medicines Act (1968) confirm when administering medicines we need to follow what has become known as the 5 Rs:
* **Right** medicine is given.
* To the **right** patient.
* At the **right** time.
* In the **righ** t form.
* At the **right** dose.
There are multiple routes and preparations available, often for the same medication. The choice of route or preparation may be a result of a patient's symptoms; for example, if a patient is vomiting, oral medication may have to be changed to an alternative route, such as rectal administration. Healthcare assistants and assistant practitioners involved in medicine administration will follow local policies and procedure, which will determine the level of knowledge required about the medicine and the side-effects that may present.
Qualified personnel must prescribe all medications and the role of the healthcare assistant and assistant practitioners must be clearly defined. There are many different routes of administration and the most common are discussed below. Before and after all medicine administration, hands should be washed to prevent infection, as discussed previously.
# Think about it
Think of some other medication routes and why and when they may be used.
### Oral route
This can take the form of either tablets (e.g. paracetamol tablets) or liquids (e.g. amoxicillin preparation for children). Consider if the patient has difficulty swallowing and, if so, report to the nurse in charge where the medicine may need to be changed from tablets to a liquid; for example a patient who has had a cardiovascular accident (CVA or stroke) and who may have dysphagia (problems swallowing), especially if the tablets are large.
When administering tablets, their placement can vary, but this will be clearly indicated on the medicine bottle and the accompanying leaflet. Examples of different oral placement include buccal (which is placement between the gum and the inside of the mouth) or sublingual, which is under the tongue (Dougherty and Lister 2011).
Tablets should not be crushed or opened to release the medication unless the manufacturer states that this is acceptable, because this can alter the chemical properties of the medication (Boyd 2013). The advice on the label or leaflet will show if the medication needs to be administered depending on digestion, such as medication to be taken with/after meals. Tablets can be broken with a file if scored, or a tablet cutter can be used where appropriate, provided that the manufacturer's instructions are consulted.
Accurate measurement of liquid preparations is essential to prevent medication errors, and in some instances this may require a drug calculation to be performed. Local policy dictates whether a healthcare assistant or assistant practitioner can measure liquids. In the case of mixtures, many have a relatively short shelf-life, and some need to be kept in the fridge, for example antibiotics. Tablets and capsules may be susceptible to moisture and need to be kept in a cool dry place (Dougherty and Lister 2011).
### Topical creams
This refers to the application of cream, ointments or gels that have been prescribed to relieve symptoms experienced by the patient, for example hydrocortisone (steroid) cream or E45 cream for dermatological (skin) complaints.
As the cream/liquid is the active ingredient and is applied by direct contact, gloves should be worn. This prevents the person applying the cream or ointment receiving a dose of the medication, or a reaction on their skin. Where the application site includes broken skin, an aseptic technique (a technique that involves using sterile gloves and minimal touch to prevent infection) is required.
After application, the site should be observed for a local reaction or worsening of the condition, and reported to the nurse in charge. Patients may require assistance to apply topical creams due to difficulty in the patient reaching the site, for example if the area for application of the medication is on the patient's back.
Storage should be in conjunction with the manufacturer's recommendations, but extremes of temperature should be avoided because deterioration may occur (Dougherty and Lister 2011). Creams and ointments containing a medicine should have a date recorded, preferably on the medication, because many should only be used for a specific time after opening, for example 4 weeks after opening.
Topical creams, such as local anaesthetic creams like emla, can be applied in preparation for a further procedure in either children or anxious patients, for example during venepuncture (taking blood; see Chapters 12 and ). Please check with your local policies and procedures.
### Ear
Administration via the ear canal is to relieve the symptoms of local symptoms, for example eardrops to soften wax. Correct positioning of the patient both before and after administration is essential to ensure that the medication has the desired local effect and does not run out of the ear. This involves the patient tilting the head to the opposite side, which allows access to the ear canal and prevents the medication coming out of the ear. The use of cotton wool can prevent this. Local training and achievement of relevant competencies are required to undertake this task.
### Eyes
Administration into the eyes is to relieve local symptoms, for example due to infection, or post-operatively (after surgery), for example after cataract surgery.
Correct positioning of the patient both before and after administration is essential to ensure that the medication has the desired local effect. The patient will need to tilt the head back and look upwards. Care should also be taken to ensure that the medication does not run out of the eye before absorption. Local training and competency are required to undertake this task.
Eyedrops and ointment may become contaminated with microorganisms during use and then pose a danger to the recipient. Therefore, in the hospital environment they are discarded 7 days after they are first opened, but this may be extended to 28 days in the community (Dougherty and Lister 2011). Some products need to be kept in the fridge; ensure that this is checked and guidance followed.
### Subcutaneous
This involves a needle administering medication into the subcutaneous tissue (under the skin), for example insulin for a patient with diabetes (see Chapter 13). It is essential that correct disposal of the needle occurs to prevent needlestick injury.
It may be the patient who usually administers this medicine, but due to illness or lack of dexterity has become unable to do so. Again, training and supervision are essential to ensure competence.
Some injections may need to be kept in the fridge and manufacturer's recommendations should be followed; for example insulin needs to be kept in the fridge.
### Suppositories
Suppositories are small, torpedo shaped wax pellets inserted into the rectum. When in the rectum, the suppository melts at body temperature, and dissolves or disperses in the mucous secretion of the rectum. There are a number of different types of suppositories available. Retention suppositories deliver drug therapy, for example, analgesia and antibiotics. Suppositories can often be a useful alternative for the administration of some drugs when the person is unable to take them orally. Those suppositories administered with the intention of stimulating the bowel in order to evacuate it include glycerine and bisacodyl (Peate 2013).
Storage instructions may involve storage in the fridge, check the manufacturer's instructions. Administration by this route should only be undertaken after training and supervision, and in accordance with local policy.
### Inhalation
This can include short-term symptomatic relief, for example the use of a Salbutamol inhaler in asthma or a steroidal inhaler for long-term therapy. The actual amount of drug inhaled is small so a good technique is essential. Spacers or a bubble can be used to aid effectiveness (Figure 15.2).
**Figure 15.2** A 'spacer' inhaler.
Correct positioning: an upright position may need to be adopted to allow full lung expansion and allow correct medication delivery. A good inhaler technique is essential with this route of administration and, where healthcare assistants are involved in patient education and assessment of inhaler technique, further training and assessment must be undertaken.
Aerosol containers should not be stored in direct sunlight or over radiators, because there is a risk of explosion if they are heated (Dougherty and Lister 2011). Good oral hygiene is also required to avoid patients developing infections due to their medication.
### Oxygen
Oxygen is a medication and requires a prescription to allow administration to patients. It is delivered in varying concentrations and is measured in percentages, for example 24, 28, 35 or 40%, depending on the patient's clinical symptoms (Boyd 2013; Dougherty and Lister 2011).
Different masks exist that include simple masks with no special features, a non-rebreathing mask, and a Venturi mask, where different coloured fittings dictate the oxygen percentage and flow rate that is required, depending on the prescription (Boyd 2013). Masks are disposable and for single-patient use. They should be changed regularly to prevent infection. Nasal cannulae can be used (Figure 15.3), which make it possible for the patient to eat, drink and talk while receiving oxygen (Dougherty and Lister 2011). In the hospital setting, oxygen is often 'piped', that is available at the bedside with a meter on the wall to apply tubing. In the community or in an ambulance this would involve an oxygen cylinder.
**Figure 15.3** Nasal cannula.
### Wound dressings
If the healthcare assistant or assistant practitioner is performing simple dressing, which includes applying a dressing to a wound, a prescription for the dressing will be required. The district nurse, who has undergone additional training, or the GP may prescribe this.
Best practice would be for the same person to carry out the dressing to monitor improvement or problems at the wound and always report to the nurse in charge. Further training and competence should be undertaken in line with local policy with regard to this skill.
### Intravenous (medication administered directly into a vein)
This route should be performed only under strict local policies/procedures and competency based training. It may include administration of fluids or medications. See Chapters 16 and for further information on intravenous flush (administration of 0.9% sodium chloride via a cannula to keep it patent, i.e. prevent blockage).
The NMC (2010) state that, where a registered nurse delegates the task of giving a patient medication, this may be drawn up in advance after a full risk assessment and delegation of the task to a 'named individual' (NMC 2010). Please check your local policies and procedures.
## Errors in administration and adverse reactions
The Yellow Card Scheme is vital in helping the Medicines & Healthcare Products Regulatory Agency (MHRA) monitor the safety of all healthcare products in the UK to ensure they are acceptably safe for patients and those that use them. Reports can be made for all medicines including vaccines, blood factors and immunoglobulins, herbal medicines and homeopathic remedies, and all medical devices available on the UK market.
The Scheme collects information on suspected problems or incidents involving:
1. **1.** side-effects (also known as adverse drug reactions or ADRs);
2. **2.** medical device adverse incidents;
3. **3.** defective medicines (those that are not of an acceptable quality);
4. **4.** counterfeit or fake medicines or medical devices.
It is important for people to report problems experienced with medicine or medical devices as these are used to identify issues that might not have been previously known about. The MHRA will review the product if necessary, and take action to minimise risk and maximise benefit to the patients. The MHRA is also able to investigate counterfeit or fake medicines or devices and if necessary take action to protect public health (MRHA 2012).
### Side-effects to a medicine, vaccine, herbal or complementary remedy
All medicines can cause side-effects (commonly referred to as adverse drug reactions or ADRs by healthcare professionals).
Side-effects reported on Yellow Card are evaluated, together with additional sources of information such as clinical trial data, medical literature or data from international medicines regulators, to identify previously unknown safety issues. These reports are assessed by a team of medicine safety experts made up of doctors, pharmacists and scientists who study the benefits and risks of medicines. If a new side-effect is identified, the safety profile of the medicine in question is carefully looked at, as well as the side-effects of other medicines used to treat the same condition. The MHRA takes action, whenever necessary, to ensure that medicines are used in a way that minimises risk, while maximising patient benefit.
If the healthcare assistant or assistant practitioner is the first person to notice an adverse drug reaction or note that an error has occurred, this must be reported immediately; ensure the patient is safe and follow local policies and procedures. The registered nurse has clear accountability under the NMC Code (2015). Safeguarding the patient is always a priority.
## Summary
The evolving role of the healthcare assistant and assistant practitioner would benefit from registration and regulation, but as discussed this has not yet occurred. Whatever and wherever the role, healthcare assistants and assistant practitioners must ensure they have the knowledge, understanding, skills and training before taking on any task involving medication. Drug calculations have not been discussed, but this area remains problematic and can result in catastrophic error. If you are not confident in your numeracy skills, explore options available to you to practice and seek support and training. Many Trusts have already explored the role of healthcare assistants and assistant practitioners in the administration of medication. While medication administration can be fulfilling and rewarding as part of the holistic care of your patient, do not undertake this area of care lightly: be safe, be competent.
## References
1. Audit Commission (2002) _A Spoonful of Sugar_. London: Audit Commission.
2. Boyd C (2013) _Student Survival Skills: Medicine Management Skills for Nurses_. Oxford: John Wiley & Sons.
3. Dougherty L and Lister S (eds) (2011) _The Royal Marsden Hospital Manual of Clinical Nursing Procedures_ , 8th edn. Oxford: Blackwell Publishing.
4. Medicines and Healthcare Products Regulatory Agency (MHRA) (2012) _Medicines and Medical Devices: Regulation: What You Need To Know_. London: The Medicines and Healthcare Products Regulatory Agency.
5. NHS Education for Scotland (NES) (2015) Non-medical prescribing learning resource [online]. Available at: <http://www.prescribing.nes.scot.nhs.uk/> (accessed 3 May 2015).
6. Nursing and Midwifery Council (NMC) (2008) _Standards for Medicines Management_. London: NMC.
7. Nursing and Midwifery Council (NMC) (2010) _Standards for Pre-registration Nursing Education: Essential Skills Clusters_. London: NMC.
8. Nursing and Midwifery Council (NMC) (2015) _The NMC Code of Professional Conduct: Standards for conduct, performance and ethics_. London: NMC.
9. O'Flannagan C (2014) Should assistant practitioners be allowed to administer medicine? _British Journal of Health Care Assistants_ **8** (12): 594–601.
10. Obrey A and Caldwell J (2013) Administration of medicines – the nurse role in ensuring patient safety. _British Journal of Nursing_ **22** (1): 32–35.
11. Peate I (2013) Clinical skills series/2: enemas and suppositories. _British Journal of Healthcare Assistants_ **7** (2): 76–80.
12. Scottish Executive (2002) _The Right Medicine_. Edinburgh: Scottish Executive.
# Chapter 16
Peripheral intravenous cannulation
# Learning objectives
* Review the anatomy and physiology relating to peripheral intravenous (IV) cannulation (see Chapter 12 for the anatomy and physiology of the arm)
* Review the skills and competence with regard to undertaking peripheral IV cannulation
* Describe possible complications of peripheral IV cannulation and how to manage them
## Aim of this chapter
The aim of this chapter is to review the reasons and procedure for undertaking peripheral intravenous (IV) cannulation in the arm, and discuss possible complications and risk prevention. _This may not, however, be a role that is expected of all healthcare assistants; check your local policy and access any approved training via your manager/charge nurse_. Also insertion of a cannula requires a saline flush to confirm patency (that it is working); again many healthcare assistants may not be covered or allowed to administer this because it is classed as a medicine and many clinical areas do not allow healthcare assistants to administer any medicines (see Chapter 15); _again check your local policy for guidance_.
## Reasons for cannulation
Peripheral IV cannulation is the introduction of a cannula into a peripheral vein as a means of gaining direct access into the venous circulation. McCallum and Higgins (2012) identify that the quality of care can be significantly influenced by adopting the principles associated with the safe management and care of patients who have these devices in situ (HPS 2012; DH 2011). These procedures may cause trauma and discomfort to the patient, which is even more likely if the person performing them is not competent (Ellson 2008). Demonstrating knowledge and understanding of the effective methods that are used can ensure patient confidence is maintained and their experience of cannulation is positive (McGowan 2014). The Department of Health (DH 2011) developed High Impact Interventions (HIIs), which are evidence-based approaches that relate to key clinical procedures or care processes that can reduce the risk of infection if performed appropriately. They have been developed to provide a practical way of highlighting the critical elements of a particular procedure or care process (a care bundle), the key actions required are a means of demonstrating reliability. The peripheral intravenous cannula HII (DH 2011) highlights the associated risk of infection because of the potential for direct microbial entry to the bloodstream and emphasises the importance of training. _Please ensure that you are given local training and support, to make sure that you are competent in this role before commencing this skill_.
## Why perform peripheral IV cannulation
The following list gives some indication of why a patient may require insertion of a cannula; however, many of these are not within the scope of the healthcare assistant to carry out:
* To administer intravenous fluids for the maintenance of fluid and electrolyte balance (elements carried in the blood).
* To administer intravenous medicines (bolus, intermittently or continuously).
* To transfuse blood and blood products.
* Just in case, for example a professional judgement in case the patient collapses.
* Venesection (bleeding a volume of blood from a patient, similar to blood donation).
* To provide access for nutritional support.
* To aid in the monitoring of a patient's condition.
The decision to insert a cannula will usually be made by a doctor or registered nurse; however, in some practice settings this may also be made based on a care pathway or protocol. _Be aware of your local policy and adhere to local guidance_.
## Relevant anatomy and physiology
See Chapter 12 for the anatomy and physiology of the arm. Figures 16.1 and 16.2 are a review of the anatomy and physiology of the arm and hand relating to the veins commonly used in peripheral IV cannulation, and Figure 16.3 shows a cross-section of a vein. It is essential that the healthcare assistant or assistant practitioner undertaking peripheral IV cannulation has a good understanding of the anatomy and physiology of arteries, veins and associated nerves.
**Figure 16.1** Venous anatomy of upper arm.
**Figure 16.2** Hand veins.
**Figure 16.3** Cross-section of vein.
## How to insert and remove a peripheral IV cannula
### Assessment of the patient and their veins
#### Patient assessment
A thorough patient assessment is crucial to ensuring the patient receives the most appropriate intervention, the right device in the most appropriate site (Dougherty and Lister 2011). McGowan (2014) highlights the importance of taking into account the patient's age, condition, lifestyle, compliance and preference. Other factors that should be considered include the patient's diagnosis, treatment plan, type of therapy and duration of therapy. It is important to take time to communicate with the patient to establish their understanding and acceptance and to allay some of their anxieties (Gabriel 2012; McGowan 2014). The patient's experience is important, and yet it is easy to overlook the effect poor IV access and IV device maintenance has on them (Oliver 2015).
Use veins that feel soft and resilient, and refill when depressed, often described by practitioners as 'juicy' or 'bouncy'. Also consider the length of the cannula, so ensure that a straight vein suitable for the length of the cannula is selected, with large veins being preferable over small veins. Patient involvement is essential, so ensure that the procedure is discussed with the patient to gain consent and identify any site preference, for example the patient's non-dominant arm (Dunnnig 2011; Boyd 2013; Dougherty and Lister 2011). Coram (2015) cautions against choosing the site because of a visible vein as it might not necessarily be the best place.
Longmate et al. (2011) describe key interventions to prevent catheter-related blood stream infections that should be considered through the patient's cannulation experience or journey (Table 16.1).
**Table 16.1** Key preventative interventions
**Before insertion** | **During insertion** | **After insertion**
---|---|---
Discuss with the patient
Correct vascular access device (cannula) and site selection
Hand hygiene
Competent in skill | Skin asepsis with chlorhexadine
Use of barrier precautions
During insertion | Care of device and area once in situ
Prompt removal
Source: Longmate 2011. Reproduced with permission of BMJ Publishing Group Ltd.
### Common sites
See Figure 16.1:
* Dorsal venous arch on hand.
* Forearm vein.
* Cephalic vein on thumb side of wrist.
* Basilic vein.
This might be a useful point to revise your anatomy and physiology. Take care because the most prominent vein is not necessarily the most suitable.
### Criteria for selecting a site for cannulation
McGowan (2014) suggests the metacarpal veins found in the hand and the cephalic and basilica veins found in the forearm should be assessed first. This approach is considered best practice as further attempts above the site can then be selected. Gabriel (2012), however, recommends caution and consideration of the ageing process on veins. The ageing process results in the loss of elasticity, with the vein becoming more rigid, plus there is thickening of the vessel walls and the development of arteriosclerosis. Skin is more delicate and haematoma, bruising and damaging the vein more likely. Therefore care and caution is advised when cannulating an older person. Boyd (2013) also cautions about the number of times insertion is attempted and the need to ask a more experienced member of the team.
Witt (2011) sums up veins to avoid as those that are hard, thrombosed, thin, fragile, mobile and/or lying over a bony prominence. She also advises that skin should be intact, free from infection or damage (e.g. a burn) and any existing bruises or swelling. Areas with tattoos should also be avoided as these may also be a potential source of infection.
### Choosing the appropriate cannula
As a rule, the smallest cannula should be selected; however, as Boyd (2013) identifies, if the patient is critically ill or this is an emergency situation – for example the patient has hypovolaemic shock – then a larger device is inserted to 'push fluids' into the patient's system quickly for rapid treatment. Please check your local policy
Table 16.2 gives guidance; seek local guidance when necessary.
# Think about it
Why is the patient's age a factor that you need to think about when assessing for a site?
**Table 16.2** Cannula choice guidance
**Cannula size** | **Care situation**
---|---
14 gauge | Emergency, e.g. cardiac arrest
16 gauge | Major trauma or surgery, massive fluid replacement
18 gauge | Routine blood transfusions, rapid infusion, surgical or trauma patient
20 gauge | Routine infusions, bolus drug administration, medical, post op patient
22 gauge | Small fragile veins, short-term access
24 gauge | Small or fragile veins, children, older patient
Source: NHS Lothian (2007). Adapted with permission of NHS Lothian.
### Infection
Peripheral IV cannulation breaches the circulatory system, so healthcare assistants and assistant practitioners should consider their role in the prevention of infection and be aware of predisposing infection risk factors and subsequent management (Box 16.1). Infection control is integral to all care and robust standards of practice are therefore paramount to ensure safe and competent practice both in peripheral IV cannulation and IV care (Lavery 2010). The H.A.N.D.S acronym was created by the IV team at King's College Hospital as an aide memoire to promote safe and evidenced-based practice for the insertion and care of IV devices (Frimpong et al. 2015).
# Box 16.1 Predisposing infection risk factors and management
* Skin colonisation (surface bacterial spread) can allow bacteria to enter the circulatory system through the insertion of the needle and cannula, so ensure careful site selection and cleansing.
* Remote infection (e.g. urinary tract infection) can also lead to a risk; the patient should be educated about not tampering with the site, cannula or sterile dressing, and this should reduce the risk of transferring bacteria.
* Multi-use disinfectants can become colonised with bacteria very quickly, so use only single-use sachets when cleansing the site.
* Expired or damaged stock can be a source of infection; ensure stock is in date and has been stored correctly, and is used for its intended purpose; single-use devices must be used (Medicines Devices Agency (MDA) 2000).
* Hands of practitioners are the single most common way in which bacteria are transferred onto devices (equipment), so ensure correct hand cleansing.
(NHS Lothian 2007 with permission.)
1. **H: Hand hygiene** Before, during and after an invasive procedure such as peripheral IV cannulation, for example after contact with a source of microbes (germs): wash hands with liquid soap and warm water for at least 30 seconds; dry thoroughly with paper towels, then use alcogel before accessing the venous access devise (Frimpong et al. 2015).
2. **A: Antisepsis of the skin** The appropriate method of antisepsis to decontaminate the skin site is 2% chlorhexadine in 70% isopropyl alcohol. A single-patient use applicator should be used before insertion for at least 30 seconds using a crosshatch pattern XXX (Frimpong 2015). An area of skin that is equal to the size of the dressing should be cleaned and must be allowed to dry for 30 seconds to achieve maximum bacterial killing effect, which will reduce the risk of infection (Longmate 2011; Loveday et al. 2014).
3. **N: Non-touch technique** Centres for Disease Control and prevention (CDC) (2011) state clearly that the insertion site should not be touched once the skin is cleansed. Aseptic Non-Touch Technique (ANTT) must be performed and observed throughout. If the practitioner cannot cannulate without re-palpating the skin, the use of sterile gloves is strongly advised. Frimpong et al. (2012) also point out that ANTT should be applied when opening giving sets as the bag spike is a key part and must not be touched.
4. **D: Daily inspection; date on the dressing documentation**
Daily inspection: is the line still needed?
The removal of IV devices as soon as they are no longer needed is essential and should be part of the daily review for both the nursing and medical staff (MHPRA 3023; Boyd 2013). Loveday et al. (2014) recommend that if the cannula needs to be in situ for longer than the standard duration, the reason should be clearly documented in the patient's medical notes
Date on the dressing
A sterile, transparent semi-permeable membrane dressing should be used to cover the insertion site. The date, time and initials of the inserting clinician must be written clearly on the dressing without obstructing the insertion site for the cannula. This dressing should be left in place for no longer than seven days and reapplied as required. Please check your local policy.
Documentation: has the line been documented?
Accurate records must be kept of who inserted the cannula, where on the body it was inserted and the date on which the cannulation was performed. The cannula site should be visually inspected everyday. Local policy should be followed.
5. **S: Scrub the hub; sharps safety**
Scrub the hub
Before connecting anything, for example a syringe or a giving set, the hub of the needle-free connector should be scrubbed for at least 15 seconds, cleaning it thoroughly with 2% chlorhexadine 70% isopropyl alcohol, and allowed to completely dry before attaching the giving set or syringe (Frimpong et al. 2015). Loveday et al. (2014) recommend that this procedure is repeated every time the IV device is accessed. It is important that the healthcare assistant or assistant practitioner has been assessed as competent before undertaking any of these procedures.
Sharps safety
There is now a greater understanding of the need to be sharp aware and sharp safe. The Health and Safety Executive (HSE) (2013) regulations reinforce the need to dispose of sharps at the point of use. Frimpong et al. (2015) emphasise the importance of the following:
* NEVER re-stealth or recap needles.
* ALWAYS dispose sharps at the point of use.
* DO NOT over fill sharps containers.
### Protective clothing
Protective clothing should be worn according to local policy; and, as in Chapter 12, care should be taken using latex gloves in case the patient or member of staff has a sensitivity or allergy.
## Environment
A safe working environment is important to both the patient and the HCA. Equipment should be at hand, including the sharps bin to avoid any unnecessary hazards to the HCA. To ensure good assessment of the patient and their veins, it is important to have good lighting. The patient should be comfortable and as relaxed as possible through sitting comfortably on a chair or lying on a bed or trolley with their arm supported on a pillow (Dougherty and Lister 2011).
# Practice point
When using a tourniquet ensure it is either cleaned between patients or use single patient disposable tourniquets.
## Performing peripheral IV cannula: requirements and technique
Please refer to Box 16.2 for the equipment required for a cannulation insertion and Table 16.3 for preparation.
**Table 16.3** Preparation for procedure
**Action** | **Reason**
---|---
1. Wash hands with liquid soap, and dry hands thoroughly, followed by an alcohol hand rub, or wash with an approved antiseptic solution | To minimise the risk of healthcare-associated infection (HAI)
2. Assemble all the equipment required for the procedure on a clean trolley or a tray | In order that the procedure is carried out smoothly, efficiently and without interruptions
3. Ensure that all the equipment used is intact and within expiry dates | To maintain asepsis
4. Approach the patient and explain the procedure in a confident manner
Allow the patient time to ask questions and express concerns about the procedure, if any | To obtain patient consent and cooperation
5. Help the patient into a comfortable position, e.g. sitting in a chair or lying on bed, and support arm with a pillow
Ask patient if they have ever had problems with procedure, e.g. previous fainting episode; if so lay the patient on a bed, to prevent a vasovagal (faint) episode | To maintain the patient's comfort
To enable the operator to carry out the procedure with ease
6. Prepare the area, e.g. provide adequate lighting, privacy and heighten the bed, lower cot sides, check positioning | Safe working environment
7. Verbally check the identity of the patient – name, date of birth (DOB) against identification (e.g. patient ID bracelet) and documentation, e.g. care pathway. | Identify the need for the procedure
To ensure that the peripheral IV cannula is being inserted into the right patient
Source: NHS Lothian (2007). Adapted with permission of NHS Lothian.
# Box 16.2 Equipment required for cannulation procedure
* Tourniquet – consider quick release, latex free.
* Non-sterile gloves and apron.
* Alcohol swab (70% isopropyl).
* Appropriate size cannula.
* Closed system ( _recommended_ ), e.g. Smartsite.
* Sterile dressing (e.g. Tegaderm or IV3000).
* Pad to protect from spillage.
* Clean tray/trolley.
* 10 ml syringe.
* 5 ml ampoule sterile 0.9% NaCl flush.
* Sterile green or blue needle or sharps-less needle.
* _Appropriate IV fluid for administration._ a
* _Medical device (if required)._ a
* Sharps bin/container.
a As mentioned at the start of the chapter, some healthcare assistants may not be covered to administer either flush or intravenous fluids; check local policy. If this is the case, the healthcare assistant may require a registered nurse or doctor to flush the device once they have inserted the cannula (Figure 16.4).
**Figure 16.4** Example of cannula.
Table 16.4 outlines the specific actions and observations required throughout the procedure.
**Table 16.4** Specific actions and observations during the procedure
**Action** | **Reason**
---|---
1. Wash hands with liquid soap, and dry hands thoroughly followed by an alcohol hand rub, or wash with an approved antiseptic solution | To minimise the risk of healthcare-associated infection (HAI)
2. Consult with the patient with regard to preferences for cannulation site, based on previous experiences | To actively involve the patient in own treatment. To be aware of the patient's history and factors that may influence choice of vein
3. Apply tourniquet to the arm on the chosen side approximately 7–10 cm (3–4 inches) above selected site for cannulation
Apply enough pressure to impede (restrict) venous circulation | Increases venous pressure, aiding vein identification and entry
Check radial pulse to ensure that arterial flow is not affected
Reduce risks of cross-contamination
_Consider the use of a disposable tourniquet, if available_ |
3. To further encourage venous filling try one of the following;
(a) Stroke the vein gently
(b) Allow the arm to hang by patient's side (gravity)
(c) Immerse limb in warm/hot water for 5–10 mins
(d) Ask patient to clench fist and then relax, several times | Helps make vein more prominent and so easier to assess and cannulate
4. Palpate (feel) the selected vein | To identify its course, depth and structures, i.e. tendons, and to avoid nearby arteries or nerves
5. Release the tourniquet and check vein decompresses (returns to normal) | To prevent cell damage due to decreased oxygen (O2) supply
6. Choose and prepare the smallest practical cannula size (gauge) | Ensure appropriate size
7. Hand antisepsis; use either an alcohol hand rub or wash with an approved antiseptic solution | To minimise the risk of healthcare-associated infection (HAI)
8. Reapply tourniquet to the chosen site |
9. Cleanse the proposed cannulation site with alcohol skin prep, using a firm circular motion from centre to the periphery, for 30 s and at least a 5–7 cm (2–3 inches) area – size of dressing area | To minimise the risk of HAI
Allow the alcohol to air dry, for a minimum of 30 s
DO NOT re-palpate the vein after the site has been cleansed; use a mental marker, if necessary, e.g. freckle | Prevent stinging as cannula pierces the skin
Increases risk of infection
DO NOT shave the skin at the insertion point | Can cause microscopic damage to skin
10. Put on gloves | Gloves will give some protection from blood spillage
11. Fold down the wings of the cannula | This grip reduces the risk of contaminating the cannula
12. With the patient's arm in a supported downward position, anchor the vein by applying tension to the skin below and to side of the cannulation site | Prevents vein from rolling or moving
Prevents risk of injury to nurse inserting
13. Insert the device into the vein at an angle (depending on device used) holding the cannula firmly with a three-point grip and bevel (cut) up
_Fragile veins usually require a lower angle of insertion_
Watch for the presence of blood in the flashback chamber | Ensures correct positioning between needle and catheter tip, and stabilises cannula within the needle
Reduce overshooting
This flashback indicates that the needle has successfully entered the vein (Figure 16.5)
14. Lower the angle of the cannula to almost skin level. Advance the cannula a few millimetres into the vein and avoid contamination by holding at the wings or protection cap
No resistance should be felt as cannula advances into vein | To prevent puncture of the rear wall of the vessel
This ensures that the cannula tip also enters the vein
If resistance felt, consider if pierced rear of vein due to angle, or cannula not in vein initially. Remove cannula
15. Withdraw the introducer needle partially (approx. 2–5 mm) | To avoid exit through the rear of vein wall and provide stability to cannula
16. First hold the flashback chamber immobilising the needle. Then advance the cannula forward off the needle into the vein with the other hand; this should be in a smooth single movement | The plastic cannula advances only into the vein
Consider point 14 as cannula should advance easily; if not may require removal and new cannula insertion in different vein and site
17. Release the tourniquet | Release venous pressure
18. The needle must never be reinserted while cannula is in the vein (some devices now prevent this, e.g. Vasofix)
Apply pressure over the vein distal to the cannula tip (beyond the end of cannula) | To avoid risk of needle severing the cannula and cause plastic embolus
To avoid spillage of blood when needle is removed (raising the patient's arm also reduces risk of spillage)
19a. Remove the introducer needle completely, and dispose of immediately into sharps bin, e.g. Vasofix needle cap flips over as it is withdrawn and a slight resistance might occur | Reduces risk of needlestick injury
Ensure firm grasp of device while withdrawing needle to prevent accidental removal or dislodging of cannula
19b. Close the cannula with a closed system, e.g. Smartsite, or device cap if closed system not used | Reduce number of times cannula is reconnected to reduce infection rate and mechanical irritation
20. Flush the cannula with 5 ml 0.9% NaCl (physiological saline) or flush volume of twice the length of the cannula, plus any device, e.g. closed system, using push–pause method and positive pressure via the intermittent port or closed system connectora | To confirm correct placement of the cannula, the push–pause method helps create turbulence and so maintains flow, and positive pressure means that no blood can backflow into the cannula
21. Secure the cannula in position with sterile dressing, e.g. IV 2000 or Tegaderm IV (Figure 16.6)
Skin may be clipped adjacent to, but not at insertion site, to secure the dressing | Good fixation is essential to prevent poor position, rolling or other movements of the cannula, because can cause irritation of the vein
Reducing the risk of HAI
22. Make no more than two attempts to insert cannula. If unsuccessful, obtain assistance from more experienced staff | Patient comfort
Prevent trauma to vein
23. Ensure that patient is given appropriate education once cannula is in place | Ensure cannula safety and sustain for duration required or 72–96 hours
24. Enter date and time of insertion, site, cannula size and reason for insertion in patient notes, and record signature of operator | Good record keeping and legal requirement
Some areas may record date and time on dressing too, to aid monitoring
a Push–pause and positive pressure stage 20 – holding plunger with thumb, insert small volume then pause, then repeat, till all the saline is flushed in, then maintain pressure on plunger as syringe is removed.
Source: NHS Lothian (2007). Adapted with permission of NHS Lothian.
**Figure 16.5** Inserting the cannula. Source: Photograph by I Lavery.
**Figure 16.6** Device in place. Source: Photograph by I Lavery.
## Patient education for peripheral IV cannulation
Before and during insertion take care to use language that will not distress the patient. Rosenthal (2005) suggested avoiding the use of words such as 'needle' and 'stick', and use 'plastic tube' and 'insert' instead, and explain to the patient that it is the 'plastic' cannula that is inserted, not the needle.
Ensure that the patient has also understood the reason for the cannula, and keep them informed about ongoing treatments (Lundgren et al. 1998).
Advise the patient to report any concerns, including if the site becomes painful, swollen, hot or tender, if there is any leakage or the dressing becomes loose. Also advise patients to take care when dressing and undressing because this can dislodge the cannula. Ask them not to tamper with or touch the dressing and to try to minimise movement in the arm, especially if near an area of flexion, such as the wrist or elbow. All these should ensure a safe cannula for the duration and help the patient comply with the procedure (Ingram and Lavery 2007).
Refer to Table 16.5 for information on the maintenance and care of a cannula after insertion.
**Table 16.5** Maintenance and care of the intravenous (IV) cannula after insertion
**Action** | **Reason**
---|---
1a. Inspect the cannula each shift or more frequently depending on patient's clinical condition and type of therapy | To ensure cannula is in correct position and observe for potential complications, e.g. phlebitis
1b. Flush cannula with 5 ml 0.9% NaCl or the flush volume is twice the length of the cannula plus any device, e.g. closed system | To maintain patency of cannula and ensure flush volume adequate
_Not all healthcare assistants are allowed to administer medicines – check your local policy_
1c. The cannula site should also be monitored each shift or at least daily
Recommendations for resiting are after a period of 72–96 h
However, cannula may be left in for longer and reason documented, e.g.
• when initial cannulation was difficult
• when therapy will be completed shortly afterwards | To reduce complications including healthcare-associated infection and to ensure that length of time cannula is in place reflects individual management of each patient and needs
To provide reason and justify decisions
2. Use a rigorous aseptic technique when handling the cannula/lines:
• reduce manipulations of the system to a minimum
• keep number of stopcocks and taps to a minimum
• injection sites and bungs cleaned with an alcohol swab and allowed to dry | Any connection in an IV system is a potential point of entry for microorganisms
Recommend use of closed system to minimise infection from port
3. Maintain appropriate level of hand hygiene antisepsis before handling the cannula/lines at any time | To minimise risk of infection
4. Document in care plan/notes:
• date and time of insertion
• gauge (size) of catheter
• site of insertion
• signature
• flush and amount (volume) | Good record keeping and legal requirement
Source: NHS Lothian (2007). Adapted with permission of NHS Lothian.
# Think about it
While inserting a cannula you encounter resistance. What would you do?
### Re-siting of a peripheral IV cannula ( _once discussed and agreed locally_ )
* Follow the same procedure as for initial insertion.
* After 72–96 hours, if still required, check with senior/charge nurse or notes.
* If inserted in an emergency, re-site after 24 hours (e.g. emergency insertion may not have had time to include appropriate skin cleansing).
* If the site becomes infected, the cannula is blocked or leaking or infiltrates the surrounding area (see under Problems).
* Select another vein, alternating between arms if possible, for the new cannula, but proximal (above) to the previously cannulated site.
* Choice of cannulation site will depend on the patient's local anatomy, patient mobility and the required flow rates; however, rotation of sites is essential.
* Continue to use the distal veins of the arms if possible.
* Document reason for removal, including any signs and symptoms of infection or problems and record (see point 4 in Table 16.5).
### Use of a tourniquet
Ellson (2008) reminds us that tourniquets are a potential source of infection. Single-tourniquets are available. The tourniquet used should be sufficiently wide that it can be wrapped around the limb and gently tightened so that minimal pressure is used to suppress blood flow and achieve the dilation of the vein (Gabriel 2012). Excess pressure from a narrow tourniquet, for example, can cause trauma to the vein which may result in bleeding and scarring to the vessels, leading to unsuccessful cannulation and distress for the patient.
## Related aspects and terminology
### Consent
Explain the procedure carefully to the patient so that they understand what the procedure is and why it is being undertaken. Using good interpersonal and communication skills, not only will the patient be able to provide informed consent, but they are less likely to make any sudden movements and are more likely to be relaxed (Hart 2011). Patient education is an important part of patient care and cannot be over-emphasised.
### Anxiety
As already discussed in Chapter 12, patients may experience anxiety, so they should be asked if they have had a cannula inserted previously; because, as McGowan (2014) points out, anxiety may be due to a previous bad experience, a degree of 'needle phobia' (fear of a needle) or just a dislike of medical procedures. See Chapter 12 for suggestions on reducing or managing anxiety.
# Think about it
What options might you consider if your patient were very anxious about the procedure?
### Terminology
* _Vasovagal episode_ : blood pressure drops and patient may feel faint.
* _Erythema_ : redness.
* _Cerebrovascular accident (CVA)_ : commonly known as a stroke.
* _Phlebitis_ : inflammation/infection of the vein.
* _Rigors_ : shivering associated with high temperature.
* _Hypotension_ : low blood pressure.
* _Malaise_ : tiredness, weakness.
* _Venesection_ : blood is taken from the patient, for example to reduce the haemoglobin level; commonly this technique is used in patients with chronic bronchitis.
## Common problems/potential complications of peripheral IV cannulation
### Unsuccessful cannulation
According to Morris (2011), veins might be missed due to: poor skin stabilisation; poor vein choice; or failure to penetrate the vein due to poor insertion angle and physiological changes in the vein due to ageing. A thorough patient assessment, experience and good technique will help the practitioner to avoid or manage these problems. _Ensure that you have followed local policy to achieve competent and safe practice_.
### Damaged device
Prior to using the cannula, the packaging needs to be checked to ensure the product is latex free and that it is single use. The packaging will also display the gauge size, lot number and expiry date as well as how many millilitres per minute can be infused (Boyd 2013).
### Flushing
In order for the cannula to remain patent it needs to be flushed, usually with sodium chloride 0.9% . Ideally a 10 ml syringe should be used as a smaller syringe creates too much pressure on the vein walls resulting in damage (Boyd 2013). Please check your local policy which should reflect best practice.
### Haematoma
Morris (2011) defines this as bleeding (usually uncontrolled) that occurs as a result of infiltration of blood from a punctured vein into the tissue immediately surrounding it. A haematoma can be recognised as a blue/purplish tinged lump at the point of the needle insertion. Once this occurs the procedure should be aborted and the haematoma managed.
#### Management
If a haematoma occurs during the procedure, release the tourniquet, remove the cannula and apply firm pressure for 2–3 min and elevate the arm. Apply a sterile dressing and ensure that this is documented; also ensure regular monitoring of the site.
### Bruising
Bruising is a common risk and can be related to poor technique. Some patients, however, are predisposed to bruising, such as those with delicate skin and/or those taking certain medication (Gabriel 2012). Thorough patient assessment and good technique minimise the possibility of bruising.
### Infiltration and extravasation
Infiltration (often referred to as 'tissueing') occurs when the cannula pulls out of the vein and the infusion fluid accumulates in the tissue around the cannula site (Workman 1999; Hadaway 2004). Workman (1999) proposed careful monitoring of the site in an older patient, who may not report discomfort as quickly because loss of skin tone and elasticity mean that tissues around the site have a greater capacity to expand with the leaking fluid.
Extravasation is the infiltration of a vesicant (irritating agent) medicine from an IV line into the surrounding tissue, and can cause severe tissue injury or destruction (Hadaway 2004).
#### Prevention
* Secure the cannula firmly with a sterile dressing while in place.
* Ensure that appropriate gauge of cannula is selected.
* Replace cannula after 72–96 h (Ingram and Lavery 2007).
* Secure lines and extensions to the limb to prevent accidental pulling (Workman 1999).
#### Signs
* Swelling.
* Discomfort.
* 'Tightness' at the site.
* Pain.
* Burning sensation – associated with extravasation.
* Blanching and coolness of the skin.
#### Management
1. **1.** Immediately stop the infusion and disconnect the tubing; alert medical staff.
2. **2.** If a cannula is needed, re-site in the other arm to allow swelling to subside.
3. **3.** Where infiltration has occurred, elevate the arm and apply a warm compress.
4. **4.** Intervene rapidly to any suspected extravasation injury; for example, either apply an ice pack or warm compress depending on vesicant (agent), elevate the arm and administer antidote; _this would be the role of registered nurse or doctor only, and would require a local policy_.
5. **5.** Reassure the patient that the swelling will subside in a few days.
6. **6.** Document and monitor the patient and site to prevent permanent damage (Workman 1999.)
### Phlebitis
Mc Callum and Higgins (2012) identify three main types of phlebitis. This is inflammation of the vein and can be caused by mechanical damage, chemical irritation or infection (Ingram and Lavery 2005).
* Mechanical damage is caused by the rubbing of the cannula against the inner (intima) wall of the vein if a cannula is not secured with a sterile dressing.
* Chemical irritation is caused by the infusion of irritant medicines/fluids or a reaction to the cannula material.
* Infection is caused by the contamination of the cannula by microorganisms.
#### Prevention
* Remove the cannula as soon as it is no longer clinically indicated.
* Change the IV cannula every 72–96 h.
* Regularly inspect the IV site (at least daily).
* Remove the cannula at the first sign of phlebitis.
* Use strict aseptic technique during insertion and manipulation of cannula.
* Secure the device with a sterile dressing.
(Lavery and Ingram 2007.)
#### Signs
* Erythema.
* Pain at the insertion site.
* Localised skin temperature.
* Swelling.
* Leakage.
* In extreme cases, pus at the insertion site on removal of cannula.
#### Management
It is recommended to use a phlebitis scale for monitoring (Jackson 1997; Davies 1998; Rosenthal 2004).
* Mechanical and chemical phlebitis: remove cannula and apply warm, moist compress.
* Bacterial phlebitis: remove cannula, take blood cultures, then apply warm compress.
* Post-infusion phlebitis: this can occur 24–96 h after the cannula is removed; apply a warm, moist compress (Macklin 2003).
### Thrombophlebitis
Tortora and Derrickson (2006) defined this as inflammation of the vein and clot formation. Thromboembolism occurs when a blood clot on the cannulated vein wall becomes detached, and could pass by venous flow to the heart and pulmonary (lung) circulation.
#### Prevention
* Use a small gauge cannula, allowing continuous blood flow around it.
* If an infusion stops as a result of clot formation, do _not_ flush the cannula because it may dislodge the clot into the circulation; remove the cannula.
* Ensure correct insertion technique.
### Air embolism
This is a possible hazard during IV therapy – _however, few healthcare assistants would be involved in administering IV fluids_ – and it is caused if lines and connections are not secure, and any attachment, for example a closed system, is not flushed first before connection.
#### Prevention
* Air must be removed from all extension lines, stopcocks and administration sets during the priming of the system.
* Ensure that Luer locks are tight fitting.
* Clamp the infusion line before the bag empties completely.
### Arterial cannulation
This is identified by bright red blood pulsating into the flashback chamber and is caused by inappropriate assessment and insertion angle.
#### Prevention
* Plan procedure carefully.
* Apply sound knowledge of venous and arterial structures in the arm.
* Insert cannula at the appropriate angle; consult manufacturer's guide.
#### Action
* Remove the cannula immediately and apply firm pressure for 5 min, until bleeding stops.
* Apply a pressure bandage for 10–15 min.
* Elevate the arm.
* Check the patient's radial pulse, to ensure that pressure bandage is not too tight.
* Inform medical staff; once they are satisfied that bleeding has stopped the pressure bandage is removed and the site covered with a sterile dressing.
* Do not use that site for a further 24 h.
* Monitor the site over 24 h and document the incident in the patient's notes.
### Nerve damage
This is a rare complication caused by poor assessment and inappropriate angle of insertion. The patient may report pain, numbness or tingling in the arm (Dougherty and Lister 2011).
#### Management
1. **1.** Remove the needle/cannula immediately.
2. **2.** Apply pressure to stop the bleeding.
3. **3.** Inform the doctor.
4. **4.** Record the incident in the patient's notes.
5. **5.** Observe and advise the patient to report if symptoms worsen.
6. **6.** Treatment is symptomatic, so analgesia may be prescribed for pain.
7. **7.** Reassure the patient.
8. **8.** Physiotherapy may be necessary (Dougherty and Lister 2004).
### Delay
In the situation where a patient has collapsed, ensure that help is on the way using the normal emergency procedures. Stay with the patient. It is essential that peripheral IV cannulation be undertaken as soon as possible, as the patient's worsening clinical condition is likely to make cannulation more difficult. _Do not delay_ in gaining access (Ingram and Lavery 2007).
# Think about it
Consider, if an emergency and a patient had collapsed, whether the insertion of a cannula would be your priority. What is your local policy?
### Other complications of peripheral IV cannulation
* Use of inappropriate sites.
* Circulatory overload: too rapid IV rate, wrongly prescribed, wrongly set rate; _this would not be an aspect in which the healthcare assistant would be involved_.
* Kinking of cannula; common if sited in an area of flexion, for example the elbow.
* Plastic embolism: this risk is reduced with safety cannula, for example Vasofix, because it is now not possible to reinsert the needle back into the cannula.
* Tourniquet left in place.
* Septicaemia: result of bacteria entering the bloodstream; patient presents with general malaise, temperature, rigors and hypotension.
Table 16.7 is a competency framework for peripheral IV cannulation.
# Think about it
While removing a cannula, you observe some redness around the site. What might be the cause and what actions will you take?
### Removal of peripheral IV cannula
Once a decision has been made to remove the cannula, explain the procedure to the patient, and obtain patient consent and cooperation (see Table 16.6 for the procedure).
**Table 16.6** Specific nursing actions during procedure – removal
**Action** | **Reason**
---|---
1. Close the flow clamp to discontinue the infusion of fluid (if necessary and if an accepted part of a healthcare assistant's role) | Prevent fluid leakage
2. Decontaminate (wash) hands, put on gloves | Prevention of infection and of healthcare assistant's hands being contaminated with blood
3. Expose the cannula site and, using aseptic technique, remove the dressing. Do not use scissors | May inadvertently cut the cannula resulting in fragments that can cause embolus (clot)
4. Apply gentle pressure with a swab/cotton ball above the cannulation site while withdrawing the cannula
On removal, apply firm pressure for approximately 2–3 min until bleeding stops | Excessive pressure applied to a cannula that is blocked could result in thrombus (fixed clot) being expelled into the blood stream causing an embolus
5. Check patient has no allergy, then cover the site with a plaster/sterile dressing, until the puncture site has healed
Continue to observe the site | To prevent bacteria from entering the puncture site
Cotton ball may adhere and when removed bleeding restarts
6. Check that cannula removed is undamaged and intact. Discard immediately into a sharps bin
However, if there are signs of infection present, report this to a senior nurse and it may be necessary to obtain a swab from the insertion site and the tip of cannula, and send to the laboratory for culture | Ensure no trauma to vein
Microbiological investigations
7. Document the date and time of cannula removal and any problems encountered or not | Good record keeping and legal requirement
Source: NHS Lothian (2007). Adapted with permission of NHS Lothian.
**Table 16.7** Practical assessment form: competency – peripheral IV cannulation
| **First assessment/reassessment**
---|---
Steps | Demonstration | Date/competent/signature
| Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
1. **1.** Washed hands and apron worn
2. **2.** Assembled all equipment required on clean tray or trolley and equipment in date and intact
3. **3.** Procedure explained, verbal consent gained
4. **4.** Patient's comfort considered and positioning appropriate for safe practice
5. **5.** Environment prepared – lighting, bed height, privacy if required, and sharps bin ready
6. **6.** Patient's identity confirmed per local policy
7. **7.** Considers with patient; vein of choice by assessing sites and patient comfort
8. **8.** Prepares cannula – depending on patient's condition and reason for cannula
9. **9.** Tourniquet applied 7–10 cm above chosen site, and vein assessed as suitable
10. **10.** Tourniquet released and vein checked decompressed
11. **11.** Hands washed or bactericidal hand rub used
12. **12.** Tourniquet re-applied to chosen site
13. **13.** Site cleansed for at least 30 s and allowed to air dry for minimum of 30 s
14. **14.** Gloves put on
| | | | | |
1. **15.** Vein cannulated successfully following approved local procedure and policy
2. **16.** Tourniquet released
3. **17.** Pressure applied distally to vein, needle is removed, while cannula supported to prevent dislodging
4. **18.** Needle disposed of as per local policy immediately
5. **19.** Considers closed system, e.g. Smartsite, to minimise trauma and infection from port site
6. **20.** Cannula flushed at appropriate rate to confirm patency and position
7. **21.** Secures cannula using appropriate dressing
8. **22.** Patient education given and aware of need for prompt communication if any concerns
9. **23.** Identification of cannula site by recording in appropriate documentation, noting gauge, site, reason for insertion, date, time and signature of operator
| | | | | |
Supervisors/Assessor(s):
Equipment required: as well as a clinical waste bag and sharps bin:
* Gloves and apron.
* Tray or clean receptacle.
* Cotton ball/gauze swab.
* Pad for spillage.
* Sterile dressing/plaster.
* Tape to secure dressing, if used.
## Summary
Peripheral IV cannulation is a specialist skill that should not be undertaken lightly, ensuring compliance with local and national policies (Lavery 2010). Care should be taken using the H.A.N.D.S. approach and it should be remembered that this skill is being undertaken on a person. Accurate documentation and good interpersonal skills are important. Perhaps the final words of this chapter that summarise cannulation belong to Lisa Dougherty (2015):
> ' _IV therapy; get it right no matter what_.'
# Case study 16.1
Miss Winifred Allsop, aged 72 years, has had a stroke (CVA) affecting her right arm and has rheumatoid arthritis. What assessment factors do you need to consider?
Below, the reader will find a self-assessment checklist; however, the reader may also wish to review Skills for Health (2004) competence HSC72.
# Self-assessment
**Assessment** | **Aspects** | **Achieved ✓**
---|---|---
Patient | _Have you considered all aspects of this section?_ |
| Patient assessment: veins and general condition |
| Infection control and asepsis aspects |
| Consent, communication and education |
| Problem solving |
Procedure | _Have you considered all aspects of this section?_ | **Achieved ✓**
| Selecting equipment and insertion technique |
| Problem solving |
| Recording |
| Monitoring, maintenance and reporting concerns |
| Removal |
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35. Workman B (1999) Peripheral intravenous therapy management. _Nursing Standard_ **14** (4): 53–60.
# Chapter 17
Recording a 12-lead Electrocardiograph (ECG)
# Learning objectives
* Review anatomy and electrophysiology of the heart as it relates to the ECG
* Review the technique for recording a 12-lead ECG and use of electrocardiograph equipment
* Identify potential problems of the procedure, and discuss actions to prevent or reduce these
## Aim of this chapter
The aim of this chapter is to provide the healthcare assistant (HCA) and assistant practitioner (AP) with a brief account of the anatomy and electrophysiology of the heart and to provide an overview of how to record an ECG. Emphasis is placed on the holistic care of the patient throughout the chapter, but it does not discuss how to interpret the recording; this is a specialised role and requires specialised training. The Society of Cardiological Science and Technology (SCST) emphasise the need for training and recommend that all personnel who record ECGs should be appropriately trained. They also point out that there are a number of reports and studies that found practitioners' lack of essential knowledge lead to wrongly recorded ECGs, which may result in incorrect diagnoses and inappropriate treatments (SCST 2014).
An ECG is a graphic tracing of electrical patterns produced by the heart (Bayés de Luna 2008). Depending on where they work, the role of the HCA and AP may include recording an ECG (Peate and Wilde 2012). Recording an ECG is an important skill that requires care, competence and confidence: it is not the role of the HCA and AP to make a diagnosis. It is important that the ECG recording is reviewed by a doctor or cardiac practitioner, which Tough (2004) suggests must be within 10 minutes of the initial recording, so you must be aware of to whom results are reported and within what time frame. Check local Trust policy.
## Relevant anatomy and physiology
Understanding the anatomy of the heart is essential if skilled, high-quality care is to be provided (Peak and Wild 2012). McChance and Heuther (2014) explain how cardiac activity consists of a number of complex processes including muscular, electrical, neural, emotional and hormonal ones. It might be useful here to review Chapters 5 and , which have covered some aspects of how the heart works. Tortora and Derrickson (2011) describe how the heart lies in the thoracic (chest) cavity and consists of four chambers divided by the vertical septum (partition). The upper chambers are known as the left and right atria and the lower chambers as the left and right ventricles. Although the heart consists of four chambers, Hampton (2006) suggests that from the electrical point of view it can be thought of as being two pumps, a right-sided pump and a left-sided pump, because both atria contract together and then both ventricles simultaneously contract. The function of the circulatory system is simple: to circulate oxygenated blood, nutrients and other substances to the tissues via the high-pressure arterial system and to pump deoxygenated blood to the lungs through the low-pressure venous circulation (McChance and Heuther 2014)
The cone-shaped heart, roughly the size of a closed fist (Tortora and Derrickson, 2011), is a muscular organ located in the thoracic cavity, immediately above the diaphragm and between the lungs, that rests in a moistened chamber called the pericardial cavity which is surrounded by the rib cage. The normal adult heart rate is said to be approximately 72 beats per minute, but can fluctuate depending on a variety of factors such as age, fitness and medication (Wild and Peate 2012). Peate and Wild (2012) estimate that since the heart beats tirelessly, it could be calculated that, from the moment it starts to the moment it stops the heart beats approximately 100 000 times per day and about 35 million times in a year. During an average lifetime, that means the human heart will have beat more than 2.5 billion times. Thus the heart pumps more than 6500 litres of blood a day. The volume of blood that reaches the tissues each minute (cardiac output) is the most important index of cardiovascular performance, and in adults with a heart rate of 70 bpm this gives a cardiac output of 4900 ml/minute.
## The cardiac conduction system
The heart uses an electrical conduction system to pump blood, as shown in Figure 17.1. An impulse is initiated by the sinoatrial (SA) node that causes the heart muscle to contract or depolarise. Each impulse spreads from the node across both atria, causing them to contract and pump blood through one-way valves into the ventricles. The SA node also controls the pace of the heart (70–80 beats per minute). The electric impulse continues depolarisation (contraction) to the atrioventricular (AV) node, with the electrical discharge passing quickly through the bundle of His – a bundle of specialised fibres within the interventricular septum that divides into right and left Purkinje fibres, which continues to allow contraction of the ventricles (Stevens 2008).
**Figure 17.1** Electrical conducting system of the heart.
A 12-lead ECG is a graphical recording of the electrical activity of the heartbeat obtained by placing 10 electrodes on specific positions in the body surface (four on the limbs and six on the chest) (Stevens 2008). This provides 12 different views of the electrical activity generated by the myocardium as it depolarises (contracts) and repolarises (relaxes) to produce the heartbeat. An ECG trace is a series of waves, the size of each wave corresponding to an electrical voltage (measured in millivolts) generated by the heart as it goes through the cycle of contraction and relaxation. The currents detected on the skin are weak, hence the ECG machine contains an amplifier. It will be helpful if you find out about the type of machine you use.
These changes in voltage create a pattern of waves that are captured on paper or viewed on a screen. In a healthy heart, the size and rhythm of these waves tends to remain constant. The most frequently seen waves are P, Q, R, S and T that occur in one cardiac cycle (Crawford and Doherty 2012).
* P wave: atrial contraction (known as depolarisation).
* P–R interval: the time required for the impulse to pass the AV node and bundle of His, and cause ventricular contraction.
* QRS complex: represents ventricular contraction.
* T wave: represents the resting stage (called repolarisation).
The QRS complex is recorded as seen in Figure 17.2.
**Figure 17.2** The QRS complex.
## Reasons for recording a 12-lead ECG
Crawford and Doherty (2012) recognise the numerous indications for recording an ECG and point out that it is important to understand that the ECG can only directly measure time and voltage, and so is useful in situations such as detecting the presence of a myocardial infarction but may be of limited use in other areas. Tortora and Derrickson (2011) explain that the standard ECG produces views from different combinations of chest and limb leads. By comparing these tracings with each other and normal records, it is possible to determine three things:
1. **1.** If the heart's conduction pathway is abnormal.
2. **2.** If the heart is enlarged.
3. **3.** If certain regions of the heart have been damaged, for example from a heart attack.
## How to perform a 12-lead ECG
The ECG test is inexpensive, uses portable equipment that is easy to operate, and can be undertaken anywhere – including at a patient's bedside, GP surgery or ambulance – giving a prompt result and allowing rapid treatment decisions and actions to be made by relevant healthcare professionals.
### Indications for performing an ECG
* The assessment of patients presenting with chest pain.
* Unexplained dizziness and/or syncope.
* The diagnosis and monitoring of cardiovascular disease.
* The assessment of therapy outcomes, both beneficial and toxic.
* Overdose.
* Presurgical assessment.
* Risk assessment for cardiac disease in individuals with two or more of the following risk factors: diabetes, hypertension, smoking history, obesity, hypercholesterolemia, strong family history of cardiac disease.
* A family history of sudden death.
* The assessment of cardiac effects in co-existing systemic disease, for example renal failure.
* Monitoring cardiac transplant success or rejection.
* Adhering to occupational requirements, for example airline pilot, divers.
* Epidemiological studies.
(Crawford and Doherty 2012: 2.)
### How to record a 12-lead ECG
This chapter focuses only on a standard 12-lead ECG where electrodes are placed at strategic points of the chest area and limbs as a diagnostic tool, and does not discuss ambulatory and/or continuous ECGs.
### Preparation for the procedure
#### Preparing the patient
A key goal of good practice as identified by SCST (2014) is to ensure the patient has a positive experience and to maintain privacy and dignity, which should also reflect Trust policy. Every effort should be made to ensure the patient has privacy and dignity, and any cultural sensitivities of the patient are addressed and embarrassment minimised. If the patient does not speak English, it may be necessary to provide an interpreter; similarly some patients may use sign language and need the same consideration. Patients should be asked to undress above the waist to allow access to the upper torso for correct placement of the electrodes, removing any jewellery from the patient's neck, arms, and wrists. Assistance should be offered and given as required. Ensure the patient is comfortable and warm and avoid drafts. The ECG reading can be affected by the position of the patient, where possible, for consistency, the SCST (2014) recommends patients lie in a semi-recumbent position of approximately 45 degrees with limbs supported by the bed to minimise artefact due to muscle tension. Any variation should be noted. Once the electrodes have been attached, the patient maybe covered with a gown to preserve their modesty, avoiding unnecessary exposure. The SCST (2014) also highlights that some patients may want a chaperone present and may also request a relative or carer.
Communication skills have been discussed in Chapter 2 and are emphasised here. The patient having an ECG should be given information about the procedure that they are able to understand. Information should be clear and precise and may take the form of a booklet, information letter or be an oral explanation. The HCA or AP should introduce themselves, explain the procedure and give the patient an opportunity to seek clarification. Reassurance is essential and careful explanations can overcome many fears, especially as many patients feel uncomfortable being touched and having their chest examined (Stevens 2008). A sympathetic, caring, compassionate manner will do much to alleviate some of the patient's apprehension. Peate and Wild (2012) also highlight the importance of explaining to the patient that the ECG is painless, there will be no electrical current entering their body and that small electrodes will be attached to the chest. Leads from the electrodes connected to the ECG machine will produce a printout.
Consent should be gained and the patient positioned comfortably, maintaining dignity at all times. It is important to always remember the person at the centre of this process and treat them with care, compassion and kindness; listen to and talk with them. Check to see if the patient has any allergies, such as electrode adhesive. Confirmation of identity is vital; record the details following local policy, checking the printed recording also has the correct patient details. Only then can consent be gained as discussed in Chapter 1.
# Think about it
Mrs Wang, aged 82 years, is to be prepared for a standard 12-lead ECG. What might you need to consider if you were going to carry out this procedure?
### Recording a 12-lead ECG
This section looks at the equipment required for the procedure, the patient preparation and the actual procedure. It also reviews the care of the equipment, before moving on to discuss potential problems and means of addressing these.
#### Equipment
The equipment for a standard 12-lead ECG is an ECG machine (with tracing paper), a patient lead cable (with limb and chest leads labelled accordingly), disposable electrodes and paper towel/tissues (Crawford and Doherty 2012). Stevens (2008) highlights the need to be familiar with local equipment, as showing a lack of familiarity and ability will not result in a calm patient. The equipment should come with a manual to which you can refer. It is also important to know how to change the recording paper; how to charge the machine and where supplies of electrodes and paper are kept; and how to order further supplies. Equipment should be maintained, kept clean and orderly, and all mains leads and cables and connectors be intact with no evidence of damage. Battery operated machines will need to have sufficient charge and mains powered ECG machines should be plugged in and be easily recognisable (SCST 2014).
##### Electrodes
Peate and Wild (2012) described electrodes as required to detect the electrical energy produced by the heart and transfer the information to the monitoring equipment. External electrodes are used to do this; they consist of adhesive tape and a conductive saline gel, on the other side there is a small metal conductor button that is snap-connected to the monitor via leads.
Manufacturers produce electrodes that are disposable, self-adhesive, latex free and hypoallergenic and prepared with an inner moist conductive gel, that need to be kept stored in the manufacturer's foil packing preventing the conductive gel on each electrode from drying out and protecting the sensor from any damage or contamination (Taylor 2015). The expiry date on the foil pack of electrodes must be checked to ensure they are in-date, stored correctly, and that they are all the same product (electrodes not mixed from different packs). When ready, remove the protective electrode backing to expose the gel-covered disc and ensure that gel is still moist and enough covers the disc.
# Think about it
You have been asked to carry out a standard 12-lead ECG. What checks of the equipment must you make before proceeding?
#### Skin preparation and infection control
Skin preparation is important to ensure good skin contact; otherwise the results may be affected or distorted. SCST (2014) identified that care must be taken for patients with sensitive skin. Skin may need cleansing; infection control measures must be taken in accordance with local/Trust policy including handwashing and disposal of clinical waste (SCST 2014). If a patient has body hair this will impair the connection, and so it may be helpful to shave the patient. Exfoliation (removal of hair) may be required and should be undertaken using abrasive tape especially designed for this purpose (SCST 2014). Chest hair may need to be removed to ensure adequate contact with the skin (Peate and Wild 2012). Caution is advised, as razors may break the skin and pose a potential infection risk. Oral consent should be obtained from the patient and an unused razor should be used and disposed of, as per local policy. After the procedure, remove the electrodes and clean the skin.
#### Electrode placement
##### Placement of the four limb electrodes; right arm; right leg; left arm and left leg
The correct positioning of electrodes is essential to obtain a diagnostically accurate recording because each lead records a specific surface of the heart. Misplacing the electrodes may alter the appearance of the ECG (SCST 2014). By attaching electrodes to the right arm, left arm and left leg, just proximal to the wrist and ankle, three major planes for detecting electrical activity can be recorded. These three planes form a hypothetical triangle (Einthoven's Triangle) with the heart in the middle. A fourth electrode is attached to the left leg, but serves only as an earth and is not used for recording purposes (Stevens 2008). The electrodes are usually placed on the outer aspect 3–4 cm above the forearm (wrist) and medial (inner) aspect 3–4 cm above the foreleg (ankle) (Figure 17.3a gives the placement). The electrodes can be placed on another area, such as on the right, if, for example, the patient has a right arm amputation; this should be clearly noted and documented on the recording (SCST 2014) (see Table 17.1 for the procedure).
**Figure 17.3** Electrode and lead placement for standard 12-lead ECG: (a) Limb electrode placement and (b) electrode placement on the chest.
**Table 17.1** Procedure for recording a standard 12-lead ECG
**Action** | **Reason**
---|---
Position ECG machine close to patient | Minimise risk of leads, cables, etc. becoming disconnected during the procedure
Check that power cable and patient lead fitted correctly to machine, and route power cable away from patient | Working correctly and minimise any electrical interference
Press power on; multi-lead machine will do self-test, then check machine set at: | To ensure that machine set and working correctly
1 mV or 10 small squares (two large squares)
Paper speed is 25 mm/s
Filter is on; check local policy
Introduce self and patient provides name and date of birth (DOB); this is checked against identification, e.g. ID bracelet | Ensure correct patient
Patient explanation given to reassure and inform, to allow questions and gain consent | Understand reason for procedure and how it is done, so relaxed and cooperative
Offer patient chaperone, if appropriate | If female patient and male operator this is good practice
Ensure privacy, screens or close door | To protect patient and ensure privacy
Patient resting comfortably, lying if able (semi-recumbent or supine), with limbs supported, arms at sides | To ensure best recording and patient safety and comfort
Ask or assist the patient to undress exposing forearms, chest and forelegs. Ensure modesty; also the patient may need to remove jewellery | To prepare patient for the procedure and ensure no contact with leads from jewellery, e.g. watch
Wash hands or use alcohol gel | To prevent infection
Check that patient has understood that, once the electrodes are in place and test starts, must keep still and breathe normally | Reduce electrical noise (Henderson 1997)
Clean limbs and chest area as outlined earlier: select flat fleshy areas, avoid bony or muscular areas | To ensure that skin has good contact for electrodes and good placement
Place the 10 electrodes, as per Figure 17.3; first ensure electrodes are in date, in foil pack and gel is still moist, e.g. RA = right arm | To ensure accurate reading, and check the patient has no allergy with the adhesive on the electrodes
Attach leads to electrodes correctly (follow colour coding and labelling), e.g. LA = left arm and yellow (refer to Figure 17.3) | Correct monitoring (Henderson, 1997; SCST 2014). NHS Lothian (2004) noted that manufacturers use different colour schemes so follow UK colour code
Extend patient cable along the side of patient or centre of body from feet to chest | To ensure that all cables fully supported and prevent pulling on the electrodes
Also ensure that the leads are not pulling on the electrodes or lying over each other | To reduce electrical noise from movement and so get good reading
Make sure that patient is ready and relaxed, remind him or her not to talk or cough and allow 10 s for the patient to settle and relax | Procedure proceeds safely
Commence the 12-lead ECG recording by pushing auto-button | Allow machine to automatically run rhythm strip and leads one at a time to obtain ECG recording
Observe that paper strip is moving and recording | Ensure connected and recording correctly
Observe recording; do not alarm the patient; however, if anxious about the recording, seek advice or support, e.g. ask a colleague to get a senior nurse or doctor, and reassure the patient | It is not the role of the healthcare assistant to interpret; however, if any irregularity is observed in the rate or rhythm, it may be prudent to get a doctor or experienced nurse to come and check immediately
During procedure reassure patient and explain what's happening | So patient informed and relaxed
If poor tracing (noise – muscle movement), check electrodes, connections and leads, then redo (repeat) recording | Ensure best recording
Before finishing ECG, check first that the recording is free from artefact (noise) and confirm settings: paper speed 25 mm, standard setting 1 mV, 10 mm | Recording technically accurate, so ready for interpretation by doctor
Let the patient know that procedure is finished, what you will do with recording, and then remove the electrodes. Offer to help wipe off the gel and redress, if necessary | Ensure that patient comfortable and aware of next steps
Document as local policy, suggested that ECG has full patient name, DOB, date and time of recording, relevant clinical details, e.g. chest pain during test, ward/department, operator signs (on the reverse of the ECG recording strip) and before leaving patient | Record maintained and accurate details
Avoid errors and risk of ECG being filed in the wrong patient's notes
Turn off machine | Save power
Inform a doctor or senior nurse and ensure that doctor sees recording at earliest or agree time frame, e.g. 10 min (Tough 2004) | To ensure that results acted upon and procedure documented
Remove machine and restock; remember to plug into mains if battery operated | Good practice
Adapted from Dougherty and Lister (2011) and NHS Lothian (2004), with permission from G Brady Education Coordinator Cardiology, NHS Lothian (2004).
##### Placement of the six chest or precordial leads V1, V2, V3, V4, V5, V6
The electrodes are placed on the chest wall at the designated positions (see Figure 17.3 for placement). Clinical Guidelines by Consensus for Recording a standard 12-lead ECG produced by the Society for Cardiological Science and Technology (SCST 2014) clearly identify the correct positioning of the chest leads.
A common error occurs when counting the intercostal spaces from the clavicle: the small space between the clavicle and the first rib is not the first intercostal space. To avoid this error, the manubriosternal joint (also called the Angle of Louis) should be used as the main reference point. To locate the Angle of Louis, a finder should be run down the sternum from the top, until a bony horizontal ridge is met. Sliding the finger down and to the right side will locate the second intercostal space. From here it is possible to count down to the third and fourth intercostal spaces. Slide the finger towards the sternum until the edge is felt and place the electrode for V1 in this position. This procedure should be repeated on the left side to correctly position V2. Note that the left- and right-sided rib spaces may be offset, thus avoiding placing V2 adjacent to V1 without counting the rib spaces.
Next, the V4 electrode should be placed in the fifth intercostal space in line with the mid-point of the clavicle. The V3 electrode should be placed in the fifth intercostal space in line with the mid-point of the clavicle. The V3 electrode should then be placed midway between the V2 and V4 electrodes.
The V5 and V6 electrodes should then be positioned in horizontal alignment with the V4 electrode. The V5 electrode should be placed in the anterior axillary line; the V6 electrode should be placed on the mid-axillary line.
It is convention to place the V4, V5 and V6 electrodes beneath the left breast when breast tissue overlies the correct anatomical positions when recording an ECG from female patients. There is some evidence that suggests minimal disruption to the signal may be caused; however, further research is required to confirm or refute this. Using the back of the hand to lift the breast with care and sensitivity to place the electrodes is required.
### Times and calibration of ECG
It is of interest to note, as Stevens (2008) identified, that ECG machines are standardised using paper where each large square = 5 mm and this represents 0.2 seconds, so there are five large squares per second and 300 for 1 minute. The standard signal of 1 millivolt (mV) moves the stylus (recording needle) vertically 1 cm (two large squares).
## Related aspects and terminology
Even though this chapter does _not cover how to interpret an ECG recording_ , it is useful to have an understanding of some terminology relating to the procedure, especially what a normal ECG recording is.
* _Sinus rhythm_ : normal rhythm and usually 60–100 bpm; it is regular and complexes (PQRST wave) are identical. The word sinus indicates that the heartbeat originated in the SA node (Hand 2002) (Figure 17.4). Hampton and Adlam (2013) noted that in a child up to 1 year of age, the rate is 140–160 bpm, falling slowly to 80 bpm by puberty (approximately 10 years old).
* _Sinus bradycardia_ : regular rate originating from the SA node but less than 60 bpm. Hampton (2003) indicated that this can be due to physical fitness or caused by, for example, hypothermia (low temperature) or some medicines, such as digoxin
* _Sinus tachycardia_ : regular rate also from SA node but 100–180 bpm; this can be in response to stressors, for example fever, anxiety, pain, exercise (Hampton 2003). Some stimulants, for example caffeine, alcohol, also can cause tachycardia; check the patient history.
* _Sinus arrhythmia_ : a known phenomenon (condition) in younger people; heart rate increases as they breathe in and decreases as they breathe out.
* _Atrial fibrillation (AF)_ : rapid chaotic depolarisation (contraction) of impulses through the atrial myocardium, replacing normal rhythmic activity by the SA node; can lead to palpitations as the heart rate is increased (low risk rate below 100 bpm, medium risk heart rate 100–150 bpm, and high risk if rate over 150 bpm – Hand 2002).
* _Atrial flutter_ : less common than AF; in contrast with AF the rate is regular and often the tracing is described as 'saw tooth' and rate is often 150, 100 or 75 bpm (Hand 2002).
* _Ventricular tachycardia_ : a serious arrhythmia and requires urgent action
* _Ventricular fibrillation_ (VF): the rhythm of cardiac arrest, fast irregular rate as the ventricles contract in a chaotic uncoordinated manner. In VF the heart ceases to pump and after about 10 s, the blood pressure falls and the patient loses consciousness. If left untreated, death follows in 3–5 min (Hand 2002).
* _Artefact_ : muscular movement that can affect ECG reading/tracing
* _Electrical noise_ : as above, but also occurs if leads or power cables are crossed, or the tracing picks up electrical energy from elsewhere, such as beds or infusion devices (NHS Lothian 2004).
**Figure 17.4** Example of sinus rhythm.
Hampton (2006) also describes the difference in an ECG (with a 12-lead ECG) where the signal is detected by only five electrodes. One electrode is placed on each limb and the fifth is held on by a suction cup and is then manually (by hand) moved to different positions over the patient's chest.
## Common problems and actions
Hand (2002) outlines several tracing problems and indicates that they can usually be easily rectified (Table 17.2). Table 17.3 is a competency framework for recording a standard 12-lead ECG.
**Table 17.2** ECG recording common problems
**Problem** | **Action**
---|---
Poor electrode technique often appears as irregular fluctuations (artefact) on the tracing | Improve skin contact, so remove any body sweat or hair, or change electrodes and ensure good skin preparation
Defective cables or a loss of contact with the electrodes produces sharp waveform fluctuations | Replace cable or insert further into machine
Muscular activity (artefact) appears as fast irregular fuzzy fluctuations | Ensure that patient is comfortable and relaxed or reposition electrodes
AC interference – fuzzy, thickened, regular pattern | Ensure that filter is on, check connections, make sure leads, etc. are not being pulled or crossing over. Do not touch during the procedure, and remind the patient to lie still
If possible switch off other electrical source, e.g. bed; discuss with senior nurse first
Wandering baseline – up and down movement of ECG tracing | Ensure good skin contact, re-apply electrodes, make sure that the machine is close to the patient so that there is no pull on the leads or cable, etc.
Incorrect placement of limb leads – commonly right and left arm leads reversed | Check and swap right and left arm leads if incorrect
Misplacement of chest leads/electrodes | Check and confirm placement of electrode, e.g. V1 and V2 fourth rib space
Adapted from Hand (2002) and NHS Lothian (2004). (Reproduced with permission from NHS Lothian 2004.)
**Table 17.3** Competency framework competency: recording a standard 12-lead ECG
| **First assessment/eeassessment**
---|---
Steps | Demonstration/supervised practice | Date/competent/ signature
Recording a standard 12-lead ECG | Date/sign | Date/sign | Date/sign | Date/sign | Date/sign |
| 1 | 2 | 3 | 4 | 5 |
1. **1.** Patient's identity confirmed as per local policy
2. **2.** Procedure explained, verbal consent gained
3. **3.** Assembled all equipment required, checked that ECG machine stocked
4. **4.** Machine checked, cable/leads correctly in place, machine self test done, confirmed all settings set as standard
5. **5.** Patient screened and prepared, undressed and jewellery removed
6. **6.** Patient's comfort considered and positioning appropriate for safe practice
7. **7.** Washed hands or used alcohol gel
8. **8.** Skin sites on limbs and chest area selected correctly
9. **9.** Selected sites correctly cleaned and prepared – sweat or hair removed
10. **10.** Electrodes applied to designated sites, connections pointing in line with direction of cable and lead wires
11. **11.** Confirmed all electrodes/leads connected to power cable correctly and positioned correctly
12. **12.** Explained when procedure starts that patient must not move, talk or cough
13. **13.** Waited 10 s for patient to settle and tracing to stabilise
14. **14.** Pressed auto button and monitored tracing – ensure working correctly
15. **15.** Confirmed ECG machine working and settings correct during procedure
16. **16.** If problem with recording, checked and corrected problem
17. **17.** Reassured patient during procedure
18. **18.** Acted on concerns, if any, to appropriate person
19. **19.** Checked final recording acceptable quality, then documented required information on paper recording
20. **20.** Switched off machine
21. **21.** Helped patient clean skin and dress, as necessary
22. **22.** Explained next steps to patient
23. **23.** Washed hands
24. **24.** Machine removed and restocked, stored correctly
25. **25.** Procedure reported to designated doctor or senior nurse – check local policy and document as required
| | | | | |
Supervisors/Assessor(s):
## Summary
Recording an accurate 12-lead ECG is a crucial skill. This is because the doctor (or registered nurse if a locally accepted role) will use this recording to make a diagnosis and plan appropriate treatment. Preparation and planning for the procedure and appropriate care throughout are therefore essential.
# Case study 17.1
Fred Jones, aged 53 years, has been admitted for cardiac tests. He is anxious and has never been in hospital before. You have been asked to record a standard 12-lead ECG. Describe how you would prepare him for the procedure.
# Case study 17.2
Betty Davis (aged 76 years) has been complaining of chest pain for 5 min and you have been asked to carry out a standard 12-lead ECG recording. Describe how you would position the electrodes and leads and carry out the procedure.
# Self-assessment
**Assessment** | **Aspects** | **Achieved ✓**
---|---|---
Patient | _Have you considered all aspects of this section?_ |
| Patient assessment |
| Selection for lead and electrode placements |
| Communication and educational factors |
| Infection control and skin preparation aspects |
| Positioning patient and equipment |
Equipment | _Have you considered all aspects of this section?_ | **Achieved ✓**
| Care of the equipment |
| Storage and maintenance of equipment |
Procedure | _Have you considered all aspects of this section?_ | **Achieved ✓**
| Equipment and technique |
| Consent, communication and education |
| Problem solving |
| Recording |
| Reporting concerns and procedure completion |
## References
1. Bayés de Luna A (2008 _) Basic Electrocardiography: Normal and Abnormal ECG Patterns_. Oxford: John Wiley & Sons.
2. Crawford J and Doherty L (2012) _Practical Aspects of ECG Recording_. Keswick: M&K Update Ltd.
3. Dougherty L and Lister S (eds) (2011) _The Royal Marsden Hospital Manual of Clinical Nursing Procedures_ , 8th edn. Oxford: Wiley-Blackwell.
4. Hampton J R (2006) _The ECG in Practice_ , 4th edn. Edinburgh: Churchill Livingstone.
5. Hampton J R and Adlam D (2013) _The ECG in Practice_ , 6th edn. Edinburgh: Churchill Livingstone.
6. Hand H (2002) Common cardiac arrhythmias. _Nursing Standard_ **16** (28): 43–53.
7. Henderson H (1997) Electrocardiography. _Nursing Standard_ **11** (44): 45–56.
8. McChance K and Heuther S (2014) _The Pathophysiology: The Biologic Basis for Disease in Adults and Children_ , 7th edn. London: Elsevier.
9. NHS Lothian (2004) _Recording a Standard 12-lead ECG NHS Lothian – University Hospitals Division_. Edinburgh: NHS Lothian.
10. Peate I and Wild K (2012) Taking ECGs: being skilled, competent and confident. _British Journal of Healthcare Assistants_ **6** (7): 328.
11. Society for Cardiological Science and Technology (SCST) (2014) Clinical Guidelines by Consensus. _Recording a 12-lead Standard ECG. An Approved Methodology by the Society for Cardiological Science and Technology Guidance_. London: Society for Cardiological Science and Technology.
12. Stevens N (2008) 12-lead ECG recording. _Practice Nurse_ **36** (9): 1.
13. Taylor Industries Inc. (2015) Electrode Reference Guide Taylor Industries. <http://www.taylor-ind.com/>.
14. Tortora G J and Derrickson B (2011) _Principles of Anatomy and Physiology_ , 13th edn. Hoboken, NJ: Wiley & Sons.
15. Tough J (2004) Assessment and treatment of chest pain. _Nursing Standard_ **18** (37): 45.
16. Wild K and Peate I (2012) Clinical observations 2/6: assessing the pulse rate. _British Journal of Healthcare Assistants_ **6** (6): 274–278.
# Index
1. 2. **A**
3. abbreviations
4. accessory muscles of respiration
5. accountability
6. acetone
7. active listening
8. acute retention
9. admission, hospital
10. adrenal cortex
11. adrenal glands
12. adrenaline
13. Adults with Incapacity (Scotland) Act (2000)
14. adverse drug reactions
15. age-related changes
1. blood pressure
2. peak expiratory flow rate
3. pulse rate
4. respiratory rate
5. temperature
16. air embolism
17. airway obstruction
18. alcohol intake
19. aldosterone
20. anaemia
21. aneroid sphygmomanometers
22. antidiuretic hormone (ADH)
23. anxiety
24. apathetic
25. apex heart beat
1. and radial pulse
26. apnoea
27. appearance
28. arm veins
29. artefact
30. arterial blood gases
31. arterial blood pressure
32. arterial blood sampling
33. arterial cannulation, accidental
34. arterial puncture, accidental
35. arterial walls, elasticity
36. arteries
37. arthritis
38. ascorbic acid
39. aseptic technique
40. assistant practitioners (APs)
41. asthma
42. atria
43. atrial fibrillation (AF)
44. atrial flutter
45. atrial tachycardia
46. audit
47. axillary temperature measurement
48. 49. **B**
50. babies _see_ infants
51. bags, urine drainage _see_ drainage bags, urine
52. basilic vein
53. Beer Lambert law
54. belly bags
55. bilirubin, urinary
56. bladder, urinary
1. irrigation or instillation
2. volume
57. blood, in urine _see_ haematuria
58. blood cultures
59. blood gases, arterial
60. blood glucose
1. levels
2. regulation
3. _see also_ hyperglycaemia; hypoglycaemia
61. blood glucose meters
1. common problems
2. calibration/safety
62. blood glucose monitoring
1. blood sampling for
2. common problems
3. competency framework
4. contraindications
5. documentation
6. equipment
7. frequency
8. reasons for
9. sites
10. terminology
63. blood pressure and
1. peripheral IV cannulation
2. pulse rate
64. blood pressure (BP)
1. anatomy and physiology
2. classification
3. definition
4. diastolic
5. documentation
6. factors affecting
7. normal
8. systolic
9. terminology
65. blood pressure measurement
1. 24-hour (ambulatory)
2. automated devices
3. common problems
4. competency framework
5. complications
6. equipment
7. lying and standing
8. mercury and aneroid sphygmomanometers
9. procedure
10. professionals undertaking
11. pulse oximetry and
12. reasons for
13. requests for
14. sites
66. blood sampling
1. for blood glucose monitoring
2. peripheral venous, _see_ venepuncture
67. blood transfusion
68. blood volume
69. body language
70. body movements
71. body shape, temperature and
72. body temperature _see_ temperature
73. BP _see_ blood pressure
74. brachial artery
75. bradycardia
76. bradypnoea
77. breast-feeding
78. breathing
1. depth
2. pattern
3. pulse rate and
4. rate _see_ respiratory rate
5. regularity/rhythm
6. regulation
7. sound
79. Bristol Stool Chart
80. British Hypertension Society
81. bronchi
82. bruising
83. bundle of His
84. butterfly (winged) infusion devices, insertion
85. 86. **C**
87. cannulae, IV _see_ intravenous (IV) cannulae
88. cannulation, peripheral IV _see_ intravenous (IV) cannulation, peripheral
89. capacity, mental
90. capillary blood sampling
91. carbon monoxide (CO)
92. cardiac cycle
93. cardiac output
94. cardiovascular disease
95. care pathways
96. carotid pulse
97. catheterisation _see_ urinary catheterisation
98. catheter specimen of urine (CSU)
99. central venous pressure (CVP) line
100. cephalic vein
101. cerebrovascular accident (stroke)
1. medicines administration
2. previous
102. chaperones
103. Cheyne– Stokes respiration
104. children
1. bladder control
2. bladder volume
3. clinical holding
4. giving consent
5. medicines administration
6. pain management
7. pain-related fear
8. peak expiratory flow rate
9. psychological assessment
10. psychological care
11. pulse/heart beat
12. pulse oximetry
13. respiratory rate
14. temperature measurement
15. urinary catheterisation
16. urinary catheters
17. urine specimen collection
18. venepuncture
105. chlorine dioxide generator
106. choice, patient
107. Cidezyme
108. circulatory failure, peripheral
109. circulatory problems
110. cirrhosis
111. cleansing/cleaning
1. meatal/genital area
2. peak flow meters
3. skin
4. clothing, protective
112. colour
113. communication
1. barriers
2. checklist for effective
3. definition
4. electronic
5. importance of good
6. methods
7. non-verbal
8. place of
9. psychological care
10. quality and safety in
11. self awareness in
12. sender/ receiver
13. strategies to improve
14. terminology
15. tone in
16. urinary catheterisation
17. verbal
18. written
114. competency framework, clinical
1. blood glucose monitoring
2. BP monitoring
3. catheter sampling
4. ECG recording
5. faecal occult blood testing
6. fluid balance
7. intermittent self catheterization
8. IV infusions
9. peripheral IV cannulation
10. pulse
11. pulse oximetry
12. record keeping
13. respiratory care
14. temperature
15. urinalysis
16. urinary catheterisation
17. venepuncture
18. _see also_ training
115. conduction, heat loss by
116. confidentiality
117. conflict
118. confusion
119. consciousness, reduced
120. consent
1. medicines administration
2. peripheral IV cannulation
3. urinary catheterisation
4. venepuncture
121. controlled drugs
122. convection, heat loss by
123. coping strategies
124. creams, topical
125. CSU _see_ catheter specimen of urine
126. cuffs (BP recording)
1. sizes
127. cultural aspects
1. ECG recording
2. non-verbal communication
3. response to pain
128. cyanosis
129. cytotoxic medicines
130. 131. **D**
132. Data Protection Act (1998)
133. dehydration
134. delegation
135. dementia
136. Department for Constitutional Affairs
137. Department of Health
138. detergents, peak flow meters
139. diabetes mellitus
1. blood glucose control
2. blood glucose monitoring _see_ blood glucose monitoring
3. causes
4. complications
5. effects
6. gestational
7. maturity-onset, of the young (MODY)
8. symptoms
9. type 1
10. type 2
11. urinalysis
140. diabetic ketoacidosis (DKA)
141. diarrhoea
142. diastolic blood pressure
143. diet
1. blood pressure and
2. faecal occult blood testing and
144. digestive system
145. disabilities, communication problems
146. disinfectants, peak flow meters
147. disinfection, peak flow meters
148. dispensing, one-stop
149. distraction
150. diuretic medications
151. DKA (diabetic ketoacidosis)
152. documentation
1. blood glucose monitoring
2. blood pressure
3. common problems
4. competency checklist
5. confidentiality
6. consent
7. importance and purpose
8. improving standards
9. legal aspects
10. medicines administration
11. peripheral IV cannulation
12. poor record keeping, investigations
13. psychological well-being
14. pulse
15. pulse oximetry
16. respiratory care
17. security of information
18. temperature
19. types
153. drainage bags, urine
1. body-worn (belly)
2. emptying/changing
154. dressings, wound
155. drugs _see_ medicines
156. duty of care
157. dysphagia
158. dysphasia
159. dyspnoea
160. 161. **E**
162. early warning score(EWS)
163. ear medications
164. eating
165. ECG machine
1. calibration
166. ECG recording, 12-lead
1. anatomy and physiology
2. common problems
3. competency framework
4. consent
5. equipment
6. patient preparation for
7. procedure
8. reasons for
9. terminology
167. education, patient
1. ECG recording
2. fluid balance charts
3. peripheral IV cannulation
4. urinary catheterisation
168. elasticity, arterial walls
169. electrical noise
170. electrodes, ECG
1. common problems
2. placement
171. electrolytes
172. electronic records
173. electronic thermometers
174. email
175. emotional factors, blood pressure
176. employers
1. accountability to
2. vicarious liability
177. Entonox
178. environmental factors
1. communication
2. temperature
179. epidural anaesthesia
180. epiglottis
181. erectile dysfunction
182. erythema
183. evaporation
184. exercise
185. extracellular fluid
186. extravasation
187. eye contact
188. eye medications
189. 190. **F**
191. facial expressions
192. faecal occult blood testing (FOB)
1. advice before
2. common problems
3. competency framework
4. equipment
5. reasons for
6. terminology
193. faeces (stools)
1. assessment
2. formation
194. fear
1. _see also_ anxiety
195. females
1. urinalysis
2. urinary catheterisation
3. urinary catheters
4. urinary system
196. fetal heart beat
197. fibrillation
198. fibrosis, vein
199. Fifteen Steps Challenge
200. finger-pricking devices (lancets)
201. fistula/shunt
202. fitness, physical
203. fluid balance
1. common problems
2. competency framework
3. physiology
4. reasons for monitoring
5. regulation
6. terminology
204. fluid balance charts
1. potential problems
205. fluid intake
206. fluid losses
207. flushing, IV cannulae/lines
208. FOG index, Gunning
209. Francis Report
210. Freedom of Information Act (FOIA) (2005)
211. 212. **G**
213. gender differences
1. blood pressure
2. peak expiratory flow rate
3. temperature
4. _see also_ females; males
214. general anaesthesia
215. general sales list medicines (GSL)
216. gestational diabetes
217. gestures
218. gloves
219. glucagon
220. glucose
1. blood _see_ blood glucose
2. oral, for hypoglycaemia
3. urinary
221. glycated haemoglobin (HbA1c)
222. glycosuria
223. goosebumps
224. gravity, blood pressure and
225. grieving process
226. group protocols
227. guided imagery
228. Gunning FOG index
229. 230. **H**
231. haematocrit, raised
232. haematoma
233. haematuria
234. haemoglobin
235. hand hygiene
236. Harm Free Care
237. HbA1c (glycated haemoglobin)
238. healthcare assistants (HCA)
1. accountability
2. care certificate
3. code of conduct for health care workers
4. competence
5. delegation to
6. documentation
7. regulation
239. heart
1. anatomy
2. conduction system
3. electricity
240. heart beat
1. apex
2. sound
241. heart murmurs
242. heart valve failure
243. heart valves
244. heat
1. loss
2. production
245. height, peak expiratory flow rate and
246. 'hello my name is' campaign
247. high impact interventions
248. holding, clinical
249. homeostasis
250. hormones
251. HORUS model
252. Hospec
253. hydration care bundles
254. hydrogen peroxide
255. hyperglycaemia
256. hyperlipidaemia
257. hyperpyrexia
258. hypertension
1. white coat
259. hyperthermia
1. non-infective causes
260. hyperventilation
261. hypervolaemia
262. hypnosis
263. hypoglycaemia
264. hypotension
1. orthostatic (postural)
265. hypothalamus
266. hypothermia
267. hypoventilation
268. hypovolaemia
269. hypoxaemia
270. hypoxia
271. 272. **I**
273. imagery, guided
274. incapacity, mental
275. incontinence, urinary
276. indemnity insurance
277. infants
1. pulse/heart beat
2. urine specimen collection
278. infections
1. peripheral IV cannulation
2. urinary tract (UTI)
3. venepuncture
279. infiltration
280. information
1. confidentiality
2. distraction in information
3. supportive
4. timing of
281. inhaled medicines
282. instrumental support
283. insulin
284. insulin resistance/sensitivity
285. insurance, indemnity
286. integrated care pathways (ICP)
287. intermittent self catheterization
288. interpreters
289. intimate zone
290. intracellular fluid
291. intravenous administration of medicines
292. intravenous (IV) cannulae
1. care and maintenance
2. choosing
3. damaged
4. dressing
5. flushing
6. infection control
7. removal
8. re-siting
293. intravenous (IV) cannulation, peripheral
1. anatomy and physiology
2. anxiety about
3. areas to avoid
4. assessment for
5. common sites
6. competency framework
7. consent
8. environment
9. equipment
10. infection risk/prevention
11. patient education
12. problems and complications
13. reasons for
14. risk factors
15. site selection
16. technique
17. terminology
18. unsuccessful
294. intravenous (IV) infusions
1. BP measurement and
2. blood
3. common problems
4. competency framework
5. discontinuing
6. gravity
7. pump
8. reasons for
9. venepuncture and
10. _see also_ winged infusion devices
295. intravenous (IV) lines
1. flushing
2. priming
296. iontophoresis
297. islets of Langerhans
298. 299. **J**
300. jargon
301. jaundice
302. 303. **K**
304. ketonuria (ketones in urine)
305. kidneys
306. Korotkoff's sounds
307. 308. **L**
309. Labia
310. Lancerzyme
311. lancets
312. language
1. barriers
2. jargon
3. written
313. large intestine
314. larynx
315. leading questions
316. learning disability, mental capacity
317. leg bags
318. leukocytes, urinary
319. liability, vicarious
320. liquid medicines
321. listening, active
322. local anaesthetics
1. urinary catheterisation
2. venepuncture
323. lung disease, chronic obstructive pulmonary disease (COPD)
324. lungs
325. lymphoedema
326. 327. **M**
328. malaise
329. males
1. urinary catheterisation
2. urinary catheters
3. urinary system
4. urine specimen collection
330. Maslows hierarchy of needs
331. massage
332. maturity-onset diabetes of the young (MODY)
333. mean arterial pressure
334. meatus
335. median cubital vein
336. medicines (medications)
1. adverse reactions
2. blood pressure and
3. causing hypothermia
4. IV administration
5. legal aspects
6. one-stop dispensing
7. patient group directions
8. prescribing
9. pulse rate and
10. temperature and
11. types
337. Medicines Act (1968)
338. medicines administration
1. allergies
2. consent
3. delegation
4. errors
5. five rights
6. HCA's role
7. legal aspects
8. nurses' role
9. by patients (self-)
10. record keeping
11. routes and methods
12. standards for practice
339. Medicines and Healthcare products Regulatory Authority (MHRA)
340. medulla oblongata
341. menstruation
342. mental capacity
343. Mental Capacity Act
344. mercury sphygmomanometers
345. mercury thermometers
346. metabolic disease
347. metabolic rate
348. MEWS/NEWS
349. midstream specimen of urine (MSU)
350. Mini-Wright peak flow meters, cleaning and disinfection
351. Misuse of Drugs Act (1971)
352. mouth breathing
353. MSU _see_ midstream specimen of urine
354. muscles of respiration
1. accessory
355. music
356. 357. **N**
358. nail varnish
359. nasal cannulae
360. nasopharyngeal suctioning
361. National bowel cancer screening campaign
362. National Health Service Core Values
363. National Institute for Health and Clinical Excellence
364. National Occupational Standards (NOS)
365. National Patient Safety Agency (NPSA)
366. near patient testing
367. needle free devices
368. needle phobia
369. needles, venepuncture
370. negligence, clinical
371. neonates, pulse/heart beat
372. nephropathy, diabetic
373. nerve damage
374. neuropathy, diabetic
375. NHS see National Health Service
376. NICE see National Institute for Health and Clinical Excellence
377. nicotine
378. nitrite, urinary
379. NMC _see_ Nursing and Midwifery Council
380. Non-medical prescribing
381. non-verbal communication
382. nose
383. nurses
1. accountability
2. delegation by
3. medicines administration
4. prescribing
5. regulatory body
384. Nursing and Midwifery Council (NMC)
1. on communication
2. on consent
3. on delegation
4. on indemnity insurance
5. on medicines administration
6. on record keeping
385. 386. **O**
387. observation chart _see_ temperature, pulse and respiratory rate (TPR) chart
388. odour _see_ smell
389. oedema
390. ointments
391. older patients, IV cannulation
392. open questions
393. oral medicines
394. oral temperature
1. measurement
395. orientation, during communication
396. oropharyngeal suctioning
397. orthostatic hypotension
398. oxygen disassociation curve
399. oxygen saturation (SpO2)
1. factors affecting
2. normal readings
3. principles of measurement
4. _see also_ pulse oximetry
400. oxygen therapy
401. 402. **P**
403. pacing, psychological care
404. pain
1. anticipatory
2. excessive, venepuncture
3. non-pharmacological management
4. pharmacological management
5. psychological factors
6. pulse rate and
7. strategies to enhance coping
405. palliative care
406. pancreas
407. pancreatitis, acute
408. panic
409. parents
410. Parkinson's disease
411. patient group directions
412. patients
1. accountability to
2. involvement in care
3. capacity to consent
4. self-administration of medicines
413. peak expiratory flow rate (PEFR)
1. common problems
2. competency framework
3. normal
4. technique
414. peak flow meter
1. cleaning and disinfection
415. peripheral intravenous cannulation _see_ intravenous (IV)
416. cannulation, peripheral
417. peripheral resistance
418. peroxygen disinfectants
419. personal space
420. pH, urine
421. pharmacy-only medicines (P)
422. pharynx
423. phlebitis
424. phlebotomy _see_ venepuncture
425. phobias
426. _ortho_ -phthalaldehyde
427. pituitary gland
428. plastic embolism
429. play, therapeutic
430. play specialists
431. plethysmographic waveform
432. polydipsia
433. polyphagia
434. polyuria
435. positioning, patient
1. BP measurement
2. IV cannulation
3. venepuncture
436. postoperative patients, urinary catheterisation
437. postural hypotension
438. posture, during communication
439. pre-eclampsia
440. pregnancy
441. prescribing, medication
442. prescription-only medicines (POM)
443. P– R interval
444. privacy
445. procedures
1. psychological preparation
2. strategies to enhance coping
446. profession, accountability to
447. professional body
448. prostate gland, enlarged
449. protective clothing
450. protein, urinary
451. proximity
452. psychological assessment
453. psychological well-being
1. behavior
2. common problems
3. importance
4. non-pharmacological options
5. pharmacological options
6. self help
7. strategies
8. therapeutic sense of self
454. public, accountability to
455. pulse
1. amplitude
2. anatomy and physiology
3. apex
4. apex and radial
5. automated devices
6. babies and children
7. common problems
8. competency framework
9. deficit
10. documentation
11. equipment
12. factors affecting rate
13. irregular
14. manual technique
15. normal
16. radial
17. rate
18. reasons for taking
19. respiratory rate and
20. rhythm
21. technique
22. terminology
23. thready
24. weak
456. pulse oximeters
457. pulse recordings
458. pulse oximetry
1. advantages
2. anatomy and physiology
3. BP recording and
4. common problems
5. competency framework
6. documentation
7. equipment
8. factors affecting readings
9. limitations
10. mechanics
11. normal readings
12. probes
13. procedure
14. reasons for
15. terminology
459. purkinje fibres
460. P wave
461. Pyrexia
1. non-infective causes
2. pulse rate
462. 463. **Q**
464. QRS complex
465. qualifications
466. questions
1. closed
2. leading
3. open
467. 468. **R**
469. radial pulse
1. apex heart beat with
470. radiation, heat loss by
471. 'rattly' chest
472. readability, written language
473. reagent test strips, urinalysis
474. reasonable care
475. record keeping
1. _see also_ documentation
476. rectal temperature
1. measurement
477. red blood cells
1. altered shape
478. registration of HCA & AP
479. regulatory body
480. relaxation
481. renal function
482. repolarisation
483. respiration _see_ breathing
484. respiratory care
1. common problems
2. competency framework
3. terminology
4. _see also_ peak expiratory flow rate; suctioning
485. respiratory centre
486. respiratory rate
1. competency framework
2. normal range
3. recording
487. respiratory system
1. lower
2. upper
488. responsibility, areas of
489. retinopathy, diabetic
490. rheumatoid arthritis
491. rigors
492. Roberts catheter
493. Royal College of Nursing (RCN)
494. 495. **S**
496. Safety Thermometer
497. saline, physiological (0.9% NaCl)
498. sedation
499. seizures
500. self awareness
501. sender/ receiver
502. septicaemia
503. sex differences _see_ gender differences
504. shaving
505. shivering
506. shock
507. sickle cell disease
508. sinoatrial (SA) node
509. sinus arrhythmia
510. sinus bradycardia
511. sinus rhythm
512. sinus tachycardia
513. Six C's
514. Skills for Health
515. skin
1. cleansing
2. heat loss
3. heat production/gain
4. preparation, ECG electrodes
516. sleep
517. small intestine
518. smell (odour)
1. faeces
2. urine
519. snoring
520. social media
521. sodium chloride (NaCl) solution, 0.9%
522. sodium dichloroisocyanurate
523. sodium hypochlorite
524. SOLER acronym
525. space, personal
526. spacer devices
527. specific gravity, urine
528. sphygmomanometers
1. aneroid
2. cuffs _see_ cuffs
3. mercury
529. standard of care
530. standards of practice
531. sterile technique
532. stethoscope
1. BP recording
2. heart beat
533. stools _see_ faeces
534. stress
1. blood glucose measurement
2. respiratory rate and
3. response
4. symptoms of
535. stridor
536. stroke _see_ cerebrovascular accident
537. stroke volume
538. subcutaneous injections
539. subjective statements, in records
540. suctioning
1. common problems
2. competency framework
3. nasopharyngeal
4. oropharyngeal
541. suction pressures
542. supervision
543. suppositories
544. suprapubic
545. suprapubic catheterisation
546. suprapubic sample of urine
547. sweat glands
548. syringe drivers
549. systolic blood pressure
550. 551. **T**
552. tablets
553. tachycardia
554. tachypnoea
555. temperature
1. anatomy and physiology
2. axillary
3. common problems
4. competency framework
5. control
6. core
7. different sites
8. documentation
9. equipment
10. methods
11. normal range
12. procedure
13. pulse rate and
14. shell
15. oral
16. reasons for
17. rectal
18. route
19. temporal artery
20. terminology
21. tympanic
556. temperature, pulse and respiratory rate (TPR) chart
1. blood pressure
2. pulse
3. temperature
557. temporal artery temperature measurement
558. temporal artery thermometers
559. tepid sponging
560. therapeutic sense of self
561. therapeutic touch
562. thermometers
1. chemical
2. electronic
3. mercury
4. temporal artery
5. tympanic
563. throat (pharynx)
564. thrombophlebitis
565. thyroid hormones (thyroxine)
566. Tiemann catheter
567. time of day
1. blood pressure and
2. peak expiratory flow rate and
3. temperature and
568. timing, psychological care
569. tone, verbal communication
570. topical creams
571. touch
572. tourniquets
573. TPR chart _see_ temperature, pulse and respiratory rate chart
574. trachea
575. training
1. medicines administration
2. _see also_ competency, clinical
576. translators
577. trauma
578. tricuspid incompetence
579. T wave
580. tympanic temperature
1. measurement
581. 582. **U**
583. urethra
584. urinalysis
1. common problems
2. competency framework
3. procedure
4. reagent test strips
5. reasons for
6. substances tested
7. terminology
585. urinary catheterisation
1. assessment
2. common problems
3. communication and consent
4. competency framework
5. equipment
6. indwelling
7. infection control
8. insertion technique
9. intermittent self-
10. patient preparation
11. reasons for
12. terminology
13. types
14. valves
586. urinary catheters
1. balloon sizes
2. care
3. common problems
4. drainage systems
5. gauges (sizes)
6. length
7. materials
8. removal
9. sampling
10. tip design
587. urinary retention
1. acute
2. after catheter removal
588. urinary system
589. urinary tract infections (UTI)
590. urine
1. catheter specimen (CSU)
2. midstream specimen (MSU)
3. observation
4. output
5. production
6. residual
7. specimen collection
591. urine drainage bags _see_ drainage bags, urine
592. urobilinogen, urinary
593. 594. **V**
595. vacuum system, venipuncture
596. vasovagal episodes
597. veins
1. arm
2. assessment
3. selection
598. venepuncture
1. anxiety
2. blood cultures
3. common problems
4. common sites
5. competency framework
6. consent
7. environment
8. equipment and technique
9. infection risks/prevention
10. procedure
11. reasons for
12. sample volume
13. unsuccessful
14. vacuum system
15. winged infusion device (butterfly)
599. venesection
600. ventricles
601. ventricular contraction
602. ventricular fibrillation (VF)
603. ventricular tachycardia
604. Venturi mask
605. verbal communication
606. vicarious liability
607. Visual Infusion Phlebitis score
608. VIP score see Visual Infusion Phlebitis
609. visualisation
610. voice box (larynx)
611. vomiting
612. 613. **W**
614. water, total body
615. water intoxication
616. weight, blood pressure and
617. wheeze
618. whistle catheter tip
619. white coat hypertension
620. WHO see World Health Organisation
621. whooping cough
622. windpipe (trachea)
623. winged infusion devices, insertion
624. World Health Organisation
625. wound dressings
626. Wright peak flow meters, cleaning and disinfection
627. written language
628. 629. **Y**
630. Yankauer catheter
631. Yellow Card reporting system
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{"url":"https:\/\/www.physicsforums.com\/threads\/elastic-collision-of-hockey-pucks.140584\/","text":"# Homework Help: Elastic Collision of hockey pucks\n\n1. Oct 29, 2006\n\n### americanforest\n\nOk, I ran across this question as I was doing my homework and I thought it looked pretty easy. I worked on it for an hour and still had no luck with getting the correct answer. Here is the full text:\n\nAn elastic collision occurs between two air hockey pucks in which one puck is at rest and the other is moving with a speed of 0.1 m\/s. After the collision, the puck initially in motion makes an angle of 35.00 deg with its original direction, and the struck puck moves at an angle of 55.00 deg on the other side of the original direction. What is the final speed of the first puck and second puck? (Also, mass is the same)\n\nFirst thing I thought was that I could use conservation of momentum and conservation of energy in x or y direction. This would give me two equations, which would allow me to solve for final velocities. I'm not going to go through the tedium of solving all the systems of equations. I'll just tell you that in the end I got\n\nV1=.0628 m\/s (This is the initially stationary puck)\nV2=.0897 m\/s\n\nIs the answer you guys get? It's not right according to my book.\n\nfrom equations:\n\n$$(.1cos(35))^2=(v_1cos(55))^2+(v_2cos(35))^2$$\n\n$$0=v_2sin(35)-v_1sin(55)$$\n\nI hate when seemingly simple problems stump me and this is a great example. I normally wouldn't be surprised if it was some math error, but I spent a large amount of time diligently checking and rechecking math. The answers look legitimate. Please help?\n\nLast edited: Oct 29, 2006\n2. Oct 29, 2006\n\n### OlderDan\n\nYour first equation should not have any trig ratios in it. It is the full velocity that contributes to the energy. You have left out some of the energy. Your second equation looks OK.\n\nThe angle between the two puck velocities should be 90 degrees, which is what they gave you.\n\nLast edited: Oct 29, 2006\n3. Oct 30, 2006\n\n### americanforest\n\nIt was a stupid misunderstanding of the problem that got me. I didn't understand where the problem was telling me the angles were. Just one more example of the fact that physics questions like this cannot be considered valid without pictures. Turns out\n\n$$V_1f=V_0cos (\\theta)$$\n$$V_2f=V_0sin (\\theta)$$\n\n$$\\theta=35$$ degrees\n$$V_0=.1 m\/s$$\n\nI didn't think of the angles being perpendicular until you brought it up. That's when I suspected I misunderstood and after that I had it right within 3 minutes. Thanks.\n\nP.S. Looking forward to becoming a member in this community. Just changed to Physics major and really love the subject. I hope I can learn a lot here.\n\nLast edited: Oct 30, 2006\n4. Oct 30, 2006\n\n### OlderDan\n\nWelcome to the forum. It is a good place to visit often. There are several people here who are very helpful. You will soon get to know who they are.\n\nYour problem was interesting in that it gave you more information than required by the situation. An elastic collision of two objects of equal mass, one being initially at rest, always results in a separtaion angle of 90 degrees. The problem could have been done even if they had given only one of the angles.","date":"2018-12-11 17:46:19","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6008861064910889, \"perplexity\": 405.88921820542424}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-51\/segments\/1544376823674.34\/warc\/CC-MAIN-20181211172919-20181211194419-00364.warc.gz\"}"}
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William Cogswell (* 23. August 1838 in Bradford, Essex County, Massachusetts; † 22. Mai 1895 in Washington, D.C.) war ein US-amerikanischer Politiker. Zwischen 1887 und 1895 vertrat er den Bundesstaat Massachusetts im US-Repräsentantenhaus.
Werdegang
William Cogswell besuchte die Phillips Academy in Andover und danach das Dartmouth College in Hanover (New Hampshire). Nach einem anschließenden Jurastudium an der Harvard University und seiner 1860 erfolgten Zulassung als Rechtsanwalt begann er in Salem in diesem Beruf zu arbeiten. Während des Bürgerkrieges diente er als Offizier in verschiedenen Funktionen im Heer der Union, in dem er es bis zum Brevet-Brigadegeneral brachte. Nach dem Krieg praktizierte er wieder als Anwalt. Überdies schlug er als Mitglied der Republikanischen Partei eine politische Laufbahn ein. Zwischen 1867 und 1869 sowie nochmals in den Jahren 1873 und 1874 war er Bürgermeister von Salem. In den Jahren 1870, 1871 sowie von 1881 und 1883 saß er als Abgeordneter im Repräsentantenhaus von Massachusetts; 1885 und 1886 gehörte er dem Staatssenat an. Im Juni 1892 war er Delegierter zur Republican National Convention in Minneapolis, auf der Präsident Benjamin Harrison zur Wiederwahl nominiert wurde.
Bei den Kongresswahlen des Jahres 1886 wurde Cogswell im siebten Wahlbezirk von Massachusetts in das US-Repräsentantenhaus in Washington gewählt, wo er am 4. März 1887 die Nachfolge von Eben F. Stone antrat. Nach vier Wiederwahlen konnte er bis zu seinem Tod am 22. Mai 1895 im Kongress verbleiben. Seit 1893 vertrat er dort als Nachfolger von Henry Cabot Lodge den sechsten Distrikt seines Staates.
Weblinks
Mitglied des Repräsentantenhauses der Vereinigten Staaten für Massachusetts
Mitglied des Senats von Massachusetts
Mitglied des Repräsentantenhauses von Massachusetts
Bürgermeister (Salem, Massachusetts)
Mitglied der Republikanischen Partei
Militärperson (Nordstaaten)
Rechtsanwalt (Vereinigte Staaten)
US-Amerikaner
Geboren 1838
Gestorben 1895
Mann
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{
"redpajama_set_name": "RedPajamaWikipedia"
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{"url":"https:\/\/www.physicsforums.com\/threads\/quantum-harmonic-oscillator-complete-system.621829\/","text":"# Quantum Harmonic Oscillator Complete System\n\n1. Jul 18, 2012\n\n### YAHA\n\nOver which interval do the wave functions of a harmonic oscillator form a complete and orthogonal system? Is it (-inf,+inf)? The case with particle in a box is rather clear(system is complete and orthogonal only for the interval of the well), however the harmonic oscillator is a bit less intuitive.\n\n2. Jul 18, 2012","date":"2017-12-13 04:06:36","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8311095237731934, \"perplexity\": 988.9751058777803}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-51\/segments\/1512948521188.19\/warc\/CC-MAIN-20171213030444-20171213050444-00715.warc.gz\"}"}
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{"url":"https:\/\/hal.archives-ouvertes.fr\/inria-00368577","text":"# Comparison of the Expressiveness of Timed Automata and Time Petri Nets\n\n1 MoVe - Mod\u00e9lisation et V\u00e9rification\nLIP6 - Laboratoire d'Informatique de Paris 6\nAbstract : In this paper we consider the model of Time Petri Nets (TPN) where time is associated with transitions. We also consider Timed Automata (TA) as defined by Alur \\& Dill, and compare the expressive- ness of the two models w.r.t. timed language acceptance and (weak) timed bisimilarity. We first prove that there exists a TA A s.t. there is no TPN (even unbounded) that is (weakly) timed bisimilar to A. We then propose a structural translation from TA to (1-safe) TPNs preserv- ing timed language acceptance. Further on, we prove that the previous (slightly extended) translation also preserves weak timed bisimilarity for a syntactical subclass $T_{Asyn}(\\leq,\\geq)$ of TA. For the theory of TPNs, the consequences are: 1) TA, bounded TPNs and 1-safe TPNs are equally expressive w.r.t. timed language acceptance; 2) TA are strictly more expressive than bounded TPNs w.r.t. timed bisimilarity; 3) The subclass $T_{Asyn}(\\leq,\\geq)$, bounded and 1-safe TPNs ''`a la Merlin'' are equally ex- pressive w.r.t. timed bisimilarity.\nType de document :\nCommunication dans un congr\u00e8s\nFORMATS 2005 - 3rd International Conference on Formal Modeling and Analysis of Timed Systems, Sep 2005, Uppsala, Sweden. Springer-Verlag, 3829, pp.211-225, 2005, Lecture Notes in Computer Science. \u300810.1007\/11603009_17\u3009\n\nhttps:\/\/hal.inria.fr\/inria-00368577\nContributeur : Franck Cassez <>\nSoumis le : mardi 17 mars 2009 - 04:53:30\nDerni\u00e8re modification le : mercredi 19 d\u00e9cembre 2018 - 15:02:04\nDocument(s) archiv\u00e9(s) le : mardi 8 juin 2010 - 21:36:00\n\n### Fichiers\n\npetri-nets-formats05.pdf\nFichiers produits par l'(les) auteur(s)\n\n### Citation\n\nB\u00e9atrice Berard, Franck Cassez, Serge Haddad, Didier Lime, Olivier Henri Roux. Comparison of the Expressiveness of Timed Automata and Time Petri Nets. FORMATS 2005 - 3rd International Conference on Formal Modeling and Analysis of Timed Systems, Sep 2005, Uppsala, Sweden. Springer-Verlag, 3829, pp.211-225, 2005, Lecture Notes in Computer Science. \u300810.1007\/11603009_17\u3009. \u3008inria-00368577\u3009\n\n### M\u00e9triques\n\nConsultations de la notice\n\n## 470\n\nT\u00e9l\u00e9chargements de fichiers","date":"2019-02-22 18:21:27","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.4488045275211334, \"perplexity\": 13109.900298235567}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-09\/segments\/1550247522457.72\/warc\/CC-MAIN-20190222180107-20190222202107-00051.warc.gz\"}"}
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using Content.Server.GameObjects.Components.Projectiles;
using JetBrains.Annotations;
using Robust.Shared.GameObjects.Systems;
namespace Content.Server.GameObjects.EntitySystems
{
[UsedImplicitly]
internal sealed class ProjectileSystem : EntitySystem
{
public override void Update(float frameTime)
{
base.Update(frameTime);
foreach (var component in ComponentManager.EntityQuery<ProjectileComponent>())
{
component.TimeLeft -= frameTime;
if (component.TimeLeft <= 0)
{
component.Owner.Delete();
}
}
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
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\section{Introduction}
\label{sec:Introduction}
When dividing discrete objects, one often strives for a fairness notion called \emph{envy-freeness} \citep{F67resource}, under which no agent prefers the allocation of another agent to its own. Envy-free outcomes might not exist in general (even with only two agents and a single indivisible good), motivating the need for approximations. Among the many approximations of envy-freeness proposed in the literature \citep{LMM+04approximately,B11combinatorial,NR14minimizing,CKM+16unreasonable}, the notion called \emph{envy-freeness up to one good} (\textrm{\textup{EF}}{1}) has received significant attention recently. \textrm{\textup{EF}}{1} requires that pairwise envy can be eliminated by the removal of some good in the envied bundle. It is known that an \textrm{\textup{EF}}{1} allocation always exists and can be computed in polynomial time~\citep{LMM+04approximately}.
On closer scrutiny, however, we find that \textrm{\textup{EF}}{1} is not as strong as one might think. Indeed, an \textrm{\textup{EF}}{1} allocation could entail the (hypothetical) removal of \emph{many} goods, because the elimination of envy for different pairs of agents may require the removal of distinct goods. To see this, consider an instance with six goods $g_1,\dots,g_6$ and three agents $a_1,a_2,a_3$ whose (additive) valuations are as shown below:
\begin{table}[ht]
\label{tab:Motivating_HEF}
\centering
\small
\begin{tabular}{ c|cccccc }
& $g_1$ & $g_2$ & $g_3$ & $g_4$ & $g_5$ & $g_6$\\ \hline
$a_1$ & $\circled{1}$ & $\circled{1}$ & $\underline{4}$ & $1$ & $1$ & $\underline{4}$\\
$a_2$ & $1$ & $\underline{4}$ & $\circled{1}$ & $\circled{1}$ & $\underline{4}$ & $1$\\
$a_3$ & $\underline{4}$ & $1$ & $1$ & $\underline{4}$ & $\circled{1}$ & $\circled{1}$\\
\end{tabular}
\end{table}
Observe that the allocation shown via circled goods is \textrm{\textup{EF}}{1}, since any pairwise envy can be addressed by removing an underlined good. However, each pair of agents requires the removal of a \emph{different} good (e.g., $a_1$'s envy towards $a_2$ is addressed by removing $g_3$ whereas $a_3$'s envy towards $a_2$ is addressed by removing $g_4$, and so on), resulting in a weak approximation overall (since all goods need to be removed over all pairs of agents).
The above example shows that \textrm{\textup{EF}}{1}, on its own, is too \emph{coarse} to distinguish between allocations that remove a \emph{large} number of goods (such as the one with circled entries) and those that remove only a \emph{few} (such as the one with underlined entries, which, in fact, is envy-free). This limitation highlights the need for a fairness notion that (a) can distinguish between allocations in terms of their \emph{aggregate} approximation, and (b) retains the ``up to one good'' style approximation of \textrm{\textup{EF}}{1} that has proven to be practically useful~\citep{GP15spliddit}. Our work aims to fill this important gap.
We propose a new fairness notion called \emph{envy-freeness up to $k$ hidden goods} (\HEF{k}) defined as follows: Say there are $n$ agents, $m$ goods, and an allocation $A = (A_1,\dots,A_n)$. Suppose there is a set $S$ of $k$ goods (called the \emph{hidden} set) such that each agent $i$ withholds the goods in $A_i \cap S$ (i.e., the hidden goods owned by $i$) and only discloses the goods in $A_i \setminus S$ to the other agents. Any other agent $h \neq i$ only observes the goods disclosed by $i$ (i.e., those in $A_i \setminus S$), and its valuation for $i$'s bundle is therefore $v_h(A_i \setminus S)$ instead of $v_h(A_i)$. Additionally, agent $h$'s valuation for its own bundle is $v_h(A_h)$ (and not $v_h(A_h \setminus S)$) because it can observe its own hidden goods. If, under the disclosed allocation, no agent prefers the bundle of any other agent (i.e., if $v_h(A_h) \geq v_h(A_i \setminus S)$ for every pair of agents $i,h$), then we say that $A$ is \emph{envy-free up to $k$ hidden goods} (\HEF{k}). In other words, by withholding the information about $S$, allocation $A$ can be made free of envy.
Notice how \HEF{k} addresses the limitations associated with \textrm{\textup{EF}}{1}: Like \textrm{\textup{EF}}{1}, \HEF{k} is a relaxation of envy-freeness that is defined in terms of the \emph{number of goods}. However, unlike \textrm{\textup{EF}}{1}, \HEF{k} offers a \emph{precise quantification} of the extent of information that must be withheld in order to achieve envy-freeness.
Clearly, any allocation can be made envy-free by hiding all the goods (i.e., if $k = m$). The real strength of \HEF{k} lies in $k$ being \emph{small}; indeed, an \HEF{0} allocation is envy-free. As we will demonstrate below, there are natural settings that admit \HEF{k} allocations with a small $k$ (i.e., hide only a small number of goods) even when (exact) envy-freeness is unlikely.
\subsection*{Information Withholding is Meaningful in \mbox{Practice}.}
To understand the usefulness of \HEF{k}, we generated a synthetic dataset where we varied the number of agents $n$ from $5$ to $10$, and the number of goods $m$ from $5$ to $20$ (we ignore the cases where $m < n$). For every fixed $n$ and $m$, we generated $100$ instances with \emph{binary} valuations. Specifically, for every agent $i$ and every good $j$, the valuation $v_{i,j}$ is drawn i.i.d. from $\textup{Bernoulli}(0.7)$. \Cref{subfig:HEFk_motivation_0.7_NOTEF} shows the heatmap of the number of instances out of $100$ that \emph{do not} admit envy-free outcomes. (Thus, a `hot' cell indicated by red color is one where \emph{none} of the $100$ instances admits an envy-free allocation.) \Cref{subfig:HEFk_motivation_0.7_maxk} shows the heatmap of the number of goods that must be hidden in the worst-case. That is, the color of each cell denotes the smallest $k$ such that each of the corresponding $100$ instances admits some \HEF{k} allocation.
\begin{figure}[h]
\centering
\begin{subfigure}[b]{0.47\linewidth}
\centering
\includegraphics[width=0.94\linewidth]{hefexistence_notef_7_binary_notnorm-eps-converted-to}%
\caption{Heatmap of the fraction of instances that are not envy-free.}
\label{subfig:HEFk_motivation_0.7_NOTEF}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.47\linewidth}
\centering
\includegraphics[width=0.94\linewidth]{hefexistence_maxk_7_binary_notnorm-eps-converted-to}%
\caption{Heatmap of the number of goods that must be hidden.}
\label{subfig:HEFk_motivation_0.7_maxk}
\end{subfigure}
\caption{In both figures, each cell corresponds to $100$ instances with binary valuations for a fixed number of goods $m$ (on X-axis) and a fixed number of agents $n$ (on Y-axis).}
\label{fig:HEFk_motivation_0.7}
\end{figure}
It is evident from \Cref{fig:HEFk_motivation_0.7} that even in the regime where envy-free outcomes are unlikely (in particular, the red-colored cells in \Cref{subfig:HEFk_motivation_0.7_NOTEF}), there exist \HEF{k} allocations with $k \leq 3$ (the light blue-colored cells in \Cref{subfig:HEFk_motivation_0.7_maxk}). This observation, along with the foregoing discussion, suggests that fairness through information withholding is a well-motivated approach towards approximate envy-freeness that could provide promising results in practice.
\paragraph{Our Contributions}
We make contributions on three fronts.
\begin{itemize}
\item On the \emph{conceptual} side, we propose a novel fairness notion called envy-freeness up to $k$ hidden goods (\HEF{k}) as a fine-grained generalization of envy-freeness in terms of aggregate approximation.
\item Our \emph{theoretical} results (\Cref{sec:Theoretical_Results}) show that computing \HEF{k} allocations is computationally hard even for highly restricted classes of valuations (\Cref{thm:HEFk_Existence_NPcomplete_IdenticalVals,cor:HEFk_Existence_NPcomplete_BinaryVals}). We show a similar result when \HEF{k} is required alongside Pareto optimality (\Cref{prop:HEFkPOExistence_NPcomplete_BinaryVals}). A related technical contribution is an alternative proof of \textrm{\textup{NP-complete}}{}ness of determining the existence of an envy-free allocation for binary valuations (\Cref{prop:EF_Existence_NPcomplete_BinaryValuations}).
\item Our \emph{experiments} show that \HEF{k} allocations with a small $k$ often exist, even when (exact) envy-free allocations do not (\Cref{fig:HEFk_motivation_0.7}). We also compare several known algorithms for computing \textrm{\textup{EF}}{1} allocations on synthetic and real-world preference data, and find that the round-robin algorithm and an algorithm of \citet{BKV18Finding} withhold close-to-optimal number of goods, often hiding no more than three items (\Cref{sec:Experiments}).
\end{itemize}
\section{Related Work}
\label{sec:RelatedWork}
An emerging line of work in the fair division literature considers relaxations of envy-freeness by limiting the information available to the agents. Notably, \citet{ABC+18knowledge} consider a setting where each agent is aware only of its own bundle and has no knowledge about the allocations of the other agents. They propose the notion of \emph{epistemic envy-freeness} (\textrm{\textup{EEF}}{}) under which each agent believes that an envy-free allocation of the remaining goods among the other agents is possible. Note that in \textrm{\textup{EEF}}{}, each agent might consider a different hypothetical assignment of the remaining goods, and each of these could be significantly different from the \emph{actual} underlying allocation. By contrast, under \HEF{k}, each agent evaluates its valuation with respect to the same (underlying) allocation. \citet{CS17ignorance} study a related model where agents have probabilistic beliefs about the allocations of the other agents, and envy is defined in expectation. \citet{CCL+19maximin} study a setting similar to \citet{ABC+18knowledge} wherein each agent is unaware of the allocations of the other agents, with the guarantee that it does not get the worst bundle.
Another related line of work considers settings where the agents constitute a social network and can only observe the allocations of their neighbors \citep{AKP17fair,BQZ17networked,CEM17distributed,ABC+18knowledge,BCG+18local,BKN18envy}. These works place an informational constraint on the \emph{set of agents}, whereas our model restricts the \emph{set of revealed goods} per agent.
Several other forms of fairness approximations have been proposed recently, such as introducing side payments~\citep{HS19fair}, permitting sharing of some goods~\citep{SE19fair}, or donating a small fraction of goods~\citep{CGH19envy,CKM+20little}.
\section{Preliminaries}
\label{sec:Preliminaries}
\paragraph{Problem instance}
An \emph{instance} $\mathcal{I} = \langle [n], [m], \mathcal{V} \rangle$ of the fair division problem is defined by a set of $n \in {\mathbb{N}}$ \emph{agents} $[n] = \{1,2,\dots,n\}$, a set of $m \in {\mathbb{N}}$ \emph{goods} $[m] = \{1,2,\dots,m\}$, and a \emph{valuation profile} $\mathcal{V} = \{v_1,v_2,\dots,v_n\}$ that specifies the preferences of every agent $i \in [n]$ over each subset of the goods in $[m]$ via a \emph{valuation function} $v_i: 2^{[m]} \rightarrow {\mathbb{N}} \cup \{0\}$. Notice that each agent's valuation for any subset of goods is assumed to be a non-negative integer. We will assume that the valuation functions are \emph{additive}, i.e., for any $i \in [n]$ and $G \subseteq [m]$, $v_i(G) \coloneqq \sum_{j \in G} v_i(\{j\})$, where $v_i(\emptyset) = 0$. We will write $v_{i,j}$ instead of $v_i(\{j\})$ for a singleton good $j \in [m]$. We say that an instance has \emph{binary valuations} if for every $i \in [n]$ and every $j \in [m]$, $v_{i,j} \in \{0,1\}$.
\paragraph{Allocation}
An \emph{allocation} $A \coloneqq (A_1,\dots,A_n)$ refers to an $n$-partition of the set of goods $[m]$, where $A_i \subseteq [m]$ is the \emph{bundle} allocated to agent $i$. Given an allocation $A$, the utility of agent $i \in [n]$ for the bundle $A_i$ is $v_i(A_i) = \sum_{j \in A_i} v_{i,j}$.
\begin{definition}[\textbf{Envy-freeness}]
An allocation $A$ is \emph{envy-free} (\textrm{\textup{EF}}{}) if for every pair of agents $i,h \in [n]$, $v_i(A_i) \geq v_i(A_h)$. An allocation $A$ is \emph{envy-free up to one good} (\textrm{\textup{EF}}{1}) if for every pair of agents $i,h \in [n]$ such that $A_h \neq \emptyset$, there exists some good $j \in A_h$ such that $v_i(A_i) \geq v_i(A_h \setminus \{j\})$. An allocation $A$ is \emph{strongly envy-free up to one good} (\sEF{1}) if for every agent $h \in [n]$ such that $A_h \neq \emptyset$, there exists a good $g_h \in A_h$ such that for all $i \in [n]$, $v_i(A_i) \geq v_i(A_h \setminus \{g_h\})$. The notions of \textrm{\textup{EF}}{}, \textrm{\textup{EF}}{1}, and \sEF{1} are due to \citet{F67resource}, \citet{B11combinatorial}, and \citet{CFS+19group}, respectively.\footnote{A slightly weaker notion than \textrm{\textup{EF}}{1} was previously studied by \citet{LMM+04approximately}. However, their algorithm can be shown to compute an \textrm{\textup{EF}}{1} allocation.}
\end{definition}
\begin{definition}[\textbf{Envy-freeness with hidden goods}]
An allocation $A$ is said to be \emph{envy-free up to $k$ hidden goods} (\HEF{k}) if there exists a set $S \subseteq [m]$ of at most $k$ goods such that for every pair of agents $i,h \in [n]$, we have $v_i(A_i) \geq v_i(A_h \setminus S)$. An allocation $A$ is \emph{envy-free up to $k$ uniformly hidden goods} (\uHEF{k}) if there exists a set $S \subseteq [m]$ of at most $k$ goods satisfying $|S \cap A_i| \leq 1$ for every $i \in [n]$ such that for every pair of agents $i,h \in [n]$, we have $v_i(A_i) \geq v_i(A_h \setminus S)$. We say that allocation $A$ \emph{hides} the goods in $S$ and \emph{reveals} the remaining goods. Notice that a \uHEF{k} allocation is also \HEF{k} but the converse is not necessarily true. Indeed, in \Cref{prop:HEFk_vs_uHEF}, we will present an instance that, for some $k \in {\mathbb{N}}$, admits an \HEF{k} allocation but no \uHEF{k} allocation.
\label{defn:HEF-k}
\end{definition}
\begin{remark}
It follows from the definitions that \HEF{0} $\Rightarrow$ \HEF{1} $\Rightarrow$ \HEF{2} $\dots$, and that an allocation satisfies \HEF{0} if and only if it satisfies \textrm{\textup{EF}}{}. It is also easy to verify that an allocation is \sEF{1} if and only if it is \uHEF{n}. This is because the unique hidden good for every agent is also the one that is (hypothetically) removed under \sEF{1}. Additionally, as discussed in \Cref{sec:Introduction}, an \textrm{\textup{EF}}{1} allocation might not be \uHEF{k} for any $k \leq n$.
\label{rem:EF_HEF_Relationship}
\end{remark}
We say that allocation $A$ is \emph{\HEF{} with respect to set $S$} if $A$ becomes envy-free after hiding the goods in $S$, i.e., for every pair of agents $i,h \in [n]$, we have $v_i(A_i) \geq v_i(A_h \setminus S)$. We say that $k$ goods \emph{must be hidden} under $A$ if $A$ is \HEF{} with respect to some set $S$ such that $|S|=k$, and there is no set $S'$ with $|S'| < k$ such that $A$ is \HEF{} with respect to $S'$.
\begin{definition}[\textbf{Pareto optimality}]
An allocation $A$ is Pareto dominated by another allocation $B$ if $v_i(B_i) \geq v_i(A_i)$ for every agent $i \in [n]$ with at least one of the inequalities being strict. A \emph{Pareto optimal} (\textrm{\textup{PO}}{}) allocation is one that is not Pareto dominated by any other allocation.
\end{definition}
\begin{definition}[\textbf{\textrm{\textup{EF}}{1} algorithms}]
\label{defn:EF1_algorithms}
We will now describe four known algorithms for finding \textrm{\textup{EF}}{1} allocations that are relevant to our work.
\paragraph{Round-robin algorithm (\textup{\texttt{RoundRobin}}{}):} Fix a permutation $\sigma$ of the agents. The \textup{\texttt{RoundRobin}}{} algorithm cycles through the agents according to $\sigma$. In each round, an agent gets its favorite good from the pool of remaining goods.
\paragraph{Envy-graph algorithm (\textup{\texttt{EnvyGraph}}{}):} This algorithm, proposed by \citet{LMM+04approximately}, works as follows: In each step, one of the remaining goods is assigned to an agent that is not envied by any other agent. The existence of such an agent is guaranteed by resolving cyclic envy relations (if any exists) in a combinatorial structure called the \emph{envy-graph} of an allocation.
\paragraph{Fisher market-based algorithm (\textup{\texttt{Alg-EF1+PO}}{}):} This algorithm, due to \citet{BKV18Finding}, uses local search and price-rise subroutines in a Fisher market associated with the fair division instance, and returns an \textrm{\textup{EF}}{1} and \textrm{\textup{PO}}{} allocation. The bound on running time of this algorithm is pseudopolynomial, i.e., has a polynomial dependence on $v_{i,j}$ instead of $\log v_{i,j}$.
\paragraph{Maximum Nash Welfare solution (\textup{\texttt{MNW}}{}):} The \emph{Nash social welfare} of an allocation $A$ is defined as $\textrm{\textup{NSW}}(A) \coloneqq \left( \prod_{i \in [n]} v_i(A_i) \right)^{1/n}$. The \textup{\texttt{MNW}}{} algorithm computes an allocation with the highest Nash social welfare (called a \emph{Nash optimal} allocation). It is known that a Nash optimal allocation is both \textrm{\textup{EF}}{1} and \textrm{\textup{PO}}{}~\citep{CKM+16unreasonable}.
\end{definition}
\begin{remark}
\citet{CFS+19group} observed that \textup{\texttt{RoundRobin}}{}, \textup{\texttt{Alg-EF1+PO}}{}, and \textup{\texttt{MNW}}{} algorithms all satisfy \sEF{1}. It is easy to see that \textup{\texttt{EnvyGraph}}{} algorithm is also \sEF{1}. Among these four algorithms, only \textup{\texttt{MNW}}{} and \textup{\texttt{Alg-EF1+PO}}{} are provably also \textrm{\textup{PO}}{}.\footnote{It is also known that \textup{\texttt{RoundRobin}}{} and \textup{\texttt{EnvyGraph}}{} fail to satisfy \textrm{\textup{PO}}{}; see, e.g., \citep{CFS17fair}.} The allocations computed by all four algorithms have the property that there exists some agent that is not envied by any other agent. Indeed, \textup{\texttt{MNW}}{} and \textup{\texttt{Alg-EF1+PO}}{} are both \textrm{\textup{PO}}{} and therefore cannot have cyclic envy relations, and \textup{\texttt{RoundRobin}}{} and \textup{\texttt{EnvyGraph}}{} algorithms have this property by design. For such an agent (not necessarily the same agent for all four algorithms), no good needs to be removed under \sEF{1}. Therefore, from \Cref{rem:EF_HEF_Relationship}, all these algorithms are also envy-free up to $n-1$ uniformly hidden goods, or $\uHEF{(n-1)}$.
\label{rem:EF1_algorithms_uHEF_n-1}
\end{remark}
\begin{restatable}{prop}{uHEFExistence}
\label{prop:uHEF(n-1)}
Given an instance with additive valuations, a $\uHEF{(n-1)}$ allocation always exists and can be computed in polynomial time, and a $\uHEF{(n-1)}+\textrm{\textup{PO}}{}$ allocation always exists and can be computed in pseudopolynomial time.
\end{restatable}
\begin{remark}
Note that for any $k < n-1$, an \HEF{k} allocation might fail to exist. Indeed, with $n$ agents that have identical and positive valuations for $m = n-1$ goods, some agent will surely miss out and force the allocation to hide all $n-1$ (i.e., $k+1$ or more) goods. Therefore, the bound in \Cref{prop:uHEF(n-1)} for \uHEF{k} (and hence, for \HEF{k}) is tight in terms of $k$.
\label{rem:HEFk_Tight_Bound_For_k}
\end{remark}
\subsection{Relevant Computational Problems}
\label{subsec:Computational_Problems}
\Cref{defn:HEFkExistence} formalizes the decision problem of checking whether a given instance admits a fair (i.e., \HEF{k}) allocation.
\begin{definition}[\textbf{\textup{\textsc{\HEF{k}-Existence}}}]
Given an instance $\mathcal{I}$, does there exist an allocation $A$ and a set $S \subseteq [m]$ of at most $k$ goods such that $A$ is \HEF{} with respect to $S$?
\label{defn:HEFkExistence}
\end{definition}
Notice that a certificate for \textup{\textsc{\HEF{k}-Existence}}{} consists of an allocation $A$ as well as a set $S$ of at most $k$ hidden goods.
Another relevant computational question involves checking whether a given allocation $A$ is \HEF{} with respect to some set $S \subseteq [m]$ of at most $k$ goods.
\begin{definition}[\textbf{\textup{\textsc{\HEF{k}-Verification}}}]
Given an instance $\mathcal{I}$ and an allocation $A$, does there exist a set $S \subseteq [m]$ of $k$ goods such that $A$ is \HEF{} with respect to $S$?
\label{defn:HEFkVerification}
\end{definition}
For additive valuations, both \textup{\textsc{\HEF{k}-Existence}}{} and \textup{\textsc{\HEF{k}-Verification}}{} are in \textrm{\textup{NP}}{}. The next problem pertains to the existence of envy-free allocations.
\begin{definition}[\textbf{\textup{\textsc{\EF{}-Existence}}}]
Given an instance $\mathcal{I}$, does there exist an envy-free allocation for $\mathcal{I}$?
\label{defn:EFExistence}
\end{definition}
\textup{\textsc{\EF{}-Existence}}{} is known to be \textrm{\textup{NP-complete}}{}~\citep{LMM+04approximately}. From \Cref{rem:EF_HEF_Relationship}, it follows that \textup{\textsc{\HEF{k}-Existence}}{} is \textrm{\textup{NP-complete}}{} when $k=0$ for additive valuations.
\section{Theoretical Results}
\label{sec:Theoretical_Results}
This section presents our theoretical results concerning the existence and computation of \HEF{k} and \uHEF{k} allocations. We will first show that \uHEF{k} is a strictly more demanding notion than \HEF{k} (\Cref{prop:HEFk_vs_uHEF}).
\begin{restatable}{prop}{HEFvsuHEF}
\label{prop:HEFk_vs_uHEF}
There exists an instance $\mathcal{I}$ that, for some fixed $k \in {\mathbb{N}}$, admits an \HEF{k} allocation but no \uHEF{k} allocation.
\end{restatable}
\begin{proof}
Consider the fair division instance $\mathcal{I}$ with five agents $a_1,\dots,a_5$ and six goods $g_1,\dots,g_6$ shown in \Cref{tab:HEFk_vs_uHEFk}. Observe that the allocation $A = (A_1,\dots,A_5)$ with $A_1 = \{g_1,g_2\}$, $A_2 = \{g_3\}$, $A_3 = \{g_4\}$, $A_4 = \{g_5\}$, $A_5 = \{g_6\}$ satisfies \HEF{2} with respect to the set $S = \{g_1,g_2\}$.
\begin{table}[h]
\centering
\small
\begin{tabular}{ c|cccccc }
& $g_1$ & $g_2$ & $g_3$ & $g_4$ & $g_5$ & $g_6$\\ \hline
$a_1$ & $1$ & $1$ & $2$ & $0$ & $0$ & $0$ \\
$a_2$ & $1$ & $1$ & $2$ & $0$ & $0$ & $0$ \\
$a_3$ & $10$ & $10$ & $1$ & $1$ & $1$ & $1$ \\
$a_4$ & $10$ & $10$ & $1$ & $1$ & $1$ & $1$ \\
$a_5$ & $10$ & $10$ & $1$ & $1$ & $1$ & $1$ \\
\end{tabular}
\caption{The instance used in the proof of \Cref{prop:HEFk_vs_uHEF}.}
\label{tab:HEFk_vs_uHEFk}
\end{table}
We will show that $\mathcal{I}$ does not admit a \uHEF{2} allocation. Suppose, for contradiction, that there exists an allocation $B$ satisfying \uHEF{2}. Then, $B$ must hide $g_1$ and $g_2$ (otherwise, at least one of $a_3$, $a_4$ or $a_5$ will envy the owner(s) of these goods). Thus, in particular, the good $g_3$ must be revealed by $B$. Assume, without loss of generality, that $g_3$ is \emph{not} assigned to $a_1$ in $B$ (otherwise, a similar argument can be carried out for $a_2$). Then, $B$ must assign both $g_1$ and $g_2$ to $a_1$ (so that $a_1$ does not envy the owner of $g_3$). However, this violates the one-hidden-good-per-agent property of \uHEF{k}, which is a contradiction.
\end{proof}
Recall from \Cref{subsec:Computational_Problems} that \textup{\textsc{\HEF{k}-Existence}}{} is \textrm{\textup{NP-complete}}{} when $k=0$. This still leaves open the question whether \textup{\textsc{\HEF{k}-Existence}}{} is \textrm{\textup{NP-complete}}{} for \emph{any} fixed $k \in {\mathbb{N}}$. Our next result (\Cref{thm:HEFk_Existence_NPcomplete_IdenticalVals}) shows that this is indeed the case, even under the restricted setting of \emph{identical} valuations (i.e., for every $j \in [m]$, $v_{i,j}=v_{h,j}$ for every $i,h \in [n]$).
\begin{restatable}[\textbf{Hardness of \textup{\textsc{\HEF{k}-Existence}}{}}]{theorem}{HEFkExistenceNPcompleteIdenticalVals}
\label{thm:HEFk_Existence_NPcomplete_IdenticalVals}
For any fixed $k \in {\mathbb{N}}$, \textup{\textsc{\HEF{k}-Existence}}{} is \textrm{\textup{NP-complete}}{} even for identical valuations.
\end{restatable}
\begin{proof}
We will show a reduction from \textrm{\textsc{Partition}}{}, which is known to be \textrm{\textup{NP-complete}}{}~
\citep{GJ79computers}. An instance of \textrm{\textsc{Partition}}{} consists of a multiset $X = \{x_1,x_2,\dots,x_n\}$ with $x_i \in {\mathbb{N}}$ for all $i \in [n]$. The goal is to determine whether there exists $Y \subset X$ such that $\sum_{x_i \in Y} x_i = \sum_{x_i \in X \setminus Y} x_i = T$, where $T \coloneqq \frac{1}{2} \sum_{x_i \in X} x_i$.
We will construct a fair division instance with $k+3$ agents $a_1,\dots,a_{k+3}$ and $n+k+1$ goods. The goods are classified into $n+1$ \emph{main goods} $g_1,\dots,g_{n+1}$ and $k$ \emph{dummy goods} $d_1,\dots,d_k$. The (identical) valuations are defined as follows: Every agent values the goods $g_1,\dots,g_n$ at $x_1,\dots,x_n$ respectively; the good $g_{n+1}$ at $T$, and each dummy good at $4T$.
($\Rightarrow$) Suppose $Y$ is a solution of \textrm{\textsc{Partition}}{}. Then, an \HEF{k} allocation can be constructed as follows: Assign the main goods corresponding to the set $Y$ to agent $a_1$ and those corresponding to $X \setminus Y$ to agent $a_2$. The good $g_{n+1}$ is assigned to agent $a_3$. Each of the remaining $k$ agents is assigned a unique dummy good. Note that every agent in the set $\{a_1,a_2,a_3\}$ envies every agent in the set $\{a_4,\dots,a_{k+3}\}$, and these are the only pairs of agents with non-zero envy. Therefore, the allocation can be made envy-free by hiding the $k$ dummy goods, i.e., the allocation is \HEF{} with respect to the set $\{d_1,\dots,d_k\}$.
($\Leftarrow$) Now suppose there exists an \HEF{k} allocation $A$. Since there are $k$ dummy goods and $k+3$ agents, there must exist at least three agents that do not receive any dummy good in $A$. Without loss of generality, let these agents be $a_1$, $a_2$ and $a_3$ (otherwise, we can reindex). We claim that all dummy goods must be hidden under $A$. Indeed, agent $a_1$ does not receive any dummy good, and therefore its maximum possible valuation can be $v(g_1 \cup \dots \cup g_{n+1}) = 3T < v(d_j)$ for any dummy good $d_j$. If some dummy good $d_j$ is not hidden, then $a_1$ will envy the owner of $d_j$, contradicting \HEF{k}. Therefore, all dummy goods must be hidden, and since there are $k$ such goods, these are the only ones that can be hidden.
The above observation implies that the good $g_{n+1}$ must be revealed by $A$. Furthermore, $g_{n+1}$ must be assigned to one of $a_1$, $a_2$ or $a_3$ (otherwise, by pigeonhole principle, one of these agents will have valuation at most $\frac{2T}{3}$ and will envy the owner of $g_{n+1}$). If $g_{n+1}$ is assigned to $a_3$, then the remaining main goods $g_1,\dots,g_n$ must be divided between $a_1$ and $a_2$ such that $v(A_1) \geq T$ and $v(A_2) \geq T$. This gives a partition of the set $X$.
\end{proof}
Another commonly used preference restriction is that of \emph{binary} valuations (i.e., for every $i \in [n]$ and $j \in [m]$, $v_{i,j} \in \{0,1\}$). We note that even under this restriction, \textup{\textsc{\HEF{k}-Existence}}{} remains \textrm{\textup{NP-complete}}{} when $k=0$ (\Cref{cor:HEFk_Existence_NPcomplete_BinaryVals}). This observation follows from a result of \citet{AGM+15fair}, who showed that determining the existence of an envy-free allocation is \textrm{\textup{NP-complete}}{} even for binary valuations (\Cref{prop:EF_Existence_NPcomplete_BinaryValuations}). We provide an alternative proof of this statement in \Cref{subsec:Proof_EF_Existence_NPcomplete_BinaryValuations} in the appendix.
\begin{restatable}[\citealp{AGM+15fair}; Theorem 11]{prop}{EFExistenceNPcompleteBinaryVals}
\label{prop:EF_Existence_NPcomplete_BinaryValuations}
\textup{\textsc{\EF{}-Existence}}{} is \textrm{\textup{NP-complete}}{} even for binary valuations.
\end{restatable}
\begin{restatable}{corollary}{HEFkExistenceNPcompleteBinaryVals}
\label{cor:HEFk_Existence_NPcomplete_BinaryVals}
For $k=0$, \textup{\textsc{\HEF{k}-Existence}}{} is \textrm{\textup{NP-complete}}{} even for binary valuations.
\end{restatable}
\Cref{prop:EF_Existence_NPcomplete_BinaryValuations} is also useful in establishing the computational hardness of finding an \HEF{k}+\textrm{\textup{PO}}{} allocation. Note that unlike \Cref{cor:HEFk_Existence_NPcomplete_BinaryVals}, \Cref{prop:HEFkPOExistence_NPcomplete_BinaryVals} holds for every fixed $k \in {\mathbb{N}}$.
\begin{restatable}[\textbf{Hardness of \HEF{k}+\textrm{\textup{PO}}{}}]{theorem}{HEFkPOExistenceNPcompleteBinaryVals}
\label{prop:HEFkPOExistence_NPcomplete_BinaryVals}
Given any instance $\mathcal{I}$ with binary valuations and any fixed $k \in {\mathbb{N}} \cup \{0\}$, it is \textrm{\textup{NP-hard}}{} to determine if $\mathcal{I}$ admits an allocation that is envy-free up to $k$ hidden goods $(\HEF{k})$ and Pareto optimal $(\textrm{\textup{PO}}{})$.
\end{restatable}
\begin{proof} (Sketch)
Starting from any instance of \textup{\textsc{\EF{}-Existence}}{} with binary valuations (\Cref{prop:EF_Existence_NPcomplete_BinaryValuations}), we add to it $k$ new goods and $k+1$ new agents such that all new goods are approved by all new agents (and no one else). Also, the new agents have zero value for the existing goods. In the forward direction, an arbitrary allocation of new goods among the new agents works. In the reverse direction, \textrm{\textup{PO}}{} forces each new (respectively, existing) good to be assigned among new (respectively, existing) agents only. The imbalance between new agents and new goods means that all (and only) the new goods must be hidden. Then, the restriction of the \HEF{k} allocation to the existing agents/goods gives the desired \textrm{\textup{EF}}{} allocation.
\end{proof}
We will now proceed to analyzing the computational complexity of \textup{\textsc{\HEF{k}-Verification}}{}. Here, we show a hardness-of-approximation result (\Cref{prop:HEFk_Verification_Hardness_Of_Approximation_BinaryVals}). The inapproximability factor is stated in terms of the aggregate envy, defined as follows: Given any allocation $A$, the \emph{aggregate envy} in $A$ is the sum of all pairwise envy values, i.e.,
\begin{align*}
E \coloneqq \sum_{h \in [n]} \sum_{i \neq h} \max\{0, v_i(A_h) - v_i(A_i)\}.
\end{align*}
Note that \textup{\textsc{\HEF{k}-Verification}}{} is stated as a decision problem (\Cref{defn:HEFkVerification}). However, one can consider an approximation version of this problem as follows: A $c$-approximation algorithm for \textup{\textsc{\HEF{k}-Verification}}{} takes as input a fair division instance and an allocation, and computes a set of goods of size at most $c \cdot k^{\textup{opt}}$, where $k^{\textup{opt}}$ is the size of the smallest hidden set for the given allocation. Under this definition, \Cref{prop:HEFk_Verification_Hardness_Of_Approximation_BinaryVals} can be interpreted as follows: Given any ${\varepsilon}>0$, there is no polynomial-time $(1-{\varepsilon}).\ln E$-approximation algorithm for \textup{\textsc{\HEF{k}-Verification}}{}, unless P=NP.
\begin{restatable}[\textbf{\textup{\textsc{\HEF{k}-Verification}}{} inapproximability}]{theorem}{HEFkVerificationHardnessOfApproximationBinaryVals}
\label{prop:HEFk_Verification_Hardness_Of_Approximation_BinaryVals}
Given any ${\varepsilon} > 0$, it is \text{NP-hard}{} to approximate \textup{\textsc{\HEF{k}-Verification}}{} to within $(1-{\varepsilon}) \cdot \ln E$ even for binary valuations, where $E$ is the aggregate envy in the given allocation.
\end{restatable}
\begin{proof}
We will show a reduction from \textup{\textsc{Hitting Set}}{}. An instance of \textup{\textsc{Hitting Set}}{} consists of a finite set $X = \{x_1,\dots,x_p\}$, a collection $\mathcal{F} = \{F_1,\dots,F_q\}$ of subsets of $X$, and some $k \in {\mathbb{N}}$. The goal is to determine whether there exists $Y \subseteq X$, $|Y| \leq k$ that intersects every member of $\mathcal{F}$ (i.e., for every $F \in \mathcal{F}$, $Y \cap F \neq \emptyset$). It is known that given any ${\varepsilon} > 0$, it is \text{NP-hard}{} to approximate \textup{\textsc{Hitting Set}}{} to within a factor $(1-{\varepsilon}) \cdot \ln |\mathcal{F}|$ \citep{DS14analytical}.
We will construct a fair division instance with $n = q+1$ agents and $m = p + \sum_{i=1}^q (|F_i|-1)$ goods. The agents are classified into $q$ \emph{dummy agents} $a_1,\dots,a_q$ and one \emph{main agent} $a_{q+1}$. The goods are classified into $p$ \emph{main goods} $g_1,\dots,g_p$ and $q$ distinct sets of dummy goods, where the $i^\text{th}$ set consists of the goods $f^i_{1},\dots,f^i_{|F_i|-1}$.
The valuations are as follows: The main agent approves all the main goods, i.e., for all $j \in [p]$, $v_{q+1}(\{g_j\}) = 1$. Each dummy agent $a_i$ approves the dummy goods in the $i^\text{th}$ set as well as those main goods that intersect with $F_i$, i.e., for every $i \in [q]$, $v_i(\{f^i_j\}) = 1$ for all $j \in [|F_i|-1]$, and $v_i(\{g_j\}) = 1$ whenever $x_j \in F_i$. All other valuations are set to $0$.
The input allocation $A = (A_1,\dots,A_{q+1})$ is defined as follows: The main agent $a_{q+1}$ is assigned all the main goods, i.e., $A_{q+1} \coloneqq \{g_1,\dots,g_p\}$. For every $i \in [q]$, the dummy agent $a_i$ is assigned the $|F_i|-1$ dummy goods in the $i^\text{th}$ set, i.e., $A_i \coloneqq \{f^i_{1},\dots,f^i_{|F_i|-1}\}$. Note that in the allocation $A$, each dummy agent envies the main agent by one approved good, and these are the only pairs of agents with envy.
($\Rightarrow$) Suppose $Y \subseteq X$, $|Y| \leq k$ is solution of the \textup{\textsc{Hitting Set}}{} instance. We claim that the allocation $A$ is \HEF{} with respect to the set $S \coloneqq \{g_j : x_j \in Y\}$ with $|S| \leq k$. Indeed, since $S$ is induced by a hitting set, each dummy agent approves at least one good in $S$. Therefore, by hiding the goods in $S$, the envy from the dummy agents can be eliminated.
($\Leftarrow$) Now suppose there exists $S \subseteq [m]$, $|S| \leq k$ such that $A$ is \HEF{} with respect to $S$. Then, for every $i \in [q]$, the set $S$ must contain at least one good that is approved by the dummy agent $a_i$ (otherwise $A$ will not be envy-free after hiding the goods in $S$). It is easy to see that the set $Y \coloneqq \{x_j : g_j \in S\}$ constitutes the desired hitting set of cardinality at most $k$.
Finally, to show the hardness-of-approximation, notice that the aggregate envy in $A$ is $q$ because each dummy agent envies the main agent by one unit of utility. The claim now follows by substituting $|\mathcal{F}| = q = E$ in the inapproximability result of \textup{\textsc{Hitting Set}}{} stated above.
\end{proof}
Our next result (\Cref{thm:HEFk_Verification_ApproxAlgo}) provides an approximation algorithm that (nearly) matches the hardness-of-approximation result in \Cref{prop:HEFk_Verification_Hardness_Of_Approximation_BinaryVals}. We remark that the algorithm in \Cref{thm:HEFk_Verification_ApproxAlgo} applies to \emph{any} instance with additive and possibly non-binary valuations.
\begin{restatable}[\textbf{Approximation algorithm}]{theorem}{HEFkVerificationApproxAlgo}
\label{thm:HEFk_Verification_ApproxAlgo}
There is a polynomial-time algorithm that, given as input any instance of \textup{\textsc{\HEF{k}-Verification}}{}, finds a set $S \subseteq [m]$ with $|S| \leq k^{\textup{opt}} \cdot \ln E + 1$ such that the given allocation is \HEF{} with respect to $S$. Here, $E$ and $k^{\textup{opt}}$ denote the aggregate envy and the number of goods that must be hidden under the given allocation, respectively.
\end{restatable}
The proof of \Cref{thm:HEFk_Verification_ApproxAlgo} is deferred to \Cref{subsec:Proof_HEFk_Verification_ApproxAlgo} in the appendix but a brief idea is as follows: For any set $S \subseteq [m]$, define the \emph{residual envy function} $f : 2^{[m]} \rightarrow \mathbb{R}$ so that $f(S)$ is the aggregate envy in allocation $A$ after hiding the goods in $S$. That is,
\begin{align*}
f(S) \coloneqq \sum_{h \in [n]} \sum_{i \neq h} \max\{0, v_i(A_h \setminus S) - v_i(A_i)\}.
\end{align*}
The relevant observation is that $f$ is \emph{supermodular}. Given this observation, the approximation guarantee in \Cref{thm:HEFk_Verification_ApproxAlgo} can be obtained by the standard greedy algorithm for submodular maximization, or, equivalently, supermodular minimization~ \citep{NWF78analysis}; see Algorithm~\ref{alg:Greedy_HEFk_ApproxAlgo} in \Cref{subsec:Proof_HEFk_Verification_ApproxAlgo}.
\section{Experimental Results}
\label{sec:Experiments}
\begin{table*
\centering
\begin{tabular}{|cccc|}
%
\multicolumn{4}{c}{\textbf{Normalized average-case regret}}\\
\hline
\footnotesize{\textup{\texttt{Alg-EF1+PO}}{}} & \footnotesize{\textup{\texttt{RoundRobin}}{}} & \footnotesize{\textup{\texttt{MNW}}{}} & \footnotesize{\textup{\texttt{EnvyGraph}}{}}\\
\includegraphics[width=0.22\textwidth]{market_regret_7_binary_norm-eps-converted-to} &
\includegraphics[width=0.22\textwidth]{rr_regret_7_binary_norm-eps-converted-to} &
\includegraphics[width=0.22\textwidth]{mnw_binary_regret_7_binary_norm-eps-converted-to} &
\includegraphics[width=0.22\textwidth]{envy_graph_regret_7_binary_norm-eps-converted-to} \\
\hline
%
\multicolumn{4}{c}{}\\
\multicolumn{4}{c}{\textbf{Number of goods that must be hidden on average} (averaged over non-\textrm{\textup{EF}}{} instances only)}\\
\hline
\footnotesize{\textup{\texttt{Alg-EF1+PO}}{}} & \footnotesize{\textup{\texttt{RoundRobin}}{}} & \footnotesize{\textup{\texttt{MNW}}{}} & \footnotesize{\textup{\texttt{EnvyGraph}}{}}\\
\includegraphics[width=0.22\textwidth]{market_k_7_binary_notnorm-eps-converted-to} & \includegraphics[width=0.22\textwidth]{rr_k_7_binary_notnorm-eps-converted-to} &
\includegraphics[width=0.22\textwidth]{mnw_binary_k_7_binary_notnorm-eps-converted-to} &
\includegraphics[width=0.22\textwidth]{envy_graph_k_7_binary_notnorm-eps-converted-to} \\
\hline
\end{tabular}
\caption{Results for synthetic data.}
\label{tab:Expt_BinaryVals_bias_0.7}
\end{table*}
We have seen that the worst-case computational results for \HEF{k}, even in highly restricted settings, are largely negative (\Cref{sec:Theoretical_Results}). In this section, we will examine whether the known algorithms for computing approximately envy-free allocations---in particular, the four \textrm{\textup{EF}}{1} algorithms described in \Cref{defn:EF1_algorithms} in \Cref{sec:Preliminaries}---can provide meaningful approximations to \HEF{k} in practice. Recall from \Cref{rem:EF1_algorithms_uHEF_n-1} that all four discussed algorithms---\textup{\texttt{RoundRobin}}{}, \textup{\texttt{MNW}}{}, \textup{\texttt{Alg-EF1+PO}}{}, and \textup{\texttt{EnvyGraph}}{}---satisfy $\uHEF{(n-1)}$.
We evaluate each algorithm in terms of (a) its \emph{regret} (defined below), and (b) the \emph{number of goods that the algorithm must hide}. Given an instance $\mathcal{I}$ and an allocation $A$, let $\kappa(A,\mathcal{I})$ denote the number of goods that must be hidden under $A$. The \emph{regret} of allocation $A$ is the number of extra goods that must be hidden under $A$ compared to the optimal. That is, $\texttt{\textup{reg}}(A,\mathcal{I}) \coloneqq \kappa(A,\mathcal{I}) - \min_{B} \kappa(B,\mathcal{I})$. Similarly, given an algorithm \textup{\textsc{Alg}}{}, the regret of \textup{\textsc{Alg}}{} is given by $\texttt{\textup{reg}}(\textup{\textsc{Alg}}(\mathcal{I}),\mathcal{I})$, where $\textup{\textsc{Alg}}(\mathcal{I})$ is the allocation returned by \textup{\textsc{Alg}}{} for the input instance $\mathcal{I}$. Note that the regret can be large due to the suboptimality of an algorithm, but also due to the size of the instance. To negate the effect of the latter, we normalize the regret value by $n-1$, which is the worst-case upper bound on the number of hidden goods for all four algorithms of interest.
\subsection{Experiments on Synthetic Data}
\label{subsec:Expt_Synthetic}
The setup for synthetic experiments is similar to that used in \Cref{fig:HEFk_motivation_0.7}. Specifically, the number of agents, $n$, is varied from $5$ to $10$, and the number of goods, $m$, is varied from $5$ to $20$ (we ignore the cases where $m < n$). For every fixed $n$ and $m$, we generated $100$ instances with \emph{binary} valuations drawn i.i.d. from Bernoulli distribution with parameter $0.7$ (i.e., $v_{i,j} \sim \textrm{\textup{Ber}}(0.7)$). \Cref{tab:Expt_BinaryVals_bias_0.7} shows the heatmaps of the normalized regret (averaged over $100$ instances) and the number of goods that must be hidden (averaged over non-\textrm{\textup{EF}}{} instances, i.e., whenever $k \geq 1$) for all four algorithms.\footnote{Additional results for $v_{i,j} \sim \textrm{\textup{Ber}}(0.7)$, and $v_{i,j} \sim \textrm{\textup{Ber}}(0.5)$ can be found in \Cref{subsec:Additional_Experiments} in the appendix.}
It is clear that \textup{\texttt{Alg-EF1+PO}}{} and \textup{\texttt{RoundRobin}}{} algorithms have a superior performance than \textup{\texttt{MNW}}{} and \textup{\texttt{EnvyGraph}}{}. In particular, both \textup{\texttt{Alg-EF1+PO}}{} and \textup{\texttt{RoundRobin}}{} have small normalized regret, suggesting that they hide close-to-optimal number of goods. Additionally, the number of hidden goods itself is small for these algorithms (in most cases, no more than \emph{three} goods need to be hidden), suggesting that the worst-case bound of $n-1$ is unlikely to arise in practice. Overall, our experiments suggest that \textup{\texttt{Alg-EF1+PO}}{} and \textup{\texttt{RoundRobin}}{} can achieve useful approximations to \HEF{k} in practice, especially in comparison to \textup{\texttt{MNW}}{} and \textup{\texttt{EnvyGraph}}{}.\footnote{In \Cref{subsec:MNW_Large_Regret} in the appendix, we provide two families of instances where the normalized worst-case regret of \textup{\texttt{MNW}}{} is large.}
\subsection{Experiments on Real-World Data}
\label{subsec:Expt_Spliddit}
For experiments with real-world data, we use the data from the popular fair division website \emph{Spliddit} \citep{GP15spliddit}. The Spliddit data has $2212$ instances in total, where the number of agents $n$ varies between $3$ and $10$, and the number of goods $m \geq n$ varies between $3$ and $93$. Unlike the synthetic data, the distribution of instances here is rather uneven (see \Cref{fig:Spliddit_data_distribution} in \Cref{subsec:Additional_Experiments} in the appendix); in fact, $1821$ of the $2212$ instances have $n=3$ agents and $m=6$ goods. Therefore, instead of using heatmaps, we compare the algorithms in terms of their normalized regret (averaged over the entire dataset) and the cumulative distribution function of the hidden goods (see \Cref{fig:Results_Spliddit}).
\Cref{fig:Results_Spliddit} presents an interesting twist: \textup{\texttt{MNW}}{} is now the best performing algorithm, closely followed by \textup{\texttt{RoundRobin}}{} and \textup{\texttt{Alg-EF1+PO}}{}. For any fixed $k$, the fraction of instances for which these three algorithms compute an \HEF{k} allocation is also nearly identical. As can be observed, these algorithms almost never need to hide more than \emph{three} goods. By contrast, \textup{\texttt{EnvyGraph}}{} has the largest regret and significantly worse cumulative performance. Therefore, once again, \textup{\texttt{Alg-EF1+PO}}{} and \textup{\texttt{RoundRobin}}{} algorithms perform competitively with the optimal solution, making them attractive options for achieving fair outcomes without withholding too much information.
\begin{figure}
\centering
\begin{subfigure}[b]{0.46\linewidth}
\centering
\includegraphics[width=\linewidth]{regret-eps-converted-to}
\end{subfigure}
~
\begin{subfigure}[b]{0.51\linewidth}
\centering
\includegraphics[width=\linewidth]{hidden_all-eps-converted-to}
\end{subfigure}
\caption{Results for Spliddit data.}
\label{fig:Results_Spliddit}
\end{figure}
\section{Future Work}
Analyzing the asymptotic behavior of \HEF{k} allocations, as has been done for envy-free allocations~\citep{DGK+14computational,MS19when}, is an interesting direction for future work. It would also be interesting to explore the connections with other recently proposed relaxations that involve discarding goods~\citep{CGH19envy,CKM+20little} or sharing a small subset of goods~\citep{SE19fair}.
\section*{Acknowledgments}
We thank the anonymous conference reviewers for their helpful comments. We are grateful to Ariel Procaccia and Nisarg Shah for sharing with us the data from Spliddit, and to Haris Aziz for bringing to our attention the proof of \textup{\textsc{\EF{}-Existence}}{} for binary valuations in \citep{AGM+15fair}. RV thanks Rupert Freeman, Nick Gravin, and Neeldhara Misra for very helpful discussions and several useful suggestions for improving the presentation of the paper. Thanks also to Erel Segal-Halevi for many helpful comments on \Cref{subsec:Proof_EF_Existence_NPcomplete_BinaryValuations}. LX acknowledges NSF \#1453542 and \#1716333, and HH acknowledges NSF \#1850076 for support.
\bibliographystyle{plainnat
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 5,226
|
Q: How to aggregate prices in OHLC-data I have a SQL Server table with columns:
ID, START_DTTM, OPEN, HIGH, LOW, CLOSE
I have to aggregate data hourly.
So, I tried this query:
SELECT
ID,
MIN(START_DTTM) START_DTTM,
MAX(HIGH) AS HIGH,
MIN(LOW) AS LOW
FROM
MY_TABLE
GROUP BY
ID, DATEPART(DAY, START_DTTM), DATEPART(HOUR, START_DTTM)
and it works, but I can't pull OPEN and CLOSE.
I tried something like this:
FIRST_VALUE(OPEN_PRICE) OVER (PARTITION BY
DATEPART(DAY, START_DTTM), DATEPART(HOUR, START_DTTM) ORDER BY START_DTTM)
And, of course, it doesn't work. What can I do?
A: You can use a subquery for that:
SELECT ID, MIN(START_DTTM) START_DTTM, MAX(HIGH) AS HIGH, MIN(LOW) AS LOW,
MAX(CASE WHEN seqnum_asc = 1 THEN OPEN_PRICE END) as open_price,
MAX(CASE WHEN seqnum_desc = 1 THEN CLOSE_PRICE END) as close_price
FROM (SELECT t.*,
ROW_NUMBER() OVER (PARTITION BY ID, DATEPART(DAY, START_DTTM), DATEPART(HOUR, START_DTTM) ORDER BY STRT_DTTM) as seqnum_asc,
ROW_NUMBER() OVER (PARTITION BY ID, DATEPART(DAY, START_DTTM), DATEPART(HOUR, START_DTTM) ORDER BY STRT_DTTM) as seqnum_desc
FROM MY_TABLE
) t
GROUP BY ID, DATEPART(DAY, START_DTTM), DATEPART(HOUR, START_DTTM);
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 2,771
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Home/Politics and Current Affairs/CONSCIENCE OF THE NATION, The Hindu
There are basically two kinds of autobiographies. The first kind lays bare the individual self, speaking in detail—sometimes too much detail—about the autobiographer's life, loves, conquests and failures. The second kind seeks to subordinates the life to the times, using individual experience to illuminate wider social trends and processes. In the Indian context, Gandhi's autobiography might easily be identified as being of the first type; Nehru's autobiography, as being of the second. (In fact, most self-testimonies fall into one or the other category; rare is the work that successfully straddles or combines both.)
I have recently been reading the autobiography of Victor Navasky, the long-time editor and now publisher of the American radical weekly, The Nation. Entitled A Matter of Opinion, the book consistently privileges the public over the personal. Navasky's wife and children make only fleeting appearances. The focus, squarely, is on impersonal events, as they unfolded in the life of the nation and, indeed, in the career of The Nation.
The Nation was founded in 1865 as an abolitionist paper, and played a vanguard role in the struggle against slavery in the United States. The magazine's founding editor, E. L. Godkin, said that it 'was not to be a party paper', for 'too close identification with a factional or partisan cause was bad journalism as well as bad policy'. Godkin added that while the paper would 'devote a good deal of attention to the social and political condition of the blacks [in] the South', it would not degenerate into a 'mere canting organ of the radical wing'. His ultimate aim was to produce a paper which might not make monetary profit, but 'whose influence on those who read it, and on the country's papers, would be enlightening, elevating, and refining'.
Among later Nation editors was Freda Kirchwey, perhaps the first woman anywhere to edit a political weekly of import. She joined the journal shortly after the First World War, and ran it during the Second, when it played a critical part in uncovering the horrors of the Holocaust. Kirchwey, writes Navasky, was 'a leader on many issues—sexual freedom, birth control, democracy vs. Fascism and Nazism, the Spanish Civil War, collective security, refugees, McCarythism and censorship, the peaceful use of atomic energy, and Zionism'.
Reading Navasky's book, I wished there was a similar account of India's longest-running radical weekly, the Economic and Political Weekly. Many who read it—and all who write for it—regard the 'EPW' as this nation's conscience. It began life in 1949 as the Economic Weekly, adding the 'Political' seventeen years later. Its founder-editor, Sachin Chaudhuri, was a bhadralok of catholic tastes who was too busy enjoying his life to write about it. His successor, the legendary Krishna Raj, had the opposite problem. He was a consistently self-effacing man, who would have regarded the genre of autobiography as an unnecessary form of self-advertisement. Perhaps some future historian will step into the breach, to trace the life of the Republic of India through the career of the EPW.
There are, it appears, some telling similarities between The Nation and the Economic and Political Weekly. For one, both are appallingly bad looking. The well loved columnist Calvin Trillin said of the American weekly that it was 'probably the only magazine in the country if you make a Xerox of it, the Xerox looks a lot better than the original'. More substantively, they have a similar philosophy or credo, this, in Navasky's words, being 'to question the conventional wisdom, to be suspicious of all orthodoxies, to provide a home for dissent and dissenters, and to be corny about it, to hold forth a vision of a better world'.
A great Nation editor, Carey McWilliams, said that his journal differed from Time and Newsweek in exploring, in depth, the underlying meaning and import of the major events of the day. Newsmagazines are mostly written by a staff of experienced and full-time reporters. On the other hand, opinion journals draw much more on freelance contributors and university scholars. As the historian Christopher Lasch pointed out, with the onset of television and the dumbing down of the mass media, these journals had become 'the only surviving media in which scholars can talk to each other. They give the intellectual community what little unity and coherence it retains'. That is true of The Nation; and even more so, one thinks, of the EPW.
There is another way in which the profitable glossy is to be distinguished from the poorly circulated journal of opinion. In the words of the critic Dwight Macdonald, 'a "little magazine" is often more intensively read (and circulated) than the big commercial magazines, being a more individual expression and so appealing with a special force to individuals of like minds'. These journals are to be judged not by the bottom-line, but by their (often considerable) impact on shaping public policy and public debate and, beyond that even, by the love and loyalty of their readers.
By Ramachandra Guha|2011-11-18T11:51:41+05:30July 2nd, 2006|Categories: Politics and Current Affairs|Tags: A Matter of Opinion, EPW, Economic and Political Weekly, Krishna Raj, Sachin Chaudhuri, The Nation, Victor Navasky, an Autobiography, dissenting opionion, editor and now publisher of the American radical weekly|
colonialism Nehru communalism C Rajagopalachari Indian democracy Cricket nationalism Hindutva foreign policy BJP Indira Gandhi Narendra Modi pluralism democracy Mahatma Gandhi ambedkar freedom of speech Verrier Elwin chauvinism governance Rabindranath Tagore secularism Congress Party Vallabhbhai Patel environment RSS corruption Manmohan Singh Rahul Gandhi Sonia Gandhi
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 2,664
|
Q: Jolt Transforme Json I have this JSON
[
{
"nomclient": "diattara",
"prix": 15,
"ville": "Paris",
"typeproduit": "boisson",
"produit": [
"COCA",
"RedBull"
]
},
{
"nomclient": "kamel",
"prix": 250,
"ville": "Marseille",
"typeproduit": "beurre",
"produit": [
"auchan"
]
}
]
I want to apply a jolt Transforme in NIFI to get a JSON like this:
[
{
"nomclient": "diattara",
"prix": 15,
"ville": "Paris"
},
{
"nomclient": "kamel",
"prix": 15,
"ville": "Paris"
}
]
I tried this spec but the result was not good
[
{
"operation": "shift",
"spec": {
"*": {
"ville": "ville",
"prix": "prix"
}
}
}
]
could you help me please
A: If you want to keep the values of the first entry's prix and ville values for all the nomclient entries, you can use the following spec in JoltTransformJSON:
[
{
"operation": "shift",
"spec": {
"*": {
"@(1,[0].prix)": "[&1].prix",
"@(1,[0].ville)": "[&1].ville",
"nomclient": "[&1].&"
}
}
}
]
If you want to just keep the 3 fields from each entry you can use the following spec:
[
{
"operation": "shift",
"spec": {
"*": {
"prix": "[&1].&",
"ville": "[&1].&",
"nomclient": "[&1].&"
}
}
}
]
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 6,073
|
{"url":"https:\/\/www.maths.gla.ac.uk\/~mwemyss\/teaching\/2algtypo2013.html","text":"Known typos in the book Groups by Jordan and Jordan:\n\n\u2022 none reported yet.\n\nKnown typos in the lecture notes:\n\n\u2022 Lecture 14: Near the end of the proof of Cauchy's theorem, I wrote \"there exists e\\neq g\\in G\". This technically should have been \" there exists g\\in G with g\\neq e\".\n\u2022 Lecture 15: When describing symmetries of the tetrahedron, I wrote \"edge-face rotations\" when I meant to write \"vertex-face rotations\".","date":"2019-02-21 13:40:17","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8412632346153259, \"perplexity\": 3024.8911348524753}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-09\/segments\/1550247504790.66\/warc\/CC-MAIN-20190221132217-20190221154217-00038.warc.gz\"}"}
| null | null |
\section{Introduction}
The set of ideas enclosed in the
Renormalization Group (RG, hereafter)
has led to a
variety of developments in many fields, as this Conference has made
apparent.
From a particle theorist point of view they englobe a bunch of ideas
form which we may understand what a quantum field theory is. Moreover,
it provides a framework for nonperturbative calculations.
In recent years, there has been an intensive development of the field
mainly for scalar theories.\cite{yuri}
It can probably be said that we thoroughly understand all the
subtleties the RG reserves for us in this case.
Nevertheless what would ultimately justify the whole approach,
as applied for Particle Physics,
is the construction of Lorentz and gauge invariant nonperturbative
equations, manageable for reliable approximations. The hope of
RG practitioners is that
we are really not that
far from there.\footnote{We have to mention that although the search
for nonperturbative gauge invariant equations is still open,
there are a variety of results for perturbative definitions of
a gauge invariant theory based on these grounds.\cite{marisa}}
Particle physicists may imagine themselves, thus,
applying in the nearby future the
powerfulness of the approach to atack long-standing nonperturbative
problems for, say, quantum gluodynamics. And the next
step would probably be the introduction of matter to have the full
physical theory.
At this point it will for sure be helpful to have already understood
the peculiarities associated to fermions on their own, both conceptual
and technical. This is the reason we believe that we should try,
as it has been done for bosons, to master as deeply
as we can fermionic theories, even with no additional fields.
We do not want to suggest that the features of fermionic equations have
to be significantly different from the ones for bosons. On the contrary,
we believe that they have to be ultimately a direct translation
of ideas from
one subject to the other.
What we do mean is that these
features may not be noticeable in any obvious way. On the other hand,
new technicalities may also appear. And
before embarking ourselves in a
more ambitious project these peculiarities must be previously
worked out and clearly understood.
We thus want to present some recent work in that direction.\cite{ours}
Namely, the study of a two dimensional sample model (the so-called
Gross-Neveu model$\,$\cite{gn})
which we will define below. This
model is sufficiently simple in order to be able to carry out the algebra
as far as we need but that
it still captures the essentials of the approach
for the Grassman case.
Let us briefly review the main ideas involved
in bosonic theories as they are studied by Polchinski.\cite{polchinski}
We first have to choose a regulator adequated for our purposes.
It is done by simply
modifying the propagator
\( P(p)
\)
\begin{equation}
P(p)=\frac{1}{p^2}
\end{equation}
to
\begin{equation}
P_{\Lambda}(p)=\frac{K(p^2/\Lambda^{2})}{p^2}
\end{equation}
where
\( \Lambda
\)
is a momentum-space cutoff and
\( K(x)
\)
a regulating function which decays sufficiently
rapid to zero when
\( x\rightarrow\infty
\).
With this kind of regulator, a quick (and somehow
sloppy) argument that leads
to an appropriate RG equation is to identify all the
\( \Lambda
\)-dependences in a partly integrated action by signaling
all possible occurrences of the propagator and multiplying by the
\( \Lambda
\)-derivative of it. In this manner we immediately obtain
\begin{equation}
\label{RGeq:bos}
-\Lambda\frac{d}{d\Lambda}S_{int}
\equiv\dot{S}_{int}
=\frac{1}{2}\frac{\delta S_{int}}{\delta \phi}\cdot\dot{P}_{\Lambda}
\cdot\frac{\delta S_{int}}{\delta \phi}
-\frac{1}{2}\mbox{tr}
\left(
\dot{P}_{\Lambda}\cdot\frac{\delta^{2}S_{int}}{\delta
\phi\delta\phi}
\right)
\end{equation}
with
\begin{equation}
S_{int}=S-\frac{1}{2}\phi\cdot P_{\Lambda}^{-1}\cdot\phi
\end{equation}
and $S$ the full action.
The first term takes into account tree-type propagators and the second
one loop-type propagators.
We are using a compact notation regarding the propagator as a matrix with
a dot standing for matrix multiplication.
The equation for a pure fermionic theory can be written in a similar form.
From the propagator
\begin{equation}
P_{\Lambda}=i\not\!{p}\,\frac{K(p^{2}/\Lambda^{2})}{p^{2}}
\end{equation}
we obtain the RG equation
\begin{equation}
\dot{S}_{int}
=\frac{\delta S_{int}}{\delta \psi}\cdot\dot{P}_{\Lambda}\cdot
\frac{\delta S_{int}}{\delta\bar{\psi}}
-\mbox{tr}
\left(
\frac{\delta}{\delta\psi}\cdot\dot{P}_{\Lambda}\cdot
\frac{\delta S_{int}}{\delta\bar{\psi}}
\right)
\end{equation}
Returning to
\( S
\)
and expressing the resultant equation in dimensionless variables
it is obtained
\begin{eqnarray}
\label{RGeq:fer}
\dot{S}
&=&2K'(p^{2})\frac{\delta S}{\delta\psi}\cdot i\not\!{p}
\cdot\frac{\delta S}{\delta\bar{\psi}}
-\mbox{tr}
\left(
2K'(p^{2})\frac{\delta}{\delta\psi}\cdot i\not\!{p}\,
\frac{\delta S}{\delta\bar{\psi}}
\right)\nonumber
\\&-&2p^{2}\frac{K'(p^{2})}{K(p^{2})}
\left(
\bar{\psi}\cdot\frac{\delta S}{\delta \bar{\psi}}
+\psi\frac{\delta S}{\delta \psi}
\right)
\\&+&dS\nonumber
\\&+&\frac{1-d+\eta(t)}{2}
\left(\bar{\psi}\frac{\delta S}{\delta\bar{\psi}}
+\psi\frac{\delta S}{\delta\psi}
\right)
-\left(
\bar{\psi}\cdot p^{\mu}\frac{\partial'}{\partial p^{\mu}}
\frac{\delta S}{\delta\bar{\psi}}
+\psi\cdot p^{\mu}\frac{\partial'}{\partial p^{\mu}}
\frac{\delta S}{\delta \psi}
\right)\nonumber
\end{eqnarray}
where we work on a $d$-dimensional Euclidean space;
\( \eta
\)
is the anomalous dimension (needed to obtain a physically
interesting fixed
point);
\( t\equiv-\ln \Lambda
\);
and the prime in
\( \frac{\partial'}{\partial p^{\mu}}
\)
means that the derivative does not act on the momentum conservation
delta functions and thus only serves to count powers of momenta.
Note the first difference between bosons and fermions. Due to the
different structure of the propagators, the fermionic equation presents
an explicit factor of $p$ in the first two terms of the right hand
side of the RG equation~\ref{RGeq:fer}
while this is not the case for bosons (Eq.~\ref{RGeq:bos}).
This may just look
like a technical
remark without any relevance. However it turns out that the
seemingly most powerful approximations to these equations are based
on the so-called derivative expansion\cite{tim}
whose first order term is obtained by restricting the action to
be a kinetic term plus a general potential term with no derivatives.
In a fermionic theory this approximation will not be feasible, because
we will be left only with a fairly simple linear equation.
The derivative
expansion should nevertheless be applicable, but it would lead to more
complicated structures even at first non-trivial order.
\section{The model}
Let us now apply the RG equation~\ref{RGeq:fer}
to the so-called chiral Gross-Neveu model.\cite{gn}
As any other field theory,
it is best defined through its
symmetries. We will consider thus
an Euclidean
invariant $N$-flavoured model,
with an
\( U(N)\times U(N)
\)
internal symmetry group. It is also chosen to obey
the discrete symmetries of parity, charge conjugation and reflection
hermiticity.\cite{zinn-justin}
When one imposes these restictions and further use Fierz reorderings,
it is easily sown that there appear only three basic structures,
\begin{eqnarray}
V_{12}^{j}&\equiv&
\bar{\psi}^{a}(p_{1})\gamma^{j}\psi^{a}(p_{2})\nonumber\\
S_{12}S_{34}-P_{12}P_{34}&\equiv&
\bar{\psi}^{a}(p_1)\psi^{a}(p_2)\bar{\psi}^{b}(p_3)\psi^{b}(p_4)
\nonumber\\
&-& \bar{\psi}^{a}(p_1)\gamma_{s}\psi^{a}(p_2)
\bar{\psi}^{b}(p_3)\gamma_{s}\psi^{b}(p_4)\\
S_{12}P_{34}-P_{12}S_{34}&\equiv&
\bar{\psi}^{a}(p_1)\psi^{a}(p_2)
\bar{\psi}^{b}(p_3)\gamma_{s}\psi^{b}(p_4)
\nonumber\\
&-& \bar{\psi}^{a}(p_1)\gamma_{s}\psi^{a}(p_2)
\bar{\psi}^{b}(p_3)\psi^{b}(p_4)\nonumber
\end{eqnarray}
which
have to be combined in an arbitrary way with combinations of
momenta.
The next step is to define a reasonable approximation to handle the
above functional-derivative equation.
We would like to choose one that closely resembles the bosonic derivative
approximation. Nevertheless,
due to the number of different structures it is not that easy to
parametrize the general action up to, say, two derivatives
while maintaining
arbitrary the number of fields. Moreover, we should keep in mind that
the allowed action is, as long as we are working with
a finite number of different
species,
composed by a finite number of operators:\ the Grassman character
of our variables constraints the number of fields allowed at one
point of space.
We have already commented that derivative terms
should also be included. In fact, this is an
important point because in
\( d=2
\)
the anomalous dimension
\( \eta
\)
usually plays an important
role: we would probably be too naive if we try to obtain numbers without
letting it to be nonzero.
In fact two derivatives may seem to do the job. However, once one
goes through the calculations, it turns out to be quite clear that
\( \eta =0
\)
is the only consistent value.
This implies that we need at least three derivatives.
The maximum number of fields was chosen to be six. This seems a number
both sufficiently low in order to keep the action relatively simple
and sufficiently high to let non-trivial results appear.
The action thus obtained has the usual kinetic term; one term with
three derivatives and only two fields; two derivative-free four-fields
operators
\begin{equation}
g_{1}(S_{12}S_{34}-P_{12}P_{34})\ ,\ \ \ \ \ g_{2}V_{12}^{j}V_{34}^{j}
\end{equation}
with coupling constants
\( g_{1}
\)
and
\( g_{2}
\);
eleven operators with also four fields but two derivatives; and
ninety-two six-fermions operators, five of them
with only one derivative and
the rest with three derivatives.
After some algebra we can now obtain the set of beta functions.
The fixed points are the solutions for these functions to vanish.
They are a set of 106 non-linear algebraic equations.
Up to this point, the function
\( K(p^{2})
\)
can be mainted arbitrary, thus keeping some freedom of chosing
a scheme. The fixed point solutions in our
approximation will in general depend on two
parameters which serve as a scheme parametrization.
In principle,
this should not worry us, because it is well known that the actual
expression of the fixed point action has no intrinsic physical
meaning.
For Particle Physics it is specially interesting the
value of the relevant directions from the fixed points.
That is, we linearize the RG transformations,
\begin{equation}
\dot{g}_{i}={\cal R}_{i}(g_{j})
\end{equation}
to
\begin{equation}
\dot{g}_{i}={\cal R}_{ij}\cdot\delta g_{j}\ ,\ \ \ \ \
{\cal R}_{ij}\equiv
\left.\frac{\partial{\cal R}_{i}}{\partial g_{j}}\right|_{g^{0}}
\end{equation}
where
\( g^{0}
\)
is the fixed-point solution and
\( \delta g_{j}
\)
are the deviations from it.
The number of positive eigenvalues of the matrix
\( {\cal R}_{ij}
\)
coincide with the number of possible parameters we can fine-tune in the
corresponding cutoff-free theory$\,$\cite{wilson}
and the actual value of these eigenvalues gives the speed of departure
from the fixed point.
These eigenvalues are directly related to the so-called critical
exponents in the terminology of second-order phase transitions.
They are universal and, therefore, they should be
free from schemes dependences.
In our approximation, however,
this is not so, as often happens with truncations.
The scheme ambiguities are solved by a translation of the principle
of minimal sensitivity used in perturbative
calculations.\cite{stevenson}
\section{Results}
We now sketch the main results.
The equations simplify enormously when
\( N\rightarrow\infty.
\)
Two fixed points can be clearly identified. One of them with vanishing
anomalous dimension (it is of order
\( N^{-1}
\)) and
with the most relevant eigenvalue
\( \sqrt{17} - 3
\)
in this approximation. Moreover the coupling constant
\( g_{2}
\)
which corresponds to
\( U(1)
\)
Thirring-like
excitations becomes free (we have, in fact, a line of fixed points) and
\( g_{1}
\)
is also of order
\( N^{-1}
\).
All these features but the anomalous dimension remind the fixed point
solution found by Dashen and Frishman.\cite{df}
The other solution, which corresponds to a different definition of
the large $N$ limit (different assumed
$N$ dependences of the coupling constants) has a non-vanishing anomalous
dimension. It is scheme dependent with a range of variation of
1.11--1.14 for most of the schemes. The most relevant eigenvalue
is also scheme-dependent with a range of 2.1--2.3 and, unlike the previous
case, there are no free parameters.
Before going on we must comment on a quite unpleasant feature of this kind
of approximations. By now it is generally believe that any approximation
based on truncations leads to a system of fixed-point equations with
many spurious solutions.\cite{spur}
It seems that a pure derivative
expansion (that is, one with a truncation in the number of derivatives
but without any further truncation in the number of fields) cures
all this kind of problems.
We work with a truncated action and thus we expect on general grounds
that this unwanted peculiarity appears and, actually, it does.
The solution of the puzzle is not always simple. One usually tries
to discriminate among solutions by checking the stability of the obtained
ones either going one step beyond in the approximation or else
tuning some parameters. In our case we are lucky to have nitid
results in the large $N$ limit. Therefore,
we take as reliable solutions only those whose limit when
\( N\rightarrow\infty
\)
concides with one of the solutions found above.
This procedure will probably not be available in all cases and one should
wonder if there is any systematic procedure to deal with the problem
without relying on technical details of the studied
model.
Of course, one can always try to perform a true derivative expansion
instead of mutilating each term as we have done. It should
eliminate at once the spurious results. In fact we have a special
case, which we will refer later on that suggests that this is true.
Nevertheless the expansion proposed is not that simple, specially for
$N$ moderately large. Moreover, it seems to be difficult to deal
with different values of $N$ simultaneously and still preserving
each term in the expansion without truncating it at some arbitrary
point.
One solution for finite $N$ matches
the first one
discussed above, with the most relevant eigenvalue smoothly decreasing
to
\( \sqrt{17} - 3
\)
and with
\( N\cdot\eta
\)
increasing with N to 4.87\ldots\@\ Unlike the strict large $N$ limit,
we do not find, nevertheless, a line of fixed points but an isolated
one. We blame this feature to the crudeness of the approximation.
The solution that matches the second one above has a much more conspicuous
behaviour. In fact it is valid only for
\( N>142.8
\).
At this value it matches another branch of solutions, which
exists even when
\( N\rightarrow\infty
\)
although the couplings do not scale with $N$ as integer powers but as
noninteger ones. Both the anomalous dimension and the most relevant
eigenvalue present strong scheme dependences, quite difficult to
disentangle.
Finally, we can consider separately the
\( N=1
\)
case. It is worth going through it because it is a simple case where
we can treat the equations in a purely derivative approximation:
due to Fermi statistics, we cannot have more than six fields
if we consider terms up to three derivatives. Our action is thus exact
in this sense. Also, we have to work out further relations imposed
by Fierz reorderings, not present for
\( N\not=1
\).
Our action is, therefore,
even shorter than that. The results are nevertheless
very messy and, probably, not reliable. When considering terms up
to two derivatives, we find a line of fixed points (as it is expected
in the Thirring model) with
\( \eta=0
\)
as stated previously. But once we go to three derivatives,
\( \eta\not=0
\) but, unexpectedly, the line of fixed points disappears and we
obtain only an isolated one. Nevertheless one piece of nice news comes
out: the spurious solutions disappear, as expected.
A final comment is in order. We have found
\( \eta
\)
by imposing that the normalization of the kinetic term is fixed at
some standard value. This is surely not the most general way to
proceed. If an exact computation is performed we know that this
normalization does not matter and we will be able to fix it safely
to whatever value we want: we will find a whole line of physically
equivalent fixed points. It is generally known that this
kind of symmetry is broken for
most of the approximations$\,$\cite{bell} (in particular it is broken by
the derivative expansion). Moreover, we generally expect that the true
physical fixed point mixes with non-local ones with similar behaviour
for the truncated action but with different anomalous dimensions.
To pick up the local solution
among the non-local ones, one should try to find the
reminiscence of the line of fixed points:\
a marginal redundant operator.
Its presence would signal that our scheme is truly approximating
the local fixed point behaviour and not something else. This would
probably fixed some, or perhaps even all, of the scheme dependences.
This analysis has not been performed.
Summarizing, we have presented
a fermionic RG equation and an example of its
application. It seems that, although technically harder to work with,
there emerges the same patterns as in the bosonic case. In particular
the annoying issue of spurious solutions is also present.
However, it does seem that with sufficiently accurate work and
restricting oneself to a derivative expansion without further
truncations reliable non-trivial results should come out.
\section*{Acknowledgments}
I would like to acknowledge J.I. Latorre and
Tim R. Morris for discussions on this
and related subjects and A. Travesset
for reading the manuscript.
This work has been supported by funds form MEC
under contract AEN95-0590.
\section*{References}
|
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| 9,447
|
{"url":"https:\/\/www.numerade.com\/questions\/sketch-the-region-and-find-its-area-if-the-area-is-finite-s-x-y-mid-x-le-0-0-le-y-le-ex\/","text":"\ud83d\udcac \ud83d\udc4b We\u2019re always here. Join our Discord to connect with other students 24\/7, any time, night or day.Join Here!\n\nWZ\n\n# Sketch the region and find its area (if the area is finite).$S = \\{ (x, y) \\mid x \\le 0, 0 \\le y \\le e^x \\}$\n\n## $A=\\int_{-\\infty}^{0} e^{x} d x=1$\n\n#### Topics\n\nIntegration Techniques\n\n### Discussion\n\nYou must be signed in to discuss.\n##### Heather Z.\n\nOregon State University\n\n##### Kristen K.\n\nUniversity of Michigan - Ann Arbor\n\n##### Michael J.\n\nIdaho State University\n\nLectures\n\nJoin Bootcamp\n\n### Video Transcript\n\nthe problem is catch the region and find it. I am area. Look at this graph. We need to find its area of this part of the safety apart we can use into girl. Um negative Infinity Want zero? The function Each works yaks to denote area off us or this improper integral a definition. This is a call to the limit a goes to make to infinity into girl from a to zero e to axe yaks this's equal Choose limit a goes to make you infinity This is Eagle Tito acts a zero This is a culture of blame It a goes to make to infinity into zero is equal to want minus into eh When a goes to make to you infinity into a goes to zero since answer is the blonde So the area of this region in secret one\n\nWZ\n\n#### Topics\n\nIntegration Techniques\n\nLectures\n\nJoin Bootcamp","date":"2021-10-16 21:35:02","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5338241457939148, \"perplexity\": 4587.718882795224}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-43\/segments\/1634323585025.23\/warc\/CC-MAIN-20211016200444-20211016230444-00399.warc.gz\"}"}
| null | null |
{"url":"https:\/\/www.biostars.org\/p\/429959\/","text":"Machine learning Algorithms on DNA sequences\n0\n0\nEntering edit mode\n22 months ago\n\ni am working machine learning project,i have 4 different sequences of human from different regions and want to develop machine learning model\n\nDNA ML R \u2022 612 views\n1\nEntering edit mode\n\nThat's great and all, but it isn't a question.\n\nA model for what?\n\nWhat sequences?\n\n0\nEntering edit mode\n\nThe sequences are not normal patient sequences ,so there must be common mutation(due to disease ) between all those sequences, on that basis i want to develop model . I am confused that from where i should start ..Any example or something else will really help full.\n\n0\nEntering edit mode\n\nRight, so if there's a mutation - why do you need to arbitrarily apply ML to this problem? Variant calling pipelines are well established.\n\nYou also haven't told us what the data is still. Have you got reads? Whole genomes? What state is the data in? Has it been QC'd?\n\n0\nEntering edit mode\n\nwhole Genome of patients..the data is in RAW form(Simple FASTA format). ML model for predict same type of sequence using RAW sequences.\n\n0\nEntering edit mode\n\nWhat will the model predict that non-ML methods do not already do?\n\n0\nEntering edit mode\n\nI don't see how ML fits with this question?\n\nYou have a dataset of sequences with mutation X. You receive new data, and need to check if it has mutation X or not. Why guess this with ML, when you can literally just look at the base-pair position in the new data and see if it has mutation X or not?\n\n0\nEntering edit mode\n\nWith respect, if you do not even know where to start and if this even will be helpful then maybe are more well-defined project might make sense and most importantly => an experienced supervisor is required.\n\n1\nEntering edit mode\n\nWhat do you want the machine to learn? A model is supposed to learn to predict something tangible based on other tangible input. You only have sequence data, what do you wish to predict from that?\n\n0\nEntering edit mode\n\nThe sequences are not normal patient sequences ,so there must be common mutation(due to disease ) between all those sequences, on that basis i want to develop model . I am confused that from where i should start ..Any example or something else will really help full.\n\n0\nEntering edit mode\n\nPlease don't copy\/paste the same content. You don't need to reply to each comment if you don't have anything specific to say for that comment.","date":"2022-01-27 03:43:09","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.31624361872673035, \"perplexity\": 1945.2115144715178}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-05\/segments\/1642320305052.56\/warc\/CC-MAIN-20220127012750-20220127042750-00277.warc.gz\"}"}
| null | null |
Home / Breaking News / Startup Closeup: Prokeep builds communication platform for distributors
Startup Closeup: Prokeep builds communication platform for distributors
By: Tommy Santora, Contributing Writer July 6, 2022 Comments Off on Startup Closeup: Prokeep builds communication platform for distributors
How do you invent a software product or service that will be deemed useful in any industry? You talk to prospective clients and research what they need to do their jobs more efficiently.
Prokeep founders, from left to right, Mark Kanof, Jack Carrere and McKay Johnson. Photo courtesy Prokeep
That's exactly what the co-founders of Prokeep did. And the hundreds of hours spent at the counters of distributors have paid off.
Prokeep is the first and only communications and commerce platform built exclusively for distributors. Since the New Orleans-born software startup launched to commercial clients in 2018, it has served more than 1,000 distributors who have used Prokeep for over 5.5 million conversations.
Contractors send orders and inquiries straight to their distributor, saving hundreds of thousands of hours monthly across the customer base. The Prokeep platform, which enables a branch's main phone number to accept communication, continues to evolve from feedback from distributors to streamline information such as ordering, deliveries and pickups – all in one workplace.
"A relationship between distributors and their customers depends on communication. We spent hours observing how that interaction took place, and how we can make these communications better," said Jack Carrere, Prokeep CEO. Carrere co-founded Prokeep with McKay Johnson, COO, and Mark Kanof, CTO. "We built an omni-channel platform to make it easier for our customers to communicate, build relationships and get work done."
Prokeep employs more than 60 people in offices in New Orleans, Atlanta, and employees working remotely across the U.S. In 2021, Prokeep was included in Silicon Bayou News' "10 Must-Watch Startups in New Orleans."
Company History: Carrere and Johnson are cousins who always wanted to launch an entrepreneurial project together. In 2011, Carrere met Kanof at a startup event in Portland. Kanof, an engineer, was living in Portland and determined on solving practical problems with technology. For several years, the two continued to share start-up ideas, and Carrere would relay these ideas back to Johnson and vice versa. Eventually, the three teamed up, and were unsuccessful at their first two business ventures. It was the third time that was the charm.
In 2015, they tried to sell HVAC On Demand. "We found HVAC technicians who would answer our call if we found a customer that needed a repair," said Carrere. "We ended up scrapping the company for several reasons, but one recurring experience we found was in conversations with contractors, we saw opportunities to improve communications and efficiency within their business."
So, the three built the product Timeline, an app for contractors to help them better manage their business and communicate easily with their team and customers. While the initial feedback of how Timeline helped contractors was positive, the problem was contractors were always jumping from job to job, and it was hard to get contractors to spend the necessary time to give Timeline traction. Carrere recalled hustling for 15-20 leads who were promised free software in exchange for feedback. Those leads were called, but hardly anyone returned calls. Timeline was taken back to the drawing board, and a fork in the road directed them to texting for distributors.
The three spent a year getting to know distributors while trying to sell Timeline. "We came up with the idea of what if we text enabled distributors' landlines, because we saw it happening on personal phones," Carrere said. "Even though we spent two years building Timeline, we decided to pivot."
The Prokeep platform enables a distributor branch's main phone number to accept communication from contractors, such as orders, invoices and construction job inquiries. Photo courtesy Prokeep
Pitch: Out of the extensive research was borne a simple pitch: Get distributors away from taking customers' messages on personal phones, storing notes on yellow notepads and job files and inquiries on basic computer software. Transition them to a cloud-based communications platform where distributors could receive, field, and file all communications – an easy-to-use mission control for distributors adding three primary values of efficiency, accountability and convenience.
Traction: Initially bootstrapped, Prokeep conducted client beta testing in 2017. Its first beta client was Flick Distributing Company, an HVAC distribution company in Harahan. Carrere and Johnson would observe customers, offer both Flick employees and customers use of Prokeep's texting platform, and then gather feedback. Baton Rouge-based Acme Refrigeration also came online as a second beta testing client. Prokeep brought on 12 beta clients, and, of those, 11 of them became full-time clients when the three decided to launch the company commercially in 2018.
"Branch Texting" was at the origin of Prokeep's business model. It allowed customers to text orders, pictures and construction job information directly to their distributor's branch landline phone, saving hold times, eliminating phone tag and preventing miscommunication. All parties access the cloud-based communications platform to conduct business. Distributors respond from their counter computers, home devices or phones. Searchable conversation history provides confirmation of details such as serial and model numbers, pricing and other final decisions.
In 2021, Prokeep upgraded its texting app to include multi-channel mobile messaging, internal messaging, broadcast messaging to customers and the ability to connect to customer inquiries and leads through distributors' websites. Prokeep's App Programming Interface (API) sends a text when triggered by a company's third-party system, communicating order status, shipping information and receipts. "With feedback and the support from our customers, we have scaled Prokeep from a focused texting app to a secure omnichannel communications and commerce platform tailored for distributors facilitating tens of thousands of orders monthly," Kanof said.
Funding: In June 2022, Prokeep announced the closing of its $9 million seed round. Johnson said the funds will accelerate marketing and product development as the company works to continue to be "mission control for distributors."
"By becoming the system of truth throughout the ordering process, we will bring better workflow and actionable data to distributors and enable an even higher level of customer service," Johnson said.
The investment seed round was led by Ironspring Ventures with participation from S3 Ventures; Benson Capital Partners; Scott Wolfe Jr., Levelset CEO; Lawrence Hester, FareHarbor former CEO; and Hugh Evans, former T. Rowe Price Head of PE/VC Portfolio; among others.
"Prokeep's ability to bootstrap to over 1,000 distributors and power 5.5 million conversations, all while deeply respecting the human element involved between distributors and their customers, blew us away and is indicative of this team's ability to build a premier SaaS business," said Austin-based Ironspring Ventures co-founder and General Partner Ty Findley.
S3 Ventures, a venture capital firm also based in Austin, was an investor in local success story Levelset, which provides construction payment software. "We believe in Prokeep's vision to become the core operating system for wholesale distributors," said S3 Ventures General Partner Charlie Plauche. "Their platform is streamlining how thousands of distributors and contractors communicate and do business."
Benson Capital Partners was founded in 2019 by Gayle Benson, principal owner of the New Orleans Saints, New Orleans Pelicans and Birmingham Squadron. Benson Capital Partners is a partnership to honor the legacy of her late husband, Tom Benson, by fostering entrepreneurship and innovation in the Gulf South.
"We are thrilled to partner with the great team of professionals at Prokeep, a software company right here in our backyard that we believe is revolutionizing the way commerce is done in wholesale distribution," said Mike Katz, BCP Managing Director.
Challenges: Carrere said Prokeep's biggest competitor and challenge in the marketplace is distributors choosing to do "business as usual."
"We have a unique product that we can offer, so our challenge is to continue to tell our story and explain the value that we bring to a distributor," said Carrere. "The opportunity we have is that the construction industry is growing, and companies are investing in technology. We need to show our communications platform can be a worthy investment for their strategic planning."
The $9 million raised will also allow Prokeep to accelerate its marketing and sales efforts in the construction industry, expand partnership channels and enter additional industries. A way Prokeep markets its company is through an extensive website blog, sharing distributor spotlights, trends and user tips on the software. The company also produces podcasts and webinars.
Growing from three founders to now 60 employees in six years, Carrere said as Prokeep continues to evolve, the company will hire across all departments.
"We are hiring across sales, customer success, product development, engineering and marketing," he said. "We are excited to grow the tech ecosystem here in New Orleans and offer careers to people who are driving innovative solutions to our clients across the United States and Canada."
prokeep 9:01 am Wed, July 6, 2022 New Orleans CityBusiness
Tommy Santora, Contributing Writer
Tagged with: prokeep
|
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| 2,492
|
© Armand Colin, 2015
Armand Colin est une marque de Dunod Éditeur
5, rue Laromiguière, 75005 Paris
Illustration de couverture : Le Changeur (La parabole du riche).
Rembrandt Harmensz van Rijn (Gemäldegalerie [SMPK])
© BPK, Berlin, Dist. RMN-Grand Palais/Jörg P. Anders
ISBN : 978-2-200-60371-7
Collection U
Sciences humaines et sociales
Delas Jean-Pierre, Milly Bruno, Histoire des pensées sociologiques, 4e édition, 2015.
Gob André, Drouguet Noémie, La muséologie. Histoire, développements, enjeux actuels, 4e édition, 2014.
Chaumier Serge, Mairesse François, La médiation culturelle, 2013.
Kilani Mondher, Anthropologie. Du local au global, 2e édition, 2013.
Bornand Sandra, Leguy Cécile, Anthropologie des pratiques langagières, 2013.
Paillé Pierre, Muchielli Alex, L'analyse qualitative en sciences humaines et sociales, 3e édition, 2012.
À notre collègue Bernard Maris,
assassiné pour ses idées le 7 janvier 2015
Table des matières
Page de titre
Page de Copyright
Collection U
[Première Partie
Analyse générale : la multiplicité des points de vue](p1.html#part-001)
Chapitre 1 - Les biens culturels : définition et délimitation
Les biens et les services en économie
Comment distinguer les biens culturels ?
Unicité et reproductibilité
À la recherche d'une définition...
Chapitre 2 - Un système hybride
Des caractéristiques particulières
Trois points de vue
Trois parties de notre personnalité – un système hybride
Chapitre 3 - La logique du marché
Le marché concurrentiel, un mécanisme autorégulateur idéal ?
La théorie du marché, boîte à outils pour saisir les mondes de l'art
Structure de l'offre et stratégies industrielles
Chapitre 4 - La logique publique
Le rôle de l'État
Raisons du soutien public
De la logique publique à l'économie planifiée
Chapitre 5 - La logique du don
Le don dans la société bourgeoise
Une triple « obligation »
Les formes du don dans le domaine des arts et de la culture
Des caractéristiques différentes
[Deuxième Partie
Approches sectorielles](p2.html#part-002)
Chapitre 6 - Les arts de la scène
Trois logiques de fonctionnement différentes
La loi de « maladie des coûts » de Baumol et la logique des subventions
Subventions et structure des recettes
Chapitre 7 - Le patrimoine
Structure du secteur
Le discours économique sur le patrimoine
Tendances générales du secteur
Chapitre 8 - L'artiste, les arts plastiques, le marché de l'art
Les différents marchés de l'art et leurs protagonistes
L'évolution des intermédiaires
Un acteur public : le rôle de l'État
Formation et variation des prix
Chapitre 9 - Les industries culturelles : définition et organisation
Définition et évaluation des industries culturelles
Une organisation de nature industrielle
Chapitre 10 - Les industries culturelles : comparaisons sectorielles
Origines et trajectoires historiques
Structure de l'offre
La régulation des industries culturelles
[Troisième Partie
Enjeux transversaux](p3.html#part-003)
Chapitre 11 - La diversité culturelle
Diversité culturelle : de quoi parle-t-on précisément en économie ?
Droit d'auteur et variété de l'offre
Les pratiques culturelles : diversité, éclectisme et omnivorité
Distribution, appariement, prescription
Chapitre 12 - Intégrer la culture dans l'économie
L'évolution du contexte industriel
Logique des industries culturelles et créatives
Protéger la créativité : le droit d'auteur et le copyright
Chapitre 13 - Temporalité, spatialité
Temps, espace, économie
Le temps du loisir
Chapitre 14 - Globalité : l'économie du star-system
Production de la star
Les analyses empiriques
Les conséquences du vedettariat : une garantie de succès ?
Chapitre 15 - L'arrivée des nouveaux acteurs du numérique
La transformation du paysage
De nouveaux modèles numériques : longue traîne et crowdfunding
Écosystèmes de la culture et stratégies de plateforme
Conclusions. Intégrer l'économie dans la culture ?
Le monde mis à prix et en chiffres
La référence continue à la gestion d'entreprise
De l'anxiété au sens de la vie
Bibliographie
Index
Introduction
Économie, Arts et culture
Un grand nombre d'acteurs du champ culturel, et non des moindres, éprouvent une certaine répulsion à l'égard de l'économie et de ses méthodes. La discipline paraît austère, reposant sur un vocabulaire quelque peu abscons et une écriture proche du langage mathématique, désorientant le profane. Le discours économique est pourtant très largement sorti des sphères académiques pour se répandre à travers les médias ; nombreux sont les représentants de la discipline qui sont invités sur les plateaux de télévision pour commenter les statistiques du chômage ou les dernières mesures prises par le gouvernement, et il y a bien longtemps que les pages économiques ont envahi la plupart des journaux et périodiques. Le public s'est progressivement adapté à l'idée qu'une telle discipline, jeune d'à peine un siècle sur le plan académique, conditionne notre société dans des proportions considérables. C'est en quelque sorte le propre d'une science que de viser au dévoilement d'une réalité du monde et l'économie, à cet égard, montre un certain type d'échanges inhérents à la vie en société. Le propre de l'économie, comme celui de la science, est d'allier théorie et pratique, d'analyser, mais aussi de conseiller ou d'agir. Le conseil du prince ou celui du gouvernement constitue largement de nos jours l'affaire des économistes, tandis que ces derniers occupent des places importantes à tous les échelons de la société et notamment dans la culture. D'une certaine manière, ce dernier domaine semblait pourtant devoir échapper, par ses références littéraires ou philosophiques, aux échanges strictement matériels, qu'étudie l'économie. Ce n'est plus le cas.
Non seulement l'expertise économique est actuellement pleinement reconnue au sein de la société occidentale, mais elle constitue probablement le mode d'argumentation, avec les sciences de gestion qui en dérivent, le plus largement utilisé. Il y a environ un demi-siècle, Charles Snow évoquait le fossé séparant les deux cultures qui, à son sens, structuraient le monde et la pensée : la culture scientifique et les humanities (lettres et sciences humaines). La difficulté du dialogue entre ces deux mondes, pour Snow, s'avérait bien réelle, mais demeurait à l'avantage des élites formées aux humanities. Si l'auteur, dans la seconde édition de son ouvrage, envisageait non sans espoir une possible troisième culture, nourrie par le dialogue entre ces deux mondes a priori hermétiques, probablement n'imaginait-il pas que c'est justement à partir d'une telle synthèse que la plus « dure » ou la plus mathématique des sciences sociales allait à la fin du xxe siècle imposer son autorité ou du moins étendre ses domaines de compétences au traitement des sujets les plus divers. À cet égard, cette ouverture opérée à partir des années 1960 par la science économique dans des champs nouveaux (la famille, la religion, le crime...), mais traités traditionnellement par d'autres disciplines comme la sociologie et la psychologie, a pu être qualifiée d'« impérialisme économique ».
Le terme d'économie de la culture, qui naguère pouvait passer pour une incongruité, est révélateur de cet état de fait : la culture qui, pour un Malraux, s'imposait comme le rempart contre les puissances de la finance, se voit ainsi traitée sans état d'âme par la discipline même sur laquelle repose l'édifice financier, sans que personne ne s'en émeuve. Le mot d'industrie culturelle, aux connotations monstrueuses pour Adorno et Horkheimer (cf. infra), s'est progressivement imposé comme un terme neutre. Longtemps, des pans entiers de la société ont échappé à la logique de l'analyse économique ; tel n'est plus le cas aujourd'hui, et l'ensemble des domaines du gouvernement, en ce compris l'armée, les soins de santé ou la culture, répondent à des impératifs essentiellement guidés par une logique économique. Une telle vision est bien illustrée par les travaux du prix Nobel (de la banque de Suède) d'économie de 1992, Gary Becker, professeur à l'Université de Chicago, célèbre pour ses travaux sur l'économie de la criminalité, de la famille et du capital humain. Une telle vision n'aurait probablement pas pu émerger quelques années plus tôt, alors qu'une grande partie du monde offrait une vision singulièrement différente de l'économie que celle qui se présente aujourd'hui comme la seule possible : l'économie de marché. Car c'est bien évidemment, d'emblée, une certaine vision de l'économie qui s'est imposée ces dernières années comme courant dominant de l'économie et présentant la logique du marché comme la plus efficace en matière d'organisation du monde. En quelque sorte – nous y reviendrons – le point de vue économiste (de marché) vise à reconnaître en tout homme un Homo œconomicus dont l'action est entièrement guidée par le calcul rationnel à partir de ses propres choix et à travers ses stratégies. Si un tel modèle peut être utilisé pour l'ensemble de la vie humaine, privée et publique, il peut évidemment donner lieu à une réflexion dans le monde de la culture. Celle-ci intéresse les chercheurs depuis les fondements de l'économie politique, il n'en reste pas moins que ce n'est que depuis une vingtaine d'années qu'une telle réflexion a progressivement trouvé des applications pratiques dans le monde de la culture lui-même.
Encore s'agit-il bien de savoir de quelle économie il est question ! Parle-t-on d'un secteur d'activité, d'une méthode, d'une discipline scientifique ? Existe-t-il plusieurs manières de la concevoir ? C'est à partir d'un tel questionnement, et de ses conséquences, que nous souhaitons aborder l'économie des arts et de la culture dans cet ouvrage. C'est également pour cette raison qu'il nous semble particulièrement important que l'ensemble de la société – et, pour ce qui nous concerne, l'ensemble des acteurs du monde de la culture – s'empare du discours économique pour en maîtriser la structure, en comprendre les enjeux et au-delà, en saisir la portée et les limites. Car en quelque sorte, en s'appuyant sur les deux territoires – le scientifique et les humanités – l'économiste est parvenu à imposer un mode de raisonnement apparemment scientifique sur l'ensemble des sujets de société, à commencer par tout ce qui a trait aux relations d'échange et notamment financières. L'organisation du secteur de la culture – des théâtres aux musées, en passant par le cinéma, le livre et la danse – constitue ainsi un terrain de choix pour l'application des théories et des méthodes économiques.
Nombreux sont les responsables, mais aussi les étudiants, qui ont pourtant choisi de s'orienter dans le monde de la culture en réaction aux difficultés du raisonnement scientifique ou, de manière plus générale, à l'abstraction mathématique. Ainsi, l'utilisation du nombre – tel qu'il s'exprime par exemple à partir de l'étalon monétaire – constitue, pour un grand nombre d'acteurs de la culture, un souvenir douloureux qui apparemment ne devrait pas être réactivé au cours de leur carrière culturelle. Mauvaise nouvelle ! Le domaine de la culture est lui aussi de plus en plus régulièrement soumis à un raisonnement de ce type, que les acteurs des institutions qui le composent se doivent de comprendre, mais également de maîtriser, sinon pour en devenir spécialiste, du moins pour argumenter dans un certain nombre de situations. D'emblée, les questions du financement de la culture, qui dépend largement des pouvoirs publics en Europe, appellent au raisonnement économique. Pourquoi faudrait-il financer cette dernière ? Les responsables politiques demandent à être convaincus, pour persuader à leur tour les citoyens, et l'argument qui actuellement tend à s'imposer est d'abord économique : investir dans la culture rapporte de l'argent, sinon directement, du moins de manière indirecte. La question est d'autant plus ardue en période de crise, laquelle semble ne plus s'être arrêtée depuis la fin des années 1970. Quoi qu'il en soit, les spectres de la crise, du chômage et de la ruine de l'État induisent d'éternelles mesures d'économies budgétaires, conduisant chaque responsable à justifier et argumenter ses budgets.
Dans de telles perspectives, c'est l'argument économique qui s'avère souvent le plus convaincant ou bien souvent, et malheureusement, le seul qui soit à la fois légitime et audible pour les autorités de tutelle et les investisseurs privés. Si celui-ci tend à s'imposer dans le monde politique, il est également omniprésent dans le monde du travail et, comme nous l'écrivions plus haut, dans les organisations liées au secteur de la culture. Ce sont aussi prioritairement des critères de rentabilité ou de non-rentabilité économique qui seront utilisés pour investir dans un projet – l'ouverture d'un musée, comme à Lens – ou pour l'arrêter. On ferme ainsi des théâtres, on arrête des festivals, moins en raison de leur faible influence en matière de culture, ou de la qualité de leurs projets, qu'en raison du déficit financier qu'ils auraient encouru. Quant au secteur des industries culturelles – cinéma, livre ou musique –, c'est depuis longtemps une logique industrielle qui prime au niveau des stratégies de développement. Certes, les spécificités du monde de la culture peuvent être mises en avant pour expliquer certaines différences en matière de choix stratégiques, ou une sensibilité particulière au niveau de la structuration de ces organisations. Il n'en reste pas moins que les acteurs majeurs de la culture tendent de moins en moins à présenter des caractéristiques majeures en matière de compétences culturelles spécifiques : on peut ainsi passer (avec des résultats divers) du secteur de la construction à la télévision (Bouygues), du traitement des eaux à la musique et au cinéma (Vivendi), ou du Conseil d'État à la direction d'un grand établissement culturel. À travers le déploiement de ces grands groupes industriels-culturels, c'est aussi une certaine vision de la culture, mainstream et à vocation mondiale, qui se dessine.
Face à un tel paysage, l'analyse économique se révèle un outil précieux pour comprendre les stratégies et les modes de fonctionnement. Dès qu'il y a marché, fixation de prix et de valeurs, problème d'incitation et de coordination, coûts d'opportunité et arbitrages associés à une décision privée ou publique, le raisonnement économique intervient : comment déterminer le prix d'une œuvre d'art ? À quels signaux et informations se fier ? Comment comprendre l'évolution du prix des œuvres ? De manière générale, si l'économie s'intéresse au marché, aux comportements individuels, aux entreprises, aux institutions et aux stratégies des organisations, elle s'intéresse également à la culture elle-même. L'histoire de l'art vue par les économistes touche à bon nombre de thèmes qui leur sont chers : prix, valeur, évolution, stratégies des acteurs etc. La curiosité économiste, en ce sens, a bien peu de limites.
Pour un non-économiste actif dans le domaine de la culture, trois réactions sont possibles face à un type d'argumentation et d'organisation qui lui paraît a priori étranger : l'acceptation, le rejet ou la compréhension en vue d'en maîtriser l'argumentaire. Les dispositifs dérivant du raisonnement économique moderne, tels qu'on les retrouve actuellement dans le monde de la culture, constituent en effet un ensemble de normes contraignantes – utilisation du nombre et des statistiques, monétarisation de la culture, valorisation économique etc. – dont la mise en œuvre requiert des compétences particulières. Il est possible d'accepter, sans pour autant les comprendre, les actions demandées (valoriser des collections, évaluer les retombées économiques d'un festival). Nombre de responsables culturels, confrontés à de telles demandes (rapports d'activités, évaluation pour des demandes de subsides, argumentation devant un panel d'investisseurs) se contentent généralement de maudire l'administration ou le donneur d'ordre, sans pour autant s'interroger sur le bien-fondé d'une telle entreprise, sinon pour constater l'importance du temps nécessaire pour répondre à de telles demandes, tout en acceptant de facto les conséquences du raisonnement économique mis en œuvre. Une autre réaction possible serait, comme cela a pu être le cas durant plusieurs générations, de décréter le monde de la culture inconciliable avec de telles manières de penser, en rejetant en bloc la doxa économique actuelle. La troisième possibilité, que nous privilégions, vise à tenter de comprendre l'argumentation utilisée, c'est-à-dire le raisonnement économique lui-même, soit pour le valider, soit pour le contester et éventuellement proposer une solution alternative.
Cette connaissance des principes de l'économie est de ce fait pragmatique. Elle nous paraît en effet vitale pour tout acteur du monde de la culture, qu'il soit résolument opposé à une certaine vision de l'économie qu'il pourrait identifier comme celle de marché et à ce que le sens commun intitule ultralibéralisme ou, au contraire, qu'il en soit partisan. Dès qu'il se présentera sur le marché du travail, lorsqu'il entrera en relation avec un employeur puis, au sein d'une organisation culturelle, lorsqu'il sera confronté au public, une grande partie de ses actions seront conditionnées par le raisonnement économique. Face à son employeur, à un banquier, à un mécène (généralement issu du monde des grandes entreprises), mais aussi face aux pouvoirs publics, les arguments qu'il sera amené à utiliser ou qui lui seront opposés seront souvent de nature économique. Il est vital, dans une telle perspective, de pouvoir en assurer une certaine maîtrise.
Avant de présenter les principaux modes de réflexion à partir de laquelle la logique économique opère (première partie), d'évoquer les principaux secteurs tels qu'ils sont analysés en économie de la culture (deuxième partie) puis de présenter les principaux enjeux auxquels le monde de la culture se trouve confronté pour les prochaines années (troisième partie), il nous paraît important de tenter de définir rapidement le sujet qui nous préoccupe soit, dans un premier temps, l'économie et la culture, puis l'économie des arts et de la culture.
Définir l'économie, les arts et la culture
Le terme d'économie souffre d'un certain nombre d'ambiguïtés. Le mot, en français, désigne en effet l'action ménagère visant à réduire la dépense (faire des économies), la discipline scientifique (l'économie ou, anciennement, économie politique, à l'opposé de l'économie domestique), mais aussi le champ qu'elle explore (l'économie de la France). L'économie – on utilise parfois le terme d'économisme – présente aussi, notamment à partir du champ disciplinaire qui a été créé, une vision particulière sur le monde, comme celle de Gary Becker évoquée plus haut. L'anglais possède deux termes pour évoquer ces différents sens : economics (pour la discipline) et economy, tandis que l'on parle d'Ökonomie, de Sparsamkeit et de Volkwirtschaftlehre, en allemand. Nous nous intéressons forcément ici à la discipline scientifique, qui bénéficie de nombreuses définitions.
Économie
Commençons par une définition classique, synthèse de la plupart de celles que l'on retrouve dans les manuels d'économie, qui pointe la relation entre des individus, des ressources (limitées) et des besoins (illimités) : « L'économie étudie la façon dont les individus ou les sociétés utilisent les ressources rares en vue de satisfaire au mieux leurs besoins. » Comment être le plus heureux possible, c'est-à-dire en langage économique satisfaire au mieux ses envies (ou maximiser son utilité), en disposant de revenus (ou de temps, ou de moyens) limités ? Acheter un tableau de Cranach ou deux Dürer ? Trois disques ou un jeu vidéo ? Bref, un jeu d'équations à plusieurs inconnues. Dans la perspective publique, l'économie vise à assurer le meilleur bonheur à ses citoyens (que l'on traduit souvent par le plus de richesses) en fonction des moyens limités qui lui sont impartis. Forcément, les ressources et les moyens peuvent différer : plus de dépenses publiques ou moins d'impôts, mais l'indicateur de base, pour discutable qu'il soit, demeure : augmenter la richesse (traduite en général par le Produit intérieur brut). L'économie s'est ainsi constituée comme une discipline scientifique dont le principal objet porte sur cette relation entre les humains, face à leurs besoins et à leurs moyens ; une science sociale étudiant les comportements de l'être humain, disposant de moyens limités et confrontés à des besoins multiples. En poursuivant dans cette voie, l'économie se fait plus englobante, « impérialiste », à la manière de la définition utilisée par Joseph Stiglitz :
« L'économie est une science sociale. Elle étudie le problème des choix dans une société d'un point de vue scientifique, c'est-à-dire à partir d'une exploration systématique qui passe aussi bien par la formulation de théories que par l'examen de données empiriques. »
Une discipline qui ne s'intéresse plus seulement à la sphère économique, mais à l'ensemble de la société (famille, culture etc.) ; si l'économie étudie les choix dans la société, tout devient économique : la répartition du budget, mais aussi le fait d'avoir ou non des enfants, de commettre ou non un crime, de choisir entre le fromage ou le dessert... Une sorte de science des choix, mais aussi des relations entre hommes et objets.
« [...] l'économie recouvre aujourd'hui une forme de médiation entre les hommes et les objets. Les hommes attribuant aux objets une valeur d'échange, l'économie relie les hommes aux objets, les objets aux objets, et les hommes entre eux. »
Si, d'un point de vue technique, l'économie peut se présenter comme un outil universel, mais neutre et rationnel, il convient de se rappeler ses fondements. Ce sont d'abord des philosophes qui ont pensé l'économie. Le biologiste Philippe Kourilsky, en présentant l'économie comme une médiation entre hommes et objets, souligne aussi le rapport d'inféodation potentiel qui peut transparaître à partir de ce point de vue, et les questions éthiques sous-jacentes : considérer d'autres hommes comme des objets ou des marchandises diffère sensiblement de la possibilité de les voir comme d'autres sujets...
Longtemps, le discours économique est demeuré largement inféodé aux considérations éthiques. La recherche du bonheur ne passe aucunement par la richesse ; l'homme n'est d'abord pas un animal économique, mais politique, un être social amené à vivre en communauté, à échanger, à entretenir sa maison (au sens large, à commencer par sa famille). Aristote prend soin de distinguer l'économie, ou l'art de gérer sa propriété, de la chrématistique (la recherche de richesse liée au commerce autre que de proximité), qu'il condamne. La méfiance des penseurs, relayés par l'Église, vis-à-vis de l'enrichissement et de l'accumulation de richesses, confine l'économie à un rôle modeste. Si au cours des xive et xve siècles, un certain type de capitalisme se développe, notamment dans le sillage de l'ordre des Franciscains, et que son essor se poursuit tout au long du xvie siècle, au gré de la contre-réforme, celui-ci n'en demeure pas moins suspect pour la plupart. C'est un tour de force pour le moins étonnant qu'opèrent Bernard Mandeville, mais surtout Adam Smith, en présentant l'intérêt égoïste, voire le vice, comme éléments moteurs de la prospérité et de la richesse, non seulement pour le citoyen, mais aussi pour l'ensemble de la nation. La mystérieuse « main invisible » de Smith, si régulièrement citée – bien que très peu utilisée dans son ouvrage majeur, Recherches sur la nature et les causes de la richesse des nations (1776) – constitue le symbole d'un retournement possible des rapports entre morale et économie : veillez strictement à vos propres intérêts, vous contribuerez ainsi à la richesse collective.
Longtemps cependant, c'est d'abord l'analyse de la richesse qui intéresse ceux que l'on n'intitule pas encore économistes. Ainsi, l'économie (politique) s'inscrit dans la continuité de l'économie domestique, visant à diminuer la dépense et accroître la richesse. Ce n'est que progressivement, à partir de la fin du xixe siècle, avec les néo-classiques (Jevons, Walras et Menger) que progressivement, l'objet de l'économie s'étend à l'analyse de l'activité économique elle-même. Une telle activité doit pouvoir être décrite de manière rationnelle, et au même titre que la physique de Newton et la loi de la gravité universelle qui a révolutionné la manière de concevoir les rapports à la nature, l'économie doit se trouver elle aussi ses principes fondateurs. Ce seront d'une part, le principe d'utilité, pensé par Bentham et Mills, et d'autre part, celui de l'Homo œconomicus, que l'on voit se développer à partir du début du xxe siècle. Au même titre que l'homme moyen des sociologues (Quételet), l'Homo œconomicus est un modèle de l'être humain, dont les caractéristiques principales sont le raisonnement rationnel, une connaissance parfaite de l'information et la recherche de son profit maximum. C'est sur de telles bases, modélisées, qu'il est notamment possible de concevoir une vision elle aussi modélisée de l'économie, que Léon Walras va tâcher de présenter sous la forme la plus objective possible, par un système d'équations mathématiques. Ce mouvement de mathématisation de l'économie (auquel s'opposent un certain nombre de penseurs, et notamment Menger et l'école autrichienne, mais également nombre d'économistes « hétérodoxes »), constituera probablement un facteur de reconnaissance sur le plan scientifique. C'est, en tout état de cause, dès ce moment qu'elle s'émancipe de la sociologie et s'autonomise progressivement au sein du système académique.
Si l'économie est rapidement enseignée en France, à partir du xixe siècle (au Collège de France, au Conservatoire national des Arts et Métiers et à l'École des Ponts), elle ne va que progressivement s'insérer, avec retard, au sein du système universitaire, et d'abord au sein de la Faculté de droit (à partir de 1864, mesure généralisée en 1877), pour ne s'affranchir réellement des autres disciplines académiques qu'après la Seconde Guerre mondiale. La modélisation mathématique de l'économie, prônée par Walras, tarde à s'imposer, confrontée à une vision souvent nettement plus historique ou sociologique. C'est pourtant cette formalisation mathématique qui va progressivement dominer la pensée économique, notamment à travers la revue Econometrica, fondée au cours des années 1930. L'apport mathématique et surtout statistique, s'il permet le renforcement des outils de calcul, induit deux conséquences. La première permet incontestablement d'imposer l'économie comme la plus « dure » des sciences humaines, renforçant son influence au sein de l'enseignement académique, mais également dans la vie politique, où la parole des économistes peut se prévaloir de l'autorité des symboles de la science. Autre conséquence, le langage de l'économiste – et a fortiori celui de l'économètre –, plus mathématique, s'il permet un niveau d'objectivation plus grande, encourt le double risque de se détacher de la réalité et de ne pouvoir être compris et partagé par le plus grand nombre.
La création en 1968 d'un « prix Nobel » d'économie, remis par la Banque de Suède, marque en quelque sorte la reconnaissance sociale mondiale de cette discipline. Il n'en demeure pas moins qu'à cette époque, l'économie demeure très largement divisée. Si, d'un côté, le modèle capitaliste connaît des variantes politiques diverses, entre son application aux États-Unis ou dans les pays européens marqués par la social-démocratie, une grande partie de l'Europe, à l'Est, partage une vision radicalement différente, à partir d'un modèle d'économie planifiée inspiré des idées de Marx et Lénine. Jusque vers la fin des années 1980, des cours d'économie planifiée ou sur les coopératives côtoient généralement ceux présentant l'économie politique générale. Dès la chute du mur de Berlin (1989) et la faillite du système soviétique, le modèle capitaliste – que l'on dénommera plus généralement, à partir de cette époque, « économie de marché » – s'impose sur les autres, au point de se présenter comme seule alternative.
Arts et Culture
La définition du mot « culture », en français, désigne prioritairement le résultat de la « fructification des dons naturels permettant à l'homme de s'élever au-dessus de sa condition initiale et d'accéder individuellement ou collectivement à un état supérieur ». La culture, en ce sens, se présente comme un acte essentiellement individuel, lié à l'attention que chacun peut prendre à « cultiver son jardin ». Associée à la notion souvent controversée de civilisation – qui est nettement plus utilisée durant le xviiie siècle – la culture témoigne de la dimension individuelle, tandis que la civilisation qualifie les traits généraux de l'esprit des Lumières. À la notion universaliste de culture telle qu'elle se développe en France, s'oppose progressivement le terme allemand de Kultur, présenté en association avec le terroir local contribuant à l'âme d'un peuple, son art, ses valeurs spirituelles et intellectuelles, en opposition avec le caractère plus universel, mais aussi plus superficiel des belles manières de l'élite de Cour. À travers le différend linguistique, se joue aussi la lutte entre un certain courant dominant et les particularismes régionaux, le développement d'une logique impérialiste de la culture, et la résistance locale menacée de disparition. Qu'elle soit grecque, romaine, française ou plus tard américaine, la culture dominante a tendance à se présenter comme la seule légitime, basée sur des jugements de classe, son déploiement ne pouvant s'opérer que sur fond de destruction des régimes précédents.
Le terme de culture s'impose donc progressivement dans la langue à partir du xixe siècle et, dans les sciences sociales, à la fin de celui-ci. On doit à l'anthropologue Edward Tylor la première définition classique du terme, tel qu'il sera utilisé dans son domaine :
« Culture ou civilisation, pris dans son sens le plus étendu, est ce tout complexe qui inclut les connaissances, les croyances, l'art, la morale, le droit, les coutumes et toutes les autres capacités et habitudes que l'homme acquiert en tant que membre de la société. »
Le terme, qui inclut les arts, prend une acception particulièrement vaste et générique, dont vont s'inspirer les premiers anthropologues, comme Boas ou Malinowski, partant à la recherche de la culture des Kwakiutl ou des Trobriandais (dont nous reparlerons plus tard). En ce sens, l'économie de la culture serait composée de l'ensemble des institutions et des types d'échanges régissant, si l'on suit Stiglitz, la question des choix au sein d'une société comme celle des Kwakiutl ou celle des Français, en matière d'art, mais aussi de croyances ou de droit. C'est pourtant une vision nettement plus réduite sur laquelle s'est progressivement construite l'économie de la culture.
Économie des arts et de la culture
Si l'on suit le manuel d'économie de la culture de Françoise Benhamou, le domaine de l'économie de la culture porte d'abord sur les secteurs strictement artistiques, soit le marché de l'art et le spectacle vivant (qu'on intitule généralement économie de l'art), ensuite, dans un sens un peu plus élargi, sur le secteur du patrimoine et des musées et les industries culturelles (édition de livre et de musique, cinéma). En ce sens, l'économie de la culture se présente prioritairement comme l'étude des institutions occidentales directement liées à la production de culture artistique (savante ou populaire).
Cette vision demeure assez proche de l'acception courante, en français, du terme « culture », lié à l'élévation de l'esprit par un certain nombre de pratiques intellectuelles ou artistiques, et c'est en effet à partir de ce socle constitué sur la base des arts que l'économie de la culture s'est développée. Au départ, durant les années 1960, l'économie de l'art s'intéresse spécifiquement aux mêmes domaines qui constituent les compétences du ministère des Affaires Culturelles, dirigé par Malraux, ou à ceux qui sont subventionnés par le National Endowment for the Arts (États-Unis) : les arts de la scène, les arts plastiques et le patrimoine mobilier ou immobilier, auxquels s'adjoignent le cinéma et les secteurs du livre ou de la musique enregistrée. Le caractère industriel de ces derniers – le cinéma comme « usine de rêves », selon Malraux – les place dans une situation mixte, alliant création artistique et procédés de reproduction et de diffusion industriels. C'est cette approche, qui s'inscrit dès le départ au cœur de la réflexion des économistes sur ce qui constitue l'originalité de ce secteur, qui est retenue dans cet ouvrage. Le développement du champ culturel – qui correspond, dans le cadre des politiques culturelles, au passage de la démocratisation de la culture à la démocratie culturelle – induit en quelque sorte celui de l'économie de la culture, dans laquelle seront parfois intégrées d'autres pratiques dites culturelles, comme le jeu vidéo et, en France, la télévision ou la presse, qui sont intégrées aux industries culturelles.
La classification du Journal of Economic Littérature donne une vision encore plus vaste du terme, les cultural economics, reléguées dans une sorte de catégorie fourre-tout (JEL Z, other special topics), place l'économie de la culture aux côtés de la sociologie économique et l'anthropologie économique. Cette catégorie comprend l'économie de l'art et de la littérature aussi bien que celle de la religion. Une telle approche, globale et en cela semblable à la définition anthropologique de la culture, laisse penser que ce domaine pourrait s'étendre plus logiquement vers l'étude économique de la langue ou des religions ; tel n'est pourtant pas ce que l'on retrouve actuellement dans la plupart des ouvrages d'économie de la culture, dont les volontés d'extensions visent plutôt (nous y reviendrons au chapitre 12) des domaines directement liés à la production à destination d'un marché, comme le design, la mode ou l'architecture.
La définition que donnent Heilbrun et Gray de l'économie des arts et de la culture insiste sur la manière dont les économistes envisagent l'étude du domaine : c'est d'abord en tant qu'économiste, et non en tant que sociologue ou anthropologue, que la culture sera analysée, avec les mêmes outils utilisés pour l'étude des finances publiques ou celle du secteur pharmaceutique.
« L'économie de l'art et de la culture [...] explique comment l'art et la culture fonctionnent à l'intérieur de l'économie générale. [...] Nous effectuons des recherches au sein du secteur de l'art et de la culture pratiquement de la même manière que les économistes peuvent analyser le secteur de l'acier, de la nourriture ou des soins de santé : nous regardons d'abord la croissance du secteur, puis nous examinons la consommation, la production, le fonctionnement des marchés de l'art, les problèmes financiers de l'industrie, et le rôle important des politiques publiques. »
C'est la même logique que reprend Ruth Towse, insistant sur les outils et les principes, pour définir l'économie de la culture en tant que discipline :
« Qu'est-ce qui détermine le prix d'un concert de musique pop ou d'un opéra ? Pourquoi existe-t-il un star-system dans le domaine de l'art ? Pourquoi tellement d'artistes sont-ils pauvres ? [...]. L'économie de la culture étudie toutes ces questions (et bien d'autres) à partir de l'analyse économique. En tant que discipline, l'économie se fonde sur la théorie – des principes économiques – pour analyser les problèmes, et utilise aussi des témoignages empiriques – l'étude de données statistiques – pour tenter d'y répondre ».
Les économistes reconnaissent toutefois que, d'une part, un tel champ possède ses spécificités qui le distinguent des autres secteurs (comme le secteur de l'acier ou la filière bovine possèdent, eux aussi, leurs spécificités), requérant donc une connaissance fine du secteur et de ses caractéristiques. D'autre part, comme Ruth Towse le signale dans son ouvrage, un tel domaine est analysé à partir d'autres disciplines développant des approches souvent complémentaires : la sociologie de la culture et la gestion des arts et de la culture, qui partagent leurs intérêts pour les mêmes objets que les économistes (à la différence, généralement, de l'histoire de l'art qui privilégie la culture elle-même).
Si l'économie de la culture peut être entendue comme discipline (ou sous-discipline), elle peut aussi être présentée comme un domaine d'activités (comme on parle de l'économie de la France). Au fur et à mesure de son développement, l'économie de la culture a étendu ses objets d'analyse, ou son domaine de recherche. Au départ largement orientée à partir du secteur artistique, elle s'est progressivement intéressée à des domaines connexes. L'organisation du secteur, telle qu'on la voit notamment au niveau des politiques publiques, est pensée de manière parfois très différente, en ce compris au sein de l'Europe. Le modèle qui tend à s'imposer repose cependant sur un système concentrique impliquant un centre, dans lequel figurent les arts (littérature, arts de la scène, arts plastiques), puis un second cercle où se trouvent les institutions et les industries culturelles, le patrimoine (archives, bibliothèques et musées, monuments), le cinéma, l'édition littéraire et musicale, la télévision et les jeux vidéos. Dans un cercle encore plus extérieur viennent s'ajouter les industries qui leur sont reliées (publicité, architecture, mode, design), l'ensemble pouvant être présenté comme le secteur des industries créatives.
Brève histoire de l'économie des arts et de la culture
On peut certes trouver quelques phrases de Turgot, de Mandeville ou d'Adam Smith ayant un rapport plus ou moins direct avec la culture, puisque s'intéressant à la production de richesse, les productions culturelles ne gravitant jamais bien loin de cette dernière. Mais l'ouvrage pionnier de l'économie, la Richesse des nations, poursuit d'autres objectifs que l'analyse spécifique d'un secteur, aussi intéressant soit-il. C'est plutôt à partir des débuts du xixe siècle, avec l'institutionnalisation de la culture, que se pose progressivement la question de la (bonne) gestion des grands établissements culturels entretenus par l'État. La gestion du British Museum par exemple, fondé en 1753, suscite de nombreux commentaires ; les multiples rapports des commissions parlementaires (en 1835 et 1836 notamment) s'interrogeant sur les mesures à prendre, en matière d'organisation de l'établissement, constituent peut-être le terreau à partir duquel va pouvoir émerger une réflexion spécifiquement économique sur la culture. C'est à partir de ce moment que, progressivement, émerge une littérature sur l'administration des beaux-arts, tant en France qu'en Grande-Bretagne. La plupart de ces réflexions ne proviennent pas d'économistes, tant s'en faut ; Edward Edwards, qui publie un essai sur l'administration des beaux-arts en Angleterre, est ainsi bibliothécaire.
Premiers ouvrages économiques
Le renforcement du pouvoir des économistes néo-classiques, que l'on observe à partir de la fin du xixe siècle, les conduit peut-être à exercer leur jugement dans de plus nombreux domaines, comme celui de la culture. Ainsi William Stanley Jevons consacre-t-il plusieurs articles à la question de l'organisation des institutions de la culture en Angleterre, et notamment celle des musées et des bibliothèques. De telles contributions demeurent cependant isolées, la culture ne constituant certes pas le noyau central de l'économie. Par ailleurs, l'économie elle-même fait l'objet de nombreux débats nettement plus virulents au cours de ces années : d'une part, celle-ci est encore largement attaquée par l'élite culturelle, comme William Morris ou Ruskin, qui prend violemment à partie les théories de Stuart Mills ; d'autre part, l'influence de Marx (et de Proudhon en France) conduit à une autre représentation du monde que celle des thèses libérales. Ici aussi, la pensée marxienne, ou celle qui lui est associée, ne traite que très indirectement de l'économie de la culture. Les points de vue de Marx et de Ruskin, pour contradictoires qu'ils soient, convergent du moins sur la position implicite de l'économie sur la culture : le mélange des deux y apparaît comme relativement incongru. C'est d'une certaine manière un point de vue que l'on peut retrouver chez Keynes, grand amateur d'art devant l'éternel, sans pour autant qu'il ait réservé à celui-ci une place dans son œuvre économique.
Industries culturelles
Le discours philosophique, en revanche, intègre culture et économie. Poursuivant l'analyse de Marx à travers la culture, l'École de Francfort – Adorno, Horkheimer ou Benjamin – va jouer un rôle considérable dans la réflexion sur les liens entre culture et économie, durant l'entre-deux-guerres. On sait la fortune de l'œuvre de Benjamin (L'œuvre d'art à l'époque de sa reproductibilité technique, Paris capitale du xixe siècle), et il convient d'insister, ici, sur l'aspect directement économique de son œuvre, associant à partir de l'analyse marxiste l'art, la marchandise et la transformation du premier par le second et par les rapports de production. Mais c'est, avant tout, la Dialectique de la raison d'Adorno et Horkheimer, publiée en 1944, qui va longtemps conditionner l'analyse du rapport entre culture et économie. C'est dans cet ouvrage que, pour la première fois, est présenté le concept d'industrie culturelle, apparemment antinomique, monstre issu de la rencontre entre les modes de production capitalistes et la véritable culture. Pour les deux philosophes, le jazz, mais surtout le cinéma, illustrent à l'envi le processus par lesquels l'industrie peut s'approprier la culture pour la régurgiter à l'usage des masses, et offrir à la consommation un ersatz renforçant leur consentement à supporter la violence des rapports de production.
D'une certaine manière, l'analyse marxiste, omniprésente en France jusque dans les années 1970, condamne largement le rôle de la culture telle qu'elle se présente dans l'Europe de l'Ouest, qu'elle soit gérée par le marché ou financée par l'État, elle vise essentiellement à protéger les intérêts de la classe dominante. Cruel retour des choses : aujourd'hui, le terme d'industrie culturelle apparaît de manière totalement neutre dans l'analyse économique...
William Baumol et la fondation de l'économie de la culture
Il n'est pas inintéressant de noter que la fondation de l'économie de la culture apparaît durant les mêmes années que celles des cultural studies et de bon nombre de disciplines nouvelles, comme les sciences de l'information et de la communication ou les sciences de l'éducation. On peut émettre l'hypothèse qu'un tel développement a été notamment influencé par l'augmentation considérable du nombre des universités dans les années 1960, conduisant les enseignants-chercheurs à développer des stratégies de différenciation en se spécialisant dans de nouveaux domaines. Tel n'est pas vraiment le cas de l'économiste William Baumol, né en 1922, professeur à Princeton à partir de 1949, spécialisé dans l'économie du marché du travail. L'ouvrage Performing arts, the economic dilemma, qu'il publie avec Bowen en 1966, est le résultat d'une enquête financée par le Twentieth Century Fund, et qui constitue la première grande étude par un économiste dans le domaine de la culture. Le secteur du théâtre, de la musique et de l'opéra, qu'il étudie ici, constitue plutôt une illustration remarquable à partir duquel Baumol tente de présenter les spécificités de certains secteurs du marché du travail, notamment ceux liés à la culture, et la « maladie des coûts » qui leur est liée (cf. chapitre 6). Les théories néo-keynésiennes, sur lesquelles s'appuie Baumol, constituent encore à ce moment le courant dominant de l'économie, tandis qu'un système public d'aide à la culture est en train de se mettre en place, tant bien que mal, à la même époque aux États-Unis.
Jusqu'à présent, le monde des arts et de la culture avait été peu abordé par les économistes, à quelques exceptions, comme celle du Français Henri Mercillon. L'ouvrage de Baumol constitue un signal important dans le monde de l'économie, et nombre d'économistes, comme Allan Peacock, Mark Blaug, William Hendon ou David Throsby commencent à s'intéresser au sujet. Les années 1970 voient ainsi la fondation de la première revue dédiée à la thématique, le Journal of cultural economics, et d'une association regroupant les économistes, organisant un congrès bisannuel (aujourd'hui ACEI, Association for cultural economics international). La production autour de ce domaine est suffisamment abondante pour qu'une première revue de la littérature soit publiée en 1994 dans le Journal of Economic Literature. Le nombre d'économistes spécialisés dans le domaine de la culture demeure relativement faible (l'association compte une centaine de membres), mais leur influence n'en demeure pas moins déterminante pour le financement et l'organisation de la culture. La diffusion de la discipline est progressivement assurée, outre les articles, par nombre d'ouvrages et de manuels, la plupart de ces derniers publiés à partir des années 2000. Parmi les plus diffusés, on retiendra deux manuels réellement conçus comme une introduction à l'économie de la culture : celui de Heilbrun et Gray et celui de Towse, ainsi que deux handbooks dont les différents chapitres ont été réalisés par les principaux économistes de la culture, celui de Towse et celui de Ginsburgh et Throsby. En France, les travaux en économie de la culture ont d'abord été empiriques, sous la forme de monographies sectorielles, en particulier à l'initiative d'Augustin Girard qui fut à l'origine du Département des Études, de la Prospective et des Statistiques au sein du ministère de la Culture et participa également à la création en 1983 de l'Association pour le développement et la diffusion de l'économie de la culture (Addec). Mais c'est essentiellement l'ouvrage de Bruno Frey et de Walter Pommerhenne, traduit en français en 1993, ainsi que les contributions de Dominique Leroy et Alain Herscovici, puis le petit manuel de Françoise Benhamou, L'économie de la culture, publié pour la première fois en 1996, qui ont permis de diffuser, auprès du grand public, l'état des recherches des économistes universitaires dans ce domaine. Bien sûr, de nombreux chercheurs, notamment Xavier Greffe, Dominique Sagot-Duvauroux, Joëlle Farchy, Philippe Bouquillon ou Laurent Creton contribuent depuis tout aussi longtemps à la production scientifique dans ce domaine, nous y reviendrons dans les chapitres qui suivent.
Méthodes et sources
En tant que discipline, l'économie des arts et de la culture peut être définie comme l'application des théories et des méthodes des sciences économiques pour expliquer les phénomènes, les comportements, les institutions culturelles. Dans une perspective plus large – économique, mais également historique, sociologique etc. – elle peut être présentée comme l'étude des activités de production, de distribution, de valorisation et de consommation des biens culturels. Dans tous les cas, elle se nourrit de données empiriques. Ces données peuvent être de natures variées : qualitatives ou quantitatives, études de cas, retranscriptions d'entretiens, données statistiques etc. ; elles peuvent servir à décrire, à expliquer, voire à justifier les phénomènes observés.
Les données chiffrées sont utilisées pour étudier des phénomènes très différents : les comportements de consommation et les préférences individuelles, les ventes d'exemplaires d'un livre ou d'un disque, la fréquentation des institutions culturelles, l'emploi dans les activités artistiques, la concentration sur les marchés des biens et services culturels, les dépenses publiques et le mécénat en faveur de ces activités, la part des canaux de distribution pour tel ou tel bien culturel etc. De telles statistiques permettent de mesurer le poids et l'impact économique des activités culturelles dans une économie (nationale, régionale...), de suivre les évolutions des comportements et des activités économiques, d'établir des comparaisons (dans le temps, dans l'espace, entre pays...) et d'évaluer la performance des stratégies des firmes et des politiques publiques dans ce domaine.
Les économistes disposent de deux moyens principaux pour obtenir des données chiffrées : ils peuvent s'approvisionner auprès de producteurs tiers de données ou ils peuvent produire ces données par leurs propres moyens (enquêtes par questionnaire, expérimentations en laboratoire, expérimentations de terrain, collecte de données par l'observation directe des médias et d'internet etc.). Dans le premier cas, trois grands types de producteurs proposent des statistiques :
des organismes publics : en France, il peut s'agir de l'INSEE, des services statistiques des administrations centrales ou locales, des établissements publics du ministère de la Culture (centres nationaux de la Cinématographie, de la Danse etc.), des autorités de régulation (Conseil supérieur de l'audiovisuel, Autorité de la concurrence, Autorité de la régulation des communications électroniques et postales...) ;
des entités privées : les entreprises et les syndicats professionnels (Syndicat national de l'édition, Syndicat national de l'édition phonographique...), les sociétés de gestion collective des droits d'auteur et voisins (Sacem, SACD...), les consultants et les instituts de sondage (Idate, Gfk etc.), les organisations non gouvernementales ;
des institutions internationales comme l'Unesco ou l'Unctad/Cnuced.
Pour autant, dans certains cas, les données recueillies s'avèrent insuffisantes, soit parce qu'il n'existe tout simplement pas de données produites par des tiers ou accessibles au public, soit en raison des méthodes utilisées par certaines institutions contestables ou jugées insuffisantes. Par exemple, les échantillons des enquêtes peuvent être considérés comme non représentatifs d'une population donnée. C'est parfois le cas des données sectorielles produites par les syndicats professionnels lorsqu'ils ne comptabilisent que les chiffres d'affaires de leurs membres et donc minimisent le marché réel ou ne rendent simplement pas compte d'autres stratégies, créneaux etc. d'entreprises non affiliées ou représentées par d'autres syndicats. Parfois, l'évaluation est impossible en raison du secret professionnel : comment quantifier les droits d'auteur dans les domaines du livre et du cinéma où les contrats sont de nature confidentielle et, comme en France, lorsque le régime fiscal ne fait pas de distinction spécifique ? De même, les conditions de réalisation d'une enquête par questionnaire, qu'il soit administré par téléphone, en face à face ou auto-administré sur internet (la personne répond alors seule aux questions) peuvent affecter la qualité des données (effets du mode de recueil). Elles peuvent être ainsi entachées de biais multiples : biais de sélection, de non-réponse, de couverture, déclaratifs etc.
Plus spécifiquement, certaines données s'avèrent imparfaites en raison précisément de leur nature. Par exemple, évaluer l'emploi dans les secteurs culturels apparaît comme problématique, tant est importante la part de bénévolat, de double emploi (avec l'emploi principal dans un secteur non artistique) etc. De même, les catégories analytiques retenues sont parfois en pleine mutation : les pratiques de lecture peuvent-elles encore être mesurées uniquement sur la base du livre à l'heure des blogs de bandes dessinées très appréciées de catégories populaires jugées « philistines » par rapport à une élite intellectuelle dont les pratiques constituent la norme par ces enquêtes ? La délimitation des objets étudiés pose également souvent des problèmes en matière de comparaisons internationales. L'impact des industries culturelles ou créatives sur la croissance et l'emploi ou le poids de la consommation culturelle peuvent évidemment varier d'un pays à l'autre en fonction du nombre d'éléments (activités, biens et services) que ces catégories analytiques regroupent.
Dans ces conditions, les chercheurs sont parfois amenés à produire leurs propres données en conservant ainsi la maîtrise sur les méthodes qu'ils emploient. Les enquêtes par questionnaire constituent une méthode courante en économie de la culture. Lorsqu'il n'existe ni de prix ni d'offre marchande, l'évaluation contingente est une méthode souvent utilisée pour évaluer la demande de certains biens comme l'environnement, les parcs naturels... et les biens et les services culturels non marchands. Les expérimentations en laboratoire ou sur le terrain permettent également de produire des données statistiques en éliminant nombre de biais affectant la qualité des données produites par sondage. Plus récemment, de nouvelles possibilités s'ouvrent avec internet, notamment à travers la collecte manuelle ou automatique des traces laissées volontairement ou non par les producteurs et les utilisateurs de services en ligne : prix, caractéristiques des biens, des organisations etc.
L'exploitation des données statistiques varie selon les objectifs. Elles peuvent simplement servir à décrire quantitativement les faits observés via l'usage d'indicateurs élémentaires comme la moyenne, l'écart-type ou le taux de croissance. Elles permettent également d'établir des faits stylisés et des intuitions motivant l'élaboration de modélisations. Elles sont enfin utilisées pour élaborer des analyses statistiques afin de confronter ou de réfuter des propositions théoriques. L'analyse de données et l'économétrie constituent les méthodes statistiques les plus couramment mobilisées par les économistes. En effet, les phénomènes observés en économie de la culture sont souvent multidimensionnels et il est souvent contestable sur un plan scientifique de les expliquer par la seule corrélation entre une variable explicative et une variable expliquée. D'autres facteurs entrent bien souvent en ligne de compte et peuvent s'avérer plus fondamentaux pour expliquer un comportement, une stratégie etc.
Ainsi, le fait de consommer des jeux vidéo peut certes s'expliquer par l'âge (« être jeune » augmente la probabilité d'une telle pratique). Pour autant, ce facteur n'est pas forcément surdéterminant : la localisation, la profession, l'influence de l'entourage social etc. peuvent tout aussi bien expliquer cette pratique. À la condition de disposer d'un échantillon d'individus suffisamment large, l'analyse de données permet de mettre en évidence très finement des profils de joueurs ou des tendances en matière d'évolution des préférences et des pratiques. Quant à l'économétrie, elle permet de tester simultanément des variables explicatives plausibles (identifiées notamment à travers des revues de littérature) et de déterminer lesquelles influencent significativement, positivement ou négativement, la probabilité d'être consommateur de jeu vidéo. Ou en couplant les deux types d'analyse, d'expliquer l'appartenance d'un individu à l'un des profils identifiés.
. Snow C. P., The Two Cultures and the Scientific Revolution, Cambridge, Cambridge University Press (The Rede Lecture), 1959.
. Becker G. S. (1964), Human Capital: A Theoretical and Empirical Analysis, with Special Reference to Education, Chicago, University of Chicago Press, 1993 (3e éd.).
. D'un point de vue épistémologique, ce qui n'est pas l'objet de notre ouvrage, l'économie n'a pu jusqu'à présent prétendre au même statut que celui des sciences exactes (la possibilité d'une économie expérimentale montrant rapidement ses limites), telles que la physique ou la chimie, notamment pour la quasi-impossibilité de ses modes d'expérimentation. L'utilisation de la modélisation mathématique et du traitement statistique des données lui permet de présenter un régime de scientificité dont les modèles s'apparentent néanmoins à ceux de la science. Voir Latour B., Le métier de chercheur. Regard d'un anthropologue, Paris, INRA, 2001. Pour une introduction décapante, voir Maris B., Antimanuel d'économie, Paris, Bréal, 2 t., 2002 et 2006. Toutefois, la science économique prétend se rapprocher des sciences exactes en mobilisant de manière croissante les expérimentations en laboratoire et sur le terrain (voir les travaux recensés sur <http://www.fieldexperiments.com>).
. Ginsburgh V., Mairesse F., « Dimensions of Dialogue: Art history and the discourse of economics », in Rampley M. (dir.), Art History and Visual Studies in Europe. Transnational Discourses and National Frameworks, 2012, p. 167-184.
. Genereux J., Introduction à l'économie, Paris, Le Seuil, 2001 (3e éd.), p. 9. Soulignons toutefois que cette définition n'est pas acceptée par tous les économistes, en particulier ceux appartenant aux écoles de pensée hétérodoxes (marxiste, institutionnaliste, évolutionniste etc.) en désaccord avec le courant néoclassique.
. Stiglitz J. et al., Principes d'économie moderne, Bruxelles, De Boeck, 2009 (3e éd.), p. 17.
. Kourilsky P., Le temps de l'altruisme, Paris, Odile Jacob, 2009, p. 137.
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. Il faut néanmoins noter que la première école de pensée en économie fut fondée en France autour des travaux de François Quesnay et son fameux Tableau publié en 1758. Cet auteur et ses disciples furent alors qualifiés d'« économistes » (cf. chapitre 3).
. Passet R., Les grandes représentations du monde et de l'économie, Paris, Les liens qui libèrent, 2010.
. Pour une discussion sur l'Homo œconomicus, de Pareto à nos jours : Demeulenaere P., Homo œconomicus, enquête sur la constitution d'un paradigme, Paris, PUF, 2003.
. Le Van-Lemesle L., Le Juste ou le Riche. L'enseignement de l'économie politique 1815-1950, Paris, Comité pour l'histoire économique et financière de la France, 2004.
. Trésor de la langue française informatisé, disponible sur internet : http://atilf.atilf.fr/
. La notion de civilisation est notamment régulièrement utilisée pour soutenir la supériorité des croyances, valeurs et modes de vie associés au monde occidental. Pour une approche critique, voir notamment Latouche S., L'occidentalisation du monde, Paris, La Découverte, 2005 (3e éd.).
. Tylor, 1871, cité par Cuche D., La notion de culture dans les sciences sociales, Paris, La Découverte, 2010 (4e éd.), p. 18.
. Benhamou F., L'économie de la culture, Paris, La Découverte, 2008 (6e éd.).
. Urfalino P., L'invention de la politique culturelle, Paris, Hachette Littératures, 2004.
. Heilbrun J, Gray Ch., The economics of Art and Culture, Cambridge, Cambridge University Press, 2001 (2e ed.) (notre traduction).
. Towse R., A textbook of Cultural Economics, Cambridge, Cambridge University Press, 2010, p. 5 (notre traduction).
. Throsby D., Economics and Culture, Cambridge, Cambridge University Press, 2001 ; Bouquillion P. (dir.), Creative economy. Creative Industries, Des notions à traduire, Saint-Denis, Presses universitaires de Vincennes, 2012.
. Goodwin C., « Art and culture in the History of Economic Thought », in Ginsburgh V., Throsby D., Handbook of the Economics of Art and Culture, Amsterdam, Elsevier, vol. 1, 2006, p. 25-68. Smith s'intéresse notamment aux rémunérations des comédiens.
. Brunet A. G., De l'administration des beaux-arts en France, Paris, Brunet, 1826 et Edwards E., The Fine arts in England; their state and prospects considered relatively to national Education. Part 1 : Administrative Economy of the Fine Arts, Londres, Saunders and Otley, 1840.
. Jevons W. S., Methods of social reforms and other papers, Londres, MacMillan, 1883.
. Adorno T. W., Horkeimer M., (1944) Dialectique de la raison, Paris, Gallimard, 1974 (pour la trad. fr.).
. Charle C., Verger J., Histoire des universités. xiie-xxie siècle, Paris, PUF, 2012.
. Martel F., De la culture en Amérique, Paris, Gallimard, 2006.
. Mercillon H., Cinéma et monopoles. Le cinéma aux États-Unis : étude économique, Paris, Armand Colin, 1953. Voir aussi, du même, « Les musées : institutions à but non lucratif dans l'économie marchande », in Revue d'économie politique, 4, 1977, p. 630-641.
. Throsby D., « The production and consumption of the Arts: a view of cultural economics », Journal of Economic Literature, XXXII, March 1994, p. 1-29.
. Heilbrun J. et Gray Ch., The Economics of Art and Culture – Second Edition, Cambridge, Cambridge University Press, 2001 ; Towse R., A textbook of Cultural Economics, Cambridge, Cambridge University Press, 2010.
. Towse R. (dir.), A Handbook of Cultural Economics, Cheltenham, Edward Elgar, 2003 ; Ginsburgh V., Throsby D. (dir.), Handbook of the Economics of Art and Culture, Amsterdam, Elsevier North-Holland, 2006.
. Martin L., L'enjeu culturel. La réflexion internationale sur les politiques culturelles, Paris, La Documentation française, 2013.
. Pommerehne W. W., Frey B. S., La culture a-t-elle un prix ?, Paris, Plon, 1993 ; Leroy D., Économie des arts du spectacle vivant, Paris, L'Harmattan, 1992 ; Herscovici A., Économie de la culture et de la communication, Paris, l'Harmattan, 1994 ; Benhamou F., L'économie de la culture, Paris, La Découverte, 1996. On doit également noter, à la même époque, l'importance de l'approche communicationnelle sur l'économie de la culture, à travers les travaux de Bernard Miège ; Miège B., Les industries du contenu face à l'ordre informationnel, Grenoble, Presses universitaires de Grenoble, 2000.
. Le Département des études, de la prospective et des statistiques (DEPS) du ministère de la Culture et de la Communication produit ou finance de nombreuses études et analyses économiques et sociologiques. En particulier, cette entité a réalisé cinq enquêtes sur les Pratiques culturelles des Français échelonnées entre 1973 et 2008, 1981, 1989, 1997 et 2008 (www.pratiquesculturelles.culture.gouv.fr).
. Throsby D., « Cultural statistics », in Towse R. (dir.), A Handbook of Cultural Economics, Cheltenham, Edward Elgar, 2011 (2e éd.).
. Les personnes ne sont pas représentatives de la population étudiée. Un biais commun à tout questionnaire est qu'il ne concerne que les personnes acceptant de répondre à des questionnaires... Il s'agit d'un biais d'auto-sélection qui, pour certains phénomènes (opinions politiques, pratiques illégales etc.), peut affecter fortement la qualité des données collectées. On se référera utilement aux ouvrages de la collection 128, chez Armand Colin, dont plusieurs sont consacrés à l'enquête et à ses méthodes.
. Par exemple, interroger des personnes sur leurs pratiques de consommation musicale uniquement par le téléphone fixe élimine de l'échantillon les utilisateurs exclusifs de téléphone portable dont les comportements peuvent être fort différents.
. Arrow K., Solow R., Portney P. R., Leamer E. E., Radner R. et Schuman H., Report of the NOAA panel on contingent valuation, Federal Register 58 (10), 1993, p. 4601-4614 ; Cuccia T., « Contingent valuation », in Towse R. (dir.), A handbook of cultural economics, Cheltenham, Edward Elgar, 2011 (2e éd.).
. Bouroche J. M., Saporta G., L'analyse de données, Paris, PUF, coll. « Que sais-je ? », 2005 (9e éd.).
. Behaghel L., Lire l'économétrie, Paris, La Découverte, coll. « Repères », 2006.
Première Partie
Analyse générale :
la multiplicité des points de vue
De nos jours, l'essentiel de la production en économie de la culture présente une vision constituée essentiellement à partir de l'économie de marché. Certes, l'intervention publique, mis à part quelques économistes directement liés aux courants les plus libéraux, comme William Grampp, est largement acceptée, justifiée et encouragée dans le domaine de la culture. Mais ce sont donc d'abord les méthodes classiques de l'économie qui constituent les principaux outils de l'économie de la culture. Il convient d'insister sur de tels outils, forcément bien connus par le monde de l'économie, mais parfois relativement ésotériques aux yeux des milieux culturels. À commencer par un certain nombre de notions générales déterminantes pour l'économiste, mais qui se heurtent immédiatement à l'appréciation de la culture : la question de la valeur. Comment évaluer un bien culturel ? Comment les critères esthétiques rencontrent-ils (ou non) les critères économiques ? Comment les prix se forment-ils ? Un grand nombre de conséquences en découlent, qui visent notamment des questions liées au marché de l'art, au marché du travail dans le secteur de la culture, à la fixation des prix et aux palmarès dans le cinéma, le secteur de l'édition ou celui de la musique. Ce sont ces différents éléments que nous abordons au sein de la première partie.
Un premier chapitre permettra de mieux cerner la notion de bien culturel à travers les différentes typologies couramment mobilisées par les économistes de la culture. Nous exposons ensuite le point de vue général qui structure notre ouvrage, à savoir la proposition de ne pas penser seulement la culture à partir de deux points de vue – le marché ou les pouvoirs publics –, mais de trois, en y ajoutant la logique du don. Nous passerons ainsi en revue, dans les trois chapitres suivants, les différents types de mécanismes qui, à notre sens, structurent de manière particulièrement forte le champ de la culture. Forcément, la logique de marché, que détaille particulièrement l'économie néoclassique, constitue le mécanisme qui apparemment concentre les antagonismes les plus virulents : machinerie diabolique pour les uns, ordre naturel pour d'autres, il constitue néanmoins le modèle de base à partir duquel les sciences économiques se sont développées. La logique publique, redistributive, constitue pour certains un mal nécessaire (et donc à limiter au maximum), pour d'autres la principale planche de salut de la culture. Faut-il rappeler que c'est cette logique qui, en quelque sorte, constituait également le principe de l'économie planifiée ? Pour tenter de dépasser la querelle stérile d'un monde bipolaire, partagé entre droite et gauche, entre marché et étatisme, dont l'une et l'autre parties s'accusent de tous les maux, nous proposons de rendre sa place à un troisième principe, à notre avis largement sous-évalué de nos jours, qui est la logique du don. Ce point de vue a notamment pour mérite d'insister sur certains mécanismes souvent négligés par l'une ou l'autre des explications classiques, qui nous apparaît particulièrement important au sein du monde de la culture. Cette dernière pourrait-elle d'ailleurs exister sans la logique du don ?
Chapitre 1
Les biens culturels : définition et délimitation
L'économie des arts et de la culture analyse la manière dont sont créés, financés, produits, distribués, valorisés et consommés les « biens culturels ». Comment appréhender la notion de la culture ? Dans un sens très général, s'inscrivant dans une perspective anthropologique, la culture renvoie à un ensemble d'attitudes, de croyances ou de valeurs communes à un groupe social donné, lesquelles permettent non seulement de l'identifier et de le singulariser, mais également de lier ses membres (par exemple, une culture nationale ou religieuse). Dans un sens plus fonctionnel, la culture renvoie aux pratiques sociales et aux modes de production associés aux activités culturelles, en particulier celles qui se présentent comme artistiques et/ou récréatives. Dans ce sens plus restreint, les économistes distinguent implicitement culture populaire, culture de masse et culture « cultivée », cette dernière renvoyant à la notion de culture classique (théâtre, musique classique, Beaux-arts...). La culture se distingue également selon qu'elle soit individuelle ou collective, la première renvoyant à l'idée de « culture générale » d'un individu, mais également à celle de son identité culturelle, laquelle peut être multiple : culture(s) d'origine, pratiques culturelles actuelles...
Cet ouvrage s'intéresse plus particulièrement à un sous-ensemble de la culture délimité par les activités littéraires et artistiques. Celles-ci regroupent la création et la consommation, mais également la production ou l'édition, ainsi que les activités de valorisation (distribution, diffusion, mise à disposition, prescription etc.) nécessaires pour faire rencontrer l'offre de biens littéraires et artistiques et leur demande. Les produits de ces activités sont précisément regroupés sous l'appellation très générale de « bien culturel ». Or, celle-ci regroupe des catégories analytiques souvent bien différentes : un livre imprimé, une pièce de théâtre, la retransmission d'un concert de musique, un tableau, un happening, un film visionné sur un écran d'ordinateur, une chapelle romane...
Certes, l'ensemble de ces produits de l'activité humaine présente des points communs : tous sont issus de processus de production incorporant une part significative de travail artistique et tous représentent potentiellement des valeurs d'usage spécifiques naissant de besoins désintéressés, bien distincts de ceux, plus utilitaires, liés au fait de s'alimenter, se protéger, se déplacer ou se distraire. Néanmoins, tous renvoient à des biens très hétérogènes tant dans leur substance que dans leurs modes de production et de valorisation. Comment dès lors donner sens à une telle appellation pour la rendre opérationnelle sur un plan théorique et empirique ?
Les biens et les services en économie
Différentes classifications et typologies sont utilisées en économie pour catégoriser les biens et les services. Elles reposent sur l'utilisation d'une ou plusieurs variables discriminantes pour obtenir des catégories analytiques communes aux travaux en économie et donc pour rendre possibles la comparaison et la réfutabilité des résultats obtenus par les chercheurs.
La nature des besoins à satisfaire
Une première typologie assez classique des biens et des services est basée sur leur valeur d'usage, soit l'importance des besoins qu'ils satisfont. Si l'on considère par exemple les besoins physiologiques, l'eau et l'alimentation se situent à un extrême (besoins primaires, essentiels à la vie biologique), l'habillement et le logement à un niveau intermédiaire (besoins secondaires) et les biens culturels et de loisirs à l'autre extrême (besoins tertiaires). Pour autant, cette classification pourrait tout aussi bien être établie en référence aux besoins de la vie sociale et aboutir de cette façon, dans une approche à la Rousseau, à un renversement de cette hiérarchie : le lien social nourri par la culture n'apparaît-il pas comme une condition sine qua non de l'activité de production de biens plus utilitaires ?
Cette première classification est implicite dans la manière de mesurer et d'interpréter les variations de la demande de biens culturels par rapport à d'autres variables : le revenu des ménages, les prix des biens etc. L'élasticité est l'indicateur statistique habituellement utilisé pour mesurer la sensibilité des quantités demandées d'un bien à d'autres variables susceptibles de l'influencer comme les prix, la qualité des biens et le revenu des individus (cf. chapitre 3). Elle permet notamment de qualifier les comportements de consommateurs qui, dans certains cas (démonstration sociale, snobisme...), peuvent augmenter sensiblement leur demande pour un bien culturel lorsque son prix augmente !
Matérialité, rivalité et excluabilité
Les biens peuvent être catégorisés à partir de leurs caractéristiques intrinsèques, en particulier leur degré de matérialité. Selon Peter Hill, deux caractéristiques objectives permettent de distinguer les biens matériels, les biens immatériels et les services : leurs coordonnées géographiques (latitude et longitude) et leurs dimensions physiques (longueur, hauteur, profondeur). Ainsi, à l'inverse d'un bien immatériel, un bien matériel possède des dimensions physiques et des coordonnées spatiales, tandis qu'un service sera caractérisé uniquement par sa localisation géographique. Pour illustrer cette distinction, un DVD a une localisation précise et des dimensions physiques : c'est un bien matériel. La représentation d'une pièce de théâtre a bien une localisation géographique, en revanche, il semble difficile de pouvoir la caractériser par des dimensions matérielles : c'est un service. Enfin, une œuvre cinématographique ou un poème n'ont ni localisation géographique précise, ni dimensions physiques : il s'agit de biens immatériels.
Notons également que pour Hill, une des caractéristiques essentielles d'un bien économique est qu'il représente une entité sur laquelle des droits de propriété sont établis et échangés, et à partir de laquelle son propriétaire retire des bénéfices économiques. De ce point de vue, malgré leur immatérialité, les œuvres s'avèrent des biens : il s'agit d'entités qui procurent une valeur positive à leur possesseur (symbolique, à partir de la conception du monde que l'œuvre peut proposer ; utilitaire à travers le plaisir de la posséder, de la faire admirer ; financière lorsque l'œuvre est durable et susceptible d'être l'objet de spéculations) et sur lesquelles sont établis des droits d'auteur pouvant donner lieu à des transactions.
Une autre typologie des biens, basée également en partie sur le critère d'immatérialité et très utilisée en économie de la culture, est la partition biens privés/biens collectifs/biens clubs/biens communs. Elle est établie via le croisement de deux critères : la rivalité en usage et la difficulté d'exclusion des utilisateurs de la ressource.
La rivalité en usage signifie que la consommation d'un bien ou d'un service par un individu en réduit la quantité disponible pour les autres : la pomme qu'achète et mange Jacques n'est plus disponible pour Bernadette, ce qui les place donc en situation de concurrence. En revanche, il existe des biens « non rivaux » : l'écoute d'une émission à la radio par un auditeur, la visite d'un musée ou l'utilisation de la signalisation routière par un automobiliste ne réduisent pas la quantité (ni la qualité) disponible pour les autres usagers de ces services. La quantité produite du service est la même pour chacun.
La difficulté d'exclusion des utilisateurs d'un bien ou d'un service renvoie à la situation dans laquelle il est techniquement coûteux d'empêcher leur accès à ceux qui n'auraient pas ou ne voudraient pas contribuer au financement du bien ou plus généralement, d'en réserver l'accès et l'utilisation à ceux qui accepteraient les conditions d'utilisation du bien ou du service (par exemple, payer un prix pour pouvoir en bénéficier, être exposé à de la publicité, ne pas le revendre à ou le partager avec des tiers). Cette « excluabilité » varie selon les produits : il est quasiment impossible d'empêcher les piétons de bénéficier de l'éclairage urbain (quand bien même ils n'acquitteraient pas la totalité de leurs impôts...), mais il est possible, bien que coûteux, d'exclure les consommateurs qui souhaiteraient acquérir ou utiliser une voiture sans payer de contreparties. Les techniques d'exclusion sont alors très variées : la serrure d'une voiture, l'embauche d'un gardien, le guichet à l'entrée d'une salle de cinéma, les logiciels anti-copiage, le recours à la loi (police, justice, prison...). Les droits d'auteur sur une œuvre (un roman) visent à empêcher (« exclure ») les contrefacteurs qui ne contribuent pas au financement des biens culturels qui en sont issus (un livre, une adaptation cinématographique).
Le croisement de ces deux critères fait apparaître quatre catégories de biens et de services :
– les biens privés (rivalité en usage et coût d'exclusion économiquement supportable) : l'alimentation, des vêtements etc. ;
– les biens collectifs (non-rivalité et difficulté d'exclusion relativement forte) : la défense nationale, une émission radiodiffusée sans cryptage etc. ;
– les biens clubs (non-rivalité et difficulté d'exclusion relativement faible) : une piscine ;
– les biens communs (rivalité et difficulté d'exclusion relativement forte) : une ressource naturelle. | |
Rivalité en usage
---|---|---
| | oui | non
Difficulté d'exclusion | Faible | Biens privés | Biens communs
forte | Biens clubs | Biens collectifs
Chacune de ces catégories renvoie à des problèmes économiques et sociaux spécifiques, notamment liés à des défaillances de marché (cf. chapitre 3). En particulier, les biens collectifs posent la question du financement de leur production : comment procéder sachant que les non-payeurs ou les non-contributeurs auront accès au bien, qu'ils participent à son financement ou non ? Les comportements contributifs (le don) sont alors essentiels pour l'existence de certains services collectifs (un forum de conseils en ligne par exemple). Quant aux biens communs, ils renvoient à la fameuse tragédie éponyme identifiée par Garrett Hardin en 1968 : comment préserver une ressource naturelle renouvelable si chacun peut y avoir accès et l'utiliser librement sans supporter les coûts de son renouvellement et donc au risque de la surexploiter et de la dégrader et l'épuiser ? Et quid des ressources non renouvelables ?
Envisagée sous cet angle, en tant que bien collectif pur et bien immatériel, une œuvre artistique apparaît comme un cas d'externalités inépuisables (undepletable externalities) que Baumol et Oates distinguent des externalités non renouvelables, à l'instar les ressources naturelles partagées (common-pool resources). Pour autant, dans le cas des industries culturelles, le partage illégal de copies numériques, par exemple, s'il ne porte pas atteinte au « stock » existant des œuvres, peut générer une forme de tragédie intertemporelle des biens communs, en diminuant potentiellement les sources de financements des œuvres futures, donc en menaçant leur existence et leur diversité. Cet argument est communément mobilisé contre le partage illégal de fichiers protégés par le droit d'auteur (cf. chapitres 10 et 12).
L'incertitude sur la qualité des biens
Une typologie traditionnellement utilisée en économie se fonde sur la capacité des individus à connaître les caractéristiques des produits. C'est un problème assez courant auquel sont confrontés les individus ou les organisations lorsqu'il s'agit de prendre des décisions dans une situation d'incertitude radicale.
Un bien ou un service peut être représenté comme un ensemble de caractéristiques. Par exemple, une voiture est un vecteur d'attributs : cylindrée, marque, couleur, nombre de places etc. Chaque voiture se présente alors comme un vecteur distinct des autres. Or, ces caractéristiques se répartissent en trois grandes catégories :
– les caractéristiques de recherche, qui peuvent être connues avant l'achat ou l'utilisation du produit ;
– les caractéristiques d'expérience, qui ne peuvent être connues qu'après l'achat et l'utilisation du produit ;
– les caractéristiques de croyance (ou de confiance), qui elles ne peuvent être connues ni avant, ni immédiatement après.
Le consommateur ne connaît pas forcément tous les services que peut rendre un bien. Pour George J. Stigler, la recherche de l'information peut nécessiter du temps et un apprentissage (search costs). L'information existe, mais le fait de la collecter constitue une activité coûteuse. Cela peut expliquer, par exemple, l'existence de prix multiples pour un même produit sur des marchés pourtant concurrentiels et donc devant conduire à la formation d'un prix unique. Cependant, en raison des coûts de collecte et de traitement de l'information, les consommateurs ne peuvent connaître tous les prix pratiqués par les vendeurs, ce qui peut expliquer le maintien d'une certaine dispersion des prix.
Et même une fois ces informations sur les caractéristiques de l'œuvre collectées, il demeure souvent impossible pour le consommateur d'en déduire la valeur du bien. Selon George Akerlof, l'asymétrie d'information conduit le consommateur à utiliser la qualité moyenne comme indicateur pour calculer sa disposition maximale à payer. Or, si celle-ci s'avère inférieure au prix des biens de bonne qualité, les producteurs de biens de bonne qualité retirent ces derniers du marché, ce qui abaisse la qualité moyenne... il ne subsisterait donc à terme que des produits de mauvaise qualité sur le marché. Le fait que l'asymétrie d'information conduise le consommateur à utiliser la qualité moyenne comme indicateur de qualité rend de ce fait l'échange impossible. Ce processus de « sélection adverse » explique que les agents victimes de l'asymétrie informationnelle refusent d'engager la transaction en raison précisément de l'incertitude dans laquelle ils se trouvent et que, sur un marché sans intermédiaire, les vendeurs de produits de bonne qualité et les acheteurs ont besoin d'un signal de qualité. Celui-ci peut être apporté soit par le marché (garanties apportées par le vendeur, tout dépend de la croyance ou de la crédulité... de l'acheteur), soit par une institution (certification légale du produit comme le contrôle technique obligatoire des voitures, prix littéraires).
Comment distinguer les biens culturels ?
Bien souvent, les économistes de la culture définissent et distinguent les biens culturels à travers la part prépondérante du travail artistique dans leur processus de production. En d'autres termes, la créativité humaine représente un facteur de production essentiel pour l'élaboration de ces biens. Ce critère semble évident et commun à tous les biens culturels, jusqu'au ready-made Fontaine (1917) et à la performance Shoot (1971).
Cette approche s'avère cependant insuffisante pour délimiter les biens culturels dans le domaine des arts. De fait, d'autres domaines non reconnus ou légitimés socialement comme artistiques incorporent une part prépondérante de travail artistique, comme la publicité, le design, la décoration d'intérieur, l'« artisanat d'art » ou le jouet. Comment tracer dès lors la frontière et distinguer clairement les biens culturels des autres biens économiques ? Une solution consiste à reprendre les différentes caractéristiques et typologies évoquées précédemment. À l'analyse, le bien culturel ne se détermine pas à partir de sa valeur d'usage, mais il apparaît comme un bien d'expérience et de croyance, essentiellement non-rival et source d'externalités positives. Autant de notions sur lesquelles il convient de s'arrêter un instant.
La valeur d'usage
La nature non utilitaire des biens culturels artistiques permet de les différencier plus nettement des autres biens et services. Si l'on se place dans une perspective kantienne, les biens artistiques donnent lieu à un plaisir esthétique désintéressé, contrairement au plaisir visant l'agréable, donc le désir et l'intérêt. Un trait commun aux biens culturels dans le domaine des arts est qu'ils contiennent ou donnent naissance à des formes de valeur qui ne sont pas totalement exprimables et donc évaluables en termes monétaires.
Vecteurs de messages symboliques pour ceux qui en bénéficient, ces biens représentent plus que des produits utilitaires en remplissant en plus des finalités communicationnelles. En d'autres termes, leur valeur symbolique l'emporte dans tous les cas sur leur valeur utilitaire (embellissement, démonstration sociale, réserve de valeur). Ainsi un aspirateur au design original (forme, couleur...) demeure un bien dont la valeur dépend à la base de sa capacité à aspirer la poussière, même s'il peut embellir un placard...
Pour autant, dans quelle mesure un objet reproductible industriellement, jetable, utilitaire, mais dont le design est signé Philippe Starck ou Jony Ive ne constituerait-il pas un bien artistique ? On rejoint ici en partie la démarche de Marcel Duchamp lorsqu'il « déplace » un urinoir de l'espace des biens utilitaires à celui des arts : les caractéristiques utilitaires s'estompent grâce à la médiation de cet artiste générant de nouvelles caractéristiques esthétiques et discursives à l'objet.
Des biens d'expérience et de croyance
Plus généralement, la valeur d'une œuvre n'a pas d'existence en soi, mais dépend de son interprétation, de son acceptation ou de sa légitimation sociale. Les biens culturels sont typiquement des biens d'expérience : il est difficile pour quiconque n'ayant pas eu accès à une œuvre de savoir à l'avance s'il va en tirer du plaisir, émettre un jugement, prendre part à une discussion avec ceux qui l'ont déjà consommée. On ne peut donc pas connaître la valeur des œuvres artistiques et donc celle des biens culturels qui en sont tirés avant de les avoir vus, écoutés, lus...
Pour faire un choix dans cette situation d'incertitude radicale, le consommateur a besoin de méta-informations (informations produites autour des biens, sur les caractéristiques des œuvres), de conseils, d'avis fiables de la part de sources et de prescripteurs très diversifiés : critiques, marketing de masse, bouche-à-oreille, présence de stars ou d'artistes déjà connus, etc. Les conventions de qualité et le rôle des prescripteurs, des instances de légitimation jouent un rôle fondamental tant au niveau du statut social des arts qu'à celui individuel des œuvres.
De là découle une incertitude sur la valorisation de ce type de biens (le fameux « nobody knows » de Richard Caves) : il est impossible de connaître à l'avance les chances de succès d'une œuvre, les mécanismes par lesquels elle va être valorisée et connue du plus grand nombre. Les méta-informations et le rôle des prescripteurs deviennent donc essentiels pour stimuler l'acte d'achat ou l'utilisation d'un bien culturel. D'où la variété des stratégies mises en œuvre par les producteurs et les distributeurs des biens culturels pour anticiper et orienter la demande.
Par ailleurs, les biens culturels sont des biens de croyance. Certaines caractéristiques ne se dévoilent ni avant, ni immédiatement après le visionnage d'un film, la lecture d'un livre, l'écoute d'une musique etc. Les conventions de qualité évoluent, l'évaluation par la critique peut connaître des revirements. La valeur esthétique change et la qualité d'une œuvre peut se dévoiler bien après, révélant alors à l'individu certaines facettes nouvelles, certains plaisirs esthétiques pouvant renverser le jugement émis initialement. Un film d'Éric Rohmer ou un roman de Frédéric Dard peuvent irriter de prime abord, mais plaire quelques années plus tard, la critique aidant, la légitimation s'imposant, l'expérience de l'individu s'étoffant et faisant évoluer ses goûts et préférences...
Non-rivalité et difficulté d'exclusion variables
Une œuvre d'art se présente comme un bien immatériel par essence : une œuvre filmique, musicale ou littéraire ne peut ni être localisée, ni posséder de dimensions physiques : contrairement à une bouteille de vin, Colloque sentimental n'a ni hauteur, ni largeur, ni profondeur physiques, encore moins de coordonnées spatiales précises. Mais ce poème peut prendre une forme matérielle s'il est inclus dans un recueil édité et imprimé, à savoir un bien culturel doté de dimensions physiques et de coordonnées spatiales. Il peut également se transformer en service s'il donne lieu à une lecture publique dans un endroit précis (sur un quai du métro parisien ou au bord d'une rivière). Son support peut en outre être à son tour « dématérialisé » sous la forme d'un fichier numérique : sa concrétisation change fondamentalement de nature en n'étant plus dépendante d'un type de support donné.
Ces différences substantielles ont des incidences du point de vue des critères de rivalité et d'« excluabilité ». À l'instar d'une connaissance fondamentale, une fois qu'elle est connue du public, une œuvre artistique s'avère un bien collectif pur. Une séance de cinéma, une exposition et un concert représentent des services à effet club : le public bénéficie de la même prestation (non-rivalité), mais doit payer pour y accéder. Un livre, un film sur DVD ou un album de musique sur CD représentent des biens privés soumis au principe de rivalité (le fait de revendre ou de prêter un vieux 33-tours prive son possesseur initial de son bénéfice) et dont l'exclusion est relativement peu coûteuse. La même œuvre fixée sur un « support » numérique (un fichier) devient un bien immatériel, c'est-à-dire non-rival et dont la difficulté d'exclusion augmente avec la possibilité d'une circulation sur des réseaux numériques, des stockages hors-ligne etc.
D'une manière générale, la capacité à exclure les non-payeurs et, plus généralement, ceux qui n'acceptent pas les conditions d'utilisation dépend de la nature du « support » de fixation et de valorisation des œuvres. Il est plus difficile d'exclure les non-payeurs d'une représentation lorsqu'elle a lieu en plein air, sur une place publique, que produite dans un lieu fermé (une salle de concert, de cinéma, un gymnase...). Il en est de même pour les œuvres reproduites sur des exemplaires physiques (CD, DVD...) ou diffusées à travers des réseaux numériques sécurisés par rapport aux œuvres reproduites et distribuées sous la forme de fichiers numériques. La banalisation des technologies de reproduction au cours de l'histoire et davantage encore la numérisation et internet ont augmenté le coût des mécanismes d'exclusion technique et légale en facilitant la circulation des contenus et en rendant plus difficiles la détection ou l'exclusion (vulnérabilité des logiciels de lutte contre la copie).
Sources d'externalités positives
Les agents économiques, individus, entreprises, associations etc. vivent bien souvent dans les mêmes environnements : naturel, informationnel, sonore, cognitif etc. Des interdépendances en découlent : le comportement ou l'abstention économique des uns peuvent affecter le bien-être des individus ou les objectifs des organisations (le profit pour les entreprises). On parle alors d'externalités, car ces effets externes bénéficient (externalités positives) ou créent un préjudice (externalités négatives) à leurs récepteurs sans qu'il n'y ait de compensation et de prise en compte de ces effets par le marché.
L'exemple le plus simple d'externalité négative est la pollution. L'activité du pollueur représente un coût social supérieur à son coût privé, car elle génère également des coûts « externes » que subissent d'autres agents (et en particulier les générations futures qui voient les ressources naturelles se réduire et se dégrader). Tout l'enjeu de la régulation environnementale vise alors à minimiser ces coûts, par exemple en les faisant prendre en compte par le pollueur (qui les « internalise ») par des normes réglementaires ou une redevance.
Les biens culturels sont source d'externalités positives. Cette notion fut inventée par Alfred Marshall pour montrer comment certains facteurs extérieurs aux mécanismes du marché pouvaient influencer positivement ou négativement les fonctions de bénéfices ou de coûts des entreprises : l'éducation, la santé, la connaissance ou la culture sont ainsi de bons exemples d'externalités exerçant un rôle positif sur l'environnement social et économique dans lequel opèrent les agents économiques. En effet, les entreprises bénéficient pleinement d'une main-d'œuvre bien éduquée et en bonne santé sans payer directement pour cela.
Dans une perspective différente, autour des travaux de Tibor Scitovsky, la culture peut améliorer les capacités des individus à percevoir finement le degré de nouveauté associé à une expérience de consommation, qui peut s'avérer source de bien-être. L'offre de culture générale se présente ainsi comme une source d'externalité positive en fournissant la partie des connaissances d'un individu qui produit la redondance nécessaire à rendre la source de divertissement agréable. À la manière de la productivité dans le domaine de l'offre, Scitovsky parle de « consuptivité » : les effets d'apprentissage permettent d'améliorer l'utilité, le plaisir retiré de la consommation d'un bien au cours du temps.
Les externalités positives constituent plus généralement un argument majeur en faveur de l'intervention publique dans le financement de l'art et de ses supports de valorisation (musée, festivals...). En effet, faute de solutions marchandes pour l'appropriation de ce type d'effets positifs, le marché est généralement supposé défaillant pour financer et produire un niveau optimal d'activités artistiques. Un festival régional peut ainsi apparaître comme un levier majeur pour l'image d'une ville ou d'une région, la vie culturelle de ses habitants, le dynamisme de son tissu d'entreprises... sans pour autant réunir suffisamment de financements de la part des individus (dons) ou des entreprises. Le financement par les collectivités territoriales est alors essentiel pour la survie de ces manifestations culturelles.
Unicité et reproductibilité
Une œuvre artistique se présente donc comme un bien immatériel et le qualificatif « artistique » renvoie à une dimension symbolique très forte pour ces biens, qui domine très largement leur nature utilitaire. Les biens culturels renvoient à la fois à la « matérialisation » des œuvres d'art et aux formes de valorisation inhérentes. Chacun de ces niveaux renvoie à des problèmes théoriques et méthodologiques différents, et notamment pour ce qui concerne leur reproductibilité mécanique, thème largement analysé en esthétique, mais tout aussi important en économie.
Envisageons quelques exemples. Dans le domaine du spectacle vivant, une œuvre dramatique ou chorégraphique peut donner lieu à des représentations (des spectacles, leur télédiffusion) et à des reproductions (un enregistrement édité sur DVD ou à travers un fichier numérique téléchargeable sur internet).
Dans la littérature, le livre apparaît historiquement comme un support physique sur lequel est éditée une œuvre littéraire. Plus récemment, cette matérialisation a également pris la forme de fichiers, séries de 0 et de 1, qui nécessitent l'utilisation de biens complémentaires : un logiciel de lecture associé à un ordinateur, une tablette ou une liseuse. L'idée de « dématérialisation » renvoie ici plutôt à la déconnexion entre le fichier support de l'œuvre et l'appareil où ce fichier est stocké, reproduit, exécuté. À cet égard, le terme de « dématérialisation des supports » habituellement utilisé pour qualifier la numérisation des contenus nous semble erroné et trompeur. En effet, qu'un morceau de musique soit édité et enregistré sur un CD ou sur un disque dur, l'endroit où l'œuvre se matérialise reste bel et bien un support physique. La « dématérialisation des supports » renvoie davantage à l'idée d'accroissement à la fois (1) de la dé-spécialisation des supports d'enregistrement des œuvres (un support n'est plus associé strictement à un type de bien culturel) et (2) de la reproductibilité des supports (le temps et les manipulations nécessaires à cette fonction sont réduits). Le terme de liquidité semble a priori plus adéquat pour rendre compte de cette situation.
Dans le cinéma, la « matérialisation » de l'œuvre a pris historiquement la forme d'un service : la projection cinématographique. Il s'agit d'un « dispositif » spécifique associant une salle, un projecteur, un écran et une pellicule sur laquelle l'œuvre éditée est reproduite. Cette matérialisation s'est progressivement diversifiée avec l'édition et la reproduction sur cassette, puis sur DVD, et plus récemment, avec la projection numérique et l'utilisation des DCP (Digital Cinema Package) se substituant progressivement à la pellicule argentique dans les salles obscures.
Les biens culturels artistiques sont de nature très diversifiée : peintures, sculpture, livres, films etc. Schultze distingue deux catégories selon que le support originel où se matérialise l'œuvre s'avère reproductible ou non : les biens culturels uniques et reproductibles.
Les biens culturels uniques regroupent des biens comme les peintures originales ou les sculptures. Les supports de ces biens sont en général durables : ils ne se détruisent pas à la consommation. Contempler une peinture, un retable ou une sculpture ne les use pas a priori. L'unicité et la durabilité en font donc potentiellement des réserves de valeur à l'instar d'un placement financier. Cela a pour conséquence une prépondérance du marché secondaire où s'organise la revente de biens culturels (via des intermédiaires) par rapport au marché primaire (cf. chapitre 8). Cela s'explique également par l'imparfaite substituabilité entre les œuvres d'art nouvelles et anciennes. La réputation d'artistes et le système de côtes sont en effet des mécanismes permettant de pallier les défaillances causées par la caractéristique de biens d'expérience des œuvres artistiques : comme elles sont nouvelles, on ne peut par définition en connaître la valeur à l'avance et il serait donc risqué d'investir dans leur acquisition.
Les biens culturels reproductibles renvoient aux livres, à la musique enregistrée ou aux films. Ces biens sont produits en deux étapes : la phase de création durant laquelle l'artiste crée l'original ou premier exemplaire (le manuscrit, le master d'un album de musique ou d'un film) et la phase de reproduction durant laquelle l'exemplaire original est produit/édité, puis répliqué industriellement, parfois sur différents supports, pour être valorisé sur un ou plusieurs marchés. Chaque œuvre originale est différenciée, tandis que chaque exemplaire tiré ou reproduit à partir de cet original (la « copie première ») est strictement identique à tout autre exemplaire de la même œuvre pour chaque mode d'exploitation.
D'un point de vue économique, la reproductibilité des biens culturels est caractérisée par des rendements croissants d'échelle : les coûts fixes de production sont nettement plus élevés que les coûts variables de reproduction. Dès lors, il peut être plus intéressant de tirer 100 000 exemplaires au lieu de 100 d'un bien culturel dont le coût de production serait de 100 000 euros : dans le premier cas, si l'on considère le coût de reproduction comme négligeable, le coût unitaire est de 1 euro, dans le second cas, il est mille fois plus élevé ! Le même raisonnement peut être tenu pour l'activité de promotion ou pour l'utilisation du réseau de distribution. Par ailleurs, les marchés sur lesquels sont valorisées les œuvres ou plutôt les exemplaires qui en sont tirés sont principalement des marchés « primaires », reliant via une chaîne d'intermédiation les producteurs aux consommateurs de biens culturels. Les marchés secondaires (entre utilisateurs de second rang comme les bibliothèques et entre consommateurs via le marché de l'occasion) sont en général nettement moins développés. Toutefois, la numérisation des copies pose d'ores et déjà un certain nombre de problèmes de concurrence entre marchés primaire et secondaire (cf. prêt de livres numériques dans les bibliothèques, dépôt d'un brevet par le géant du numérique Amazon sur le marché de l'occasion des fichiers numériques).
Aussi séduisante soit-elle, cette distinction rencontre certaines limites. Quid des services culturels comme le spectacle vivant qui n'entrent dans aucune des deux cases ? Tantôt uniques (un happening, une représentation unique), tantôt reproductibles à l'instar des séances de cinéma, tantôt répétables (et non « réplicables »), les représentations théâtrales, les spectacles de danse ou les concerts de musique étant alors marquées par des variations plus ou moins sensibles selon la prestation présente des acteurs ou des interprètes, la réaction du public, le lieu, le choix parfois diffèrent des interprétations d'un concert à l'autre lors d'une même tournée musicale etc.
À l'opposé, qu'en est-il du marché des « chromos » comme ceux que l'on retrouve sur la place du Tertre à Montmartre, caractérisé par une offre abondante de peintures de bonne qualité, mais dont les thèmes sont standardisés, stéréotypés, voire reproduits à une échelle massive ?
Enfin, les frontières entre ces deux catégories sont parfois poreuses. Dans quelle catégorie classer des biens culturels comme les sérigraphies ou les photographies non numérotées, donc difficiles à singulariser à moins de marques particulières héritées au cours de leur histoire ? Moins problématique est sans doute le cas des « ersatz » dans un sens proche de la réflexion de Walter Benjamin sur la perte d'aura liée à la reproductibilité, par exemple les reproductions photographiques d'œuvres plastiques ou graphiques (dans des livres d'art, des catalogues d'exposition ou sur des sites de musées virtuels) ou les performances filmées et diffusées à la télévision alors qu'il ne s'agit que d'un mode de valorisation secondaire, d'un dispositif pour lequel l'œuvre n'a pas été conçue.
À la recherche d'une définition...
Les arts ne se laissent que très difficilement enfermer dans des catégories analytiques données, ce qui rend bien délicate la définition des biens culturels. L'ensemble des caractéristiques et des typologies examinées jusqu'à présent permet néanmoins de mieux saisir la spécificité de ces biens et services dans leur dimension économique. Pour David Throsby, ce sont huit caractéristiques au total qui distingueraient les biens culturels artistiques par rapport aux autres biens et services. D'autres propriétés peuvent être toutefois ajoutées, telles que la différenciation et le renouvellement constant des biens culturels, des modes de rémunération et des contrats de travail plus diversifiés que dans d'autres secteurs industriels. Pour autant, si ces traits discriminants permettent de mieux cerner cette catégorie de biens et services, il s'agit au mieux d'une check-list, comme l'indique David Throsby, qui permet de circonscrire le champ d'analyse de l'économie de la culture et des arts. Toutes ces caractéristiques ne sont pas forcément présentes dans tous les biens culturels, de même qu'aucun sous-ensemble ne constitue une condition suffisante pour définir un bien culturel. Au fond, ces biens demeurent hétérogènes à de nombreux égards, même si, pour ce qui nous intéresse ici, ils ont tous une essence commune : la valorisation des œuvres artistiques dont il est difficile à la fois d'esquisser l'essence, à moins d'approfondir des réflexions relevant davantage des théories esthétiques qui dépassent le cadre de cet ouvrage, et de délimiter précisément le champ, car celui-ci est conventionnel et contingent selon les périodes, les sociétés, les groupes sociaux, les institutions... et les individus eux-mêmes.
. Hill P., « Tangibles, Intangibles and Services: A New Taxonomy for the Classification of Output », CSLS Conference on Service Sector Productivity and the Productivity Paradox, Ottawa, 11 et 12 avril 1997.
. Hardin G., « The Tragedy of the Commons », Science, vol. 162, no 3859, 13 déc. 1968, p. 1243-8.
. Baumol W. J., Oates W. E., The Theory of Environmental Policy, New York, Prentice Hall, 1975.
. Nelson P., « Information and Consumer Behavior », Journal of Political Economy, vol. 78, 1970, p. 311-329 ; Darby M., Karni E., « Free Competition and The Optimal Amount of Fraud », Journal of Law and Economics, vol. 16, 1973, p. 67-88.
. Stigler, G. J. « The Economics of Information », Journal of Political Economy, 69(3), 1961, p. 213-25.
. Akerlof G., « The market for lemons: quality uncertainty and the market mechanism », Quarterly Journal of Economics, 84 (3), 1970, p. 488-500.
. Towse R., 2011, op. cit.
. Les gestes esthétiques de Marcel Duchamp (« Richard Mutt ») et de Chris Burden constituent l'essentiel de la valeur de ces deux œuvres. Ici, à la différence de la théorie de la valeur travail qui explique la valeur d'une marchandise par la quantité de travail nécessaire pour la produire ou sa difficulté de production, c'est la qualité du travail (artistique) qui semble déterminer la valeur du bien.
. Moulin R., L'artiste, l'institution et le marché, Paris, Flammarion, coll. « Champs Arts », 1997 (2e éd.).
. Caves R., Creative Industries. Contracts between art and commerce, Cambridge, Harvard University Press, 2000.
. Adelstein R. P., Peretz S. I., « The competition of technologies in markets for ideas: copyright and fair use in evolutionary perspective », International Review of Law and Economics, no 5, (1985) p. 217-218.
. Marshall A., Principles of Economics, Londres, MacMillan, 1890.
. Scitovsky T., The joyless economy – An inquiry into human satisfaction and consumer dissatisfaction, Oxford, Oxford University Press, 1976.
. Benjamin W., L'œuvre d'art à l'époque de sa reproductibilité technique [1939], Paris, Allia, 2006.
. En nous inspirant du cadre analytique de l'école de pensée autrichienne (Carl Menger, Eugen von Böhm-Bawerk, Friedrich von Wieser), on pourrait ainsi distinguer des biens d'ordres différents : la télédiffusion d'un film sera un bien d'ordre 1 (ici un service), le film en question, édité sur une bande, un bien d'ordre 2 (ici un bien matériel) et l'œuvre filmique, un bien d'ordre 3 (en l'occurrence, un bien immatériel).
. Schulze G. G., « International trade », in Towse R., op. cit., (2011), p. 236-244.
. Un original, en sculpture – et notamment pour les bronzes – peut être constitué par le tirage d'un certain nombre de copies (sept à douze en général), mais ce tirage, limité, diffère largement de la reproduction en série.
. Il existe certes des contextes ou des pratiques qui accélèrent leur usure et peuvent en détériorer la qualité : la photographie en constitue un, l'exposition de certaines œuvres (aquarelles) à la lumière en constitue un autre.
. La qualification de « bien » est excessive s'agissant du cinéma en salle. Ce dispositif est davantage un service culturel, la projection, produit par l'utilisation conjointe d'une salle (obscure), d'un projecteur et de copies.
. Moulin R., op. cit.
. Throsby D., « Introduction and Overview », in Ginsburgh V., Throsby D., Handbook of the Economics of Art and Culture, Amsterdam, Elsevier, vol. 1, 2006, p. 7. David Throsby ajoute trois caractéristiques à celles déjà énoncées dans ce chapitre : la nature addictive de la consommation culturelle ; le fait que tout bien culturel contient, au moins potentiellement, des éléments protégeables par la propriété intellectuelle ; et l'impossibilité d'estimer systématiquement sur une base monétaire toutes les formes de valeur générée par les biens culturels.
. Zallo R., Economia de la communicacion y de la cultura, Madrid, Akal, 1988.
. Pour une analyse détaillée en sciences de la communication, voir Tremblay G., « Industries culturelles, économie créative et société de l'information », Global Media Journal, vol. 1, no 1, 2008, p. 65-88.
. Le lecteur intéressé pourra toutefois approfondir ce point en consultant l'ouvrage de Hutter et Throsby qui confronte l'histoire de la pensée économique à celle de la philosophie de l'art. Hutter M., Throsby D., Beyond Price. Value in Culture, Economics and the Arts, Cambridge, Cambridge University Press, 2008.
Chapitre 2
Un système hybride
Nous partons d'un point de vue particulier, qui nous apparaît très important dans le secteur de la culture – et à notre sens dans l'ensemble de l'économie –, mais demeure largement sous-évalué dans les présentations générales, en introduisant la logique du don. Généralement, en effet, ce sont essentiellement deux systèmes qui sont présentés (comme partiellement antinomiques, par ailleurs) : les règles du marché et celles des pouvoirs publics. L'histoire de l'économie actuelle est essentiellement présentée à partir de ces deux angles, par le biais du développement ou de la diminution de l'influence publique (de l'État) dans la logique de marché, présentée comme l'ordre naturel des échanges en société.
La volonté d'introduire un troisième principe, fondé sur le don, nous a d'abord été dictée par l'examen pratique du champ de la culture, essentiellement à partir des activités historiques de celui-ci : Beaux-arts, arts de la scène, patrimoine. Il importe, afin de rendre compte des principes d'échanges au sein du secteur, d'évoquer cette logique omniprésente dans la plupart des petites organisations. Le terme que nous utilisons recouvre en effet un grand nombre de pratiques importantes dans le secteur, que l'on présente notamment à travers les catégories d'altruisme, de réciprocité, de mécénat, de libéralités, de bénévolat, de legs, de cadeaux, mais aussi de crowdfunding ou de crowdsourcing. De telles pratiques, qui font l'objet d'analyses en économie, sont très anciennes – plus anciennes que les règles du marché – et demeurent fondamentalement enracinées dans nos modes de vie en société. On parle parfois d'économie solidaire, partiellement non monétaire (une grande part des échanges n'est pas valorisée monétairement), bref, d'une « autre » économie. Ces pratiques, si elles témoignent parfois d'altruisme, ne peuvent être pour autant présentées comme désintéressées : bien souvent, elles impliquent un retour, du calcul, et participent d'une logique complexe tissée à partir des liens sociaux. On n'observe certes pas ces pratiques dans tous les secteurs : la logique du don n'intervient pas vraiment dans les grandes places financières et dans le système bancaire tel que nous le connaissons de nos jours, et on pourrait en dire autant au niveau des différents secteurs industriels, y compris celui des technologiques numériques. En revanche, on peut envisager un lien entre ce que l'on présente sous la forme d'un secteur archaïque – pour lequel les gains de productivité sont faibles ou inexistants, nous reviendrons sur ce principe au chapitre 6 – et la logique du don. Et c'est bien pour une grande partie dans ce secteur que se situe le cœur de l'économie de la culture.
Des caractéristiques particulières
La logique du don, que nous présentons plus précisément dans le chapitre 5, diffère sensiblement des règles prévalant dans l'économie classique : l'Homo œconomicus n'est pas un Homo donator, et la logique de répartition ou de redistribution publique n'équivaut pas à la logique des libéralités. Chaque système, en ce sens, repose sur des caractéristiques particulières plus ou moins bien adaptées à certaines situations, aucun des trois systèmes ne les possédant toutes de manière identique. Un tel modèle apparaît comme relativement simple et pourrait être complexifié, il n'en demeure pas moins, à notre sens, suffisant pour montrer les avantages et les inconvénients de tout système, dès lors qu'il se présente comme la seule alternative.
Enrichissement personnel/altruisme et solidarité
La logique du marché repose sur la recherche de profit de l'Homo œconomicus. On peut gloser sur le caractère imparfait de ce modèle, il n'en demeure pas moins présenté – au moins depuis Adam Smith (1776) – comme le moteur de l'économie. Cette logique de profit suppose l'enrichissement personnel, induisant lui-même la concentration du patrimoine et la fortune du capitaliste. Si longtemps, une telle attitude a été présentée par l'Église comme moralement répréhensible et demeure combattue à ce titre par certaines religions, l'enrichissement personnel est plutôt vu de nos jours, dans les pays occidentaux, comme un modèle à suivre, puisque constitutif de l'accès aux biens matériels valorisés par la société de consommation. En suivant Pierre Bourdieu, on peut voir dans le capitalisme économique l'un des aspects d'un système plus vaste, comprenant également du capital social, symbolique et culturel. Dans cette perspective, c'est d'abord la recherche des intérêts de chaque individu qui prime, et non celle de son semblable.
À l'inverse, la logique du don et celle des pouvoirs publics partent d'un présupposé différent, fondé sur l'altruisme, l'acceptation et le souci des autres, dont découle la solidarité. C'est au titre de l'égalité et de la fraternité que l'État prélève une partie de la richesse de chacun, par la voie de l'impôt, pour la redistribuer (notamment) sous la forme d'aides à l'insertion sociale, de couverture des soins de santé etc. La logique publique, partiellement consentie, demeure néanmoins contrainte : tout citoyen en mesure de payer ses impôts est obligé de participer à cet effort collectif (tout en ayant le droit de choisir la voie la moins imposée), et toute tentative de fraude est punie par la loi. Ce principe de solidarité existe également dans la logique du don, mais de manière volontaire (encore pourrait-on discuter à ce niveau) : le don à un proche, à une organisation ou à un inconnu peut s'avérer plus ou moins spontané ou calculé, il constitue néanmoins un geste par lequel le donateur marque sa solidarité en redistribuant une partie de son avoir à un autre. Si l'on suit toujours Bourdieu, on pourrait envisager que la redistribution économique entraîne une capitalisation symbolique (en forme de prestige), mais de nombreux donateurs, anonymes, ne rentrent pas dans cette catégorie – ce qu'on observe notamment dans le crowdfunding ou les sociétés d'amis de musée par exemple. En ce sens, ces deux logiques se présentent de manière opposée à celle de l'Homo œconomicus du marché (tableau 2.1).
Tab. 2.1. Principales caractéristiques des logiques du Marché, de l'État et du Don | Marché | État | Don
---|---|---|---
Enrichissement personnel | ■ | □ | □
Solidarité | □ | ■ | ■
Contrat | ■ | ■ | □
Lien social | □ | □ | ■
Rapidité | ■ | □ | ■
Durée | □ | ■ | □
Équité | □ | ■ | □
Domination | ■ | □ | ■
Contrat/lien social
C'est l'une des institutions les plus anciennes du droit, que l'on retrouve dès la plus haute antiquité. Le contrat scelle l'échange ; souvent écrit, parfois tacite, il constitue le symbole de l'architecture complexe mise en œuvre pour garantir sa bonne réalisation. C'est évidemment bien moins le bout de papier qu'il constitue que l'ensemble des éléments qu'il suppose qui représente le pouvoir de ce document. Qu'il s'agisse d'un paquet de cigarettes, d'un immeuble ou du droit de reproduction d'un roman, si les transactions diffèrent par la complexité du contrat mis en œuvre ou par le temps de la transaction, il n'en reste pas moins que ces deux éléments sont régis par un même système, constitutif de devoirs et d'obligations – transférer un bien contre une certaine somme d'argent –, mais que leur garantie est assurée par l'arsenal juridique mis en place par l'État, ainsi que par la force légitime dont il a le monopole pour la faire appliquer. Ce sont les tribunaux et, au besoin, la prison qui attendent celui qui contreviendrait aux règles du contrat. Même dans un système aussi libéral que celui décrit par Ayn Rand, chantre de l'égoïsme parfait, l'État doit exister pour faire respecter les échanges contractuels (et les libertés personnelles). La même logique se retrouve au fondement de l'appareil public, pour l'organisation du système de répartition ou de redistribution. C'est aussi le tribunal et au besoin, la prison, qui attendent celui qui refuserait de payer l'impôt.
Ce principe contractuel ne se retrouve pas dans la logique du don, pour lesquelles les règles sont tacites et ne sauraient être contractualisées – sous peine de ne plus s'inscrire dans le registre du don – nous parlons ici du don dans son principe pur, lequel, nous le verrons plus bas, n'existe que très rarement sous cette forme. L'ingrat a le droit de ne pas rendre, et le principe de la contestation d'un échange par don s'avère impossible (à quelques exceptions près) à plaider devant un tribunal. La logique du don n'est pas pour autant dénuée de celle de réciprocité, comme nous le verrons plus précisément au chapitre 5 : donner, recevoir et rendre constituent trois étapes de cette logique qui, si elle ne s'appuie pas sur l'institution du contrat et, de manière plus générale, le droit privé ou public et les forces de l'ordre, repose sur un lien parfois nettement plus solide, liant le donateur et le récipiendaire. Le don peut s'observer envers des inconnus (de l'argent à un mendiant, du sang ou un rein à l'hôpital), mais c'est surtout à travers une communauté qu'il circule : la famille dans un sens plus ou moins large, les réseaux d'amis et les réseaux sociaux, bref, ce qui fonde en quelque sorte la communauté. Le don, dans cette perspective, s'appuie essentiellement sur la force du lien social – et sur les conséquences qui pourraient advenir si ce lien était brisé – pour induire un retour. Ce principe du lien social, s'il n'est pas totalement étranger aux relations de marché et des pouvoirs publics, n'est jamais présenté comme le fondement de ces deux logiques qui, au contraire, revendiquent, pour la première, l'égoïsme individuel de l'Homo œconomicus, et pour la seconde, l'indifférence zélée de l'agent d'État qui, de manière volontairement impersonnelle, traitera toute transaction à partir de la réglementation votée et organisée par les pouvoirs publics.
Rapidité/durée
On oppose souvent la rapidité d'intervention de la logique de marché – telle qu'elle se présente par exemple au niveau des marchés financiers, à la lenteur de l'initiative publique. Il est vrai que la logique administrative requiert un temps particulier, lié aux vérifications de la conformité d'une action avec les règlements, à la nécessaire validation des prises de décision par la hiérarchie etc. On sait l'exaspération que peut entraîner ce que l'on perçoit comme un temps d'indécision de la part des pouvoirs publics, dont les principes de fonctionnement – le traitement équitable des citoyens doit passer par la vérification de l'ensemble des lois ; toute nouvelle loi ou règlement doit tenter de prendre en considération tous les cas de figure – ralentissent de manière aussi bien théorique que pratique le processus de décision. C'est évidemment le contraire que l'on peut observer pour une organisation fonctionnant à partir d'une logique de marché ou du don. Qu'elles soient guidées par le lucre ou l'altruisme, les organisations commerciales ou à but non lucratif s'avèrent souvent premières, dès lors qu'il s'agit de réagir à un événement : la perspective d'un nouveau marché, donc l'espérance de gains (ou de liens) constitue sans doute un vecteur puissant, dont se trouve dépourvue la logique publique. Dès lors qu'il s'agit, par exemple, de réaction face à un séisme, un tsunami ou une famine, mais aussi en matière de financement lors de cas extrêmes, ce sont d'abord des entreprises et des organisations non gouvernementales que l'on retrouve les premières sur place, alors que les pourparlers en vue d'une possible intervention sont souvent encore en train de se poursuivre à l'échelon public.
En revanche, la logique publique, s'appuyant notamment sur un principe de continuité et de permanence de son action, peut se targuer d'une plus grande longévité de son action. La taille relativement modeste des opérateurs du marché ou du secteur associatif les contraint souvent à un avenir généralement moins assuré que celui des pouvoirs publics, et s'il n'est pas impossible que la faillite puisse guetter une administration communale ou un État, elle n'en demeure pas moins exceptionnelle en regard de la survie des entreprises ou des organisations non publiques. L'octroi de subventions publiques, en ce sens, permet à tout établissement œuvrant dans le secteur culturel de bénéficier d'une garantie de pérennité, sinon parfaite, du moins généralement efficace.
Équité/domination
Si la logique administrative ou bureaucratique présente une certaine lenteur, c'est notamment parce qu'elle part d'un présupposé fondamental : le traitement égalitaire des citoyens, dont le respect exige une prise en compte relativement complexe : il convient en effet d'envisager tous les cas de figure d'un dispositif réglementaire afin d'éviter que des citoyens ne bénéficient indûment d'un avantage particulier. Tous les citoyens naissent libres et égaux en droits, le principe s'inscrit au cœur du dispositif législatif et réglementaire sur lesquels s'appuient les échanges entre les pouvoirs publics et les citoyens. C'est notamment ce principe qui impose le respect de règles antidiscriminatoires (selon le sexe ou l'origine des citoyens), permettant par exemple à chacun d'accéder, théoriquement avec les mêmes chances, aux concours de la fonction publique. En suivant ce même exemple, force est de reconnaître que les examens de recrutement dans le secteur privé – qu'il soit lucratif ou non lucratif – bien que réglementés par les pouvoirs publics, prêtent plus généralement à des discriminations à l'embauche ou à l'avancement dans la carrière, ce dont témoignent régulièrement les médias (pour la simple raison que l'application et la surveillance du respect de règlements, dans ces deux secteurs, s'avèrent nettement plus difficiles à opérer).
Le principe du traitement inéquitable entraîne, d'emblée, la possibilité d'un autre rapport, fondé sur une relation de pouvoir : lorsqu'il revient à un responsable de décider de l'engagement d'un candidat, en dehors de toute procédure de concours ou de choix objectif, se tisse une relation de pouvoir entre celui-ci et la personne engagée (sélectionnée, promue, favorisée), qui entraîne une possible domination du premier sur le second. En quelque sorte, le don et le marché présupposent l'inégalité : chacun naît avec un capital (économique ou social) différent et peut en tirer parti, dans ses relations, sur ceux qui lui sont inférieurs. Ce principe se retrouve régulièrement au niveau du marché, lorsqu'une entreprise plus importante bénéficie d'un pouvoir économique suffisamment considérable pour contraindre ses concurrentes à accepter ses choix. La chose est paradoxalement identique au niveau du don : celui qui donne acquiert un certain pouvoir (bien que non contractuel) sur celui qui reçoit, nous y reviendrons, certaines relations au niveau du don, dans certains contextes précis, peuvent aller jusqu'à « écraser » un adversaire qui ne pourra jamais rendre ce qui lui a été donné.
Trois points de vue
Il serait erroné d'imaginer trois systèmes « purs » pouvant fonctionner de manière autonome au détriment des autres. La plupart des libéraux, à la droite d'Adam Smith, reconnaissent la nécessité d'un État permettant de garantir les libertés individuelles, tandis que dans la Russie soviétique ou la Chine maoïste, une partie des transactions se poursuivait selon des règles de marché. De la même manière, la logique du don continue d'irriguer le système économique actuel, à travers de nombreux échanges monétaires et non monétaires. Il n'en reste pas moins que chacun de ces systèmes semble avoir pour ambition de se développer comme seule alternative possible. C'est pourtant, depuis toujours semble-t-il, un composé de solutions qui règle les questions économiques dans le monde.
Il serait assez logique d'envisager que certains systèmes fonctionnent mieux que d'autres, en fonction de leurs caractéristiques, dans l'un ou l'autre contexte. L'histoire nous enseigne, en tout état de cause, que même dans les lieux présentés comme idéaltypiques de la logique du don – chez les Trobriandais du Pacifique ou les Kwakiutl d'Amérique du Nord, présentés par Marcel Mauss, comme dans les villes antiques – il existe également des échanges que l'on peut catégoriser selon les règles du marché, et d'autres selon celles des pouvoirs publics.
Il est cependant indéniable que, d'un point de vue strictement historique, certains processus d'échange précèdent les autres. Le seul mode d'échange, pour l'enfant, n'est pas fondé sur une relation de marché ; il est d'abord lié à l'économie du don – de la mère ou de la famille à l'enfant. Ce n'est que dans un second temps que l'enfant, qui a très rapidement appris à accepter et à rendre symboliquement, se voit progressivement apprendre les règles d'un échange marchand, fondé sur l'emploi d'un étalon monétaire. Les premiers principes de l'échange, qui occupent l'essentiel de notre humanité – depuis la préhistoire jusqu'à nos jours – reposent d'abord sur les règles d'un don plus ou moins sophistiqué, puis du troc, auquel s'adjoint progressivement la nécessité de fixer une mesure étalon pour les échanges. La fixation d'une telle mesure (que l'on retrouve assez tôt dans la plupart des civilisations) ne suppose pas pour autant le développement des principes du marché. Si l'on suit Karl Polanyi, les règles de marché régulièrement présentées comme naturelles (pour fixer les prix en fonction d'un rapport offre-demande) ne sont progressivement advenues, de manière très restreinte, qu'à partir du ve siècle avant notre ère en Grèce (le siècle de Périclès). Avant cette date, les grandes civilisations (comme l'Égypte) se fondent essentiellement sur des systèmes de répartition organisés par l'État.
Le développement du marché permet de résoudre certains problèmes, notamment liés à la complexification des systèmes d'échange au sein d'empires toujours plus vastes, mais aussi de développer un contre-pouvoir à la fois à l'égard du donateur (le riche patricien de l'Antiquité ou l'Église) et du prince. Le développement des principes du libéralisme se fonde sur une logique politique autant qu'économique. Mais cette logique, une fois arrivée à sa position dominante – ce qui est le cas de son évolution actuelle, à la suite de l'effondrement du système soviétique – s'avère tout aussi hégémonique que les autres. Si l'on suit les préceptes de Friedrich von Hayek et des économistes de l'École de Chicago (notamment ceux d'un Gary Becker, appliquant l'analyse économique néolibérale à la famille et au système judiciaire), le raisonnement de l'Homo œconomicus apparaît comme le plus approprié pour comprendre le fonctionnement humain et gérer l'ensemble des échanges sur le globe, y compris ce qui est actuellement pris en charge – de manière imparfaite – par l'État ou la philanthropie. Le monde de la culture constitue ainsi un marché certes spécifique, mais fonctionnant essentiellement à partir des règles de l'économie libérale, tout comme les raisons qui poussent certains philanthropes à donner de l'argent (afin de convertir du capital économique en capital social).
La logique publique s'avère, somme toute, tout aussi hégémonique dans sa volonté de régenter les autres, qu'il s'agisse de briser les monopoles autrefois détenus par l'Église, ou de brider, voire d'annihiler la logique du marché. Si on peut en quelque sorte considérer, en France, l'évolution politique des idées républicaines et laïques comme une volonté de mettre un terme au pouvoir de l'Église – notamment en matière d'éducation et de soins de santé, mais aussi de culture – force est de reconnaître que le rôle des pouvoirs publics est demeuré confiné à un certain nombre d'interventions, en comparaison avec l'emprise des régimes soviétiques et chinois, et celui qui prévaut encore en Corée du Nord. C'est soit par le biais de nationalisations (dans le cas des sociétés commerciales), soit par le lancement de politiques alternatives (notamment dans le domaine de la culture) que progressivement, l'État entreprend d'imposer ses vues. Si les pouvoirs publics entendent ainsi encadrer les règles du marché, afin d'en conserver la maîtrise, c'est dans une même perspective de régulation qu'ils envisagent la réglementation du mécénat ou du bénévolat. En quelque sorte, les deux logiques – marché et don – apparaissent à nouveau par le prisme public, qui se présente comme seul mode d'organisation de la société.
La puissance publique s'est progressivement imposée, en Europe, durant l'époque contemporaine, avant de connaître un brusque déclin à partir des années 1980, mais cette confrontation doit aussi être vue avec l'économie du don, paradigme longtemps dominant, car principal mode d'échange dans les systèmes religieux. L'Église (le christianisme de nos régions, mais aussi l'hindouisme, le bouddhisme ou l'islam) a longtemps joué un rôle central en matière de réglementation des doctrines économiques, face au contrôle de l'État (au bénéfice des patriciens ou de l'Église) ou à celui du marché (en privilégiant par exemple la gestion monastique ou celles d'associations charitables). Mais qu'il s'agisse de l'Église ou de riches patriciens, la logique du don, par-delà les questions de générosité ou d'altruisme, entraîne également des répercussions analysables en termes de rapports de pouvoir : « À ce jeu de qui donne et qui reçoit, qui gagne ? Celui qui a le mérite de donner, et à ce jeu, toujours, les pauvres perdront, par nécessité mathématique. [...] Renforcez donc la pratique donataire au détriment de l'échange marchand, vous obtiendrez au mieux un patriarcat romain, ou des Médicis ou des Borgia, au pire, des jeux du cirque et des guerres civiles qui mettront aux prises des César et des Crassus », remarque Alain Testart.
Trois parties de notre personnalité – un système hybride
Si nous présentons trois logiques, il nous apparaît que celles-ci coexistent, non seulement au sein de la société, mais probablement dans le fonctionnement de tout être humain. On sait combien, par exemple, de grands capitaines d'industrie, à l'instar d'un Carnegie ou d'un Rockefeller, ou plus près de nous Bill Gates, se sont aussi présentés comme des philanthropes. Nombre de patrons d'entreprise – surtout au xixe et au début du xxe siècle, ont par ailleurs conjugué les trois modèles, exerçant simultanément des fonctions d'actionnaires et d'administrateurs de sociétés, de député ou de maire, voire de ministre, tout en pratiquant la philanthropie. On pourrait envisager que ces trois figures répondent à un seul modèle capitaliste s'exerçant à la fois sur du capital économique, symbolique et culturel. Le point de vue que nous adoptons diffère sensiblement de cette position, reconnaissant à de tels personnages des modes de raisonnement particuliers – la possibilité de privilégier des intérêts différents en fonction des rôles joués. Certes, on peut imaginer qu'un patron représentera d'abord les intérêts de la classe dirigeante à l'Assemblée nationale, mais l'on peut également remarquer qu'il en accepte de facto le jeu et qu'une partie de son action, dans cette perspective, dépasse ses seuls intérêts d'Homo œconomicus ou ceux de sa classe sociale. De manière inverse – et les exemples abondent, à commencer par la figure ambiguë d'un Malraux – de nombreux hommes politiques dédiés à l'avènement d'une logique publique, peuvent également, en privé, agir de manière nettement plus prosaïque en fonction de leurs propres intérêts, même si ceux-ci s'avèrent contradictoires (c'est ce principe qui a par ailleurs été largement analysé par les économistes du public choice, comme James Buchanan, nous y reviendrons). Qu'il s'agisse de différents moments de la vie, voire de différents moments de la journée, l'être humain, dans cette perspective, peut aborder les choses de plusieurs manières différentes. Ainsi, un fonctionnaire dédié à son travail peut également, le même jour, passer des ordres en bourse et envoyer de l'argent à une ONG...
Si les sciences économiques reposent sur des modèles, c'est parce qu'elles présupposent, à l'instar de la physique, qu'à l'état naturel, l'économie ne présente pas de caractère parfaitement pur et homogène. La logique de marché, si elle se fonde sur les principes de l'Homo œconomicus, ne se retrouve pas – même dans les compagnies de Bill Gates ou dans les salles d'arbitrage de Goldman Sachs – chez tous ses employés. En ce sens, on peut observer des comportements relevant de modèles publics ou de don, même dans des transactions essentiellement portées par le marché.
Ainsi, le fonctionnement de l'économie – et, dans le cas qui nous intéresse, celui de l'économie des arts et de la culture – nous semble relever intrinsèquement de trois principes distincts, dont les caractéristiques diffèrent, ainsi que les avantages ou les inconvénients qui leur sont liés. Théoriquement, les possibilités de fonctionnement sont, dans cette perspective, innombrables, reposant selon des proportions diverses de logique publique, de marché ou de don. L'hybridité connaît cependant des limites : si l'altruisme ou la logique du don est présenté par certains comme une voie d'avenir, elle ne saurait être envisagée de manière globale pour tous les échanges. De la même manière, la gestion collective et l'économie planifiée ont montré leurs limites, du moins au niveau de leur application en Union soviétique. Si nous pouvons douter du principe « naturel » du marché comme mode de fonctionnement optimal pour tous les échanges, nous devons remarquer que celui-ci s'est particulièrement bien adapté dans un contexte de mondialisation des échanges, et en fonction des caractéristiques du régime démocratique libéral. Mais ce contexte diffère déjà sensiblement dans certains pays émergents (comme la Chine), induisant une combinaison différente des modes d'échange. On peut ainsi certes évoquer, au niveau de la culture, les grandes industries culturelles dont le fonctionnement se rapproche des règles du marché des produits manufacturés ou des services classiques. En revanche, au sein de certains secteurs plus confidentiels tels qu'on peut en observer souvent dans les mondes de la culture – par exemple le secteur de la poésie –, c'est une autre combinaison qui sera privilégiée, s'appuyant sur des réseaux plus informels et associatifs, et nettement plus centrés sur l'échange par dons.
Ce principe nous conduit à évoquer la métaphore du moteur hybride, maintenant répandue chez nombre de constructeurs automobiles depuis quelques années. Le principe d'un tel moteur s'appuie sur les avantages de plusieurs systèmes mécaniques, en fonction des différents contextes de la conduite. Ainsi, au démarrage, est-il préférable d'utiliser un système électrique, tandis que les moteurs thermiques s'avèrent plus performants pour une conduite en vitesse de croisière (par ailleurs, le moteur électrique peut profiter des décélérations pour se recharger). De tels niveaux d'hybridité permettent une diminution certaine de la consommation de carburant, mais ne sont pas exempts de critiques. Longtemps accueillis avec scepticisme, ils s'avèrent plus fragiles, et de coûts de production plus onéreux. Mais la réduction de la consommation permet également celle de la pollution. Le parallèle avec les secteurs de la culture et les logiques de financement est simple. Si tout secteur a forcément besoin de flux financiers pour l'alimenter, certaines autres logiques d'échange peuvent s'avérer plus performantes dans certains contextes.
Encore convient-il de s'interroger sur les raisons qui poussent certains à vouloir alimenter le moteur : pourquoi financer la culture ? Les réponses venant du marché diffèrent de celles des pouvoirs publics et de celle d'un philanthrope. Ce n'est pas pour les mêmes raisons que l'État, le marché ou des citoyens décident de consacrer de l'argent pour consommer, soutenir ou investir. Une telle réflexion nous conduit à ne pas séparer le modèle, quel qu'il soit (État, marché et don) et ceux qui l'alimentent, d'abord composés de citoyens plus ou moins intégrés, et plus ou moins regroupés : individus consommateurs ou citoyens politiquement actifs, partis politiques, gouvernements ou lobbys, organisations de taille réduite ou grands groupes mondiaux...
. Kolm S.-C., Ythier J.-M. (dir.), Handbooks of the Economics of Giving, Altruism and Reciprocity, Amsterdam, North Holland, 2006.
. Colin B., Gautier A., Pour une autre économie de l'art et de la culture, Ramonville Saint-Agne, Érès, 2008.
. Voir par exemple la synthèse de Jourdain A., Naulin S., La théorie de Pierre Bourdieu et ses usages sociologiques, Paris, Armand Colin, 2011.
. Rand A., La vertu d'égoïsme, Paris, Les Belles Lettres, 2008. Cela mis à part, un certain nombre de théories libertariennes, telles que celles de David Friedman. Voir Friedman D., Vers une société sans État [« The Machinery of Freedom »], Paris, Les Belles Lettres, 1992.
. Sur cette question, voir le classique Tönnies F., Communauté et société, Paris, PUF, [1887] 2010.
. Polanyi K., La subsistance de l'homme. La place de l'économique dans l'histoire et la société, Paris, Flammarion, [1977] 2011. C'est en fait plutôt pour affaiblir la mécanique électorale du repas gratuit, favorisant le clientélisme, que Périclès instaure le principe du marché alimentaire local.
. Testart A., Critique du don : Études sur la circulation non marchande, Paris, Syllepse, 2007, p. 170.
Chapitre 3
La logique du marché
Le monde de la culture est souvent perçu comme un ensemble d'activités bénéficiant de ou survivant grâce à de multiples soutiens publics et protections réglementaires : subventions au spectacle vivant, loi sur le prix unique du livre, régulation de l'investissement dans le cinéma (compte de soutien du CNC), quotas de diffusion audiovisuels, propriété intellectuelle etc. L'essentiel de cette économie est cependant à la base régulée et donc structurée autour de marchés plus ou moins concurrentiels sur lesquels se rencontrent une offre et une demande de biens et de services culturels. Ce chapitre vise précisément à expliciter la notion de marché et les discours qui l'entourent. À l'instar de l'intervention publique, on peut en effet adopter une approche normative : la théorie cherche ici à justifier le marché concurrentiel comme le seul mécanisme efficace pour allouer les ressources et stimuler les acteurs économiques. Les aides publiques seraient a contrario des freins au progrès économique et social. Le marché peut également faire l'objet d'une démarche positive : il s'agit alors davantage d'étudier les processus économiques et sociaux à travers le prisme de l'échange marchand entre des offreurs et des demandeurs.
La presque totalité des secteurs de la culture se retrouve confrontée, de près ou de loin, à la logique du marché. D'un point de vue historique, une grande partie du secteur du théâtre et de celui de la musique (classique), mais aussi une partie du monde des musées et des expositions, est directement liée au monde des foires et à celui des marchés (au sens littéral du terme) et à une logique d'indépendance des pouvoirs publics. Il en va de même du marché de l'art, et bien sûr des industries culturelles, à commencer par celle du livre, à partir du xve siècle. Certes, nombre de stratégies individuelles ou d'organisations reposent dès le Moyen Âge sur des modèles hybrides, s'appuyant sur des mécènes, des réglementations publiques puis un soutien de l'État, mais elles se développent également, parfois presque en totalité, à partir d'une logique de marché.
Le marché concurrentiel,
un mécanisme autorégulateur idéal ?
L'histoire de la pensée économique fourmille de définitions et d'approches du marché. Les économistes classiques du xixe siècle proposent une vision dynamique du marché où interviennent des acheteurs et des vendeurs adoptant des comportements de « batailles en affaires », les premiers demandant « à l'enchère », les seconds offrant « au rabais ». Dans la perspective libérale dans laquelle s'inscrivent leurs travaux, de tels comportements concurrentiels permettent une certaine justice sociale, car les prix de marché ne s'écartent jamais durablement des prix naturels des marchandises, éliminant ainsi à terme toute rente injustifiée. Le libéralisme économique stipule que ce mécanisme décentralisé d'allocation des ressources est supérieur à la centralisation des décisions par un agent central, l'État. Les individus et les entreprises sont ainsi supposés être les meilleurs arbitres quant à leurs propres intérêts. Le marché se voit ainsi pensé comme le lieu idéal et efficace de socialisation des rapports humains et de pacification d'intérêts égoïstes et souvent contradictoires.
La main invisible et le libéralisme économique
Le xviiie siècle est celui de l'apologie de la liberté. Dans ce contexte, la liberté économique accompagne la liberté politique, l'individu étant perçu comme capable de se gouverner dans tous les domaines. Le fondement du libéralisme économique est de supposer qu'il n'existe pas d'antagonismes entre les individus, mais une harmonie spontanée entre leurs intérêts.
Le libéralisme économique trouve ses origines modernes dans la contestation des doctrines mercantilistes (Antoine de Monchrestien, Jean-Baptiste Colbert, Thomas Gresham etc.) selon lesquelles l'intervention de l'État est constamment nécessaire afin d'assurer l'enrichissement de la nation et donc la puissance du Prince. La régulation de l'activité économique est avant tout l'affaire de l'État : restreindre les importations de biens manufacturés et les sorties de métaux précieux, favoriser le travail du plus grand nombre, protéger les industries nationales etc. La contestation de ces doctrines et de leurs excès sera notamment le fait de l'école française de la Physiocratie. Ainsi dans son Tableau économique en 1758, François Quesnay modélise l'économie nationale à l'image de la circulation sanguine et rejette toute entrave qui pourrait gêner le fonctionnement et l'épanouissement du système. Il existe en effet selon cet auteur un ordre naturel, c'est-à-dire un système de lois naturelles, universelles, gouvernant tout phénomène économique, antérieur à toute convention sociale entre les individus. Cet ordre naturel est fondé sur les aptitudes de chacun, les besoins physiques et sur les intérêts communs de tous face aux lois immuables de la nature. Il s'agit de respecter avant tout cet ordre pour assurer la prospérité générale.
Les physiocrates vont inspirer largement les travaux d'un philosophe écossais, Adam Smith (1723-1790), considéré comme le père de l'économie classique anglaise. Son constat de départ est simple : les acteurs du marché sont tous poussés par le désir de gagner de l'argent. Comment un agencement socialement viable peut-il naître d'une motivation aussi antisociale que l'amélioration de son propre sort ? Adam Smith fait l'hypothèse de l'harmonie des intérêts individuels utilisant la métaphore de la « main invisible ». Ce principe s'inspire largement de la fameuse Fable des abeilles du hollandais Bernard Mandeville parue en 1714 et selon laquelle l'égoïsme des individus travaille pour le bien commun. Mais alors que Mandeville ramène à l'égoïsme tous les motifs de l'action humaine, pour Smith, ce n'est vrai que pour la sphère économique. Pour lui, en opposition à la sphère générale des sentiments moraux fondée sur l'altruisme (titre d'un livre de Smith antérieur à la Richesse des nations), l'activité économique est la seule où il n'y ait besoin que d'égoïsme, chacun travaillant pour son intérêt particulier, tous concourent à leur intérêt commun : « nous n'attendons pas notre dîner de la bienveillance du boucher ni du boulanger, mais bien de la considération qu'ils ont de leur propre intérêt ». Le capitaliste augmente ainsi ses richesses et contribue à la croissance économique. Ses choix le conduiront naturellement à utiliser son épargne dans les emplois les plus avantageux pour la société. En ce sens, chaque individu est conduit par une main invisible pour faire avancer une fin qui n'était pas intentionnelle.
Sous certaines conditions concurrentielles, en particulier la libre entreprise (« laissez faire ») et la libre circulation des marchandises (« laissez passer »), les intérêts privés s'harmonisent avec les intérêts sociaux. L'idée de base est simple : en limitant les gains excessifs (les profits de monopole), la concurrence conduit à l'allocation optimale du travail et du capital entre les activités. On retrouve ici à la fois le principe de l'ordre naturel cher à l'école classique et la loi de l'offre et de la demande. L'ordre social, lui aussi, est présenté comme le reflet de l'ordre naturel. Dans la sphère économique, cela se traduit notamment par le fait que les prix des marchandises et des facteurs de production tendent toujours vers leurs taux naturels : le salaire versé aux travailleurs tend toujours vers le minimum de subsistance social (soit, à l'époque des classiques, essentiellement les biens alimentaires et les vêtements ; à notre époque, on y adjoindrait un téléphone portable...), la rente payée aux propriétaires terriens est fixée par la rareté naturelle des terres (leur fertilité) et le profit prélevé par les capitalistes dépend en partie des conditions techniques de production (elles-mêmes déterminées en dehors du champ économique, étant calquées sur les lois de la nature).
C'est précisément ici qu'intervient la loi de l'offre et de la demande, et plus précisément le libre jeu de la concurrence. Le phénomène de la « gravitation » proposé par Adam Smith garantit que les prix de marché ne s'écartent jamais durablement des prix naturels : chaque personne cherchant à améliorer son propre sort sans se soucier des autres se heurte à une foule de personnes avec la même motivation ; il en résulte que chaque acteur du marché est contraint d'offrir les mêmes prix que ses concurrents. Par exemple, un industriel ne trouvera aucun acheteur s'il propose un prix supérieur à celui de ses concurrents, mais aucun n'offrira le bien à un prix inférieur sous peine de disparaître, faute de rentabilité. Le prix de marché reflète ainsi forcément les conditions techniques et sociales de la production. De même, un demandeur d'emploi ne trouvera pas de travail s'il demande plus que le salaire courant, puisqu'il est en concurrence avec d'autres ; ce salaire courant tend dès lors mécaniquement vers le minimum de subsistance (le niveau en dessous engendrant une défaillance de main-d'œuvre en raison de la surmortalité et de la précarité qu'il provoquerait).
Ce concept de concurrence (dont la main invisible se présente comme la métaphore) est central pour l'analyse libérale. Ainsi, plutôt que mettre l'accent sur l'idée d'un contrat social fondateur (Rousseau), la perspective libérale montre que la conciliation entre intérêt individuel et bien-être collectif s'opère dans la sphère économique par le jeu de la concurrence.
Libéralisme, utilitarisme,
lois de l'offre et de la demande
Après Adam Smith, Léon Walras, économiste français (1834-1910), tente de formaliser le principe de la main invisible en s'inspirant pour cela d'un modèle en biologie. Il déplace le questionnement de la dynamique de la richesse des nations vers la satisfaction des besoins individuels et l'allocation optimale des ressources, sans gaspillage, afin de lutter au mieux contre la rareté. Ce faisant, il va néanmoins « figer » la représentation de la concurrence et de la dynamique des marchés.
Walras développe une vision globale de l'activité économique et de la répartition des richesses basée sur l'analyse des comportements individuels. C'est le projet ambitieux de l'équilibre général défini comme l'équilibre simultané de l'ensemble des marchés interdépendants tel qu'aucun agent économique ne désire modifier le niveau de ses échanges avec chacun des autres agents économiques. Les revenus que les agents économiques perçoivent (salaire, rente, profit, dividendes, intérêts) et les dépenses qu'ils effectuent sont étudiés dans le cadre d'un système complet de marchés interdépendants sur lesquels chacun peut être tantôt offreur, tantôt demandeur d'un bien ou d'un service. Les individus offrent leurs services sur le marché du travail et reçoivent un salaire de la part des entreprises ; celles-ci combinent ce travail à d'autres facteurs de production ; les ménages offrent leur épargne sur les marchés financiers où les entreprises sont demandeuses de fonds pour financer leurs investissements et donc paient des intérêts aux offreurs de moyens de financement. Les ménages sont en revanche demandeurs sur les marchés de biens et services de consommation finale où les producteurs sont offreurs. Les revenus de chacun sont fonction des prix d'équilibre qui se déterminent sur les marchés des « services producteurs » (les facteurs de production : travail, capital, technologie...) où les agents acquièrent les ressources nécessaires à la production des biens de consommation finale qui font l'objet d'échanges entre les entreprises et les ménages.
Pour Walras, tout agent économique est supposé être doté d'un comportement rationnel visant à rechercher le maximum de satisfaction de ses besoins. La filiation avec Adam Smith est ici évidente : l'Homo œconomicus est défini comme un individu égoïste qui recherche son bien-être à travers des rapports sociaux réduits à des liens marchands. Ce modèle économique est fondé sur les règles du « laissez faire, laissez passer », caractérisée par un certain nombre d'hypothèses, soit l'atomicité des agents (aucun offreur ni demandeur ne dispose du pouvoir de marché suffisant pour modifier à lui seul les prix : les agents sont preneurs de prix), la fluidité de l'offre et de la demande (liberté d'établissement, aucune barrière à la mobilité des biens et des services), la transparence (les prix sont annoncés de manière gratuite aux agents, l'information a un coût nul) et l'homogénéité des biens et des services (deux produits dont une seule des caractéristiques différerait correspondent à deux marchés distincts).
La libre concurrence apparaît comme une condition essentielle de validité de toute la construction théorique de Walras. Le rôle de l'État vise selon Walras à « instituer et maintenir la libre concurrence économique », car la tendance spontanée des agents est de rechercher et d'instaurer des situations de monopoles pouvant conduire à des défaillances du point de vue collectif. Dans la pensée walrassienne, la concurrence n'est pas seulement une structure de l'offre et de la demande (définie par les conditions de la concurrence parfaite), mais également un type de comportement des agents. Il reprend ainsi l'idée de comportements de « batailles en affaires » d'Adam Smith. La concurrence est alors définie par les réactions des agents économiques à des désajustements entre l'offre et la demande : augmenter le prix en cas de demande excédentaire (D>O) et le diminuer en cas d'offre excédentaire (O>D). La concurrence permet ainsi l'ajustement des quantités offertes aux quantités demandées et garantit ainsi l'efficacité du système productif. Selon le modèle, au final, les produits sont vendus à leur prix de revient, sans bénéfice, ni perte, à l'avantage des consommateurs. Par conséquent, la libre concurrence assure à la fois l'efficacité et la justice dans l'échange.
L'analyse de marché proposée par Walras s'avère pourtant statique : le système étant en position d'équilibre, toute perturbation engendre instantanément les forces qui le ramènent à sa position initiale d'équilibre. Ce processus de « tâtonnement » ne renvoie à aucune réalité observable, mais constitue une abstraction par laquelle Walras cherche le processus idéal qui permet sur un marché lui-même idéal de parvenir aux prix d'équilibre idéaux théoriquement déterminés de façon à maximiser le bien-être de tous les agents et de parvenir à un idéal de justice.
Sur cette base, Walras suppose un marché unique réunissant l'ensemble des offreurs et des demandeurs pour tous les biens et services et fonctionnant avec un « crieur de marché » (il n'emploie jamais cette expression, ni même celle de commissaire-priseur, mais affirme que « des prix sont criés »). Cet agent fictif, situé au-dessus du marché et ne prenant pas part aux échanges, centralise toute l'information sur les prix, les offres et les demandes, la diffuse et propose des prix qui se rapprochent peu à peu des prix de l'équilibre général. Cet agent fictif fait des propositions de prix auxquelles réagissent les offreurs et les demandeurs. À partir de là, il centralise les informations sur la situation du marché : si l'offre et la demande s'équilibrent du premier coup (ce qui est évidemment hautement improbable), alors l'ajustement est terminé et les échanges peuvent avoir lieu. Si certains biens sont trop demandés et d'autres pas assez (s'il apparaît des demandes excédentaires ou des offres excédentaires), alors le crieur modifie en conséquence les prix pour provoquer une variation de l'offre et de la demande, les agents fixent sur la base de ces nouveaux prix leurs quantités offertes et demandées de manière à atteindre leur objectif (maximisation de leurs fonctions-objectif individuelles en respectant leur contrainte budgétaire donnée). En prenant compte des excédents d'offres et de demandes que cette nouvelle situation génère, de nouveaux prix sont criés (ou non si l'équilibre est atteint). Et ainsi de suite jusqu'à l'établissement d'un équilibre général. Les oscillations de prix sont, en quelque sorte, des propositions successives, des tâtonnements qui acheminent les échanges vers les prix définitifs de l'équilibre général où toutes les offres vont être égales à toutes les demandes.
Cependant, une condition essentielle à l'efficacité du processus de tâtonnement est l'hypothèse d'échanges suspendus tant que l'équilibre général n'est pas atteint. En effet, si des échanges ont lieu alors que les prix annoncés ne permettent pas d'établir un équilibre qui satisfasse l'ensemble des agents économiques, alors ces « faux » prix modifieraient les dotations individuelles, et partant, les demandes et les offres réciproques. Toutes les solutions changeraient en permanence, créant un déséquilibre perpétuel, donc rendant tout équilibre impossible. La condition de validité essentielle au modèle proposé par Walras repose sur l'hypothèse qu'aucun échange n'a lieu en dehors de l'équilibre.
L'agent fictif centralisateur jouerait ainsi en première analyse le rôle de la « main invisible ». Mais ce mécanisme peut fort bien fonctionner dans une économie planifiée (comme celle mise en place dans le système soviétique) : selon certains économistes, un bureau central idéal pourrait tout à fait jouer le même rôle. En fait, le tâtonnement walrassien s'oppose à la spontanéité et au pouvoir autorégulateur du marché : tout au long du processus de tâtonnement, il n'y a pas d'échange (l'échange reste virtuel) et c'est seulement au prix d'équilibre que les échanges peuvent avoir lieu. D'autre part, il s'agit d'un marché centralisé. Or, selon Smith, le fonctionnement du marché reposait sur la réunion des marchands dont les relations d'échanges suffisaient et limitaient le rôle de l'État à un rôle d'arbitre. Qui plus est, le marché, toujours selon Smith, était un ordre qui s'est mis en place progressivement par des expériences successives, des relations répétées entre les vendeurs et les acheteurs. Dans le cadre walrassien, le marché est centralisé par un agent non privé, qui ne prend pas part aux échanges et qui n'est pas preneur de prix. En extrapolant un peu, ce système pourrait correspondre à une planification indicative de l'État, renvoyant à l'idée de centralisation contraire aux échanges décentralisés permis par le marché.
L'équilibre général qu'obtient Walras sur la base d'une « concurrence parfaite » se présente dès lors comme un état idéal et non réel. Cela n'est pas surprenant dans la mesure où Walras veut faire de l'économie une science, c'est-à-dire un modèle d'explication des phénomènes qui ne soit pas prisonnier des contingences de la réalité, et qui pourra être modélisé mathématiquement. C'est pourquoi il distingue soigneusement cette économie pure, qu'il veut élaborer, de l'économie appliquée. Un économiste anglais, Alfred Marshall, adoptera par la suite une démarche plus pragmatique et positive permettant de mener des travaux sur des marchés spécifiques sans avoir à prendre en compte tout le reste de l'économie, à partir de la notion d'équilibre partiel. Les outils forgés par les auteurs néoclassiques dont Walras est l'un des plus grands représentants sont alors utilisés dans une perspective plus positive.
La théorie du marché, boîte à outils pour saisir les mondes de l'art
La notion de marché évoque inévitablement l'idée de marchandisation, laquelle, en matière de culture, est le plus souvent connotée négativement, car elle renvoie à l'extension de la recherche de profit dans des domaines jusqu'alors préservés ou non touchés directement par le capitalisme. La mise en concurrence des artistes serait susceptible de dénaturer le produit de leur travail, dès lors que leur créativité est orientée en fonction d'objectifs autres qu'esthétiques. La marchandisation est également associée à l'idée d'industrialisation de la culture, de standardisation de la production artistique et des pratiques culturelles. Sans nier toute la pertinence et tout l'intérêt de ces critiques, que l'on retrouve par exemple déjà avec l'École de Francfort et le principe des industries culturelles, on peut envisager une perspective quelque peu différente à partir de l'analyse de marché comme une boîte à outils permettant une certaine lecture, un décryptage, du fonctionnement des activités culturelles.
Qu'est-ce que le marché ?
Le marché constitue une abstraction pour représenter les modes de coordination entre les agents économiques, obtenue grâce à la formation de prix qui résulte de la confrontation entre des offreurs et des demandeurs d'un bien ou d'un service. Les prix servent alors de signal pour déterminer des quantités échangées. Toutefois, le marché n'est pas le seul moyen pour gérer et affecter des ressources entre des individus et des organisations. D'autres systèmes coexistent, voire peuvent prédominer dans certains pays ou à certaines époques : le lien solidaire (échanges entre les membres d'une famille, au sein d'une communauté...), la planification (décision d'affectation des ressources prises par l'État), la hiérarchie (l'organisation des transactions à l'intérieur d'une organisation, comme dans le cas des corporations) ; ou encore des formes hybrides (par exemple, une coopération entre deux entreprises pour décider comment allouer une ressource, à quel prix etc.).
Mais pour la théorie microéconomique, les rapports sociaux sont essentiellement marchands. Toute transaction s'inscrit ou s'analyse dans le cadre d'un marché. Dans le monde de la culture, la vente de biens culturels à des consommateurs, mais également les collaborations entre artistes, la cession de leurs droits sur leurs créations à un exploitant, les contrats entre les annonceurs et les chaînes de télévision, entre celles-ci et les vendeurs de programmes etc. correspondent à des marchés.
L'économie appliquée analyse les marchés séparément. On parle alors d'analyse en « équilibre partiel » et on ne s'intéresse alors qu'aux conditions de confrontation de l'offre et la demande pour un produit donné, en considérant les conditions d'équilibre sur les autres marchés comme fixées. C'est généralement cette approche qui est retenue par les économistes de la culture. Il s'agit évidemment d'une abstraction, mais c'est à ce prix que l'analyse est possible. Comprendre la consommation de films nécessiterait certes d'analyser la demande de tous les autres biens, mais également les comportements d'offre comme l'épargne etc. Or, la complexité d'une telle analyse la rendrait impossible et ses résultats difficiles à déchiffrer... On préfère alors considérer la demande pour les autres biens ou la propension à épargner... du consommateur de films comme données pour se concentrer sur certaines variables, telles que sa réaction au prix des films, à l'offre de substituts proches, à des variations de son revenu, de son temps libre etc.
Il existe ainsi plusieurs typologies des marchés selon leur localisation (locale, nationale, internationale, mondiale), la nature des produits qui y sont échangés (produit de consommation finale ou facteurs de production comme le travail, capital, connaissance, qui servent eux-mêmes à produire d'autres biens et services), leur degré de segmentation lié à la différenciation plus ou moins forte des produits qui y sont échangés, le nombre d'offreurs et de demandeurs qui y interagissent. Ce dernier critère permet notamment d'établir la fameuse « table de Stackelberg » qui croise simplement le nombre des demandeurs et celui des offreurs (cf. infra).
Demande et utilité marginale
La demande sur un marché de bien consommation finale peut être analysée de différentes manières. Elle indique quelles seraient les quantités demandées en fonction des divers prix hypothétiquement possibles. À un niveau microéconomique, l'économie (et après elle le marketing) tente d'expliquer les choix du consommateur. À un niveau agrégé, il s'agit de caractériser la fonction de demande totale sur un marché.
Les premiers économistes néoclassiques (Léon Walras, Stanley Jevons, Carl Menger) ont forgé les fondements de cette analyse en mariant le marginalisme (issu des fameuses fonctions de Gottfried Wilhelm Leibniz) et l'utilitarisme (Jeremy Bentham) à travers le modèle de l'Homo œconomicus. Le consommateur est l'une des représentations fictives utilisées par le courant néoclassique pour fonder sa théorie du fonctionnement du marché.
À la base de cette approche, on trouve la notion de besoin. Pour qu'il y ait production pérenne d'un bien ou d'un service, il faut normalement qu'il y ait un besoin, donc qu'une demande se crée. Un besoin est le désir d'un individu, étant donné un état de privation, d'obtenir le moyen de combler un manque, d'atténuer une sensation désagréable ou d'accroître une sensation agréable. Un besoin se traduit par un acte ou une demande visant à obtenir un bien ou un service permettant de le satisfaire. Le but de l'activité économique est alors de satisfaire les besoins solvables compte tenu de la rareté des ressources disponibles.
Chaque consommateur a des besoins illimités qu'il doit satisfaire avec des ressources limitées (des revenus fixés sur une période donnée) – c'est le propre de la définition des sciences économiques (cf. Introduction). Il cherche alors à maximiser son utilité totale, à savoir la satisfaction qu'il retire des quantités consommées de biens et de services. En règle générale, ce calcul s'opère sur la base du principe de satiété ou de saturation dans la satisfaction des besoins. Cette hypothèse comportementale est qualifiée de « loi de l'utilité marginale décroissante » : plus un individu consomme d'un bien, moins le plaisir qu'une quantité supplémentaire de ce bien lui procure est important. Par exemple, plus un individu amateur de cinéma visionne de films chaque semaine, plus sa satisfaction globale va augmenter. Mais l'utilité apportée par chaque nouveau film visionné est moindre par rapport au film vu précédemment. Au pire, la saturation est atteinte, et un cinéphile qui consacrerait ses jours et ses nuits à visionner des films pourrait souffrir de migraines au-delà d'un certain seuil.
L'individu consomme par conséquent une quantité supplémentaire d'un bien tant que le surcroît d'utilité que cette quantité lui apporte est supérieur au prix payé. Le bien-être doit tout simplement être supérieur au sacrifice, selon cette approche hédoniste. Si l'utilité marginale est décroissante et le prix donné, il existe forcément une quantité d'équilibre en deçà de laquelle le consommateur peut encore obtenir un surcroît d'utilité en augmentant sa consommation et au-delà de laquelle le consommateur va voir son niveau d'utilité totale diminuer, car le gain de satisfaction obtenu par cette quantité supplémentaire est inférieur au prix acquitté pour l'obtenir. Ce point définit précisément l'équilibre du consommateur.
Évaluer la demande
La disposition à payer des individus pour chaque unité d'un bien donné constitue une manière d'évaluer la demande des biens. Il s'agit de la somme qu'un individu est prêt à consacrer pour obtenir une unité supplémentaire d'un bien. Ce montant va dépendre des préférences et du revenu de l'individu (si vous n'aimez pas l'opéra ou si vous n'avez pas les moyens d'acheter une place, vous serez prêt à payer zéro euro pour y aller).
Le surplus du consommateur est alors défini par la différence entre son consentement à payer pour une unité de marchandise donnée et le prix de marché de cette unité de marchandise. Si l'individu est prêt à payer 100 euros pour assister à un opéra et qu'il obtient une place pour 60 euros, son surplus (ou gain psychologique à l'échange) sera de 40 euros. Il s'agit de ce fait à la fois d'un stimulant à l'échange marchand et d'une limite (étant déterminée par les préférences et le revenu de l'individu).
Mais comment estimer la demande pour des biens subventionnés, dont le prix d'entrée, par exemple, ne reflète aucunement les coûts réels de production ? En d'autres termes, en l'absence de prix (il n'y a pas d'offre pour les paysages...), comment estimer leur valeur économique et ainsi justifier le financement public ? L'évaluation contingente est une méthode habituellement utilisée en économie du patrimoine (naturel, culturel...) et qui consiste à estimer directement auprès des individus leur disposition à payer pour la préservation des monuments, l'entretien des parcs régionaux etc. D'autres méthodes existent comme les évaluations par analogie par lesquelles on estime la valeur d'un bien ou d'un service culturel par les dépenses monétaires et non monétaires qu'un individu effectue pour être en mesure d'en bénéficier (par exemple, temps de déplacement pour aller à l'Opéra, temps de préparation, abonnement à des revues spécialisées etc.).
Au niveau collectif, on obtient le surplus total des consommateurs en additionnant leurs surplus individuels pour chaque quantité en considérant la quantité totale du bien consommé par l'ensemble des consommateurs. Cela suppose que l'utilité soit mesurable et comparable d'un individu à l'autre. La courbe de demande d'un produit est alors obtenue simplement en additionnant pour chaque quantité du produit les dispositions à payer de tous les consommateurs.
Au niveau du marché, les économistes s'intéressent à la fonction de demande totale pour un bien ou un service. Celle-ci est obtenue par agrégation simple des quantités individuelles demandées pour chaque prix de ce bien ou de ce service. La demande totale est régie par une loi générale s'appliquant à la plupart des marchandises (« biens normaux ») : les quantités demandées d'un produit par les consommateurs diminuent avec son prix, « toutes choses étant égales par ailleurs ». Cette condition stipule tout simplement que le revenu du consommateur ou les prix des autres marchandises ne varient pas. Plus généralement, ce type d'analyse isole une variable (le prix ou le revenu, par exemple) pour expliquer la demande des ménages qui peut être par ailleurs soumise à de nombreux aléas comme l'évolution des pratiques et des effets de mode, de la conjoncture économique etc.
Dans certains cas, comme celui des biens addictifs (la cigarette, ou un concert pour un accro à la musique), la demande peut être insensible au prix. Dans d'autres cas, elle peut augmenter avec les prix (« biens supérieurs ») : on parle alors d'« effet Veblen » qui caractérise les comportements de snobisme ou de démonstration sociale (il s'agit notamment des produits de luxe, que les classes sociales élevées utilisent pour se distinguer). À l'inverse, la diminution du prix d'autres biens ou l'augmentation du revenu pour certaines catégories sociales peut entraîner une baisse de la consommation (les « biens ordinaires » comme le pain, que l'on abandonne au profit d'autres biens dès que ses revenus augmentent).
L'élasticité : mesurer la réactivité de la demande
L'outil généralement utilisé pour caractériser la demande pour un bien ou un groupe de consommateurs spécifique est la notion d'élasticité. Il s'agit d'un rapport de variations : quel est l'impact d'une variation de prix, de revenus, du prix d'autres biens, de la qualité du bien etc., sur la variation de la quantité consommée d'un bien ?
L'élasticité-prix ou élasticité directe de la demande par rapport au prix permet d'évaluer l'effet d'une augmentation de prix sur la quantité consommée d'un bien. Elle est généralement négative (une augmentation des prix provoque une diminution des quantités consommées d'un bien) ; elle est parfois positive (une augmentation des prix provoque une augmentation des quantités demandées, effet de snobisme). Lorsque l'élasticité-prix est inférieure à 1 (ou à -1), on dit que la demande est inélastique : par exemple, une hausse des prix du gaz en hiver n'entraîne qu'une baisse modérée, moins que proportionnelle de la consommation de gaz (ce qui traduit l'importance du besoin de se chauffer !). En revanche, pour les biens culturels, nous le verrons par la suite, la demande peut être très élastique.
Deux autres types d'élasticités sont également utilisés : l'élasticité-revenu et l'élasticité-croisée. La première se réfère à la sensibilité de la consommation en regard de l'évolution du pouvoir d'achat des consommateurs, et décrit la variation de la consommation d'un bien lorsque le revenu d'un consommateur ou d'un groupe augmente. Selon les lois de Engel, il existe trois catégories de biens : les biens inférieurs (élasticité-revenu inférieure à 1) : lorsque le revenu augmente, leur poids dans les dépenses diminue (ex. : le pain, les biens de mauvaise qualité etc.) ; les biens supérieurs (élasticité-revenu supérieure à 1) : leur part augmente avec l'accroissement du revenu (ex. : les biens de luxe, les biens culturels etc.) ; et les biens neutres (élasticité-revenu égale à 1) dont la part reste constante (la consommation d'eau).
L'élasticité-croisée met en relation les variations du prix d'un produit et de la quantité demandée d'un autre produit. Ce rapport est très utile pour analyser les frontières d'un marché et les liens existants entre les marchandises. Il permet de qualifier trois cas de figure selon que deux biens sont complémentaires, concurrents ou indépendants l'un de l'autre. Lorsque cette élasticité est négative, les deux biens sont complémentaires (c'est le cas lorsque l'augmentation du prix de l'essence provoque une baisse des achats ou de l'usage des voitures, les deux biens étant complémentaires à l'usage) et lorsqu'elle est positive, les deux biens sont substituables, donc concurrents (par exemple, l'augmentation du prix des voitures peut accroître l'usage des transports collectifs). À l'heure des services numériques, l'élasticité-croisée est particulièrement élevée entre les tablettes et autres mobiles substituables, et tout accroissement du prix ou du coût d'un service en ligne peut rapidement conduire les internautes à changer d'offre.
Structure de l'offre et stratégies industrielles
Léon Walras inventa la concurrence pure et parfaite comme outil pour mesurer l'efficience des marchés et les effets de leur fonctionnement sur le bien-être social. Les économistes ont par la suite étudié les situations de concurrence imparfaite. Les entreprises ont en effet une tendance forte à éviter la guerre des prix lorsqu'elles le peuvent.
Les firmes se distinguent des autres acteurs par leur objectif principal, qui est de maximiser leurs profits. Celui-ci est défini comme l'excès de recettes (chiffre d'affaires défini par la quantité vendue multipliée par le prix moyen par unité vendue) sur les coûts de production (la quantité produite totale multipliée par le coût unitaire moyen). Donc augmenter ses profits pour une firme consiste à accroître ses recettes (par exemple, en produisant ou en vendant plus, ou bien par l'innovation de produits, en se différenciant des concurrents, en offrant des produits nouveaux, ou encore en éliminant ses concurrents) ou à diminuer ses coûts de production. Les entreprises agissent généralement sous contrainte, en fixant les quantités et parfois les prix en réaction aux conditions du marché.
La productivité est définie comme le rapport entre une quantité produite (le « volume de production ») et les moyens (les « facteurs de production ») mis en œuvre pour l'obtenir. La productivité mesure ainsi l'efficacité des facteurs de production et de leur combinaison. Les gains de productivité sont obtenus lorsque la firme produit plus avec les mêmes moyens de production (une heure de travail aboutit à plus de bien ou de service produit) ou lorsqu'elle produit autant avec moins de moyens (réduire le nombre de salariés aboutit au même niveau de production). Les gains de productivité s'expliquent par de nombreux facteurs, comme l'adoption d'une technique de production supérieure, un changement dans l'organisation du travail, les effets d'apprentissage... La notion de gains de productivité apparaît d'une importance capitale au sein du système de la concurrence parfaite, puisqu'elle permet (en réduisant les coûts) de potentiellement maximiser les profits de l'entreprise. Cette dynamique particulière constitue le moteur de notre société actuelle, mais d'autres stratégies peuvent apparaître afin de permettre aux entreprises de développer leurs profits. Une firme peut ainsi jouer sur la quantité produite pour tenter d'exploiter des rendements d'échelle (stratégie de volume). Grâce aux gains de productivité obtenus, elle peut gagner des parts de marché sur ses concurrents, voire les éliminer, en réduisant ses prix ou en augmentant la qualité de son offre par le réinvestissement des marges bénéficiaires ainsi dégagées.
Monopoles
La concurrence parfaite suppose la confrontation d'un grand nombre d'acteurs de part et d'autre, de telle sorte que nul ne peut imposer sa stratégie aux autres, mais chacun se voit imposer les conditions du marché, en particulier des prix égaux aux coûts de revient. Il faut pour cela des conditions supplémentaires, très strictes et de ce fait difficilement observables dans la réalité : les firmes doivent fournir le même produit (pas de différenciation) selon des quantités insignifiantes par rapport à l'offre totale (on appelle cette hypothèse l'« atomicité ») de telle sorte que leur stratégie d'offre n'a aucune influence possible sur les prix et les quantités offertes sur un tel marché.
Le cas diamétralement opposé à la concurrence parfaite est celui du monopole : une seule firme offre un produit sur un marché donné avec un grand nombre de demandeurs (consommateurs, entreprises clientes etc.). Par définition, le monopoleur ne subit la concurrence d'aucun produit substituable et donc ne fait face qu'à la réaction de demandeurs dont dépendra le niveau de son « surprofit », sa rente de monopole. Une telle situation peut s'expliquer par l'existence de barrières à l'entrée qui empêchent l'apparition de concurrents qui pourraient amener le monopole à réduire ses prix et donc réduire ou faire disparaître sa rente de monopole. Ces barrières peuvent être artificielles : le monopole peut bénéficier d'une protection réglementaire par exemple (durant l'Ancien Régime, certains théâtres étaient les seuls à pouvoir jouer un certain répertoire). Elles peuvent être technologiques, un innovateur crée par définition de la nouveauté et donc est seul sur le marché qu'il vient de créer ; il bénéficie ainsi d'une rente de « premier arrivé » qui lui permet de financer parfois les coûts de développement de son innovation ou d'être simplement récompensé pour sa créativité. Elles peuvent être enfin stratégiques : une entreprise peut s'accaparer une ressource essentielle et empêcher tout concurrent de l'obtenir et donc d'entrer sur son marché (cela peut être le cas pour les contrats d'exclusivité que certaines firmes réalisent avec des auteurs ou des acteurs célèbres).
Les alternatives à la guerre des prix
Il est habituel de penser que le mode normal de concurrence entre les firmes est la guerre des prix. Or, quand elles le peuvent, les firmes créent les conditions pour éviter autant que possible ce type de concurrence. Dans bien des cas, elles préfèrent la concurrence hors prix, moins destructrice pour elles :
– la différenciation par la localisation ou par la qualité (le prix d'un produit différencié peut être supérieur aux autres produits) ; on distingue les différenciations horizontale (les firmes créent des produits de qualité différente en fonction de l'hétérogénéité des préférences des consommateurs) et verticale (à un prix donné, les consommateurs préfèrent de manière unanime un niveau de qualité d'un produit : un fauteuil confortable à un strapontin dans une salle de cinéma...) ;
– l'intégration verticale (rachat ou extension de l'activité en amont ou en aval de son activité – les stratégies d'intégration verticale se justifient par la baisse des coûts ainsi obtenue (moins d'intermédiation), mais également par la sécurisation et l'exclusivité en matière d'accès à une ressource rare ou à un marché) ;
– la concentration horizontale (par le rachat des concurrents) ;
– la coopération qui peut se traduire par une entente restrictive entre deux firmes pour éliminer les rivales ou empêcher l'entrée de nouveaux concurrents sur leur marché, ou par des coopérations en recherche et développement pour se différencier ensuite de la concurrence ou créer de nouveaux produits rendant obsolète l'offre existante.
Oligopole, oligopsone et concurrence monopolistique
Dans les faits, aucune activité n'est parfaitement concurrentielle ni parfaitement monopolistique. L'étude des marchés montre donc plutôt des cas intermédiaires parmi lesquels deux structures de marché sont particulièrement présentes dans les activités de la culture et de la communication, à savoir l'oligopole et la concurrence monopolistique.
L'oligopole est une situation où un petit nombre d'offreurs dominent le marché face à un très grand nombre de demandeurs. C'est une structure de marché fréquemment observée dans le domaine des activités culturelles, en particulier les majors dans les industries culturelles (cf. chapitre 9). Cette structure de marché ne poserait pas de problème si les concurrents agissaient en tant que tels. Or, dans les faits, le petit nombre facilite la communication entre les offreurs. Ainsi des entreprises peuvent s'entendre sur les prix de manière à recréer stratégiquement les conditions d'un monopole et se partager ainsi la rente inhérente à un tel comportement d'entente restrictive de la concurrence. Elles peuvent également ériger des barrières à l'entrée en excluant des fournisseurs, en verrouillant la distribution ou en ralentissant le changement technologique pour préserver leur position de marché.
Une structure de marché symétrique à l'oligopole est l'oligopsone, dans laquelle un petit nombre de demandeurs font face à un grand nombre d'offreurs. Il caractérise par exemple les relations marchandes entre écrivains et éditeurs ou entre distributeurs et producteurs de films et il s'analyse de manière similaire à l'oligopole. Ces structures de marché se retrouvent très fréquemment dans les activités artistiques, et notamment les industries culturelles, les ventes aux enchères d'œuvres d'art etc. Toutefois, nous le verrons, les majors coexistent (parfois en symbiose) avec une constellation de petites et moyennes structures dynamiques (petits labels, réseaux de distribution indépendants, petits vendeurs...) qui ne dépassent cependant guère le dixième de parts de marché (cf. chapitres 9 et 10).
La concurrence monopolistique est, comme son nom l'indique, une hybridation de la concurrence parfaite avec des éléments monopolistiques. De nombreux offreurs sont présents, mais leur offre est suffisamment différenciée pour qu'ils bénéficient d'un certain contrôle sur la fixation des prix. La concurrence s'établit en fonction des modifications apportées par chaque producteur à la qualité objective ou subjective de ses produits pour influencer les choix des consommateurs en augmentant l'élasticité-croisée entre son offre et les produits substituables. Chaque offreur bénéficie de la sorte d'un monopole « local » dans l'espace géographique ou dans celui des produits. Cette différenciation peut s'expliquer par un monopole géographique (des librairies éloignées les unes des autres, mais proposant la même offre de livres) ou par la publicité. Les prestations des artistes, les stations de radios ou les galeries d'art en constituent de bonnes illustrations.
La concurrence imparfaite est associée à des stratégies économiques très variées. Toutes ces stratégies visent à obtenir des avantages concurrentiels pour augmenter ses parts de marché, voire empêcher toute concurrence. La suite de cet ouvrage explore plus en détail certaines de ces stratégies.
. Voir notamment les chapitres de Scherer F. M., de Marchi N. et Miegroet H. in Ginsburgh V., Throsby D., Handbook of the Economics of Art and Culture, Amsterdam, Elsevier, vol. 1, 2006 ; ainsi que Dorléac B. L. (dir.), Le commerce de l'art de la Renaissance à nos jours, Besançon, La Manufacture, 1992.
. Cependant, pour David Ricardo (1772-1823), un des grands représentants de l'économie classique, certaines marchandises échappent à cette loi générale : c'est le cas des œuvres d'art dont le prix dépend du « caprice » et du « revenu » des acheteurs face à leur rareté découlant d'une non-reproductibilité par le travail.
. « Dans toute l'histoire, les ravages causés par les excès d'assertion individuelle sont quantitativement négligeables comparés aux boucheries organisées par transcendance altruiste pour la plus grande gloire d'un drapeau, d'un chef, d'une foi ou d'une conviction politique. » (Arthur Koestler, Janus. Esquisse d'un système, Paris, Calmann-Lévy, 1979, p. 88. Cité par Godbout J. T., Ce qui circule entre nous. Donner, recevoir, rendre, Paris, Le Seuil, 2007, p. 39).
. Sur l'histoire économique, on pourra se référer à Blaug M., La pensée économique : origine et développement, Paris, Economica, 1999 (Blaug est par ailleurs l'un des premiers auteurs à avoir écrit, en 1976, sur l'économie de l'art) ; le classique Schumpeter J., Histoire de l'analyse économique [1954], Paris, Gallimard, coll. « Tel », 2004 ; ou pour une introduction rapide : Valier J., Brève histoire de la pensée économique, Paris, Flammarion, coll. « Champs », 2005.
. Mandeville B. [1705], La ruche bourdonnante ou les crapules virées honnêtes, Paris, La bibliothèque, 1997. La fable raconte l'histoire d'une ruche prospère, bien que cette communauté vive dans la corruption (c'est-à-dire la dépense). La prospérité naît du jeu de ces pratiques moralement condamnables, le système absorbant les défauts individuels. Pour Mandeville, le progrès social s'explique par la recherche du bien-être, du luxe et non par des vertus d'abnégation et d'épargne. La fin est néanmoins triste : un jour, la ruche éprouve la nostalgie de la vertu et les citoyens renoncent à leur vie luxueuse pour épargner, la dépense devient une faute. Lorsque la ruche retrouve la vertu, le vice disparaît, mais également la prospérité. Pourquoi ? Parce que se développent alors l'inactivité et l'ennui. Cette fable fournit un enseignement essentiel : ce qui est vrai au niveau privé (le vice, le gaspillage par la dépense) devient faux au niveau collectif (la prospérité) ; le sous-titre de la fable des abeilles est d'ailleurs : « vices privés, bénéfices publics ».
. Voir Smith A., Recherches sur la nature et les causes de la richesse des nations [1776], Paris, Flammarion, 1991, vol. 2, p. 42-43.
. Walras L., Études d'économie appliquée, Lausanne, Corbaz. 2e édition, Paris, Pichon [1898] (1936), OEC, vol. X, Paris, Economica, 1992, p. 476.
. Du nom d'un économiste allemand, Heinrich von Stackelberg (1905-1946), qui représenta de la sorte différentes structures de marché du monopole à la concurrence parfaite en passant par l'oligopole, le monopsone etc.
. Nous n'envisageons pas ici les autres marchés comme ceux du travail ou du capital.
. On utilise souvent des scénarisations pour amener l'individu à révéler son véritable consentement à payer (par exemple, « L'État envisage de fermer l'Opéra Bastille faute de moyens. Combien seriez-vous prêt à payer pour pouvoir maintenir en activité cette institution ? »). Voir par exemple, pour le cas des musées : Martin F., Une méthode d'évaluation économique des musées, Montréal, HEC, Chaire de gestion des arts, 1993.
. Par exemple, si le prix de l'essence augmente fortement, mais que son revenu augmente dans les mêmes proportions, la consommation d'essence d'un individu ne diminuera pas. Le même résultat peut prévaloir si le prix de l'essence augmente, mais que le prix des principales alternatives (transports collectifs...) augmente également. D'où la précaution de la clause « toute chose étant égale par ailleurs » ou « ceteris paribus ».
. Veblen parle de consommation ostentatoire. Veblen T., Théorie de la classe des loisirs, Paris, Gallimard, 1970 (1899 pour l'éd. originale).
. Ernst Engel (1821-1896) était un statisticien allemand.
. Le critère de maximisation du profit n'est en fait pas le seul objectif de la firme, qui peut également être motivée par des objectifs philanthropiques (sponsoring par exemple), d'influence politique ou sur l'opinion (dans les médias, journaux associés à des partis politiques ou des religions). De même, il ne s'agit pas d'un objectif univoque : ainsi la théorie du « gouvernement d'entreprise » a montré que les dirigeants pouvaient ne pas maximiser les profits au détriment des actionnaires, lorsque cet objectif général ne coïncidait pas avec leur stratégie de carrière et de rémunération...
. De plus, l'information sur les technologies, l'offre de produits et les prix est parfaite, « transparente » (nulle possibilité de se différencier des autres concurrents), de même que les coûts d'entrée et de sortie du marché sont nuls.
. Il s'agit davantage de catégories analytiques permettant de mesurer l'écart entre des marchés existants et ces idéaux-types. Par exemple, plus un marché sera éloigné de l'idéal de la concurrence et donc proche de conditions monopolistiques, plus cela justifiera des procédures en matière de politique antitrust.
Chapitre 4
La logique publique
Si les penseurs libéraux privilégient depuis toujours l'économie de marché, la plupart d'entre eux reconnaissent – dès l'origine – qu'il existe des exceptions au système, conduisant la puissance publique à intervenir dans les échanges. Ainsi, la force publique et la défense nationale font partie des domaines pour lesquels la logique publique est reconnue : il s'agit notamment de garantir la défense des droits de propriété, le fonctionnement des transactions sur le marché intérieur, mais également de protéger les intérêts du pays de menaces extérieures, ou de parties extérieures qui ne respecteraient pas les accords conclus à l'étranger. Dans cette même perspective, la construction des routes, des ponts ou des ports, bref des infrastructures lourdes équipant le territoire et permettant de développer les échanges, recueille un consensus pour les envisager de manière publique.
Assez rapidement, certains risques du marché sont pointés du doigt : si les économistes néoclassiques privilégient les ajustements naturels réalisés par le marché, à terme, ils se doivent de reconnaître que celui-ci peut induire des pertes de revenu immédiates ainsi que des inégalités très importantes, du moins pendant une période déterminée. C'est notamment durant de telles périodes, qui constituent une grande partie du paysage économique du xixe siècle, que de nombreux auteurs, dans le sillage de Proudhon ou de Marx, décrivent la pauvreté, la misère et les révolutions engendrées par le système capitaliste. C'est évidemment dans une telle perspective que le rôle de l'État comme régulateur – par l'octroi d'un système de sécurité sociale ou de financement des périodes de chômage, peut intervenir afin de corriger de telles inégalités, ou d'éviter la disparition de certains secteurs d'activité. À la fin du xxe siècle, c'est aussi la question de la diversité des cultures et leur possible extinction – qui donnera lieu à la Convention sur la protection et la promotion de la diversité culturelle, initiée en 2005 à l'Unesco – qui va notamment être présentée comme nécessitant l'intervention publique (cf. chapitres 11 et 12).
Ainsi se dégagent trois modes à partir desquels la logique de marché peut être acceptée par tous, dont deux dépendent, paradoxalement, des pouvoirs publics. (1) Si comme le soulignent certains économistes, tout le monde y trouve son avantage, la logique de marché s'imposera d'elle-même ; une telle affirmation est cependant difficile à expliquer aux citoyens voyant leurs ressources diminuer au gré des fermetures d'usines. (2) La seconde possibilité qui dépend directement des pouvoirs publics est le recours à la force, afin de garantir les citoyens des risques d'émeutes ou de révolution, les invasions permettant le développement, dans une logique impérialiste, de nouveaux débouchés. (3) Enfin, la solution la plus couramment utilisée vise une certaine redistribution de la richesse par le biais de l'État, afin de désamorcer les risques les plus importants de révolte (les politiques d'austérité augmentant, à l'inverse, ce type de risques).
Si l'organisation du marché nécessite ainsi le recours à la puissance publique, afin d'en imposer les règles – notamment le respect des contrats et celui de la propriété privée – cette règle s'applique non seulement aux citoyens les plus pauvres (les plus démunis ne pouvant pas payer leurs dettes), mais aussi aux grands groupes pouvant développer une fâcheuse tendance à vouloir les contourner. La concurrence induit en effet, sur le plan théorique, la réduction des prix pour le consommateur et, dans le cas d'une concurrence parfaite, des profits nuls pour les producteurs vendeurs. En revanche, les ententes entre concurrents (cartels et oligopoles), de même que les monopoles, sont perçus comme des systèmes nettement plus favorables aux entreprises qui s'en rapprochent. C'est dans cette perspective que l'État a également pour rôle de veiller au respect de la concurrence, raison pour laquelle, au niveau de l'Union européenne par exemple, un commissaire est spécialement chargé des questions visant les fusions et acquisitions des grands groupes industriels (en ce compris dans le domaine des grandes industries culturelles). Les pouvoirs publics ont également le rôle ambigu de promouvoir les exportations de leur pays, tout en favorisant la production locale – et donc en freinant les importations étrangères. Les barrières douanières et les réglementations diverses ont ainsi pour objet de restreindre les importations, tandis que les subventions plus ou moins déguisées visent à promouvoir les exportations. De telles mesures – qui s'opposent aux principes de la liberté des marchés et des avantages comparatifs – appliquées par toutes les puissances commerciales de manière plus ou moins détournée, font l'objet de nombreux litiges réglés au niveau international, à l'Organisation mondiale du commerce notamment.
Le rôle de l'État
Le marché, régulièrement présenté comme le système optimal d'organisation des échanges, requiert cependant qu'un certain nombre de règles soient respectées. Pour autant, producteurs et consommateurs souhaitent contourner ces dernières, le bénéfice de l'un s'opérant au détriment des autres. Les pouvoirs publics, dans une telle perspective, ont un premier rôle d'arbitrage et de contrainte, visant à faire respecter les règles par toutes les parties voire, lorsque la partie s'échauffe, à les changer. De manière plus générale, ils peuvent également jouer un rôle plus actif, par le biais de politiques spécifiques, visant notamment à maintenir et développer l'offre culturelle, mais aussi faire bénéficier l'ensemble des citoyens des effets indirects entraînés par la présence d'organisations culturelles.
Fonctionnement et contrôle
Globalement, les pouvoirs publics exercent une action à deux niveaux : d'une part, ils encadrent les systèmes d'échanges et assurent un contrôle de la régularité des transactions ; d'autre part, ils visent, par des systèmes de prélèvement et de redistribution, à exercer une influence sur le développement de la richesse commune.
Encadrement et contrôle. L'organisation générale du dispositif public repose sur un système législatif (qui va de l'échelon communal au mondial) adopté par les citoyens ou leurs représentants. Outre les règles générales portant sur la question des échanges, que l'on retrouve dans le doit privé, le droit public ou le droit commercial, l'État peut intervenir, dans le domaine de la culture notamment, par le biais de dispositifs légaux particuliers, comme le règlement des droits d'auteur, la législation sur le prix unique du livre, l'organisation de réseaux de musées, l'encadrement du bénévolat etc. Si l'État encadre, il se doit également de disposer d'instruments pour s'assurer que les règlements – ainsi que les politiques qu'il met en œuvre, sont bien assurées. La question du contrôle s'exprime de deux manières différentes : la plus classique consiste à vérifier – par le biais de son administration – que les directives sont bien appliquées, mais les questions d'évaluation des politiques font également partie de ce dispositif général, incluant nombre d'indicateurs statistiques dont la collecte occupe une place importante de l'activité des organisations contrôlées (cf. conclusion générale).
Fonctionnement et subventions. L'instrument auquel une organisation culturelle pense immédiatement, en matière de politique publique, est le financement public par le moyen de subventions. Celles-ci, décidées au niveau politique, sont organisées par les administrations (ministère de la Culture, DRAC etc.). Sous cette appellation, on retrouve en fait nombre de possibilités différentes : une instance publique peut en effet décider d'organiser complètement un service culturel (un musée, une bibliothèque) en l'intégrant dans son administration, déléguer sa gestion à un organisme public ou mixte, ou contribuer à son financement en lui octroyant des subventions. À ce niveau également, les subventions peuvent être directement octroyées par le ministère, combinées par le biais de partenariats entre plusieurs instances publiques, voire privées, ou versées à un organisme indépendant qui les redistribuera (c'est le cas de la Grande-Bretagne, qui la première a créé en 1940 le Council for the Encouragement of Music and the Arts (CEMA), baptisé Arts Council après la guerre, et qui fut présidé par Keynes).
Dispositifs incitatifs. L'État peut également présenter des mesures incitatives, laissées à l'appréciation du marché. Ainsi, les lois en faveur du sponsoring ou du mécénat (déductibilité fiscale pour les dons en nature ou en espèce), ainsi que le mécanisme de dation, de même que la création de niches fiscales spécifiques (tax shelter), comme il en existe pour le financement du cinéma, visent à promouvoir un certain nombre de mesures par le biais non pas de subventions, mais de la possibilité de moindres prélèvements, et donc aussi de moindres recettes fiscales. Ce principe, bien plus que celui des subventions, est privilégié aux États-Unis.
Prélèvements et redistributions. Le mécanisme des subventions repose forcément sur l'agent que le contribuable verse par le biais de ses impôts, ou par les taxes qu'il paie sur les produits qu'il achète, par les amendes ou par les recettes que l'État percevrait de l'exploitation d'une activité. C'est à partir de ces recettes que les budgets de l'État et des collectivités locales sont constitués. Un tel mécanisme peut également être envisagé à un niveau sectoriel, la perception des taxes permettant ainsi d'alimenter un fonds lié à l'activité du secteur. Au niveau des industries culturelles, nombre de secteurs sont ainsi alimentés par de telles taxes : les taxes sur les billets de cinéma alimentent le Centre national du cinéma et de l'image animée, le même principe s'appliquant pour les spectacles de variétés et le théâtre privé (pour le livre, le Centre national du livre est surtout alimenté par une taxe sur les appareils de reproduction).
Une histoire ancienne
La logique publique remonte donc, en théorie, au moins aussi loin que celle du marché. Il semblerait même qu'elle le précède. C'est selon cette logique que le principe d'une mise en commun des efforts et des ressources a permis de réaliser des travaux bénéficiant à l'ensemble d'une population (ponts, routes, armées), dont les bénéfices pouvaient être (partiellement) redistribués à l'intérieur de la population. Peu importe, dans de telles conditions, le système politique : la logique publique, si elle donne des résultats différents en fonction du mode d'organisation (royaume, empire, république, tyrannie, dictature) est d'abord associée à son ou ses dirigeants personnifiant le système. C'est à partir de ces mêmes dirigeants que s'est également organisé le lien entre culture et pouvoirs publics.
D'emblée, on remarque ainsi depuis l'Antiquité une logique de capitalisation de la richesse passant par les objets d'art, au travers de collections dans les cours princières, l'accueil et la protection des artistes dans les cours ainsi que la construction d'infrastructures spécifiques administrées par le prince (ou son représentant). Si, durant le Moyen Âge, cette prérogative est largement dominée par l'Église (nous y reviendrons en abordant la logique du don), à partir de la Renaissance, le pouvoir temporel reprend progressivement la main sur le secteur, lui assurant son soutien de manière à la fois privée (en tant que protecteur et philanthrope) et publique (à partir de capitaux clairement identifiés comme n'appartenant pas au prince).
La société de l'Ancien Régime, qui sera aboli à la Révolution française, repose sur une structure très largement hybride, combinant à la fois dons, protection et organisation publique. Ainsi, le système d'organisation des métiers – et, dans une large partie, celui des échanges ou de la fixation des prix – constitue une combinaison particulière différant singulièrement des règles du marché : les peintres, les orfèvres, les libraires, sont regroupés en autant de corporations dont l'organisation privilégie le protectionnisme et des modes de recrutement par parrainage (de l'apprenti au maître). Un tel système, accepté et défendu par les pouvoirs publics, sera largement combattu par les théoriciens du libéralisme (il ne privilégie pas assez les règles du marché), puis supprimé à la Révolution française.
Le domaine public et les premières institutions culturelles (xvie\- xviie siècle)
L'un des acquis de l'Ancien Régime, visant à séparer la personne privée du Roi et la personne publique, est la notion de domaine public. Le principe du domaine public, tel qu'il est établi en France au xvie siècle, vise à identifier certains biens dont le Roi ne peut disposer à sa guise, afin de maintenir l'intégrité du patrimoine à transmettre et la puissance économique du territoire. C'est dans cette perspective que, sous François 1er, les joyaux de la Couronne sont déclarés inaliénables, mais c'est surtout l'Édit de Moulins, signé par Charles IX en 1566 et proclamant l'inaliénabilité des domaines royaux, qui constitue la référence du domaine public. Il s'agit de prévenir, en l'occurrence, une possible fragmentation du territoire français, alors encore bien fragile. Mais l'Édit marque, symboliquement, le fait que la propriété de certains biens, transmise de générations en générations, ne peut être organisée selon des règles identiques à celles d'autres biens. La notion de domaine public, consacrant l'ensemble des biens possédés par l'État, demeure fondamentale de nos jours : les biens qui lui appartiennent sont inaliénables et imprescriptibles. Ils peuvent cependant faire l'objet d'une mesure de déclassement (pour cause d'obsolescence, ce qui permet leur destruction ou leur vente). Dès la Révolution française, un lien fort entre les biens du patrimoine et la notion de domaine public se crée, marquant les principes particuliers qui en découlent – par exemple l'impossibilité de vente des collections des musées, en France.
La France constitue sans doute un modèle particulier pour le développement de grandes institutions culturelles publiques. Un tel modèle diffère de celui d'autres pays, comme la Grande-Bretagne où les théâtres privés se développent de manière nettement plus rapide à Londres qu'à Paris. Durant le siècle de Louis XIV, la culture s'impose progressivement comme instrument politique. L'architecture de Versailles, de même que l'ensemble des arts (musique, théâtre, danse, peinture...) participent du prestige de la France, tandis que la politique de Colbert permet le développement des grandes manufactures (de porcelaines ou de tapisseries), dans lesquelles l'art se décline comme facteur de développement économique. Le monopole de l'Académie royale des beaux-arts (sous Louis XIII), de même que la création de l'Académie royale de musique (l'opéra) et la Comédie française, présente les traits d'une véritable politique culturelle, par ailleurs moins liée au développement qu'au prestige de la France et de la personne du Roi.
Vers un nouveau mode d'organisation (xviiie-xixe siècles)
L'effritement progressif de la puissance royale en France s'accompagne du développement du libéralisme, tant sur le plan de la pensée (politique) que dans ses applications économiques. L'esprit de l'encyclopédisme prêche pour un changement des privilèges, tant au niveau politique que dans le domaine des arts, afin que s'instaure une nouvelle relation entre l'artiste et ses commanditaires. C'est dans un tel contexte qu'est notamment créée par Beaumarchais, en 1777, la Société des auteurs et compositeurs dramatiques (SACD). La période révolutionnaire conduit à la nationalisation des institutions autrefois propriétés du prince. Ainsi en va-t-il de l'Opéra, mais aussi du Jardin du Roi ou des collections royales, qui sont instituées en musées en 1793 (le Musée central des Arts, au Louvre). C'est dans cette même logique que la nation révolutionnaire entend se doter d'outils publics. Ainsi le Conservatoire national des arts et métiers est créé un an plus tard, afin de développer l'économie. Nationalisations d'une part, réglementation de l'autre. S'il se substitue au Roi, le nouveau régime – tiraillé entre partisans d'une réglementation très libérale fondée sur la propriété privée, et la tentation d'une gestion collective – entend bien appliquer les nouvelles libertés, tout en ne laissant pas au marché l'ensemble des matières qui étaient autrefois traitées par l'entremise du pouvoir royal. Ainsi, certains théâtres sont-ils directement gérés par l'État, tandis que les autres font l'objet d'une réglementation et que l'on légifère sur le droit d'auteur.
Tout au long du xixe siècle, la succession des régimes – république, empire, royauté – entraîne une variation des libertés et des mesures de soutien en matière de gestion et d'organisation de la culture. Les premières réglementations – politiques en matière de théâtre ou de bibliothèques, puis de musées – nécessitent la mise en place d'une administration afin d'appliquer les mesures. Ainsi l'administration des beaux-arts se constitue-t-elle lentement, d'abord au sein d'autres ministères, avant de connaître son autonomie, de manière très éphémère en 1848 et 1936, puis de manière plus pérenne, en 1959 avec Malraux.
La Troisième République, un moment contrasté
La Troisième République (1870-1940) constitue un moment de référence pour le développement de la culture en France. Elle est marquée par une politique très libérale, qui n'est pas sans rappeler celle que les États-Unis mènent actuellement, et les contours de sa « politique culturelle » (le terme n'existe pas encore) demeurent extrêmement réduits. Le rôle de l'État s'est largement concentré sur les questions du maintien de l'ordre dans la société, et de l'unité nationale. Dans cette perspective, l'idée de former des citoyens, aptes à décider de leur prise en charge, s'impose sur les autres. L'École de Jules Ferry, creuset des valeurs de l'État laïque et républicain, constitue un vecteur de la cohésion nationale. S'il s'agit bien de former des citoyens (raisonnant), c'est à ceux-ci qu'il reviendra de décider, en consommateurs éclairés, des éléments de culture qu'ils entendront soutenir. Aussi l'intervention de l'État en matière de culture, demeure-t-elle largement limitée, sinon pour ce qui concerne la protection du patrimoine (vecteur d'histoire et d'unité nationale). En revanche, les arts vivants (musique, théâtre ou beaux-arts) sont largement laissés aux mains du marché. Dans le contexte international que connaît alors la France, Paris s'impose comme principale capitale de la culture, tant pour ce qui concerne le marché de l'art que pour la diffusion du goût et de la mode. Si la situation au niveau des musées et du patrimoine s'avère relativement prospère, les arts du spectacle connaissent une situation plus difficile : le recours au marché privilégie le répertoire de boulevard, au détriment du théâtre d'auteur. La politique culturelle des années 1980 sera parfois fustigée en référence à cette période marquée par l'absence de soutien public, présentée comme source de vitalité de la création artistique à cette époque.
Durant cette époque, un modèle alternatif se met progressivement en place, alimenté par la pensée de Proudhon, puis celle de Marx. La première internationale des travailleurs, en 1864, a lieu à Londres, et trois ans plus tard est publiée la première partie du Capital. La révolution russe, en 1917, et les bouleversements qui s'ensuivent durant l'entre-deux-guerres constituent une alternative en matière de politique économique, mais aussi pour ce qui concerne le financement de la culture. La liberté picturale ou cinématographique, que l'on observe durant les premières années du régime soviétique laisse quelques années plus tard la place à un encadrement plus rigoureux, conditionné par la volonté d'un art plus réaliste, la culture – comme dans tous les pays tentés par le totalitarisme – s'imposant comme un vecteur potentiel de propagande du régime. Ainsi, l'URSS connaît un développement considérable de son réseau culturel (musées, théâtres, salles de concert, cinémas), pris en charge par l'État. D'une certaine manière, ce principe va influencer largement, jusque dans les années 1980, la définition de l'intervention de l'État dans la culture. Car qu'il s'agisse du New Deal, lancé au début des années 1930 aux États-Unis, ou de la politique du Front populaire (les deux comprenant un volet relativement important de subventions en faveur de la culture), chacune des alternatives se doit de se positionner face aux propositions communistes ou aux régimes d'extrême-droite, les deux privilégiant l'investissement culturel.
Les suites de la Seconde Guerre mondiale et la démocratisation de la culture
Cette logique va se poursuivre au sortir de la Seconde Guerre mondiale, durant les trente glorieuses. L'intervention publique, prônée par la pensée keynésienne, constitue non seulement une réponse aux logiques trop libérales précédentes, mais se confronte également au système en vigueur au sein du bloc soviétique. La social-démocratie, qui en résulte, privilégie un renforcement de l'État, certes pas dans des proportions aussi importantes qu'en Union Soviétique ou qu'en Chine, mais néanmoins suffisamment fortes pour avoir une influence dans de nombreux secteurs, notamment celui de la culture.
Cette époque constitue un tournant important pour la culture en France. C'est à ce moment que Paris perd sa place, comme « capitale de l'art », au bénéfice de New York. Mais si les États-Unis se présentent alors comme le lieu de l'art moderne par excellence, ils sont aussi le domaine des industries culturelles et, d'une certaine manière, le théâtre d'une transformation de la culture, tel qu'elle est dénoncée aussi bien par Hannah Arendt que par Adorno et Horkheimer. En France, la Troisième République (on entre alors dans la cinquième) est utilisée comme repoussoir pour promouvoir, progressivement, la démocratisation de la culture. Un tel principe est largement conditionné par l'action culturelle qui est progressivement mise en place – notamment à travers la politique du Théâtre national populaire, de Jean Vilar – et vise à faire partager une même culture, pour conduire à promouvoir la démocratie. C'est dans cette perspective que la mise en place du ministère des Affaires culturelles, avec à sa tête André Malraux, positionne son action : faire partager au plus grand nombre les grandes œuvres de l'humanité, faire « aimer » l'art, non l'enseigner ou éduquer, en donnant l'accès à tous, notamment par la constitution d'un réseau de maisons de la culture à travers la France. Ministre emblématique, car le premier et l'un de ceux dont l'action sera la plus longue (1959-1969), André Malraux dispose cependant d'un budget relativement restreint, son action étant essentiellement limitée aux beaux-arts et au cinéma.
De la démocratie culturelle aux industries culturelles
Une certaine vision de la culture conçue comme l'ensemble des grandes œuvres de l'humanité est progressivement remise en cause (de part et d'autre de l'Atlantique, par ailleurs). Contre la culture de Malraux, des voix s'élèvent pour exiger un agrandissement du périmètre de l'intervention en matière d'art et de culture. Il ne s'agit plus de démocratiser une certaine culture, mais de soutenir de manière démocratique des pratiques culturelles plus étendues, et notamment en matière de culture populaire. Cette logique, que l'on perçoit au travers de l'intervention du ministre de la Culture de l'époque, Jacques Duhamel, va connaître un développement considérable durant les deux septennats de François Mitterrand et le ministère de Jack Lang (1981-86 et 1988-93). Le doublement des crédits de la culture, pour arriver à l'obtention d'1 % du budget global de l'État, constitue une victoire en matière d'intervention culturelle, en permettant le renforcement du soutien aux arts classiques, mais aussi l'ouverture à de nombreuses formes plus récentes (rap, tag etc.), tout en développant la dimension festive de la culture (fête de la musique, fureur de lire, journées du patrimoine etc.).
Deuxième grand moment après Malraux en France, le ministère Lang constitue une période d'abondance et de transformations au niveau de l'intervention publique en matière de culture. Il s'agit, d'une part, de poursuivre le programme de déconcentration entamé vingt ans plus tôt, afin de doter l'ensemble du territoire d'infrastructure d'accueil contemporaine, soit par de nouvelles constructions, soit par des rénovations importantes. Parallèlement, un mouvement de déconcentration du pouvoir de décision voit le jour (avec la création des DRAC et FRAC), tandis que certaines compétences culturelles, naguère portées par l'État central, sont confiées aux régions. Une telle logique décentralisatrice s'observe en fait progressivement à travers toute l'Europe, qui dès cette époque se pense à travers ses régions. Si l'on se réfère à la période des années 1980 comme celle du doublement des budgets consacrés à la culture, permettant l'intervention dans de nouveaux secteurs, paradoxalement, cet accroissement des compétences passe également par un lien plus soutenu entre la culture et le secteur industriel qui lui est proche, soit le livre, le cinéma et la musique enregistrée. C'est à partir de ce moment que la culture est également présentée comme un secteur économique. Une telle logique s'inscrit dans un mouvement plus vaste, déjà évoqué au chapitre précédent, visant à promouvoir la logique de marché dans les échanges, en ce compris ceux de la culture.
Raisons du soutien public
De manière plus générale, en effet, la contestation du rôle de l'État (son inefficacité et ses choix discutables), dès la fin des années 1970 (Friedmann ou Hayek), vise à promouvoir la diminution de son périmètre d'intervention, notamment en matière de culture.
Un a priori négatif
Dans tout système démocratique, le débat sur le financement public constitue un défi pour le monde de la culture. Le soutien public, en la matière, est loin de faire l'unanimité. Trois raisons principales sont souvent mentionnées. D'une part, certains secteurs (la pauvreté, les soins de santé ou la criminalité) sont présentés comme prioritaires par rapport à la culture et le soutien public, en outre, pourrait provoquer la diminution des contributions privées (la philanthropie). D'autre part, la créativité s'accommode mal, selon certains, avec les subventions : l'artiste ne devrait pas bénéficier d'un trop grand confort, au risque de voir sa créativité s'émousser (ce serait la même chose pour les organisations culturelles). Enfin, l'intervention publique est vue comme un risque possible de censure pour l'art – en dictant ses choix.
De manière plus générale, dans la logique libérale, le test du marché est présenté comme vital pour le bon équilibre des échanges : il revient aux consommateurs ou aux citoyens de décider, et non à l'État. Dans cette perspective, le principal devoir de l'État, en matière de culture, serait de former des citoyens responsables... en mesure de décider, eux-mêmes, ce qu'ils jugeront bon d'acquérir, ou de soutenir par la philanthropie. C'est notamment le cas de Tyler Cowen, qui voit dans la logique de marché un système idéal pour l'innovation artistique et la promotion de la culture. Dans une optique (caricaturalement) darwinienne, seuls, les bonnes idées et les bons produits parviennent à prospérer, tandis que les artistes médiocres disparaîtraient.
On peut s'interroger, bien sûr, sur le test du marché, tel qu'il est ici présenté : apparemment démocratique – puisqu'il repose sur le plébiscite par l'achat, auquel tous les citoyens pourraient théoriquement participer – il repose de manière sous-jacente sur le principe d'un pouvoir d'achat plus ou moins équivalent pour tous, ce qui est loin d'être acquis. S'il s'agit d'une sorte de suffrage, c'est bien plus directement à un suffrage censitaire, tel qu'il s'appliquait justement à la fin du xixe siècle dans de nombreux pays, que l'on peut se référer.
Biens publics, biens mixtes et études d'impact
Par-delà ces premiers arguments, les économistes s'accordent généralement sur le fait que certains biens dits « publics » ne peuvent être totalement pris en charge par le marché (cf. chapitre 3). La logique des biens culturels n'échappe cependant pas totalement aux lois du marché, comme nous l'avons évoqué plus haut. William Baumol, parmi les premiers, évoque ce débat pour la culture, et remarquant le caractère non public des biens culturels, souligne cependant leur caractère mixte. Les biens ou services mixtes, en ce sens, sont constitués d'une partie fonctionnant selon les règles du marché, mais d'une autre échappant partiellement à celles-ci. Ainsi, un théâtre lyrique ou un musée célèbre ne sont pas des biens publics, mais leur fonctionnement contribue au prestige ou au dynamisme économique de toute une région, prestige qui retombe sur tous les citoyens, consommateurs ou non de culture. De tous ces éléments – prestige, possibilité pour la population d'utiliser les infrastructures, impact économique – seul le dernier peut être directement estimé d'un point de vue économique (les autres pouvant faire l'objet d'une enquête sur la disposition à payer).
La question des études d'impact ou d'évaluation économique, qui est devenue très importante de nos jours, part de ces présupposés. La logique est assez simple : un festival, un concert ou une exposition attirent des spectateurs qui sans cela ne seraient pas venus et vont consommer, dans la région, bien plus que l'entrée au spectacle : nuits d'hôtel, restaurants, achats dans les boutiques, constituent des revenus indirects qu'il importe de prendre en compte. À ces revenus s'en ajoutent d'autres, induits par cette consommation (les restaurateurs ou les hôteliers etc., vont à leur tour consommer davantage). Cet effet multiplicateur, largement discuté, a été longuement utilisé dans tous les secteurs pour justifier l'intervention publique. L'une des premières études, dans le secteur de la culture en France, a été lancée en 1986 sur le festival d'Avignon montrant que les flux indirects générés par le festival dépassaient largement les subventions octroyées par les pouvoirs publics. C'est en effet à cette époque que, un peu partout dans le monde, sont publiées de nombreuses études visant à montrer l'importance du secteur culturel sur le plan économique sont réalisées, et ce sont surtout les revenus considérables générés par le Musée Guggenheim de Bilbao qui ont constitué, à partir des années 2000, la référence en matière d'investissement culturel et d'impact économique.
De telles méthodes sont à manier avec prudence, et toutes les études, à cet égard, ne se valent pas : de nombreuses enquêtes sont réalisées à des fins de justification, voire de propagande afin de montrer l'intérêt d'une dépense, et il s'avère souvent aisé de multiplier les effets, en gonflant les estimations supposées des dépenses des visiteurs, ou en estimant de manière un peu plus généreuse le multiplicateur.
Soutien public et passagers clandestins
Mis à part les questions économiques, d'autres raisons sont évoquées pour justifier le soutien économique à la culture. Parmi celles-ci, les questions d'égalité d'accès à la culture – tout le monde ne dispose pas du même pouvoir d'achat – et celles de l'éducation des plus jeunes sont régulièrement citées. De nombreux biens culturels (l'opéra ou l'art contemporain) sont effectivement présentés comme des biens d'expérience (cf. supra), dont un premier contact (une première visite...) ne permet pas d'apprécier toutes les qualités. Aussi les pouvoirs publics se doivent-ils de favoriser cet accès, du moins aux plus jeunes qui pourraient ainsi, durant leur scolarité par exemple, se former progressivement à certaines disciplines artistiques d'un abord difficile. Un tel principe revient à permettre aux plus jeunes générations de bénéficier d'une offre que leurs parents pourraient ne pas leur offrir, soit parce qu'ils n'en auraient pas les moyens, soit parce qu'ils n'en ressentiraient pas le besoin. Enfin, et nous le développerons plus loin, la dernière raison régulièrement évoquée pour le soutien public, développée par William Baumol pour le secteur des arts de la scène, réside dans le fait que le secteur artistique ne bénéficie pas de gains de productivité et, à ce titre, est concurrencé par les autres secteurs, au risque de disparaître ; nous y reviendrons au chapitre 6.
Qu'il s'agisse de biens publics ou de biens mixtes, une partie de la « production » du secteur de la culture est disponible pour tous (critère de non-exclusion) : tous les consommateurs peuvent en bénéficier, même ceux qui n'auraient pas payé indirectement pour le service, par exemple sous forme d'impôts. Le problème de ces « passagers clandestins » (ou free riders) se pose dans nombre de prestations culturelles subventionnées, par exemple lorsqu'un festival propose une entrée gratuite : les touristes étrangers peuvent en bénéficier, sans jamais participer à leur financement. Cet argument a par exemple été évoqué dès le xixe siècle pour les musées qui, traditionnellement, étaient gratuits en France, alors qu'ils étaient payants dans d'autres pays.
La diversité culturelle et ses dérèglements
La question de la diversité culturelle va, au début du xxe siècle, constituer une nouvelle pomme de discorde entre les partisans et les opposants à l'intervention publique (cf. chapitre 11). Les enjeux, à ce niveau, sont moins idéologiques que clairement financiers, opposant les États entre eux, notamment la France et les États-Unis dont l'industrie cinématographique constitue l'un des moteurs de la balance commerciale américaine. Les accords commerciaux à travers le monde, longtemps réglés par les accords du GATT (General Agreement on Tariffs and Trade), sont transposés, à partir de 1995, au sein de l'Organisation mondiale du commerce (OMC). Cet organe, composé en 2014 de 160 membres, est chargé de développer les principes (et les bénéfices) du libre-échange à travers le monde, ce qui suppose l'abaissement des barrières douanières et des subventions ou autres règles visant à protéger les États. Pendant longtemps, les négociations concernant le domaine de la culture vont être évitées, l'Union européenne (qui représente ses pays adhérents) évoquant le principe d'exception culturelle – notion complexe, mais vague et jamais réellement définie – afin de ne pas aborder ces matières. Un tel principe soulève progressivement nombre de critiques quant aux limites de sa mise en œuvre, mais aussi pour ce qui concerne les résultats obtenus en matière de développement culturel. Les négociations menées au sein de l'OMC s'avérant de plus en plus ardues, et le maintien du principe d'exception culturelle de plus en plus hasardeux, le débat va être partiellement déplacé (par le biais d'un jeu diplomatique largement mené par la France) au sein de l'Unesco, avec la préparation de la Convention sur la protection et la promotion de la diversité des expressions culturelles, en 2005. La notion de diversité, elle aussi définie de manière relativement vague (du moins d'un point de vue économique), s'appuie cependant partiellement sur le potentiel économique de la culture (cf. chapitre 12). La Convention entre en vigueur deux ans plus tard, après avoir été ratifiée par plus de 30 États. Cela n'empêchera pas les industries culturelles de poursuivre leur évolution, ni le scepticisme de nombreux économistes de persister et les États-Unis de se lancer dans des négociations bilatérales avec l'Union européenne, évitant pour l'instant le domaine culturel.
De la logique publique à l'économie planifiée
La logique de l'intervention publique implique la mise en place d'une administration chargée d'exécuter les tâches dévolues à l'autorité, qu'il s'agisse de surveiller, de réguler ou de subventionner des actions. La logique administrative n'est pas l'apanage des pouvoirs publics : on la retrouve dans toute organisation de taille moyenne. Au niveau public, certains principes administratifs récurrents ont été dégagés, que l'on présente sous le concept de « lois de Rolland », du nom du juriste qui les a émises. Il s'agit du principe de continuité du service public (l'assujetti doit bénéficier d'un fonctionnement continu et régulier), du principe de mutabilité (afin d'adapter l'organisation à l'évolution des besoins de l'intérêt général), des principes d'égalité et de neutralité (garantir l'égalité de traitement de tous les citoyens). Ces quelques principes (il en est d'autres, tel que la valeur ajoutée nulle, la légalité ou la transparence) permettent de comprendre, notamment, certaines des caractéristiques essentielles de la logique publique. L'égalité de traitement, par exemple, s'oppose aux rapports de force pouvant se présenter dans une situation de marché ; de même, l'idée de continuité dépasse le court terme pour s'inscrire dans une logique de longue durée.
Lourdeurs administratives
De tels principes visant à promouvoir la raison et l'équité engendrent cependant de possibles dysfonctionnements. Ainsi, la préparation d'une loi ou d'un règlement se doit de respecter toutes les règles visant à assurer la légalité des principes qu'elle met en œuvre, et examiner toutes les situations possibles dans lesquelles celle-ci serait appliquée. Mais de telles procédures, comme celles qui visent à valider une décision, requièrent un temps parfois considérable, souvent plus long que celui qu'on observe dans une temporalité de marché. Ainsi, entre la décision ministérielle et sa mise en œuvre pratique, plusieurs mois (ou plusieurs années) peuvent s'écouler...
La machinerie administrative, visant à garantir l'équité du traitement de tous les citoyens, engendre ainsi de multiples lourdeurs, ressenties parfois avec exaspération par les mêmes citoyens : « C'est peu de dire que l'administration de la culture est devenue impopulaire : elle exaspère. Elle encourt bien sûr les habituels reproches faits à l'État : suffisant et insuffisant, pingre et gaspilleur, paperassier pour les autres, négligent pour lui-même, omniprésent dans la vie quotidienne, absent ou impuissant dans les coups durs, lent ou aboulique dans l'action, précipité dans la bêtise, arrogant aux petits, lâche devant les puissants, prompt à proliférer, rétif à la réforme ».
L'économie planifiée, ou la lourdeur à son paroxysme
La logique politique qui prévalait dans l'économie planifiée, en cours dans les pays de l'Est, constitue en quelque sorte l'archétype du sentiment de lourdeur ou d'inertie administrative, bloquant les processus de décision ou de redistribution par l'État – tout en engendrant, par défaut, des zones de passe-droit à partir d'autres rapports de pouvoir.
Marx, présenté comme le dernier des classiques, part d'une définition de la valeur fondée à partir du processus de production, et non de l'utilité des consommateurs (selon l'approche marginaliste des néo-classiques). Si l'un des axiomes de l'économie de marché postule la fixation des prix et des quantités par la rencontre de l'offre et la demande, le raisonnement est tout autre en économie planifiée. C'est l'État, en effet, qui détermine les prix (calculés en fonction des coûts de production) et la production dont les moyens ont été collectivisés. La détermination de la production (par l'administration ou les conseils ouvriers) nécessite une connaissance fine des besoins de la population ; les défauts de prévision engendrant des files dans les magasins ou le stockage des surplus.
L'implosion du système soviétique est partiellement liée à la faillite de son système de production, la complexité de plus en plus grande des produits manufacturés ne pouvant être gérée par un tel système de calcul, et les pénuries résultant des failles de la planification.
La critique néolibérale... mais aussi marxiste
Pendant longtemps, le système soviétique a fait office d'épouvantail permettant de dénoncer les maux liés à la prise en charge, par l'État, des besoins du citoyen. La chute du mur de Berlin a plus directement permis de montrer que la critique néolibérale, à partir des années 1970, visait toute forme d'intervention publique – et pas seulement les régimes totalitaires – afin de prôner un marché « pur ».
Globalement, même dans les régimes démocratiques, la puissance publique est présentée comme forcément contrôlée par des groupements d'acteurs agissant non par altruisme, mais pour leur propre profit. Ainsi, de nombreux travaux de l'école du public choice représentent le jeu politique comme biaisé par les intérêts particuliers de groupes auxquels les responsables politiques sont amenés à s'adresser. Dans de telles conditions, il s'avère presque inéluctable, afin de préserver les intérêts de chacun – responsables politiques et groupes de pression – d'allouer des dépenses publiques de manière non optimale.
Selon cette vision, le gestionnaire culturel vivant des dépenses publiques va tenter, par tous les moyens, de conserver sa position. L'une des critiques qui peuvent lui être adressées visera le possible déficit qu'il induirait. Aussi veillera-t-il, le plus souvent, à demander – sauf contre ordre – un budget plutôt supérieur à celui qu'il avait reçu les années précédentes.
C'est dans une telle perspective qu'un certain nombre de critiques liées aux politiques culturelles ont été réalisées, dénonçant la gabegie financière entraînée par des politiques peu responsables. Ainsi, l'économiste William Grampp voit-il dans le fonctionnement des musées subventionnés par l'État, une logique guidée par la recherche de subventions perpétuelles, comme de véritables rentes (rent seeking) : les directeurs et conservateurs préfèrent accroître leur déficit et miser sur des politiques favorables à leurs pairs, comme le fait d'accroître la collection, plutôt que de véritablement satisfaire le marché en proposant des expositions populaires. Sa solution : supprimer toutes les subventions afin de diminuer l'offre muséale, mais de la mettre aux dimensions du marché... De la même manière, l'analyse par Xavier Dupuis du fonctionnement de l'opéra, comme celle du Festival de Salzbourg par Werner W. Pommerehene et Bruno S. Frey, visent à montrer que les gestionnaires des organisations culturelles, confortés par la logique de subvention privilégient largement la qualité (susceptible de plaire à leurs pairs autant qu'au public) sur les impératifs de maîtrise des dépenses, entraînant une augmentation importante des budgets et des contributions publiques.
Si l'intervention publique est régulièrement critiquée à droite, pour des raisons de gabegie financière, il est important de rappeler qu'elle fut également dénoncée à gauche, parce qu'inféodée à l'appareil de l'État. Selon la logique marxiste, l'infrastructure (l'économie et les rapports de production) détermine la superstructure, soient les formes politiques, juridiques et intellectuelles. Dans cette perspective, théorisée par Louis Althusser, le contrôle de l'État s'exerce par la contrainte (police), mais aussi par l'idéologie. L'école, la famille, les médias ou la religion, ainsi que la culture, constituent ainsi des instruments permettant de favoriser une certaine idéologie. L'intervention publique de l'État dans la culture permet ainsi de garantir la diffusion d'une certaine culture – qui, en Occident, vise à consolider la domination de la classe bourgeoise – et de reproduire les schémas sociaux qui lui sont favorables.
. Throsby D., The Economics of Cultural Policy, Cambridge, Cambridge University Press, 2010.
. Moulinier P., Les politiques publiques de la culture en France, Paris, PUF, 2010 (9e éd.).
. On observe de grandes différences entre les politiques culturelles en Europe. Voir Van der Ploeg F., « The making of cultural policy: a European perspective », in Ginsburgh V., Throsby D., Handbook of the Economics of Art and Culture, Amsterdam, Elsevier, vol. 1, 2006, p. 1183-1221 ; Poirrier P., Pour une histoire des politiques culturelles dans le monde, 1945-2011, Paris, La Documentation française, 2011. Une référence pratique : Barthelemy P., Financer son projet culturel : Méthode de recherche de financement, Voiron, Territorial Éditions, 2011.
. Debiesse F., Le mécénat, Paris, PUF, coll. « Que sais-je ? », 2007.
. Netzer D., « Cultural policy : an american view », in Ginsburgh V., Throsby D., op. cit., p. 1223-1251.
. Schuster M., « Tax incentives in cultural policy », in Ginsburgh V., Throsby D., op. cit., p. 1253-1298.
. Polanyi K., La subsistance de l'homme. La place de l'économique dans l'histoire et la société, Paris, Flammarion, [1977] 2011.
. Sur les origines et le développement de l'administration des beaux-arts, voir notamment Boussu N., L'administration des Beaux-arts, Paris, Edouard Baltenweck, sd (1877).
. Fumaroli M., L'État culturel, Paris, Éd. de Fallois, 1992.
. Guilbaut S., Comment New York vola l'idée d'art moderne, Nîmes, Jacqueline Chambon, 1996.
. Arendt H. (1954), La crise de la culture, Paris, Gallimard, 1972 (pour la trad. fr.) ; Adorno T. W., Horkeimer M., (1944) Dialectique de la raison, Paris, Gallimard, 1974 (pour la trad. fr.).
. Laurent J., Arts et pouvoirs en France de 1793 à 1981. Histoire d'une démission artistique, Saint-Étienne, CIEREC, 1982.
. Chaumier S., Mairesse F., La médiation culturelle, Paris, Armand Colin, 2013.
. Barnavi E., Saint-Pulgent M. (dir.), Cinquante ans après. Culture, politique et politiques culturelles, Paris, La Documentation française, 2010.
. Unesco (Collectif), Les industries culturelles. Un enjeu pour l'avenir de la culture, Paris, Unesco, 1982.
. Camarero C., Garrido M. J., Vicente E., « How cultural organizations' size and funding influence innovation and performance: the case of museums », Journal of Cultural Economics, 35, 2011, p. 247-266.
. Baumol W. J., Bowen W. G., Performing arts. The Economic Dilemma, New York, The Twentieth Century Fund, 1966.
. Cowen T., In Praise of Commercial Culture, Cambridge, Harvard University Press, 1998. Un bon résumé est donné dans Chong D., Arts Management, Londres, Routledge, 2010 (2e éd.), chapitre 2 : « Art and the State ».
. Baumol W. J., Bowen W. G., op. cit.
. Bille T., Schulze G. G., « Culture in urban and regional development », in Ginsburgh V., Throsby D., Handbook of the Economics of Art and Culture, Amsterdam, Elsevier, vol. 1, 2006, p. 1051-1097 ; Seaman B., « Economic impact of the Arts », in Towse R. (dir.), A Handbook of Cultural Economics, Cheltenham, Edward Elgar, 2003, p. 224-231.
. Pflieger S., Les retombées économiques du festival d'Avignon, rapport pour Avignon Emploi Développement, BIPE, 1986.
. Throsby D., The Economics of Cultural Policy, Cambridge, Cambridge University Press, 2010, p. 58 sq.
. Voir à ce sujet le site Scholars on Bilbao, rassemblant plus de 80 articles produits autour de cette question : <http://www.scholars-on-bilbao.info/list.php?var=list> (consulté en décembre 2014).
. Nicolas Y., « L'analyse d'impact économique de la culture », Ministère de la Culture et de la Communication, Documents de Travail, 1271, juillet 2006. Disponible sur : <http://www.enluminures.culture.fr/culture/deps/2008/pdf/dt1271.pdf> (consulté en août 2013). Les études produites par l'association American for the Arts constituent, à cet égard, un bon exemple de la manière d'utiliser les évaluations à des fins de lobbying. Voir le site de l'association : <http://www.artsusa.org/information_services/research/services/economic_impact/iv/reports.asp> (consulté en mai 2013).
. Peacock A., « The arts and economic policy », in Ginsburgh V., Throsby D., Handbook of the Economics of Art and Culture, Amsterdam, Elsevier, vol. 1, 2006, p. 1123-1140.
. Voir le site de l'OMC qui contient une description précise de ses activités et de son histoire : http://www.wto.org/indexfr.htm.
. Farchy J., La fin de l'exception culturelle ? Paris, CNRS Éditions, 2002 ; Benhamou F., Les dérèglements de l'exception culturelle, Paris, Le Seuil, 2006. Voir aussi le discours américain en faveur de l'ouverture : Cowen T., op. cit.
. Cowen T., op. cit.
. Sur les développements de l'industrie culturelle en regard de ces accords : Bouquillon P. et Combès Y. (dir.), Diversité et industries culturelles, Paris, L'Harmattan, 2011.
. Crozier M., Le phénomène bureaucratique, Paris, Le Seuil, 1963 ; Weber M., Économie et société, Paris, Plon, 1971.
. Rolland L., Précis de droit administratif, Paris, Dalloz, 1953 (10e éd.).
. Saint-Pulgent M. de, Le gouvernement de la culture, Paris, Gallimard, 1999.
. Kornai J., Socialisme et économie de la pénurie, Paris, Economica, 1984.
. Buchanan, J. M., Tullock G., The Calculus of Consent: Logical Foundations of Constitutional Democracy, Chicago, University of Michigan Press, 1962.
. Van der Ploeg F., op. cit.
. Grampp W. D., Pricing the Priceless, Art, Artists and Economics, New York, Basic books Inc., 1989.
. Dupuis X. « La surqualité, le spectacle subventionné malade de la bureaucratie ? », Revue économique, 1983, 34,6, p. 1089-115 ; Pommerehne W. W., Frey B. S., La culture a-t-elle un prix ?, Paris, Plon, 1993.
. Althusser L., « Idéologie et appareils idéologiques d'État » [1970], in Positions, Paris, Les éditions sociales, 1976, p. 67-125.
Chapitre 5
La logique du don
Le débat économique porte largement sur l'intervention – ou non – des pouvoirs publics, éclipsant presque totalement ce qui peut apparaître comme un mécanisme particulier, très important dans le secteur de la culture : la logique du don. La question est abordée dans les manuels d'économie de la culture, mais de manière ancillaire.
La place que le don occupe, au sein des sociétés occidentales et, notamment, à l'échelle de la famille, demeure centrale. C'est d'abord par un mécanisme de don que se règlent les échanges au sein du cercle familial. Presque toujours non contractualisés ou décrits précisément, leur mise en œuvre permet de faire fonctionner la cellule familiale. C'est de la même manière que fonctionnent les systèmes d'échange de cadeaux, durant les fêtes, ou les invitations à manger, au niveau du cercle amical. Mais le don fonctionne également de manière plus large, et notamment, dans nos sociétés modernes, avec des inconnus. La question de l'altruisme et de la réciprocité n'a pas échappé à Smith, qui en discute dans sa Théorie des sentiments moraux, et ce principe, au même titre que la solidarité, est également rappelé par Pareto ou Walras. Gary Becker, lui-même, évoque l'altruisme au sein de la famille – mais l'égoïsme en dehors de celle-ci. Pour autant, l'ensemble des transactions gagne, pour les mêmes auteurs, à être privilégié par le mécanisme du marché. Faut-il cependant lâcher l'un pour l'autre ? Le principe hybride, que nous soulignons, opte pour un système très largement mixte. Si cette dimension a donc été quelque peu éclipsée par l'économie, on la rencontre en revanche de manière importante au niveau de la sociologie et de l'anthropologie, que nous utilisons largement dans les pages qui suivent.
Une partie de la population vivant en marge de la société subsiste par le biais de dons, octroyés soit directement (dans la rue), soit par le biais de sociétés dites de bienfaisance, œuvrant à la redistribution des dons. De manière plus générale, certains objets dont la morale réprouve à définir la valeur, comme l'être humain ou les organes qui le constituent, circulent par le don : on donne du sang, des organes et, parfois, son enfant, mais il est (actuellement) réprouvé de les monnayer. Une petite partie du monde de la culture s'est, dans cette perspective, accommodée de telles manières, jouant « au chapeau », dans le métro ou dans les marchés, invitant chacun à contribuer. Mais c'est une relation, sinon identique, du moins fonctionnant partiellement avec les mêmes ressorts, que l'on peut observer dans les cours princières et dans l'Église, protégeant et entretenant les artistes, dans une relation – la plupart du temps non contractualisée – souvent ambiguë entre mécène et artistes, ces derniers dépendant largement du bon vouloir (et des humeurs) de leur protecteur.
Nombre d'associations fonctionnent ainsi à partir d'une logique ne reposant ni sur les principes du marché, ni sur ceux des pouvoirs publics : les différents clubs philanthropiques (Rotary, Lyons etc.), mais aussi des organisations comme les alcooliques anonymes, partagent une logique de fonctionnement identique, reposant moins sur les cotisations ou les contrats que sur la bonne volonté de chacun, et sur la philia qui résulte des échanges informels entre les membres. C'est évidemment sur une même logique que se sont développées la plupart des églises, qu'il s'agisse de la tradition chrétienne, islamique ou hindouiste. On doit aux Églises (et, pour l'Europe, à l'Église catholique et au protestantisme, essentiellement), pendant des siècles, la prise en charge de secteurs entiers de la société, à commencer par les soins de santé et l'enseignement, mais aussi une grande partie des arts et de la culture. C'est à partir de dons que le fonctionnement actuel de l'Église catholique (en France, par le biais du denier de l'église, mais aussi des quêtes) est assuré, mais c'est aussi par ce moyen que les chapelles ou les grandes cathédrales ont pu être construites, pour la plus grande gloire de Dieu, mais aussi pour celle des donateurs.
L'Église s'est très largement imposée comme alternative aux lois du marché : « ne faites pas de la maison de mon père une maison de trafic » (Jean, 2 : 16), s'exclame le Christ en chassant les marchands du temple. Mais si dans les lieux de prière, la logique qui prévaut dépasse celle que l'on trouve dans les rapports marchands, si la religion promeut la charité au bénéfice des pauvres, qui recevront l'enseignement et les soins gratuitement, ce sera sous l'influence de la croix, et c'est bien pour contrer cette vision que, durant le xixe et les débuts du xxe siècle, les républicains visent à asseoir l'État laïc. Car par-delà la charité s'imposent aussi des relations de domination entre celui qui donne et celui qui ne peut que recevoir et remercier, étant redevable jusqu'à la fin de sa vie.
La notion d'altruisme, en économie, a longuement été évincée par les penseurs classiques, considérée comme peu intégrée dans une économie productive. L'économie s'est essentiellement intéressée au don et à l'altruisme à partir de la double logique privée/publique. Becker, déjà cité, développe l'idée d'une utilité du don – contraire au sens commun du don désintéressé et du sentiment d'altruisme –, l'Homo œconomicus donateur cherchant son intérêt dans les marques de sympathies ou le sentiment agréable produit par l'action de donner. Selon un autre point de vue, le système de la charité est présenté comme un bien public auquel les gens contribuent de manière personnelle : les parents d'un enfant, à l'intérieur du cercle familial, agissent comme si la famille était un bien public, et la logique du don peut apparaître, dans ce contexte, comme un système de redistribution neutre par un système de taxes. D'où l'idée que l'État pourrait évincer la charité par des subventions envers ce bien. James Andreoni, pour sa part, relie les deux principes, développant un système mixte où les gens contribuent à un bien public parce qu'ils reçoivent en retour quelque chose (remerciements etc.) s'apparentant à un bien privé – soit donc un « altruisme impur ». D'autres approches, comme celle de Serge-Christophe Kolm, sont développées à partir d'une réflexion plus globale sur l'échange, la notion de réciprocité et le développement d'une économie fondée sur des relations sociales complexes et réciproques, plutôt que sur la logique d'un échange marchand trop simplifié.
Nous souhaiterions, pour notre part, envisager – à partir d'un constat fondé sur la réalité des échanges tels qu'ils ont été observés par les sociologues et les historiens, notamment dans le domaine de la culture – sur l'hypothèse d'un système très largement indépendant de celui de la logique publique ou privée, présentant sa propre logique, ses avantages, mais aussi ses inconvénients.
Le don dans la société bourgeoise
C'est essentiellement au travers des grandes familles patriciennes que l'on perçoit le mieux l'influence du don dans les sociétés occidentales. L'ouvrage de Paul Veyne, le pain et le cirque, témoigne de la place qu'occupait cette pratique distincte des règles publiques ou de marché et largement codifiée durant l'Antiquité, tant en Grèce qu'à Rome. L'évergétisme, la tendance des classes les plus riches à distribuer une partie de leurs richesses au bénéfice de la collectivité, soit à travers la constitution de monuments (temples, forums, thermes), soit par le biais de financement de liturgies ou de jeux, n'est jamais tellement loin du clientélisme, entretenu par les cadeaux. Le pouvoir de la richesse permet, avec de telles transactions, de confirmer le rang des grandes familles au sein de la société.
Une telle logique, que l'on retrouve durant l'Ancien Régime, constitue également une dimension importante de la société bourgeoise du xixe siècle, telle qu'on la trouve en Europe. La structure de la société se présente alors de manière nettement plus structurée, et le fossé entre les différentes classes sociales, s'il s'exprime à travers les quartiers et les consciences collectives – le prolétariat ouvrier contre la bourgeoisie capitaliste – s'exprime aussi à travers les dons que la bourgeoisie ne manque pas de faire aux plus démunis. Il est vrai que les taux d'imposition, à l'époque, sont relativement faibles et ne permettent pas d'assurer une couverture sociale telle qu'elle sera appliquée à partir de la seconde moitié du xxe siècle. Ainsi, c'est notamment par le biais des libéralités que sont financées bon nombre d'infrastructures sociales (hôpitaux, écoles, chauffoirs, soupes populaires...). Les libéralités d'une grande famille bourgeoise peuvent ainsi régulièrement atteindre les 10 %, voire plus, rappelant en quelque sorte la règle ancestrale de la dîme, promue par les religions du livre.
Une telle pratique s'impose, pour une famille qui tient à affirmer son nom, et par là même s'affirmer comme supérieure à ceux qui reçoivent. Ainsi, les nombreux petits gestes, cadeaux ou gratifications, permettent-ils d'affirmer, incessamment, les relations de pouvoir : « Les supérieurs seuls (par l'âge, la position, l'ascendance etc.) font des cadeaux de Noël et du jour de l'An. Les inférieurs n'en rendent pas. Mais ces derniers peuvent offrir un présent à leurs supérieurs, à l'occasion du jour de fête ou du jour de naissance de ceux-ci », écrit la Baronne Staffe.
Les catégories du don
Parmi tous les termes utilisés – altruisme, réciprocité, transfert – nous retenons celui de don, qui bien qu'encore insuffisamment délimité, se présente néanmoins de manière clairement distincte comme une troisième voie, entre l'échange marchand et la redistribution publique. De tels dons apparaissent comme (1) des actes dont l'espérance d'une contrepartie directe (non symbolique) est nulle. C'est la même logique qui préside dans les actes de mécénat, les cotisations dans des sociétés de bienfaisance ou les liturgies antiques. De tels dons s'opposent (2) à ceux dont la contrepartie attendue est centrale, qui existent de manière tout aussi régulière, mais dans d'autres contextes. Ainsi, dans le monde du commerce, les bakchichs ou les rabais accordés, ainsi que les cadeaux d'affaires, mais aussi les offrandes à un dieu ou les ex-voto une fois la prière ayant été accordée, participent d'une logique qui, si elle prend la forme d'un don, n'en attend pas moins, de manière plus ou moins explicite, un retour direct. Entre les deux, (3) une troisième catégorie peut être constituée par les dons dont la contrepartie n'est pas centrale, sans pour autant disparaître. Ainsi, les cadeaux que l'on offre à Noël, ou les invitations lancées et rendues, les potlatchs, participent-ils de la logique du don, tout en développant une dimension essentiellement fondée sur la sociabilité, ou la relation qui permet d'activer une telle logique du don.
Si l'on peut ainsi catégoriser le don en fonction de la contrepartie attendue, on peut également le classer à partir de l'ampleur des échanges et l'étendue de leur pratique au sein de la société. (1) Dans une première catégorie, on pourrait ranger les dons d'affaire et de sociabilité, que l'on retrouve dans toutes les catégories de la population, en ce compris chez les plus pauvres, si ce n'est à une moindre échelle. Ainsi, les repas et les réceptions, les petits cadeaux que l'on offre à la Noël, en famille ou dans les relations de travail, constituent des pratiques très largement partagées par toutes les classes sociales. Forcément, l'importance de ces gestes peut différer en fonction de la richesse, les classes les plus fortunées pouvant régulièrement organiser des banquets... (2) Seule, une partie des classes les plus aisées de la société pratique ce qu'on pourrait intituler les dons philanthropiques, finançant par leurs cotisations ou des achats divers des associations et sociétés philanthropiques s ou de bienfaisance, œuvrant dans les domaines culturels ou sociaux. Ici aussi, les classes les plus élevées jouent un rôle considérable, le montant de leurs interventions les plaçant parmi les contributeurs les plus importants, les conduisant régulièrement à accepter des postes soit honorifiques, soit de direction au sein de ces associations. (3) Enfin, on peut regrouper un certain nombre de pratiques – nettement plus rares et réservées à une élite – sous la dénomination de monuments philanthropiques. La notion même de monument, au sens premier du terme, vise la création d'une œuvre édifiée dans le but de conserver le souvenir d'une action ou d'une personnalité particulière. C'est bien dans cette perspective que, depuis l'antiquité, un certain nombre de bâtiments (hôpitaux, chapelles, musées, universités, bibliothèques...) sont construits et offerts par de riches patriciens, associant leur nom à une réalisation prestigieuse, dans le but de préserver leur mémoire. Tandis que les deux premières catégories de dons disparaissent de manière assez rapide, la pierre ou l'objet de patrimoine, offert et conservé, permet d'associer la mémoire du donateur. C'est ce que des générations de grands capitaines d'industrie ont bien compris, offrant à leur pays de riches monuments associant leur patronyme de manière positive. Probablement le nom des Calouste Gulbenkian (Lisbonne), Paul Getty (Los Angeles) ou Henry Tate (Londres) aurait-il disparu des mémoires collectives – sauf pour quelques spécialistes de l'histoire économique – s'il n'avait pas été associé à des musées. À Paris, de nombreux établissements ont ainsi été offerts par les Camondo, Cernuschi, Jacquemart-André ou Cognacq-Jay, tous grands financiers ou patrons d'industrie de la fin du xixe et du début du xxe siècle.
Capitalisme et philanthropie
Les exemples précédemment cités montrent le lien très étroit entre le grand capitalisme et la philanthropie. De nos jours encore, certains des hommes les plus riches du monde, à l'instar de Bill Gates ou de Warren Buffet, se présentent également comme les plus grands philanthropes. De tels liens semblent exister depuis les débuts du capitalisme, conduisant à chaque génération les plus grands capitaines d'industrie, parfois vilipendés de leur vivant pour leurs pratiques commerciales scandaleuses, à s'acheter une respectabilité (pour leurs détracteurs) ou rendre une partie de leurs richesses (pour leurs partisans), au bénéfice de leur postérité. Les musées, bibliothèques et autres fondations constituées par les Morgan, Carnegie ou Rockefeller, à l'époque des « barons voleurs », les placent tous en situation « d'hommes de biens », redistribuant – à leur gré et en fonction de leurs choix, plutôt que de celui de l'État – une partie des sommes accumulées durant leur vie professionnelle. À chaque génération, ses nouveaux philanthropes : l'époque de la libéralisation bancaire, durant les années 1980, avec ses scandales d'initiés, a elle aussi donné naissance à de nouveaux donateurs.
Une triple « obligation »
La référence probablement la plus souvent citée et commentée par les anthropologues (Lévi-Strauss, Godelier etc.) sur le don est l'article de Marcel Mauss, paru en 1923 : Essai sur le don. Mauss n'est certes pas le premier à parler du don, mais son intervention se présente à une époque charnière, au moment même où s'opposent la logique capitaliste et le nouveau système soviétique, l'un et l'autre s'accusant des pires exactions. C'est une sorte de troisième voie que présente Mauss, appuyant ses revendications d'une prise en charge par les pouvoirs publics au nom du don et des sacrifices que la population a endurés, durant la guerre. Pour ce faire, Mauss tente une vaste synthèse historique et géographique, retrouvant cette logique particulière dans l'Antiquité, à travers le système féodal, mais aussi en Inde ou chez les Vikings, ainsi que chez les populations autochtones d'Amérique du Nord ou du Pacifique.
Cette logique particulière, Mauss la présente comme articulée autour de trois principes, apparemment spontanés et reposant sur la bonne volonté, mais dont le caractère s'avère pratiquement obligatoire. Donner, recevoir et rendre, trois temps particuliers conditionnant la logique du don, aucun de ces temps ne pouvant être réellement effacés, malgré l'apparente spontanéité. Parmi les populations étudiées, Mauss reprend les analyses par Malinowski des « argonautes du Pacifique », les Trobriandais, et d'un système d'échanges par dons et contre-dons particulièrement complexe de coquillages entre les îles : le kula. Mais c'est surtout le phénomène du potlatch, analysé par Boas chez les Indiens Kwakiutl, qui apparaît comme le plus étonnant. Durant de grandes cérémonies rassemblant de nombreuses tribus, des dons somptueux – de grands cuivres, des couvertures, mais aussi des objets modernes, comme des machines à coudre – sont offerts entre tribus, parfois jetés aux pieds du chef, voire détruits. Les plus grands dons engendrent les plus grands honneurs : gloire à celui qui donne, malheur à celui qui ne peut rendre (pas immédiatement, mais lors d'un prochain potlatch). Ainsi peut s'engager une lutte d'honneurs particulière, permettant d'écraser symboliquement un adversaire par des cadeaux tellement somptueux qu'ils ne pourront être rendus...
Une telle logique, présentée comme obligatoire par Mauss, est effectivement ancienne, et a fait l'objet de nombreuses analyses depuis l'Antiquité. Sénèque, dans l'un des traités consacrés à ce geste particulier, insiste déjà sur le triple moment du don, mais en soulignant l'aspect volontaire, et non obligatoire : si des ingrats ne veulent pas rendre un bienfait qui leur aurait été accordé, ils en ont le droit, au risque d'encourir l'opprobre public.
Il n'en reste pas moins que même non obligatoire, la pratique du don entretient avec elle une part sombre et peu évoquée. S'il est possible de donner pour ne pas rendre, il est donc possible d'inféoder un sujet qui ne pourra au mieux que manifester sa reconnaissance, établissant à jamais un rapport de domination entre le donateur et le récipiendaire. Le don, parce qu'il repose sur une relation – pas toujours équitable – participe d'un échange dont les deux parties ne peuvent réellement se défaire, même une fois la transaction établie. Ainsi, une partie de la personnalité du donateur semble toujours inscrite dans l'objet du don et, pour autant que celle-ci ne soit pas exempte de tous soupçons, l'ambiguïté demeure, quant à la nature de l'objet donné, aussi beau soit-il.
Les formes du don dans le domaine des arts et de la culture
C'est notamment au niveau patrimonial que la logique du don s'exprime de la manière la plus active, permettant au donateur d'afficher son statut dans la durée. Ainsi retrouve-t-on de très nombreux monuments – châteaux, hôpitaux, chapelles... – donnés à des fondations ou aux pouvoirs publics, afin que ceux-ci en assurent la protection. Dans cette même perspective, les musées, de nos jours et en ce compris dans nos régions, fonctionnent largement à partir d'une logique inspirée par le don. Leurs collections ne seraient pas les mêmes si elles n'avaient pas été enrichies par de très nombreux donateurs, certains parfois anonymes. Le fonctionnement de ces établissements repose largement, dans les pays anglo-saxons, sur le volontariat (de très nombreux bénévoles accompagnent le travail des professionnels), tandis que des dons en nature ou en argent sont régulièrement sollicités et reçus au bénéfice du musée, tant de la part de mécènes privés que d'associations d'amis de musée.
Les sociétés philanthropiques, qui collectent les dons et cotisations au bénéfice du musée, sont également développées dans d'autres secteurs ne pouvant dépendre seulement du marché. C'est parce que certaines œuvres musicales ne pouvaient aisément reposer sur les seuls mécanismes du marché que les sociétés philharmoniques sont créées en Europe dès le début du xixe siècle, notamment à Saint-Pétersbourg (1802), à Londres ou à Liverpool. De manière identique, dès la fin du siècle précédent, des sociétés d'Amis des arts avaient été mises en place afin d'aider les jeunes peintres et graveurs. C'est en effet le secteur de l'art vivant et des artistes qui fait l'objet d'un soutien particulier. Qu'il s'agisse de Mozart ou Vivaldi, Rubens ou Rigaud, le développement de l'art passe par les cours princières ou ecclésiastiques, mais dans une relation qui tient bien plus au mécénat qu'aux règles du marché ou aux subventions publiques. La philanthropie, dans le domaine des arts de la scène et des arts plastiques, constitue une réalité, encore très importante dans les pays Anglo-saxons et dont la logique est intégrée dans la démonstration qu'entreprendra Baumol pour évoquer la nécessité d'un soutien public.
À la logique du mécénat, qu'il soit particulier ou collectif (comme les associations d'amis), il convient d'ajouter la pratique du don à l'entrée d'un établissement, symbolisé par le tronc que l'on retrouve dans la plupart des églises, mais aussi de nombre de musées, permettant à tout anonyme de verser son obole, de manière plus ou moins discrète. C'est dans cette même catégorie que l'on peut ranger les quêtes qui, traditionnelles durant les cérémonies liturgiques, prennent d'autres formes dans les institutions culturelles. Les campagnes de levées de fonds, qui sous-tendent ces pratiques, privilégient en effet plutôt les soirées, galas ou banquets de bienfaisance, dont la logique demeure identique, mais pour lequel l'acte du don – remise d'espèces ou de chèques – semble parfois s'apparenter aux règles du Potlatch, ce que n'avait pas manqué de relever Thorstein Veblen. On notera encore, dans cette même logique reposant essentiellement sur le don en argent, le caractère parfois hybride du don à l'entrée, tel qu'on peut le remarquer dans certains musées américains, comme le Metropolitan Museum. Si, la plupart du temps, le prix d'entrée est fixé par la loi ou estimé d'après le marché, il est laissé, dans ces établissements, à l'appréciation du visiteur qui est invité à fixer lui-même ce qu'il va donner au musée. Certes, un prix (plutôt élevé) est souvent suggéré, et le montant de la contribution est affiché en grand sur les caisses enregistreuses (privilégiant ainsi le conformisme social). Il n'en demeure pas moins qu'il s'agit, dans une telle perspective, d'un don certes plus ou moins contraint, mais qui engage nettement plus le visiteur que dans le cas d'un prix fixé à l'avance.
Enfin, un grand nombre d'organisations culturelles fonctionnent, en tout ou en partie, avec l'aide de bénévoles. Pour la plupart des structures récentes et de statut plus ou moins amateur, ne dépendant pas (encore) des pouvoirs publics et ne pouvant s'attendre à dégager suffisamment de chiffres d'affaires à partir du marché, le bénévolat constitue un principe vital. Tout le théâtre amateur, un très grand nombre de festivals, de petits musées associatifs ou de lieux de patrimoine ne pourraient fonctionner qu'à partir d'une telle logique. Le bénévolat, dans les pays anglo-saxons, est encore nettement plus répandu, notamment dans les musées les plus renommés.
S'il est relativement aisé de trouver des ordres de grandeur afin de présenter l'activité du bénévolat et les dons financiers, en France ou aux États-Unis, force est de reconnaître que les statistiques mesurant l'activité économique générée par le marché ou les pouvoirs publics sont nettement plus développées. Il existe en effet des enquêtes officielles (INSEE), associatives et universitaires, mais par nature, l'engagement bénévole ou les flux financiers transitant par le don s'avèrent plus difficiles à mesurer, aussi sont-ils souvent ignorés.
Le secteur associatif est estimé à environ 1,3 million d'associations, employant 1,8 million de salariés, tandis que 32 % des Français exerceraient une activité bénévole, ce qui équivaudrait à une activité estimée entre 700 000 et 1 000 000 d'équivalents temps plein. Forcément, la part culturelle, dans ce contexte global, n'équivaut qu'à une faible proportion de ces activités que l'on retrouve aussi dans le secteur des loisirs, du sport, de la religion ou du social : quelques pourcents au plus pour les activités d'aide dans le secteur de la production culturelle. Il n'empêche que cette activité permet le fonctionnement de dizaines de milliers de petites structures, dans le domaine des arts de la scène, du patrimoine etc. Une partie des dons transitent par ces associations, d'autres sont directement versés à des établissements publics (musées, théâtres...). Certaines fédérations d'associations ont tenté de se regrouper au sein de l'UFISC (Union fédérale d'intervention des structures culturelles), en 1999, afin de promouvoir ce tiers secteur reposant sur une alternative à l'économie de marché ou publique. On dispose également, afin de déterminer les montants, de résultats parcellaires – de nombreux dons sont par exemple directement réalisés en espèces lors de quêtes etc. Une partie de ces dons fait en effet l'objet de déductions d'impôts, les déclarations transitant par le ministère des Finances ; l'autre partie fait alors l'objet d'estimations. Plus de cinq millions de foyers fiscaux déclarent environ deux milliards d'euros chaque année, mais la valeur estimée des dons en France serait de l'ordre de 3,7 milliards (en 2011). De telles sommes s'avèrent nettement moins importantes que celles qui sont récoltées sur le territoire américain (une enquête de 2010 évoque la somme de plus de 300 milliards de dollars, dont plus des deux tiers sont versés par des particuliers). En revanche, sur l'ensemble de ces dons, seul un faible pourcentage (3 à 4 % aux États-Unis) est consacré à l'art et à la culture. À l'échelle des établissements cependant – et bien plus dans les pays anglo-saxons, qui en dépendent plus directement – le secteur de la philanthropie constitue une source de revenus importante. Le montant des sommes récoltées par les Amis du Louvre, par exemple, avoisine les trois millions d'euros. Une telle somme ne constitue qu'un faible pourcentage de l'investissement public (près de cent millions, pour un budget évalué au double), mais se présente néanmoins comme un apport crucial pour certains postes budgétaires, comme celui des acquisitions du musée.
Le rôle de l'État
Si la philanthropie ressort du domaine de l'initiative privée, il n'en reste pas moins que c'est à partir d'un mécanisme mis en place par les pouvoirs publics, lesquels encadrent le marché autant que ce type particulier d'échange. Les trois principes les plus importants, dans ce contexte, visent l'encadrement du travail bénévole (essentiellement afin de garantir que celui-ci ne soit pas exploité au détriment des salariés), l'encouragement du mécénat, qu'il soit issu des particuliers ou des entreprises, enfin l'établissement d'un régime spécial pour les organisations créées à partir de dons privés, et dont l'objet vise essentiellement à œuvrer dans une optique non lucrative, notamment en distribuant de l'argent. Ce principe est celui des fondations, largement plus présentes dans les pays anglo-saxons qu'en Europe continentale. Ici encore, le rôle de l'État est primordial, qui peut décider d'assurer seul (ou aidé par des commissions indépendantes) la redistribution de l'argent perçu (subventions etc.), ou de déléguer de manière plus ou moins complète cette tâche à la société civile, par le biais de fondations ou par l'action des particuliers eux-mêmes. Il est fort probable que la logique révolutionnaire, inversant les mécanismes de l'Ancien Régime (reposant notamment sur les fondations gérées par l'Église), ait privilégié l'action publique. Quoi qu'il en soit, bien que les différences persistent de part et d'autre de l'Atlantique, le mécénat et l'activité des fondations jouent un rôle important dans les domaines non lucratifs, et notamment celui de la culture.
Mécénat. Dans cette perspective, c'est par le biais de régimes fiscaux particuliers, permettant aux donateurs de déduire de leurs impôts (66 % dans la limite de 20 % du revenu imposable, voire 75 % pour certains organismes aidant les personnes en difficulté), que le mécénat est encouragé en France. La notion de mécénat, pour le droit, est associée à un don offert sans contrepartie ou dont les contreparties sont négligeables (contrairement au sponsoring), et octroyé à des associations dont l'objet social est désintéressé et largement public. Ces associations peuvent, lorsqu'elles sont reconnues d'utilité publique, délivrer un reçu d'impôt qui permettra la déductibilité. Un tel mécanisme, s'il ressort encore d'une logique de don – car il diffère des règles du marché ou de celles des pouvoirs publics – n'en demeure pas moins largement différent du don pur, si tant est que celui-ci puisse exister... Ce même principe a été également mis en place pour les entreprises, celles-ci pouvant déduire 60 % de leurs dons dans la limite de 0,5 % de leur chiffre d'affaires. Par ailleurs, les entreprises peuvent également valoriser du mécénat en nature (l'apport de matériaux ou de services), et du mécénat de compétence (le travail gratuit du personnel de l'entreprise, durant leurs heures de service, au profit d'une organisation). Les dépenses en vue de l'achat d'œuvres contemporaines (d'artistes vivants), ainsi que de trésors nationaux, la rénovation de monuments historiques, de même que la diffusion de spectacles vivants et d'expositions d'art contemporain, bénéficient également, sous certaines conditions, d'avantages fiscaux dans le cadre des mêmes mesures de mécénat.
Fondations et fonds de dotation. Les fondations sont des organisations bénéficiant d'un statut juridique particulier, rassemblant des donateurs afin d'accomplir une action d'intérêt général. Contrairement aux associations Loi 1901 (associations à but non lucratif), elles disposent d'une personnalité juridique de droit privé. Les fondations peuvent revêtir plusieurs types. On distingue les fondations d'utilité publique (créées par un individu ou un groupe), des fondations sous égide ou abritées (au sein d'une fondation d'utilité publique, comme la Fondation de France), ainsi que les fondations d'entreprises (permettant de mieux valoriser ses activités de mécénat). Le mécanisme de base des fondations repose sur le fonds de dotation (endowment) dont elles disposent et dont les intérêts sont utilisés à des fins philanthropiques. De tels fonds peuvent atteindre, dans le cas des grandes fondations américaines (comme celle de Bill et Melinda Gates, ou la fondation Ford) plusieurs milliards de dollars (leur montant fluctue largement au gré des cours boursiers, dont elles dépendent). Le système des fondations est en effet peu important, en France et dans les pays latins, tandis qu'il joue un rôle majeur au sein de la société américaine, les nombreuses fondations contribuant largement, par leurs dons, à la vie culturelle – de manière nettement moins importante que dans les domaines sociaux ou de la santé, cependant. La logique de participation de tels fonds, initiés à partir des grandes fortunes industrielles ou financières, si elle relève de la philanthropie, diffère des principes de redistribution de l'État-providence, puisque leur fonctionnement et leurs critères de choix peuvent s'opérer de manière privée et discrète, privilégiant certaines actions au détriment d'autres. Il n'en reste pas moins qu'un certain nombre de fondations d'entreprise, notamment, en France, contribuent activement – mais de manière relativement modeste – au financement de la culture, comme la Fondation Groupama Gan, œuvrant dans le domaine du cinéma, la fondation Cartier pour l'art contemporain ou la fondation Louis Vuitton pour la création.
Fonds de dotation et levées de fonds. Les grands établissements culturels (musées, orchestres symphoniques, opéras) disposent tous, en Amérique du Nord, de fonds de dotation considérables (ceux du Metropolitan Museum de New York et du Museum of Fine arts de Boston dépassent le milliard de dollars), auxquels contribuent les puissants trustees, chargés de veiller au fonctionnement du musée. Le Louvre, très récemment, s'est doté d'un tel fonds de dotation, principalement alimenté par le projet du Louvre Abu Dhabi, constituant une exception dans le paysage français. De tels fonds, par nature, demandent à être accrus ; aussi les établissements culturels ont-ils développé, depuis de nombreuses années, des outils visant à attirer les mécènes. Si, de manière structurelle, un certain nombre de démarches sont entreprises pour attirer et fidéliser des donateurs potentiels, mais aussi inviter (via un tronc ou d'autres moyens) un donateur anonyme à participer au financement des activités d'un musée ou d'un théâtre, certaines campagnes, plus ponctuelles, sont régulièrement mises en œuvre afin de réaliser un projet particulier (acquisition d'une œuvre d'art, construction d'un nouveau bâtiment) ou, de manière plus générale, à renforcer le fonds de dotation via une campagne de levée de fonds (fundraising). En fonction de la taille des établissements, ceux-ci font appel à des spécialistes extérieurs ou à un service particulier du musée (mécénat, levée de fonds), dont les effectifs, ces dernières années, se sont régulièrement accrus, en ce compris en Europe.
Nouvelles formes
Ces dernières années, les méthodes de levées de fonds qui n'ont pas cessé de se perfectionner ont largement bénéficié du développement des technologies numériques et de celui d'internet, notamment à travers la révolution « 2.0 ». L'extension prodigieuse de la toile et de ses utilisateurs, sur laquelle nous reviendrons au chapitre 15, permet en effet, selon un principe qui n'est pas sans rappeler la logique de la longue traîne, de Chris Anderson, de tenter de joindre tous les collaborateurs ou donateurs potentiels ne pouvant s'investir énormément, mais dont la somme des contributions constitue néanmoins un apport significatif.
Le crowdfunding. La notion de crowdfunding, qui est apparue ces dernières années, à travers des sites de financement participatifs, constitue un certain renouveau des formes de recherche de dons. Ce sont d'abord les petites firmes œuvrant dans le domaine de la musique et du cinéma, pour le lancement d'albums et la réalisation de courts-métrages ou de documentaires, qui ont bénéficié de tels projets. Ainsi, des sites internet comme My Major Company, ou Kiss Kiss Bank Bank, proposent aux internautes de nombreux projets, présentés par leurs concepteurs, dont le lancement nécessite un financement (relativement modeste la plupart du temps, de l'ordre de quelques milliers ou dizaines de milliers d'euros). Bien que le processus soit généralement hybride (les promoteurs offrent une contrepartie, relativement symbolique, pour toute participation, celle-ci évoluant au gré du montant de la participation) et que le discours soit souvent présenté comme une sorte de « coproduction », le système repose largement sur la logique du don. Récemment, le Musée du Louvre, profitant de sa notoriété, a ainsi pu rassembler assez rapidement plusieurs centaines de milliers d'euros pour acquérir des œuvres d'art (un tableau de Cranach ou deux sculptures médiévales).
Le crowdsourcing. De manière plus générale, la même logique peut être envisagée à partir d'un mécanisme non financier, reposant essentiellement sur le don de temps et l'investissement en nature que de nombreux internautes peuvent ainsi produire. Dans de telles conditions, forcément, la notion de distance, très importante pour les associations classiques, compte nettement moins, et on a ainsi vu des internautes participer depuis les quatre coins du monde, selon la même logique que celle qui permet à Wikipedia de se développer, à des projets de films (scénarios, effets spéciaux etc., comme pour le film finlandais « Ironsky ») ou des projets d'expositions (au Tech Museum ou à Brooklyn).
Des caractéristiques différentes
Si, apparemment, de telles méthodes sont également utilisées par des organismes dépendant essentiellement des pouvoirs publics (comme les musées) ou par des entreprises culturelles, reposant sur une logique de marché (qui ont de plus en plus souvent recours à du crowdfunding), il convient à nouveau d'insister sur certaines caractéristiques très particulières que l'on retrouve dans la logique du don, induisant un fonctionnement différent des règles classiques de l'échange.
D'une part, dans nombre de dons, le contrat liant le donateur et le récipiendaire demeure largement implicite. Aucun texte juridique, la plupart du temps, ne lie celui qui offre un objet de collection et celui (le musée) qui le reçoit (mais certains souhaitent l'enregistrer devant notaire, ou établir un contrat en bonne et due forme), aucun texte ne vient engager l'établissement qui reçoit des dons dans un tronc, ou des dons anonymes. Dans bon nombre de cas, la force légale ne s'applique pas ; c'est plutôt la pression sociale qui force à rendre : « la force qui pousse à rendre est celle de l'obligation, quelle que soit sa nature, sociale, juridique ou seulement morale. Et obligare, faut-il le rappeler, c'est se lier : la force qui pousse à rendre est celle du lien social ». Le don vient en quelque sorte renforcer le lien social qui unit un organisme à son donateur (ou à sa communauté) ; il peut aussi servir à tenter d'initier un tel lien. À travers cette logique, c'est une certaine histoire de la solidarité qui peut être esquissée, mais également une logique de domination, à tout le moins, une histoire de rapports de force plus ou moins équilibrés, influencés par les transferts d'objets ou d'argent entre les différentes parties.
Une partie de la personnalité du donateur transite par le don, ce que l'on observe de manière particulière à travers les dons d'organes (et qui amène souvent le receveur à ne pas souhaiter connaître l'identité de celui – ou la famille de celui – qui lui aurait donné un cœur ou un rein). Mais si l'argent n'a pas d'odeur, les objets qui sont donnés, notamment dans les musées, conservent une part de l'identité de leur propriétaire antérieur, du moins aux yeux de la société, qui ne saurait aisément accepter qu'un riche criminel offre sa collection à un lieu de patrimoine.
Enfin, les échanges entre donateurs et récipiendaires, s'ils ne sont pas influencés par le droit contractuel (principe que l'on retrouve au niveau des pouvoirs publics), sont largement dépendants de rapports subjectifs, notamment de l'émotion qui peut nous atteindre, qu'elle soit heureuse ou malheureuse, face à un événement agréable (la visite d'un musée, la réception d'une pièce de théâtre ou d'une œuvre musicale) ou désagréable (un tsunami). Ce sont de tels rapports qui, en quelque sorte, déterminent autant le montant que la rapidité de transfert des dons, mais ce sont probablement ces mêmes caractéristiques qui induisent une certaine instabilité au niveau des sources de financement. S'il existe une logique du don plus ou moins rationnelle, à partir de laquelle une fondation ou un trustee peuvent tenter de dégager des stratégies de développement, il existe donc une part largement instable et dépendant de l'engouement ou de la désaffection, parfois des modes. Un tel phénomène s'observe par ailleurs largement au niveau des mécanismes du marché, ce que les publicitaires ont intégré depuis longtemps.
. Katz S. N., « Philanthropy », in Ginsburgh V., Throsby D., Handbook of the Economics of Art and Culture, Amsterdam, Elsevier, vol. 1, 2006, p. 1299-1321 ; Klamer A., « Gift economy », in Towse R. (dir.), A Handbook of Cultural Economics, Cheltenham, Edward Elgar, 2003, p. 243-247.
. Kolm S.-C., « Introduction to the economics of giving, altruism and reciprocity », in Kolm S.-C., Ythier J.-M. (dir.), Handbooks of the Economics of Giving, Altruism and Reciprocity, Amsterdam, North Holland, 2006, p. 1-122.
. Godbout J., Caillé A., L'esprit du don, Paris, La Découverte/Syros, 1992 ; Godbout J. T., Ce qui circule entre nous. Donner, recevoir, rendre, Paris, Le Seuil, 2007 ; Chanial P. (dir.), La société vue du don. Manuel de sociologie anti-utilitariste appliquée, Paris, La Découverte, 2008. Pour l'anthropologie, ce sont les ouvrages de Mauss, Godelier ou Testart, que nous évoquons plus bas, qui peuvent être mentionnés d'emblée.
. Bremond C., Dieu aime-t-il l'argent ? Don, piété et utopie sociale chez les catholiques en France, Paris, L'Harmattan, 2006.
. Kolm S. Chr., « Efficacité et altruisme : les sophismes de Mandeville, Smith et Pareto », Revue économique, 32, 1, 1981, p. 5-31.
. Becker G. S., « A theory of social interactions », Journal of Political Economy, 82, nov./déc. 1974, p. 1063-1093.
. Andreoni J., « Giving with impure altruism: applications to charity and ricardian equivalence », Journal of Political Economy, 97, 6, déc. 1989, p. 1447-1458; « Impure altruism and donations to public goods: a theory of warm-glow giving », The Economic Journal, 100, juin 1990, p. 464-477.
. Kolm S.-C., Reciprocity. An Economics of Social Relations, Cambridge, Cambridge University Press, 2008.
. Veyne P., Le pain et le cirque : sociologie historique d'un pluralisme politique, Paris, Le Seuil, 1976.
. Mairesse F., Mariemont, capitale du don : des Warocqué aux Amis de Mariemont, Morlanwelz, Musée royal de Mariemont, 2007.
. Staffe B., Usages du Monde : règles du savoir-vivre dans la société moderne, Paris, Victor-Havard, 1892, p. 245.
. Mis à part Testart, cité plus bas, cf. Athané F., Pour une histoire naturelle du don, Paris, PUF, 2011.
. On trouve cette catégorisation chez Testart A., Critique du don : Études sur la circulation non marchande, Paris, Syllepse, 2007.
. On notera également la proposition de Marcel Hénaff de distinguer don cérémoniel (potlatch), don gracieux ou unilatéral (en famille ou à des inconnus) et don d'entraide. Henaff M., Le don des philosophes, Paris, Le Seuil, 2012, p. 65 sq.
. Guilhot N., Financiers, philanthropes. Vocations éthiques et reproduction du capital à Wall Street depuis 1970, Paris, Raisons d'agir, 2004.
. Mauss M., « Essai sur le don » (1923), in Sociologie et anthropologie, Paris, PUF, 1950, p. 143-279. Réimprimé seul, dans la même collection, en 2007. Une critique classique (outre celle de Lévi-Strauss, dans l'introduction de 1950) : Godelier M., L'énigme du don, Paris, Fayard, 1996.
. Sénèque, Les bienfaits (De beneficiis), Paris, Arléa, 2005.
. <http://www.philharmsociety.spb.ru/english/index.php> ; Van de Sandt U., La Société des Amis des Arts (1789-1798). Un mécénat patriotique sous la Révolution, Paris, École nationale supérieure des Beaux-Arts, 2006.
. Veblen T., Théorie de la classe des loisirs, Paris, Gallimard, 1970 (1899 pour l'éd. originale).
. Archambault E., Tchernonog V., Quelques repères sur les associations en France aujourd'hui, Centre d'économie de la Sorbonne, CNRS – Paris 1, 2012. Disponible sur : https://www.associatheque.fr/fr/fichiers/divers/reperes_asso-paris_CPCA.pdf (consulté en juin 2013). Voir également Bazin C. et al. (dir), La France bénévole, Paris, France Bénévolat et Recherche & Solidarité, mai 2012 (9e éd.). Disponible sur : <http://www.recherches-solidarites.org/media/uploads/lafrancebenevole2012.pdf>
. Colin B., Gautier A., Pour une autre économie de l'art et de la culture, Ramonville Saint-Agne, Érès, 2008.
. Bazin C., Malet J., La générosité des Français, Paris, Recherche et solidarité, 2012 (17e éd.).
. Giving USA Foundation, Giving USA 2010. The Annual Reoport on Philanthropy for the Year 2010. Indiana University. The Center on Philanthropy, 2010. Disponible sur : <http://www.cfbroward.org/cfbroward/media/Documents/Sidebar%20Documents/GivingUSA_2010_ExecSummary_Print.pdf> (consulté en juin 2013).
. Alline J.-P., Carrier R., La culture au risque du marché. Le mécénat face à ses acteurs, Paris, L'Harmattan, 2010.
. Martel F., De la culture en Amérique, Paris, Gallimard, 2006.
. La liste des fondations est disponible sur le site du ministère de l'Intérieur : http://www.interieur.gouv.fr/A-votre-service/Mes-demarches/Fondations.
. Bouquillon P., Matthews J. T., Le web collaboratif. Mutations des industries de la Culture et de la communication, Grenoble, Presses universitaires de Grenoble, 2010.
. Testart A., Critique du don : Études sur la circulation non marchande, Paris, Syllepse, 2007.
Deuxième Partie
Approches sectorielles
Le domaine des arts et de la culture, s'il affirme une certaine cohésion à partir des objets qu'il regroupe – arts de la scène, arts plastiques, patrimoine et industries culturelles – en regard des autres secteurs de production (la chimie ou l'agriculture), présente cependant un certain nombre de différences qu'il importe ici de préciser. L'ensemble des matières culturelles, au niveau des pouvoirs publics, est généralement traité par le même ministère, mais ce ne sont ni les mêmes professionnels, ni les mêmes services administratifs qui en ont la charge ; et pour cause, chacun des secteurs requiert un savoir-faire et des connaissances spécifiques.
Les catégories que nous avons choisi d'explorer de manière plus précise s'avèrent relativement classiques, en matière de culture ; ce sont elles qui à nos yeux expriment réellement les spécificités de la logique du secteur de la culture, notamment à travers l'histoire de leur reconnaissance comme des arts à part entière, à la différence de la logique médiatique, comme la presse ou la télévision. Nous reviendrons sur ces spécificités lorsque nous évoquerons la question des industries créatives (design, architecture, mode ; voire la gastronomie...) que l'on associe de plus en plus régulièrement au secteur culturel, mais qui présentent un caractère utilitaire nettement plus développé. Il n'en reste pas moins que les différences entre secteurs sont parfois floues (certains acteurs/créateurs peuvent travailler aussi bien dans le domaine de la création pure, et donc dans la culture que dans le domaine de la reproduction industrielle, comme un artiste plasticien travaillant comme designer pour une manufacture). Mais le caractère artistique et culturel, tel qu'il est reconnu par la société depuis la Renaissance, s'affirme prioritairement dans certains secteurs particuliers qui sont directement liés à l'histoire de l'art occidental : théâtre et opéra, musique, arts plastiques, cinéma, patrimoine.
Il n'empêche que si ces secteurs présentent une certaine cohérence qui les amène à être considérés, du moins à un certain niveau, comme artistiques, leur nature entraîne des modes de production, de diffusion et de présentation différents, induisant autant de systèmes d'organisation divergents. L'économie du théâtre, si elle se rapproche de celle de l'opéra, diffère en cela de celle des arts plastiques et du marché de l'art, dont les lieux de réception (galerie, salons, musées...) supposent des modes d'organisation spécifiques. Nous avons choisi de regrouper en quatre ensembles ces modes de fonctionnements des arts et de la culture, à travers la logique des arts de la scène, celle du patrimoine, celle des arts plastiques et celle des industries culturelles. Nous aurions bien entendu pu préciser en autant de sous-chapitres cette typologie (l'organisation de l'opéra n'est pas la même que celle des comédies musicales), mais nous avons plutôt cherché à décrire ce qui rassemble, notamment dans les industries culturelles, des organisations parfois relativement différentes (comme le livre, la musique enregistrée ou le cinéma).
Chapitre 6
Les arts de la scène
On rassemble, sous l'étiquette d'arts de la scène ou du spectacle vivant, un ensemble de pratiques dont la structure apparaît comme relativement identique, bien que les modes d'expression puissent largement varier. Des artistes proposent, à un public, une prestation généralement présentée dans un lieu spécifique (la scène), plus ou moins délimité (de l'opéra au théâtre de rue). Les prestations d'un orchestre de musique classique ou non classique, l'opéra, le théâtre, la danse, les arts de la rue, les arts du cirque ou les comédies musicales entrent dans cette catégorie dont le modèle économique fonctionne de manière plus ou moins similaire – le cas hybride des performances, en art plastique, bien que très proche du modèle des arts de la scène, dans sa forme, obéit plutôt aux règles du marché de l'art, qui sont examinées plus loin.
Ce secteur représente une partie considérable de l'emploi dans le domaine de la culture : près de 290 000 salariés y travaillaient en 2006, soit 34 % de l'emploi culturel, mais à peine plus de 20 % bénéficiaient de contrats à durée indéterminée. Le nombre d'unités marchandes œuvrant dans le domaine du spectacle vivant, c'est-à-dire l'organisation des spectacles, des tournées, la préparation des décors ou l'éclairage, mais aussi la gestion des salles, est d'environ 18 000 unités (soit 11 % du secteur culturel), employant un effectif d'environ 20 000 salariés équivalents temps plein. Entre ces deux chiffres, figurent nombre d'artistes ou de techniciens du spectacle, engagés pour des productions déterminées et bénéficiant, pour la plupart, du statut d'intermittents, sur lequel nous reviendrons. Ces chiffres ne tiennent cependant pas compte de la production amateur non rémunérée, pourtant considérable, mais dont la logique d'échange échappe largement aux relevés statistiques. Si l'image des arts de la scène apparaît largement comme celle d'un secteur subventionné, le domaine n'en demeure pas moins très largement fondé sur une logique marchande, qui s'exprime à travers le secteur privé du théâtre, mais aussi, surtout, celui des salles de concert, le monde des entrepreneurs de spectacles, des organisateurs de tournées etc. Au total, près de 80 % du chiffre d'affaires est réalisé par des entreprises marchandes (pour un montant de 4,4 milliards d'euros).
Trois logiques de fonctionnement différentes
Les économistes Pommerehne et Frey, dans un ouvrage déjà ancien, présentaient le développement de la production théâtrale à partir de trois modèles, qu'il est intéressant de décrire ici afin de comprendre l'imbrication des logiques économiques différentes en œuvre dans certains lieux, par exemple dans le théâtre privé et le théâtre public. C'est justement à partir du théâtre que les deux économistes évoquent, de manière chronologique, les manières de fonctionner différemment, en fonction d'une logique coopérative, privée et publique. Une telle présentation pêche cependant d'un point de vue historique : d'emblée, le soutien public, durant l'Antiquité, mêlé au mécénat des grandes familles, permet l'organisation des fêtes et liturgies. Par ailleurs, la notion de théâtre amateur (ou d'amateur) que l'on accolerait au modèle coopératif, essentielle pour comprendre l'histoire du spectacle, n'a pris un sens péjoratif que depuis quelques années (en opposition avec les professionnels du secteur). Le plaisir du partage entre les acteurs et le public, tous deux le plus souvent membres de la même communauté, participe d'un mouvement de loisir, au sens noble du terme, qui s'inscrit au cœur des réflexions de l'éducation populaire puis, plus tard, de l'action culturelle. En ce sens, nombre de théâtres amateurs n'envisagent nullement de passer d'un modèle coopératif à un modèle privé ou subventionné.
Le modèle coopératif
Le modèle coopératif repose largement sur des principes que l'on retrouve dans l'économie du don, bien qu'il puisse également comporter des flux financiers. On le retrouve dans le théâtre amateur (sur lequel, faut-il le rappeler, le renouveau théâtral s'est appuyé au début du xxe siècle, par exemple avec le théâtre du peuple de Bussang, de Maurice Pottecher), mais aussi de manière constitutive pour nombre de jeunes troupes se formant de manière spontanée à l'issue des années de formation, voire durant celles-ci.
Ce modèle part des artistes eux-mêmes, qu'ils soient acteurs ou metteurs en scène, qui tentent de jouer et, pour cette raison, de rassembler les capitaux nécessaires (cette logique s'oppose, par exemple, à celle du théâtre privé, qui part plutôt de l'organisation). De telles structures sont de taille relativement modeste (une dizaine de personnes), et les rapports entre les membres de l'équipe sont très informels : les tâches sont largement partagées au sein de l'équipe (un acteur peut également s'occuper de la comptabilité ou des relations publiques), tandis que l'organisation est largement débattue et discutée au sein du groupe. Un tel mode de fonctionnement, que l'on peut retrouver dans le théâtre de rue et le jeu « au chapeau » (ce qui conduit le public à se rapprocher d'une logique de don) ou à partir de droits d'entrée, pour des salles louées ou prêtées (par une école, un centre culturel etc.). Mais il participe également, tout au long de l'histoire, au développement de théâtres non lucratifs, que l'on retrouve aussi bien dans les cours de province ou les hôtels particuliers et les salons bourgeois, moyennant un mécénat plus ou moins affirmé. Une telle forme d'organisation bénéficiant de coûts relativement faibles – les recettes sont souvent réparties de manière équitable entre les membres de l'équipe – peut survivre durant de nombreuses années et, parfois, permettre à certains d'en vivre au titre de métier principal. Les rapports de travail reposent sur une logique privilégiant les liens sociaux et les rapports humains, tel qu'on peut les retrouver dans la logique du don, et ce sont les mêmes principes qui induisent les travailleurs de l'organisation à régler les problèmes entre eux, de manière informelle, sans véritablement de recours à un cadre juridique précis afin de préciser les conditions de travail (contrats de travail, commissions paritaires, barèmes des salaires etc.).
C'est justement la modestie des coûts, mais aussi celle des recettes et celle des activités, qui induit un tel mode de fonctionnement. En quelque sorte, le succès de la troupe peut entraîner l'augmentation de la demande (le nombre de prestations) et, partant, ne permet plus de poursuivre un tel fonctionnement : si le nombre de représentations augmente, les questions de comptabilité, d'intendance ou de relations publiques et d'organisation générale prennent une ampleur telle que les membres ne peuvent plus s'en occuper en sus de leur prestation artistique. L'organisation est condamnée à s'agrandir, mais ce développement induit d'autres formes de relations, avec un cadre de travail nécessitant une meilleure définition. Dans un tel cas, stipulent Pommerehne et Frey, l'organisation peut être dissoute, mais également se spécialiser, ce que l'on observe au niveau du théâtre privé.
Le modèle privé
La structure d'un théâtre privé (ou d'une salle de concert) repose sur une organisation en phase avec les règles du marché, tel qu'elles avaient déjà été largement explorées depuis la révolution industrielle, à partir de la spécialisation des tâches : les acteurs ou les musiciens d'un côté, la mise en scène, les services techniques, de communication ou de direction de l'autre.
Les professions des arts vivants s'articulent selon une structure que l'on va retrouver dans d'autres domaines, notamment les industries culturelles : création, production et diffusion. (1) Le pôle de création du spectacle rassemble les tâches les plus directement liées à ces aspects, à savoir l'auteur de l'œuvre et, parfois, la mise en scène. Encore ce dernier métier bénéficie-t-il d'un positionnement à cheval entre deux pôles, celui de la création et celui de la production. C'est sans doute au niveau du théâtre amateur ou public que la fonction de la mise en scène (ou de la direction d'orchestre) peut se présenter comme créatrice ; dans le théâtre privé, elle intègre plus généralement la production. (2) Alors que le rôle de la création est largement indépendant des nécessités de financement (de nombreux auteurs, par ailleurs, ne dépendant pas de ces revenus pour vivre), celui de la production de spectacle lui est totalement lié. Le rôle du producteur, que l'on va retrouver dans d'autres domaines (cinéma, disque ou livre), vise à trouver les capitaux nécessaires pour monter un projet, réunir les artistes (acteurs ou musiciens), le metteur en scène ou chef d'orchestre, le personnel technique (son, décors, costumes etc.). (3) Le troisième pôle des métiers vise à diffuser et exploiter le spectacle, par sa présentation dans un théâtre, par l'organisation de tournées etc. C'est dans cette troisième catégorie que l'on retrouve des métiers liés à la communication de l'événement, à l'accueil des publics, à la billetterie, à la sécurité des lieux, aux changements de décor (machinistes) etc.
D'un point de vue historique, le subventionnement des spectacles n'a longtemps affecté qu'une petite partie de ceux-ci, d'abord en fonction d'un statut plus ou moins hybride liant mécénat et subvention royale, tandis que de très nombreux lieux – le théâtre londonien notamment, depuis la création du Globe en 1599, jusqu'au théâtre de boulevard, qui domine la scène parisienne sous la Troisième République, en passant par l'organisation des concerts – dépendent totalement du public. C'est encore cette logique du théâtre privé que l'on retrouve en grande partie au sein du théâtre à Londres ou à New York (une logique identique lie le théâtre et les comédies musicales, où les productions sont conçues à partir de stratégies commerciales et financières proches de celles utilisées dans l'industrie du cinéma), ainsi qu'en France, essentiellement à Paris (le Syndicat national des directeurs et tourneurs du Théâtre privé regroupe une cinquantaine de théâtres).
Certaines productions au niveau des arts de la scène peuvent en effet s'avérer particulièrement rentables, pour autant que l'organisation qui les conçoit et les gère respecte un certain nombre de règles, que se sont attaché à décrire les deux économistes.
Les coûts fixes sont bas. La logique du marché induit non seulement la maximisation des recettes, mais aussi la diminution des coûts, et notamment des coûts fixes qui, contrairement aux coûts variables, sont permanents, même lorsque le théâtre ne produit rien. Forcément, le coût fixe le plus élevé réside dans l'entretien d'un théâtre ; aussi nombre de troupes itinérantes peuvent-elles plus facilement fonctionner selon une logique de marché. Lorsqu'une telle infrastructure est possédée par l'organisation, celle-ci sera rentabilisée au maximum, par exemple en augmentant le nombre de représentations sur une même journée. De manière plus générale, l'équipe permanente d'un théâtre privé est toujours réduite au minimum ; le personnel se doit alors d'assumer plusieurs tâches (comme dans le théâtre coopératif), à cette différence que certaines tâches – notamment celles liées à la direction ou aux finances – ne sont ni partagées ni discutées en commun : c'est en fonction d'une logique contractuelle qu'il est demandé à un employé la flexibilité la plus grande possible, tant au niveau de l'horaire de ses prestations que de leur nature. La logique des économies apparaît de manière structurelle, tant au niveau du nombre de répétitions que du réemploi de décors ou de costumes, de l'envoi de courriers ou de photocopies... Selon ces mêmes principes, l'augmentation du nombre de représentations, pour un même spectacle, et sa reprise en tournée permettent d'amortir le plus directement possible les investissements liés à la production... pour autant qu'il y ait du public.
Le public potentiel est grand. La présentation d'une pièce ou d'une œuvre à de multiples reprises – pour autant qu'elle ait du succès – implique que le réservoir de spectateurs soit suffisamment important ; c'est évidemment pour cette raison que le secteur privé des arts du spectacle, du moins celui qui est lié à une salle de spectacle, est implanté dans les grandes métropoles (le secteur est essentiellement francilien). La logique de marché qui prévaut part d'un présupposé simple : pour rentabiliser un certain investissement, il est nécessaire que le public potentiel soit suffisamment important. Le bassin de population, dans cette perspective, constitue une condition nécessaire, mais pas suffisante. Parmi les autres conditions, le sujet de l'œuvre doit être suffisamment attractif – d'où des sujets populaires, boulevardiers – et le produit, lui-même, gagne à être desservi par des acteurs célèbres, qui attireront une partie du public pour leur seule prestation dans la pièce, selon la logique du star-system – le principe étant identique pour une pièce de théâtre ou une œuvre musicale. Tant que l'œuvre continue d'attirer du monde, il est préférable de la poursuivre, ainsi certains théâtres londoniens ont-ils poursuivi avec profit ce dispositif d'open end (la fin est ouverte, tant qu'il y a du public...), et La souricière, d'Agatha Christie, a pu être jouée pendant près d'un demi-siècle... Parfois, la recherche d'un nouveau public induit la nécessité de faire partir la pièce en tournée, ce que l'on observe actuellement avec le phénomène des comédies musicales en France, qui après Paris, poursuivent leur vie en province.
Le prix des places est fixé de manière discriminante. La politique de prix constitue l'un des axes majeurs des principes du marketing. Discriminer, c'est tenter d'établir le prix le plus élevé que les gens sont réellement disposés à payer. Si un riche amateur est prêt à débourser 200 euros pour une prestation, mais que le prix d'entrée est fixé à 50 euros, le théâtre (mais c'est vrai dans tous les secteurs) aura, en quelque sorte, « perdu » 150 euros... soit le surplus du consommateur. C'est pour cette raison que certains secteurs, comme celui du transport, ont mis au point un système de classes donnant accès à des prestations différentes (un peu plus luxueuses, comme un repas offert et un siège un peu plus confortable), moyennant des tarifs plus élevés. Cette logique se retrouve dans les spectacles, où le tarif des sièges des carrés VIP ou de la première catégorie est parfois dix fois plus élevé que celui des troisièmes balcons. Un tel procédé, qui s'observe plus rarement dans le spectacle subventionné (sauf à l'opéra), permet évidemment d'augmenter les recettes, et c'est une même logique, à l'inverse, qui conduit les invendus, peu de temps avant un spectacle, à être bradés, afin de remplir au mieux la jauge.
D'autres sources de revenus sont exploitées. La volonté d'accroître les recettes conduit les producteurs et les diffuseurs à tenter de générer, à partir des spectacles produits, un maximum de recettes différentes. Outre le prix des places, qui constitue le principal de la recette, on a longtemps espéré trouver des débouchés par le biais de l'exploitation des œuvres sous une autre forme : les retransmissions par la radio ou la télévision, et plus récemment, par le cinéma (pour certains opéras), ou la diffusion de cassettes vidéos et de DVD. De tels revenus, s'ils ne sont pas négligeables, ont parfois été surestimés – ce que l'on retrouve également, actuellement, sur internet à partir des usages du numérique. En revanche, le développement des boutiques (ventes de livres, de CD ou DVD, multiplication des formules de restauration, de bars) ainsi que la prestation de certains services (voituriers, baby-sitting) et, de manière générale, le merchandising lié à l'événement conduisent également au développement des recettes, probablement dans des proportions moindres que celles que l'on observe dans le milieu du cinéma.
Ainsi, le secteur du théâtre peut fonctionner, du moins en partie, à partir des règles du marché et d'un financement lié aux recettes générées par les spectateurs. Il est cependant évident que, dans de telles circonstances, tous les répertoires et toutes les œuvres ne peuvent être joués : seules, les pièces plus populaires et les moins coûteuses permettent de garantir une certaine rentabilité. Ainsi, certains secteurs entiers, comme l'opéra, ne semblent pas pouvoir reposer uniquement sur le financement du public ; de la même manière, seules les œuvres dont la distribution est relativement modeste peuvent espérer être produites. C'est évidemment pour cette raison que, d'emblée, une partie du répertoire théâtral et l'opéra, mais aussi les concerts symphoniques, bénéficient d'un soutien qui fut longtemps privé (et lié au prince), puis public. La logique du théâtre subventionné va s'étendre, dès les années 1950 (avec Jean Vilar), et se présenter d'une certaine manière comme le fil conducteur de la politique culturelle, telle qu'elle sera mise en œuvre par Malraux durant les années 1960, et développée par ses successeurs, notamment Jack Lang, issu lui-même du milieu du théâtre.
Le modèle public
L'intervention des pouvoirs publics intervient à tous les niveaux qui ont été évoqués : au niveau de la création et des compagnies, mais aussi à celui des structures de production et de diffusion.
Subventions et financements. Les subventions peuvent être envisagées de plusieurs manières différentes. Au niveau des personnes ou des compagnies, les subventions ou aides peuvent prendre la forme de commandes d'œuvres, de résidences d'artistes ou de bourses pour les auteurs, tandis que les compagnies peuvent obtenir des aides ponctuelles (à la production) ou sous forme de conventions (généralement sur base d'un contrat triennal ou quadriennal, assorti d'un cahier des charges détaillé). Des subventions au billet vendu peuvent aussi être envisagées (ce dispositif n'existant pas en France). La plus grande partie de l'enveloppe publique est cependant dévolue au financement de structures pérennes, selon une logique que l'on retrouve dans de nombreux autres secteurs – comme le patrimoine et les arts plastiques. La politique culturelle mise en place, à ce niveau, vise également un soutien à deux niveaux : production et diffusion. Ainsi, certaines scènes (scènes nationales, scènes conventionnées ou scènes de musique actuelle) sont financées pour l'accueil des compagnies et le travail de diffusion de leur œuvre au sein du public, tandis qu'un nombre plus restreint – mais mieux doté – de structures a été mis en place, tant à l'échelon national (théâtres nationaux, opéras, centres dramatiques nationaux, centres chorégraphiques nationaux, orchestres permanents, centres nationaux des arts de la rue) que régional (centres dramatiques régionaux, opéras de région, pôles régionaux du cirque) pour accueillir des compagnies, mais aussi pour créer des spectacles. L'action conjuguée du ministère de la Culture, des régions et des villes vise ainsi à l'entretien de ces différentes structures, leur assurant une certaine pérennité qu'elles ne sauraient atteindre par le seul biais du marché.
Emploi et intermittence. De nombreux emplois sont ainsi directement pris en charge par des financements publics, soit via les dotations dont disposent les établissements, soit par l'engagement direct de personnel par les collectivités, au bénéfice des structures. Mais c'est essentiellement un régime spécifique d'assurance de chômage, géré par l'Unédic en France, qui permet de maintenir un certain niveau de traitement pour les travailleurs salariés du secteur (en France, les travailleurs du secteur sont bien plus souvent salariés, contrairement à d'autres pays qui privilégient le statut d'indépendant). Les travailleurs du milieu du spectacle – arts de la scène, mais aussi télévision et cinéma – pour autant qu'ils aient travaillé un certain nombre d'heures (507 heures sur environ dix mois), peuvent ainsi revendiquer ce statut et bénéficier d'allocations. Les premiers dispositifs, créés en 1936, ont été largement développés, comme le nombre de contributeurs et de bénéficiaires. De moins de 20 000 en 1974, ils sont plus de 100 000 de nos jours. Entre-temps, le système a en quelque sorte conditionné le secteur et la manière d'employer les artistes, rémunérés pour des périodes de plus en plus courtes – et dépendant donc du système d'allocations de manière plus importante. Depuis de nombreuses années, le niveau des cotisations du système ne permet plus de financer ce mécanisme, dont le déficit est reporté sur le système général de cotisation des travailleurs (la méthode de calcul du déficit et son résultat font par ailleurs l'objet de contestations). Le protocole d'accord en 2003, visant à renégocier le système, a suscité des mouvements de grève importants parmi les bénéficiaires, et notamment l'annulation de plusieurs festivals importants, de même (mais dans une moindre mesure) que les modifications entamées en 2014. Un récent rapport de la Cour des comptes, en 2012, continue de stigmatiser les « dérives massives » et son déficit qu'elle évalue à un milliard d'euros (pour 100 000 bénéficiaires).
Encadrement et fonds de soutien. L'intervention publique, il convient à nouveau de le souligner, joue un rôle fondamental en matière d'encadrement du secteur tant en matière de sécurité en général (incendie d'un lieu de spectacle) que de sécurité juridique (contrats, relations entre travailleurs et employeurs ou avec les consommateurs). Pour ce qui est des tâches de production, de diffusion et d'exploitation des spectacles, en revanche, l'État joue un rôle d'organisation et de censure – cette dernière a rythmé toute l'histoire du théâtre occidental, son influence actuelle étant très réduite ; la notion de spectacle, cependant, doit être entendue dans un sens large, destiné à encadrer aussi bien le théâtre d'auteur que les spectacles de Pigalle. Si les règles encadrant les producteurs et les diffuseurs de spectacle ont, au départ, été envisagées pour des raisons de morale (mais aussi pour s'assurer du respect des règles comptables et du droit du travail), celles qui concernent leur exploitation sont essentiellement mises en place pour des raisons de sécurité. Les entrepreneurs doivent ainsi, pour ouvrir un lieu, obtenir une licence, qui dans le cas des exploitants de salles, diffère en fonction des jauges (le nombre de places, de moins de 301 spectateurs à plus de 1 500). Plus de 24 000 licences, qui sont renouvelables tous les trois ans, ont ainsi été délivrées en France.
Par ailleurs, un mécanisme identique à celui qui a été mis en place pour le Centre national du Cinéma et de l'image animée (CNC), permet de soutenir le secteur du théâtre privé et de la chanson, par le biais d'une taxe spéciale sur les spectacles, qui est gérée d'une part par l'Association pour le soutien du théâtre privé, d'autre part par le Centre national de la Chanson, des variétés et du jazz ou CNV (établissement public à finalité industrielle et commerciale, sous la tutelle du ministère de la Culture). La taxe rapporte actuellement, au CNV qui est en charge de redistribuer ces moments, environ 25 millions d'euros. Nous reviendrons plus précisément sur ce type de fonds en évoquant l'activité du CNC.
La loi de « maladie des coûts » de Baumol et la logique des subventions
On sait le rôle pionnier que joue William Baumol dans l'économie de la culture. L'ouvrage qui fonde, en quelque sorte, la discipline, porte sur le secteur des arts de la scène aux États-Unis : théâtre, opéra, musique et danse. L'enquête menée par Baumol et Bowen, financée par le Twentieth Century fund, vise à comprendre le financement des arts de la scène et sa possible évolution. Une telle logique est plus ancienne, le financement public de la culture ayant déjà fait l'objet d'autres justifications.
Baumol, économiste spécialisé dans le marché du travail, s'est intéressé aux arts de la scène pour illustrer un problème plus général, lié aux questions de productivité. La productivité du travail est le rapport entre la production et les facteurs mis en œuvre pour aboutir à celle-ci, par exemple le nombre d'heures de travail pour produire un bien. La production varie, en fonction de l'organisation du travail, du perfectionnement des technologies (ce qu'Adam Smith avait notamment mis en valeur à travers la notion de division du travail) etc. Ainsi, des gains de productivité peuvent être réalisés. Ces gains de productivité peuvent être redistribués à plusieurs niveaux : aux actionnaires (augmentation du dividende), aux consommateurs (diminution du prix), à l'entreprise (augmentation des fonds propres ou financement des investissements), mais aussi aux salariés, par des hausses de salaires, des primes, des promotions etc.
L'enquête de Baumol
Si la « loi » présentée par William Baumol a pu faire a posteriori l'objet d'une démonstration utilisant les mathématiques, c'est d'abord à une minutieuse enquête que se livrent les auteurs, dont le résultat – plus de 400 pages – peut être présenté comme le premier véritable jalon de l'économie de la culture. À partir de données empiriques, dont certaines remontent à la fin du xixe siècle, l'économiste de Princeton et New York, s'est attelé à comprendre l'organisation générale du secteur des arts de la scène aux États-Unis, soit ses orchestres, son théâtre, l'opéra, mais aussi le statut de l'artiste ainsi que les publics de la culture (ses conclusions sont proches de celles de Bourdieu). C'est donc à partir d'une importante enquête de terrain qu'il peut étayer son raisonnement, par ailleurs assez simple, fondé sur les gains de productivité. Car en matière de productivité, certains secteurs dépendant essentiellement de la main-d'œuvre (les arts de la scène, mais aussi la coiffure), ne peuvent réellement dégager de gains substantiels : on ne peut jouer plus vite une pièce de Shakespeare ou un quatuor de Beethoven, et on ne peut non plus enlever des rôles... Néanmoins, l'augmentation de la productivité, dans d'autres secteurs, induit une augmentation générale des salaires (pour continuer d'attirer la main-d'œuvre). En outre, constate Baumol, le prix du billet d'entrée doit demeurer relativement bas, la demande s'avérant élastique. C'est dans cette perspective que le coût des concerts a tendance à sensiblement augmenter (inflation déduite), mais sans pouvoir être répercuté pleinement au niveau du prix d'entrée. D'où, constate Baumol, le creusement d'un déficit engendré par des dépenses de plus en plus lourdes, et des recettes stagnantes. Baumol a soin d'intégrer, dans son raisonnement, la philanthropie, car il revenait justement à l'élite de compenser ce manque à gagner par une générosité accrue.
L'étude de Baumol ne porte pas seulement sur le constat d'un déficit, mais tente d'estimer son évolution dans les années ultérieures. Et le calcul de cette évolution laisse entrevoir de grandes difficultés au niveau du secteur des arts de la scène, le développement de la philanthropie ne parvenant pas à combler le déficit toujours croissant du secteur. C'est dans cette perspective que l'économiste de Princeton interroge et discute le principe d'une intervention publique. Le climat de l'époque est marqué par les projets d'intervention publique, et notamment l'ouverture du National Endowment for the Arts, en 1965. Analysant les raisons du soutien public, Baumol présente le secteur comme un bien qui n'est certes pas public, mais mixte, dont les retombées économiques ou le prestige bénéficient à l'ensemble de la région dans laquelle un orchestre, un opéra ou un théâtre se situe. Cette logique augure, on le sait, le développement d'enquêtes plus précises (cf. chapitre 4) à partir desquelles on tentera de déterminer l'impact économique d'une structure sur son territoire.
La vérification du modèle
La « loi de Baumol » a été largement utilisée comme argument pour étayer les demandes d'intervention publique – ce que Baumol ne demandait pas explicitement. De nombreuses études ultérieures ont été réalisées afin de vérifier la loi. Dans un premier temps, il importe de remarquer que les estimations de Baumol pour les années ultérieures (le creusement du déficit et l'impossibilité de combler ce dernier par la philanthropie) ne se sont pas réalisées dans les proportions calculées. La question de l'élasticité de la demande, par exemple, a largement été contestée (l'augmentation des prix n'implique pas la diminution de la fréquentation, mais l'inélasticité n'est pas pour autant vérifiée).
Par ailleurs, la loi elle-même, telle que formulée brièvement, ne permet pas de prendre en compte les stratégies parfois très diverses des établissements pour tenter de résorber le déficit. Ainsi, le développement des technologies numériques a conduit à une transformation radicale du contexte des arts de la scène et de l'emploi de nouvelles techniques afin de concurrencer l'audiovisuel. Par ailleurs, des gains de productivité ou des économies ont pu être parfois observés dans nombre de productions, notamment par la réutilisation de décors, l'utilisation d'un même acteur pour jouer plusieurs rôles, la réduction des répétitions, le recours à du bénévolat, l'utilisation de musique enregistrée ou de musique électronique etc. Parallèlement, les organisations ont également essayé de développer leurs recettes, en améliorant leur offre de produits au cours du spectacle (restaurants, bar, boutique etc.), mais aussi en tentant de coproduire (diminution des coûts) et de mieux diffuser leur spectacle.
Subventions et structure des recettes
Nous avons déjà évoqué largement la critique des subventions publiques, notamment à partir du modèle général de l'école du Public choice, mais également, de manière plus précise, au niveau des arts de la scène, qu'il s'agisse de l'opéra ou du théâtre (cf. chapitre 4). Il est sûr que l'évolution des subventions publiques, telle qu'elle se présente au cours des années 1980 (époque à laquelle se développe cette littérature critique), laisse en effet apparaître une augmentation croissante des subventions qui, de l'ordre de moins de 30 % pour le théâtre allemand par exemple, au début du siècle, dépasse les 85 % à la fin des années 1980.
Si l'on considère que le subventionnement répond à la « maladie des coûts », telle qu'elle a été mise en exergue au cours des années 1960, cela entraîne inévitablement un effet sur le comportement des organismes conventionnés, logiquement conditionnés à mettre en œuvre des stratégies visant à pérenniser l'action publique, parfois au détriment du spectateur dont ils dépendent moins. Les grandes structures subventionnées ne participent que de manière très modeste à la fréquentation des spectacles, si l'on tient compte de la musique actuelle (ainsi que des festivals, dont la quarantaine des plus importants, en France, rassemble plus de 3,5 millions de participants).
Fréquentation des principales structures des arts de la scène en France, en 2012 (milliers de spectateurs) | Nombre | Spectateurs
---|---|---
Théâtres nationaux | 4 | 581
Opéras nationaux | 2 | 871
Centres dramatiques nationaux et régionaux | 39 | 1 000
Théâtres lyriques en région | 13 | 1 000
Centres chorégraphiques nationaux | 19 | 662
Scènes nationales | 71 | 2 100
Théâtres privés de Paris | 56 | 3 300
Spectacles privés et de musique actuelle | n.c. | 21 700
Source : Ministère de la Culture et de la Communication, Chiffres clés 2013. Statistiques de la culture, disponible sur internet : <http://www.culturecommunication.gouv.fr/Politiques-ministerielles/Etudes-et-statistiques/Les-publications/Chiffres-cles-statistiques-de-la-culture/Chiffres-cles-2013>
La structure des recettes et des dépenses dépend, on l'aura compris, largement de la nature de l'institution et de ses relations avec les pouvoirs publics. Ainsi, l'acteur qui reçoit la plus importante dotation, l'Opéra de Paris, bénéficie en 2012 d'une subvention d'environ 105 millions d'euros, ce qui représente 50 % de ses recettes. Ses dépenses sont largement liées à sa masse salariale (plus de 56 %, hors artistes), soit plus de 1 800 personnes. On pourrait penser que cette vénérable institution est l'une des plus dispendieuses pour la nation, il n'en est rien. Les recettes de la billetterie, de la boutique ou du mécénat ont été largement développées ces dernières années. Le niveau de subvention du théâtre de l'Odéon, dont l'intervention publique est nettement moins importante (un peu plus de 12 millions), représente environ 72 % du budget du théâtre, somme relativement identique pour la Comédie française. Le niveau de subvention du National Theatre de Londres, en revanche, avoisine les 25 % (pour un budget de 80 millions de livres). Il convient cependant de rappeler que ces établissements, symboliquement très emblématiques, ne constituent qu'une très faible partie de l'emploi et des revenus du secteur. Ce sont d'abord les entreprises marchandes, soit les théâtres privés, les spectacles privés et de musique actuelle, qui attirent le plus de spectateurs et constituent l'essentiel de l'emploi et du chiffre d'affaires – plus de 60 % de la valeur ajoutée est par ailleurs produite en Île-de-France.
. Cléron É., Patureau F., « L'emploi salarié dans le secteur de la culture », Culture-Chiffres, 2009-1, 8 p.
. Deroin V., « Les activités marchandes de spectacle vivant en 2010 », Culture Chiffres, 2013-1, 16 p.
. Ibid.
. Pommerehne W. W., Frey B. S., La culture a-t-elle un prix ?, Paris, Plon, 1993.
. Barberis I., Poirson M., L'économie du spectacle vivant, Paris, PUF, coll. « Que sais-je ? », 2013 ; Veyne P., Le pain et le cirque : sociologie historique d'un pluralisme politique, Paris, Le Seuil, 1976.
. Mervant-Roux M.-M. (dir.), Du théâtre amateur. Approche historique et anthropologique, Paris, CNRS éd., 2004.
. Sur ces métiers, voir Urrutiaguer D., Guide des études théâtrales, Paris, Armand Colin, 2012.
. Donahue T., Patterson J., Stage Money. The Business of the Professional Theater, Columbia, University of South Carolina Press, 2010.
. Voir le site et les chiffres clés donnés par le syndicat : http://www.theatresprives.com/
. Greffe X., Pflieger S., La politique culturelle en France, Paris, La Documentation française, 2009 ; Poirrier P. (dir.) Politiques et pratiques de la culture, Paris, La Documentation française, 2010.
. Menger P.-M., Les intermittents du spectacle. Sociologie du travail flexible, Paris, éditions de l'ÉHÉSS, 2011 (nouv. éd.).
. Dans le rapport annuel de la Cour des comptes de 2012 : http://www.ccomptes.fr/Publications/Publications/Rapport-public-annuel-2012.
. Urrutiaguer D., Économie et droit du spectacle vivant en France, Paris, Sorbonne nouvelle, 2009.
. Baumol W. J., Bowen W. G., Performing arts. The Economic Dilemma, New York, The Twentieth Century Fund, 1966.
. Notamment la « Loi de Wagner », comme le rappellent Isabelle Barbéris et Martial Poirson. Barberis I., Poirson M., op. cit., p. 62-63.
. De tels gains peuvent être obtenus à partir de l'amélioration de la technologie, mais aussi, de la formation, du management, d'économies d'échelles etc. Sur ce développement, voir par exemple la synthèse qu'en donne Heilbrun J, « Baumol Cost's disease », in Towse R. (dir.), A Handbook of Cultural Economics, Cheltenham, Edward Elgar, 2003, p. 91-101.
. Seaman B. A., « Empirical studies of demand for performing arts », in Ginsburgh V., Throsby D., Handbook of the Economics of Art and Culture, Amsterdam, Elsevier, vol. 1, 2006, p. 415-472 ; Last A.-K, Wetzel H., « Baumol's cost disease, efficiency, and productivity in the performing arts: an analysis of german public theatres », Journal of Cultural economics, 35, 2011, p. 185-201. Pour un bon résumé, voir également Benhamou F., L'économie de la culture, Paris, La Découverte, 2008 (6e éd.).
. Dupuy X., « La surqualité, le spectacle subventionné malade de la démocratie ? », Revue économique, 34, 1983, p. 1089-1115.
. Pommerehne W. W. et Frey B. S., op. cit.
. Sources : rapport d'activité de l'Opéra national, et budget simplifié présenté sur le site du Théâtre de l'Odéon : http://www.theatre-odeon.eu/fr/l-odeon/quelques-chiffres.
. Deroin V., op. cit.
Chapitre 7
Le patrimoine
La notion de patrimoine est d'abord juridique et désigne, dans le droit romain, l'ensemble des biens recueillis par succession. Ce n'est que progressivement, par analogie, que l'idée d'un patrimoine culturel émerge, apparaissant au xviie siècle et se développant au siècle suivant, notamment durant la Révolution française, avec l'idée d'un patrimoine national dépassant celui des familles, puis au xxe siècle, avec le principe d'un patrimoine mondial. C'est ainsi assez logiquement que la notion de patrimoine englobe les biens immobiliers (monuments, châteaux, églises, mais aussi des granges, ascenseurs à bateaux, gares etc., relevant de l'administration du patrimoine, autrefois des monuments historiques), et les biens mobiliers, généralement conservés dans des musées. Récemment (en 2003), l'Unesco a associé au patrimoine matériel le patrimoine immatériel, constitué par les pratiques ou savoir-faire que des communautés et groupes d'individus reconnaissent comme appartenant à leur patrimoine.
L'extension du champ patrimonial suppose, en quelque sorte, que tout bien est susceptible d'être patrimonialisé. Le Code du patrimoine, en revanche, retient plus spécifiquement cinq domaines principaux relevant de son champ d'application : les archives, les bibliothèques, les musées, l'archéologie (les fouilles) et les monuments historiques, sites et espaces protégés. L'économie de ces différents domaines varie quelque peu ; ceux dont il est le plus souvent question sont les musées et les monuments historiques, sans doute en regard de leur succès de fréquentation et de leur rapprochement récent (ces trente dernières années) avec la logique de marché. Le secteur des archives ou celui des bibliothèques, par exemple, est largement oublié. Il est vrai, par ailleurs, que ce dernier secteur obéit à une logique particulière (celle de la lecture publique), au même titre que le monde des musées qui, pour son activité de recherche et de communication, ne saurait être réduit à sa seule dimension patrimoniale. C'est néanmoins à partir de cette dimension que l'économie de la culture s'est essentiellement intéressée à ce domaine. Babelon et Chastel, dans un article célèbre de 1980, publié plus tard sous forme d'ouvrage, constataient que « Le patrimoine se reconnaît au fait que sa perte constitue un sacrifice et que sa conservation suppose des sacrifices ». Ce double mouvement indique bien le mécanisme particulier qui soutient l'édifice patrimonial : si sa perte constitue un sacrifice, son entretien nécessite des financements, longtemps publics et financés par l'impôt (comme le secteur des bibliothèques et celui des archives publiques le sont encore globalement), mais de plus en plus soutenus par le marché lui-même, lorsque la chose est possible. C'est notamment pour cette raison – qui prend en charge les sacrifices ? – que la philanthropie, d'abord (le prince ou les grands mécènes), puis les pouvoirs publics, se sont largement investis dans ce domaine, l'Homo œconomicus du marché ne pouvant, par définition, avoir intérêt à les prendre en charge. Un certain nombre de musées lucratifs célèbres ont bien existé (comme celui de Charles Wilson Peale fondé en 1786 à Philadelphie), mais leur durée de vie n'a jamais dépassé les deux générations.
Structure du secteur
Le secteur du patrimoine continue – dans les pays européens – d'être largement soutenu par les pouvoirs publics. C'est notamment le cas des archives et des bibliothèques, qui bénéficient d'une longue tradition à cet égard. Il existe bien un certain nombre d'archives ou de bibliothèques privées – on peut songer aux sociétés savantes qui se sont développées à travers le monde occidental, notamment durant le xixe siècle, et qui sont à la base de la création d'un grand nombre de musées ou de centres d'études en province. Mais ce réseau relativement informel, largement fondé sur la logique du don et quoique partiellement ouvert au grand public, a été éclipsé par celui initié par les pouvoirs publics. C'est un réseau dense et relativement bien structuré qui est ainsi mis en place dès le début du xixe siècle, notamment en France, dans le sillage de la Révolution française. La logique qui prévaut, et que l'on retrouve dans l'ensemble du système culturel, mais aussi politique, part d'un dépôt central, institué dans la capitale – les Archives nationales, la Bibliothèque nationale, le Muséum et le Musée central des Arts (Louvre) – pour essaimer dans les provinces, avec un réseau assez rapidement mis en place pour ce qui concerne les archives (départementales, puis communales) et les bibliothèques (essentiellement communales) ; le secteur des musées et des monuments historiques connaîtra une évolution un peu moins structurée, évoluant au gré des ensembles ou des collections à préserver. Quoi qu'il en soit, la logique animant ces trois secteurs est d'abord similaire, liée à la protection et la préservation d'un patrimoine, à son étude et à sa communication au public. Longtemps, ce public, s'il n'exclut pas les masses, est d'abord constitué d'un cercle d'amateurs et d'érudits, dont les archives, les livres et les collections constituent les fonds nécessaires à la recherche. Les musées d'art, en revanche, sont d'abord destinés à la formation des artistes et à la délectation d'une communauté d'esthètes, notamment de touristes. Aussi, durant longtemps, l'accueil du public ne constitue-t-il qu'une dimension relativement peu importante de l'édifice patrimonial. Son inventaire et sa préservation, en revanche, nécessitent la mise en place d'une administration, qui se constitue tout au long de la première moitié du xixe siècle (décret Chaptal pour la constitution des musées de province, 1801, Inspection générale des monuments historiques, 1830, Commission des monuments historiques et début des travaux d'inventaire et de classement, 1837).
C'est assez logiquement au sein du ministère de la Culture que l'on retrouve l'administration en charge du patrimoine. Récemment, au gré de la restructuration des services publics, la Direction générale des Patrimoines de France est devenue l'un des trois pôles du ministère, comprenant le service des musées de France, les archives, l'architecture, le patrimoine et l'archéologie. En revanche, le secteur des bibliothèques est piloté à partir du Service du livre et de la lecture, qui se trouve au sein de la direction générale des médias et des industries culturelles (nous en parlerons dans le chapitre consacré au livre). Par ailleurs, nombre de services d'archives, de bibliothèques, mais aussi de musées dépendent d'autres ministères.
Les réseaux publics
Les établissements publics liés au patrimoine forment un réseau relativement dense sur l'ensemble du territoire, encore les trois principales institutions du patrimoine présentent-elles des différences numériques importantes.
Tableau 7.1 : Musées, bibliothèques et archives en 2012 | Dépôts d'archives | Bibliothèques | Musées
---|---|---|---
National | 3 | 4 | 61
Régional | 14 | |
999
Départementales | 90 | 94
|
Communales et Intercommunales | 369 | 7 500
|
Personnel | 3 940 | 27 000
|
Fréquentation totale (milliers) | 1 040
3 600 communications | 150 000 | 59 018
Source : Deps, 2013.
Le réseau des archives est le moins nombreux, mais aussi le moins fréquenté. On compte environ 250 000 lecteurs, et le dépassement du million de visiteurs comptabilise les sorties scolaires ou les fréquentations d'expositions. Il est vrai que la numérisation a permis la consultation de très nombreux documents via internet, dont les sites sont très largement consultés (près de 25 millions de consultations). À vrai dire, les trois institutions – archives, bibliothèques et musées – s'adressent à des publics relativement différents. Celui des archives est probablement celui qui a le moins changé au fil des années. Ce sont avant tout des chercheurs (et longtemps aussi des généalogistes), soit un public de spécialistes, qui viennent consulter les quelque 3 millions de mètres linéaires d'archives publiques conservées (dont 350 000 par l'État). Ce patrimoine, discret, s'accroît de 65 kilomètres d'archives par an, heureusement réparties dans quelques centaines de dépôts. Le personnel qui y travaille n'est numériquement pas le plus important, et le secteur souffre régulièrement d'un certain sous-investissement, dont l'inauguration du nouveau dépôt de Pierrefitte masque mal les difficultés.
Le réseau des bibliothèques, en revanche, s'est développé à partir d'une vision largement plus éducative que patrimoniale. C'est d'abord l'encouragement de la lecture et la formation du citoyen qui s'inscrit au cœur du projet des bibliothèques publiques – ce qui, de l'autre côté de l'Atlantique, sera essentiellement pris en charge par la philanthropie, notamment par l'action de Carnegie ; un mouvement que la France, au xixe siècle, connaît également avec la mise en place de nombreuses bibliothèques populaires (catholiques ou laïques). Actuellement cependant, c'est essentiellement un réseau public constitué de plus de 7 000 bibliothèques municipales et des services de prêt à l'échelon départemental. L'objet de ce réseau n'est pas principalement patrimonial, surtout pour les plus petits établissements, même si de nombreuses bibliothèques de ville disposent de fonds patrimoniaux remarquables. Ne sont pas comptées ici, par ailleurs, les bibliothèques universitaires, relevant d'un autre ministère et s'adressant en priorité aux étudiants et aux chercheurs. C'est à l'échelon national – la Bibliothèque nationale sur ses deux sites parisiens – que se trouve la plus grande partie de la politique patrimoniale du livre. Le public des bibliothèques est plus complexe, celles-ci s'adressant à une population d'abord locale, mais multiple (tous âges et toutes classes sociales), pour une mise à disposition optimale des supports écrits, mais aussi, pour les bibliothèques nationales ou celles des grandes villes, aux chercheurs et spécialistes français et étrangers. Les règles de prêt et de consultation diffèrent forcément en fonction des fonds, qu'il s'agisse d'ouvrages destinés au plus grand nombre ou des collections patrimoniales composées de manuscrits et incunables, de livres d'artistes ou plus simplement des productions conservées au dépôt légal, constituées pour rassembler et à conserver les livres imprimés en France. Cet ensemble dédié autour du livre est organisé par 27 000 agents et près de 12 000 bénévoles – il s'agit d'un des rares secteurs où logique publique et logique du don sont intégrées par l'État – chargés de veiller à la consultation d'un stock estimé à plus de 120 millions d'ouvrages et s'accroissant, chaque année, de plus de 8 millions de livres. Près de 6 millions d'utilisateurs sont inscrits dans ce réseau, contribuant pour plus de 160 millions de prêts (sans compter les consultations de cd etc.).
Les musées sont moins nombreux, on comptait 1 218 « musées de France » en 2012, dont un millier appartenant aux pouvoirs publics. Le réseau des musées nationaux, en revanche, est plus important que celui des bibliothèques ou des archives. On compte en effet plus d'une soixantaine de musées nationaux, dont un peu plus de la moitié bénéficient du titre de Musée national. La Réunion des musées nationaux, créée en 1895 et qui regroupe ces derniers, a pour objet initial de contribuer aux acquisitions des musées, par ses recettes issues des ventes de certains services (chalcographie, moulages, livres, organisation d'expositions) ainsi que par le reliquat de la vente des bijoux de la Couronne (dont la moitié est affectée à cette caisse). Cette logique particulière montre déjà les enjeux différents que l'on pourra observer, dès ce moment, au sein du musée. Car dès la création de la Réunion des musées nationaux, se sont posées les questions de son financement et notamment la possibilité d'imposer un droit d'entrée aux musées nationaux, alors gratuits. Jusque dans les années 1980, les musées vont néanmoins partager une logique relativement similaire à celle des archives et des bibliothèques, leurs publics se partageant entre érudits et chercheurs d'une part, et un grand public essentiellement national d'autre part, mais aussi une partie non négligeable de touristes, surtout pour les grands établissements de la capitale. Ce dernier public constitue un enjeu très différent pour les musées, n'entrant plus directement dans les politiques culturelles (étude, préservation et diffusion du patrimoine), mais économiques. La politique touristique d'un territoire est directement créatrice de richesse, et son développement n'a pas pour objectif premier d'élever le niveau d'éducation des nations étrangères, mais d'augmenter la richesse nationale. Or, si le tourisme d'archives ou de bibliothèques est relativement réduit, le tourisme culturel lié aux musées constitue un potentiel qui sera largement exploité à partir des années 1980, selon les principes évoqués au chapitre 12, de retombées économiques régionales, mais aussi d'une potentielle source de revenus directs pour les musées. Le développement général du tourisme (aussi bien à l'intérieur du territoire qu'à l'international), durant ces trois dernières décennies, est étroitement lié au mouvement de modernisation et de développement du système muséal, mais aussi à la transformation de son modèle économique, contrairement à celui des archives et des bibliothèques. Cette évolution a conduit à une augmentation considérable de la fréquentation des musées (près de 60 millions de visiteurs, dont un pourcentage très important de touristes). Si, seule la fréquentation de l'ensemble des sites de la Bibliothèque nationale arrive au million de lecteurs, sept musées français sont plus que « millionnaires » dont le Louvre, qui est arrivé à presque 10 millions de visiteurs en 2012. C'est une logique similaire que l'on observe dans les monuments historiques, dont le nombre est nettement plus important (plus de 44 000 monuments historiques classés, dont près de la moitié est entre des mains privées), mais dont seuls trois (la Tour Eiffel, l'Arc de Triomphe, l'Abbaye du Mont-Saint-Michel) dépassent le million de visiteurs. La gestion, à proprement parler, d'une centaine de monuments propriété de l'État et ouverts au public, a été confiée au Centre des monuments nationaux, sorte de pendant à la Réunion des musées nationaux. La logique économique du patrimoine, en ce sens, est loin de reposer sur la seule fréquentation d'un public, de nombreux biens sont toujours utilisés en fonction de leur destination première (habitation, bureaux, culte etc.) et la question de l'utilisation ou de la réutilisation du patrimoine constitue une dimension différente de la réflexion économique que l'on trouve dans le monde muséal.
Établissements privés
On l'aura compris, le secteur du patrimoine apparaît comme clairement coupé en deux, une partie regroupant le secteur subventionné par les pouvoirs publics, l'autre constituant le secteur privé, dont nombre d'auteurs n'hésitent pas à mélanger établissement lucratifs et non lucratifs (les plus nombreux). À l'échelon de base, celui des monuments historiques, le secteur est pour moitié entre des mains privées et son utilisation repose sur des règles générales largement identiques à celles du secteur immobilier (dans le cadre du droit patrimonial dont il est question plus bas). Un certain nombre de monuments historiques majeurs reposent ainsi encore dans des mains privées, tout en étant ouverts au public. C'est par exemple le cas de nombreux châteaux de la Loire : alors que le château de Chambord est un Établissement public à finalité industrielle et commerciale, propriété de l'État, le château d'Azay-le-Rideau, propriété de l'État, est géré par le Centre des monuments nationaux, le château de Blois est propriété de la ville (et intégré comme musée de France), le château de Cheverny ou le Clos Lucé sont des propriétés familiales. C'est Joachim Carvallo, propriétaire de Villandry, qui a fondé en 1924 l'association La Demeure historique, fédérant des propriétaires privés de monuments historiques ayant décidé d'ouvrir leur propriété au public. Les huit principales associations nationales de défense du patrimoine (notamment la Demeure historique, Sauvegarde de l'art français ou Vieilles maisons françaises) se sont regroupées, en 2005, au sein du Groupe national d'information et de concertation sur le patrimoine, plus connu sous le nom de G8 du patrimoine. Il convient de noter, d'emblée, que si ces établissements sont considérés comme privés, ils ne reposent pas pour autant sur une vision lucrative du patrimoine, et même si nombre de monuments historiques se visitent moyennement paiement, c'est d'abord une passion particulière qui anime leurs propriétaires, que celle-ci repose sur des sentiments sociaux (château de famille) ou esthétiques, et dont la logique se rapproche de celle du don.
Mais les biens les plus emblématiques du patrimoine, en revanche, ainsi que les institutions qui les gèrent – archives, bibliothèques et musées – sont essentiellement du ressort du secteur public. À tout le moins, cette remarque apparaît comme relativement exacte pour les archives et les bibliothèques, elles le sont déjà un peu moins pour les 1 218 musées de France, dont 13 % appartiennent à des associations ou à des fondations. On trouve ainsi des musées de fondation, autonomes ou gérés par des collectivités locales et de nature très différente, comme l'Institut de France, mais aussi la fondation Maeght à Saint-Paul-de-Vence. Les musées associatifs (fondés à partir d'associations de Loi 1901), très nombreux dans le monde anglo-saxon, peuvent présenter en France des profils très différents : on peut y trouver quelques très grands établissements, comme l'Union centrale des arts décoratifs de Paris, mais ce sont surtout de très nombreux petits musées ou écomusées, fondés à partir d'une initiative locale non publique, qui ont adopté cette structure. Certaines entreprises (Peugeot, Perrier, Haribo) possèdent également des musées ou centres d'interprétation, visant à préserver leur histoire, mais servant également de vitrines commerciales. Enfin, quelques sociétés commerciales, comme Grévin, font fonctionner des musées, bien que ceux-ci ne soient pas reconnus par les associations de musées.
Dispositions spécifiques en matière de patrimoine
Le code du patrimoine, mis en place en 2004, regroupe la législation dans les principaux domaines évoqués dans ce chapitre. Un certain nombre d'éléments sont notamment évoqués pour l'ensemble des domaines, visant la protection et l'acquisition des biens culturels.
Le cadre légal pour protéger le patrimoine est important. D'emblée, en envisageant de telles mesures, à partir de la seconde moitié du xixe siècle, l'État visait d'une part l'incurie d'un certain nombre de propriétaires, mais surtout la nécessité d'imposer un certain nombre de critères visant à ne pas détruire ou modifier (dans le cadre d'un monument), voire à vendre à l'étranger (dans le cas de biens mobiliers ou immobiliers : certains édifices des Cloisters du Metropolitan Museum de New York sont d'origine française), de manière à ne pas appauvrir le patrimoine national. Cette logique a d'abord été appliquée pour les monuments historiques, qui peuvent bénéficier de diverses mesures de protection, la plus contraignante étant le classement. Pour les biens mobiliers, c'est la notion de trésor national qui définit ce principe ; la mobilité des biens culturels fait l'objet d'un encadrement spécifique, en cas de sortie du territoire, temporaire notamment (lors d'expositions), mais aussi définitive, lorsqu'ils sont vendus et exportés (un certificat d'exportation doit être délivré). De même, lorsque des biens sont volés, des procédures de restitution sont mises en place et réglementées au niveau européen. Lorsqu'un bien est désigné comme trésor national (ce qui est le cas des collections des musées de France, mais peut être également celui de biens privés), aucun certificat d'exportation ne peut être délivré.
Outre le classement, l'État dispose d'autres outils pour acquérir des biens patrimoniaux. Le mécanisme de dation, qui permet de s'acquitter de certaines dettes (droits de succession) par la cession de biens patrimoniaux, a notamment été utilisé lors du règlement de la succession Picasso (ce qui a permis de créer le musée éponyme). L'État français a également le pouvoir de préempter, pour son compte, des œuvres d'art acquises au cours de ventes publiques sur son territoire, ce mécanisme lui permet de ne pas surenchérir sur un autre acquéreur. Ces deux mécanismes permettent essentiellement d'enrichir le patrimoine des musées (et plus rarement, la bibliothèque ou les archives nationales). En revanche, la bibliothèque nationale bénéficie principalement du mécanisme du dépôt légal, qui instaure l'obligation, pour tout éditeur, de déposer deux exemplaires de tout livre édité sur le territoire. Le principe du dépôt légal remonte à 1537, en France, et une mesure similaire existe dans la plupart des pays. L'évolution des techniques a vu l'application de ce principe dans les autres domaines des médias, pour le film, l'audiovisuel et les logiciels (le dépôt légal est ainsi géré par la Bibliothèque nationale, le CNC et l'INA).
Le discours économique sur le patrimoine
On peut faire remonter au moins à la fin du xixe siècle le discours économique sur le patrimoine, notamment avec l'article que William Stanley Jevons consacre aux musées, critiquant notamment le fonctionnement du Victoria & Albert Museum de Londres. C'est cependant essentiellement au cours des années 1970 – dans le sillage des travaux pionniers de Baumol sur les arts de la scène – que les économistes commencent à s'intéresser de manière plus spécifique à l'économie du patrimoine. Les premiers exercices visent à montrer que le musée peut être analysé comme toute autre organisation (ou firme), dont on s'interrogerait sur les inputs et outputs, sur le capital et la manière de l'accroître – à savoir la collection, mais aussi sur l'impact économique que peut présenter l'activité muséale pour une région, sur le caractère de la demande pour les musées etc..
Les questions que l'économiste se pose sur le patrimoine sont les mêmes que celles que l'on observe dans les autres secteurs de la culture. Le patrimoine est ainsi classiquement examiné en fonction de son offre et de sa demande, à travers une socio-économie du public. La notion de bien public est généralement associée aux établissements du secteur, et notamment aux collections muséales, encore cette question porte-t-elle à débat et est contestée par certains, notamment William Grampp qui remet en cause leur financement public ou philanthropique.
Les économistes – qui s'intéressent essentiellement aux monuments et musées d'art – soulignent le paradoxe intéressant que constitue la collection dont la valeur est souvent considérable, mais qu'ils ne peuvent utiliser comme un vrai capital. La plupart des économistes ne contestent pas la prise en charge des pouvoirs publics, mais tous s'interrogent, en revanche, sur la possibilité de générer d'autres ressources alternatives. À la suite des travaux de Pommerehne et Frey, les réformes des politiques tarifaires – privilégiant jusque dans les années 1980 des droits d'entrée modestes, voire la gratuité – ont été vivement encouragées, certains économistes suggérant notamment d'augmenter de manière très importante les droits d'entrée pour les visiteurs étrangers, d'autres présentant les avantages des politiques de forfaits. La justification de la valeur économique des musées a également fait l'objet de nombreuses études, souvent fondées sur des analyses d'impact économique plus ou moins complexes, qui remontent aux années 1980, mais se sont multipliées de manière exponentielle dans le sillage du « phénomène » causé par l'inauguration du Guggenheim Museum de Bilbao, attirant des millions de touristes et dégageant des revenus considérables au sein du Pays basque. On retrouve cette logique de manière identique avec le patrimoine immobilier (bâtiments, sites), et notamment à travers la volonté des États d'obtenir pour certains monuments le label « patrimoine mondial » promu par l'Unesco. Un certain nombre d'analyses portent sur l'efficacité ou l'efficience de ces établissements, analysés comme une firme, avec ses intrants et ses coûts de production, qui produit un certain nombre d'outputs (expositions permanentes, mais aussi temporaires, notamment les blockbusters).
Certains économistes, de manière plus explicite, suggèrent, à partir de leurs analyses, un certain nombre d'actions que les musées ou les gouvernements devraient prendre, en vue d'améliorer leur fonctionnement. La question des droits d'entrée a ainsi fait l'objet de nombreuses discussions, toutes les conclusions n'allant pas dans le même sens. Parmi toutes les propositions, l'une des plus incisives est probablement celle de William Grampp, déjà cité, suggérant d'arrêter de subventionner les musées et de les laisser uniquement fonctionner par le biais du marché. La question du deaccessioning (la sortie d'un bien de l'inventaire, et sa possible vente), par ailleurs, a fait l'objet de nombreux débats, plusieurs économistes souhaitant une ouverture plus large des musées à cette possibilité (les collections des musées dans les pays de tradition latine sont inaliénables). Comme nous l'avons déjà souligné, la plupart des travaux se fondent sur une dichotomie public-privé, mais tiennent généralement peu compte des différences d'approche, au sein de l'initiative privée, entre les objectifs lucratifs, qui peuvent exister, et la philanthropie. Cette dernière s'avère pourtant fondamentale pour comprendre le fonctionnement du secteur – notamment les dons de collections à des musées, ainsi que le mécénat –, mais aussi les réactions d'hostilité en cas d'approche trop mercantile, tel qu'elles peuvent apparaître au niveau des réflexions sur le droit d'entrée ou pour l'aliénation des collections.
La question du don, pourtant fondamentale pour comprendre ce secteur, est en revanche assez peu abordée et nous disposons à cet égard de peu de sources afin d'évaluer son importance. La plupart des petits musées associatifs, comme le réseau des petites bibliothèques, fonctionnent à partir d'une logique de bénévolat plus ou moins importante (elle est nettement plus développée dans les pays anglo-saxons). Pour ce qui est du financement direct, nombre de musées et, dans une moindre mesure, de bibliothèques ou de centres d'archives se sont dotés d'associations d'amis – il en existe 290 en France, regroupées au sein de la Fédération française des sociétés d'amis des musées –, qui contribuent par leurs cotisations à l'enrichissement des collections ou à l'organisation d'activités spécifiques. Mais c'est essentiellement par le don d'objets (livres, archives, objets, voire édifices) que les particuliers plus ou moins riches contribuent très largement à l'enrichissement du patrimoine. En témoigne la liste des donateurs du Louvre, qui compte des centaines de personnalités de toutes provenances sociales. Nous évoquons également cette question au chapitre suivant, en présentant la relation du collectionneur au marché de l'art.
Tendances générales du secteur
Le secteur du patrimoine a, ces dernières années, connu des transformations considérables, tant pour ce qui concerne le développement de son réseau – multiplication des établissements – que pour sa popularité, ce dont atteste la fréquentation des musées et des grandes expositions temporaires. D'un point de vue économique, le modèle de fonctionnement des lieux de patrimoine – du moins celui des musées et d'un certain nombre de monuments historiques – s'est largement tourné vers la logique de marché, ce que l'on observe de manière nettement moins importante dans les centres d'archives ou les bibliothèques. Ce mouvement est fort logiquement lié aux transformations des politiques économiques elles-mêmes et notamment les politiques culturelles, comme la décentralisation, mais aussi les modèles de gouvernance et la mise en marché accrue, débouchant sur des remises en question de politiques traditionnelles, telles qu'elles s'observent à travers les politiques tarifaires ou l'aliénation du patrimoine. La « spectacularisation » du secteur est elle-même à l'origine de l'émergence d'un phénomène sur lequel il nous faudra revenir à plusieurs reprises, lié au star-system.
La décentralisation du patrimoine
Le mouvement de décentralisation suit celui de déconcentration, initié par Malraux pour la culture. Le modèle très centralisateur de l'État français s'observe de manière récurrente au niveau patrimonial, tous les grands musées, la bibliothèque nationale et les archives ayant leur vaisseau amiral dans la capitale (le Musée des civilisations méditerranéennes, inauguré à Marseille en 2012, constitue le seul exemple de musée parisien – le Musée national des arts et traditions populaires – transféré en région). La logique de décentralisation qui a été mise en œuvre, depuis de nombreuses années, vise à assurer la préservation par chaque échelon de pouvoir des infrastructures liées à son niveau d'attractivité : entretien par les communes des plus petites infrastructures, par les départements ou les régions pour celles d'importance plus grande, et par l'État pour les infrastructures nationales. Ce mouvement de décentralisation s'est néanmoins opéré récemment, au niveau patrimonial, de deux manières différentes. D'une part, l'entreprise de l'inventaire général, initiée par André Malraux et répertoriant l'ensemble des richesses de la France, a été transférée aux régions ; d'autre part, le transfert de nombreux monuments appartenant à l'État a été proposé aux collectivités locales, à charge pour ces dernières de pourvoir à leur entretien. Cette proposition, mise en place durant la première décennie des années 2000, n'a eu qu'un succès mitigé, les collectivités locales ne s'empressant pas pour accepter des monuments dont l'attractivité relative laissait peu d'espoir de valorisation économique et les charges nécessaires pour pourvoir à leur entretien ou leur restauration s'avérant trop importantes en regard des bénéfices (économiques ou symboliques) escomptés.
Le spectaculaire patrimonial
Le monde des musées et du patrimoine n'a connu de réel essor commercial que récemment. S'il existe, depuis le xviiie siècle, un projet de développement économique lié au musée, c'est au cours des années 1980 que ce volet s'est particulièrement épanoui, au point de prendre parfois le dessus sur d'autres missions de l'institution – et notamment les questions de préservation et de recherche. La notion de spectaculaire muséal a ainsi été introduite pour évoquer un nouveau type de musées, à l'architecture d'avant-garde, résolument tournés vers le public, dans un rapport de plus en plus ludique et commercial. C'est à partir de ce moment que le temporaire et l'événement prennent progressivement le pas sur le temporaire, les espaces dédiés aux services du visiteur (boutique, restaurants etc.), mais aussi les départements de relation publique, de marketing et de levées de fonds se développant de manière importante. La notion de spectacle, dans ce sens, se réfère moins à l'architecture « spectaculaire » qu'au programme de la société du spectacle, tel qu'il avait été froidement analysé par Guy Debord : « le règne autocratique de l'économie marchande ayant accédé à un statut de souveraineté irresponsable, et l'ensemble des nouvelles techniques de gouvernement qui accompagnent ce règne ». C'est en quelque sorte cette logique de commercialisation et du musée marchandise, étroitement associé au marché de l'art et au monde des collectionneurs et spéculateurs, que l'on retrouve de plus en plus à travers la communication soutenue des événements rythmant la vie des musées actuels, et notamment des grandes expositions blockbusters, destinées à attirer un public le plus nombreux possible à partir de propositions flattant les goûts les plus répandus : impressionnisme, Égypte etc. Cette tendance à la promotion de l'événement et de l'éphémère au détriment du permanent n'est pas sans conséquence pour le futur du musée et du patrimoine dont il a la charge, le statut des collections apparaissant comme de plus en plus remis en question.
L'aliénation des collections
La question de la gestion des collections est abordée différemment dans les institutions du patrimoine. Ainsi, dans les bibliothèques de consultation, la pratique du « désherbage » est de rigueur, et les livres restés trop longtemps non consultés, ou les abîmés, sont évacués des rayonnages. Tel n'est pas le cas dans les lieux dédiés plus précisément à la conservation, surtout dans les pays latins, s'appuyant sur le principe d'inaliénabilité des biens publics. Les collections sont inaliénables, notamment en France, mais pas dans les pays anglo-saxons, où les objets peuvent sortir de l'inventaire selon un processus bien encadré (lorsque leur présence n'est pas jugée significative pour la collection, lorsqu'ils ne sont pas considérés comme authentiques, s'ils sont redondants etc.), afin d'être donnés, détruits ou vendus. C'est généralement ce dernier point que retiennent les économistes qui, depuis longtemps, ont souligné le paradoxe de ces institutions dont le capital (la collection) est très important, mais dont les revenus ou la trésorerie sont particulièrement faibles (cf. supra). C'est notamment dans cette perspective qu'à la suite du rapport Jouyet-Lévy sur l'économie de l'immatériel, était déposé en 2007, par Jean-François Mancel, un projet de loi visant à offrir une « réelle liberté de gestion des établissements culturels », suscitant l'indignation et la colère de la part des conservateurs. Le rapport rendu par Jacques Rigaud, interrogé par la ministre de la Culture, rendait un avis très défavorable à cette proposition qui ne fut pas retenue. Il n'empêche que le principe d'inaliénabilité des collections des musées, en vigueur en France, apparaît aux yeux de nombre d'économistes comme une aberration, les musées luttant difficilement pour leur survie alors qu'ils détiendraient un capital considérable. Cette dernière affirmation, contestable (les collections en réserves sont rarement d'une grande valeur commerciale) fait craindre aux conservateurs une baisse radicale des subventions publiques (« vendez quelques œuvres ! »). Le débat sur l'aliénation, par ailleurs, qui porte sur l'ensemble des collections, est dominé par les collections artistiques, valorisables sur le marché de l'art. La question se pose de manière totalement différente pour des muséums d'histoire naturelle et nombre de musées d'ethnographie ou d'archéologie, confrontés à de réelles difficultés d'inventaire et de gestion des réserves dont le coût est élevé, mais dont les collections, bien plus abondantes que celles des musées d'art, ne peuvent être ni détruites, ni données (la vente est difficile). Par ailleurs, le débat tient souvent bien peu compte des volontés des donateurs et du caractère particulier du don d'objets (le donateur demeure lié symboliquement à l'objet, entrant ainsi dans le musée), dont les répercussions à terme sont difficiles à établir. Bien que pour l'instant peu évoqué, le débat sur l'aliénation pourrait connaître d'autres rebondissements dans les années à venir, les collections des musées, dont les coûts d'entretien ne sont pas envisagés dans une perspective décroissante, se développant de manière continue.
Les musées superstars
Tous les musées ne sont pas égaux entre eux ; leur taille influencerait notamment, de manière positive, leur niveau d'innovation. Les transformations du monde des musées – le tournant commercial des musées et leur développement spectaculaire – à partir des années 1980, ont non seulement métamorphosé leur image, mais aussi la structure du secteur. C'est ce principe que Bruno Frey, à partir de la logique du star-system (cf. chapitre 14), a évoqué à travers le concept des musées superstars, définissant l'émergence d'une catégorie d'établissements présentant des particularités spécifiques. On trouve, dans ce cercle relativement restreint d'une soixantaine de musées (sur les plus de 50 000 dans le monde) des noms familiers, comme le Louvre, Orsay, le British Museum, l'Ermitage, le Metropolitan Museum etc. Les musées superstars sont en quelque sorte les « millionnaires » (en visiteurs) du monde muséal – mais on peut étendre ce principe à tous les lieux de patrimoine. Ce sont des lieux incontournables pour les touristes qui en constituent une part importante de leur audience. La qualité de leur collection (ce sont essentiellement des musées d'art) est mondialement connue, mais le bâtiment qui les abrite, qu'il soit historique ou d'une architecture d'avant-garde, est tout aussi reconnu. Cette fréquentation massive les amène à générer des revenus commerciaux très importants, comme le Louvre, qui avec ses presque 10 millions de visiteurs, peut fonctionner avec 50 % de recettes propres (lorsqu'un très grand nombre de lieux de patrimoine peuvent espérer en obtenir 20 ou 30, au mieux). Ce sont ces mêmes musées qui peuvent envisager de développer leurs recettes par des politiques de marque, les plus célèbres exemples demeurant la création de filiales, comme l'ont mis en œuvre le musée Guggenheim (Bilbao, Abu Dhabi, d'autres sites comme Las Vegas ou Berlin ayant fermé) ou le Louvre (Lens, Abu Dhabi). Cette logique du star-system se retrouve pour quelques très grands lieux de patrimoine, comme en France à Versailles (qui est aussi considéré comme un musée) ou au Mont-Saint-Michel, une telle dynamique poussant les pays à se positionner sur le marché mondial, à travers notamment la liste du patrimoine mondial de l'Unesco.
On est en droit de se demander si cette évolution ne conduit pas le secteur du patrimoine à se restructurer, comme les industries culturelles, selon les principes d'un oligopole à frange, quelques très grands acteurs mobilisant l'essentiel des ressources et des achats, décidant des normes du secteur, tandis que la plupart des petites organisations subissent les lois du marché et tentent de lutter pour leur survie.
La fin des conservateurs ?
La résultante de cette métamorphose progressive conduit également à une transformation à l'intérieur de l'institution, les rapports de force traditionnels, voyant la prééminence du conservateur sur les autres professions (surveillants, restaurateurs, médiateurs, gestionnaires) s'inversant au profit des gestionnaires. Le profil du directeur du musée, traditionnellement choisi parmi les scientifiques, connaît une mutation similaire, et nombre d'établissements, aux États-Unis par exemple, sont dirigés par des spécialistes ayant été sélectionnés pour leurs compétences en gestion ou en levée de fonds, plutôt que pour leur apport scientifique. C'est un mouvement similaire que l'on peut observer en France, le pouvoir des énarques et des responsables des départements financiers ou du marketing affaiblissant celui de la conservation. Près de la moitié du corps des conservateurs, recrutés dans les années 1980, prenant sa retraite dans les prochaines années, leur remplacement n'est pas systématique (pour des raisons de budget, notamment, mais aussi pour leur supposée inadaptation aux mutations du secteur), il n'est pas interdit de penser que le secteur connaisse encore des transformations profondes dans les prochaines années.
. Desvallées A., Mairesse F., Deloche B., « Patrimoine », in Desvallées A., Mairesse F. (dir.), Dictionnaire encyclopédique de muséologie, Paris, Armand Colin, 2011, p. 421-452.
. Pour une approche générale, voir Benhamou F., L'économie du patrimoine culturel, Paris, La Découverte, 2012 ; Vecco M., Économie du patrimoine monumental, Paris, Economica, 2007.
. Salaün J.-M., « The immeasurable economics of libraries », in Rizzo I., Mignosa A., Handbook on the Economics of Cultural Heritage, Cheltenham, Edward Elgar, 2013, p. 290-305.
. Babelon J. P., Chastel A, La notion de patrimoine, Paris, Liana Levi, 1994.
. Mairesse F., 2012, « Les sociétés d'histoire et d'archéologie et leurs collections », in Dartevelle A. et Toussaint J. (coord.), Cercles et sociétés archéologiques et historiques en Fédération Wallonie-Bruxelles. Passé, présent, futur, Bruxelles, Fédération Wallonie-Bruxelles (Documents du patrimoine culturel, 4), 2012, p. 28-40.
. Le nombre de visites des bibliothèques est difficile à établir. On compte près de 60 millions d'entrées pour les seules bibliothèques universitaires (source : DEPS, chiffres clés 2013) et l'estimation du taux de fréquentation dans les bibliothèques municipales est de 212 pour 100 habitants, soit environ 150 millions de visites – pour 7 100 bibliothèques et 9 200 points d'accès au livre (source : Observatoire de la lecture publique, rapport 2012).
. Poirrier P. (dir.), Politiques et pratiques de la culture, Paris, La Documentation française, 2010.
. Callu A., La Réunion des musées nationaux 1870-1940. Genèse et fonctionnement, Paris, École des Chartes, 1994. La Réunion des musées nationaux a fusionné en 2011 avec le Grand Palais pour former l'établissement public Réunion des musées nationaux et du Grand Palais des Champs-Élysées.
. Origet du Cluzeau C., Le tourisme culturel. Dynamique et prospective d'une passion durable, Bruxelles, De Boeck, 2013 ; Bonet L., « Heritage tourism », in Rizzo I., Mignosa A., Handbook on the Economics of Cultural Heritage, Cheltenham, Edward Elgar, 2013, p. 386-401.
. Seaman B., « The role of the private sector in cultural heritage », in Rizzo I., Mignosa A., Handbook on the Economics of Cultural Heritage, op. cit., p. 111-128.
. Voir le site internet du groupe : <http://www.lepinay.org/patrimoine/index.html> (consulté en août 2013).
. Davallon J., Le don du patrimoine : une approche communicationnelle de la patrimonialisation, Paris, Lavoisier, 2006.
. Cornu M., Negri V., Code du patrimoine et autres textes relatifs aux biens culturels, Paris, Lexis Litec, 2010 ; Chaumier S., Di Gioia L., Actualité du patrimoine. Dispositif et réglementation en matière de patrimoine en France, Dijon, Éditions universitaires de Dijon, 2008.
. Jevons W. S., « The use and abuse of museums », Methods of social reforms and other papers, Londres, MacMillan, 1883, p. 52-81.
. Peacock A., godfrey C., « The economics of museums and galleries », Lloyds Bank Review, 111, jan. 1974, p. 17-28 ; Mercillon H., « Les musées : institutions à but non lucratif dans l'économie marchande », Revue d'économie politique, 4, 1977, p. 630-641 ; Hendon W. S., Analysing an Art Museum, New York, Praeger, 1979.
. Grampp W. D., « A colloquy about art museums: economics engages museology », in Ginsburgh V., Menger P.-M. (dir.), Economics of the Arts – Selected Essays, Amsterdam, Elsevier, 1996.
. Ce constat est établi à partir des ouvrages, articles ou manuels (pour les chapitres consacrés aux musées) suivants : Feldstein M. (dir.), The Economics of the Art Museum, Chicago, University of Chicago Press, 1991 ; Peacock A., Rizzo I., The Heritage Game. Economics, Policy and Practice, Oxford, Oxford University Press, 2008 ; Benhamou F., Économie du Patrimoine culturel, Paris, La Découverte, 2012.
. Pommerehne W. W., Frey B. S., « Les musées dans une perspective économique », Revue Internationale des Sciences Sociales, XXXII, 2, 1980, p. 345-362 ; voir également Mairesse F., Le droit d'entrer au musée, Bruxelles, Labor, 2005.
. Benhamou F., Thesmar D., Valoriser le patrimoine culturel de la France (rapport au Premier ministre), Paris, Conseil d'analyse économique, disponible sur internet : <http://www.cae.gouv.fr/IMG/pdf/rapport_culture_1_mars.pdf> (consulté en juillet 2013).
. Ginsburgh V., Zang L., « The museum pass game and its value », Games and Economic Behavior, 43, 2003, p. 322-325.
. Voir la liste des articles sur le site internet : Scholars on Bilbao : http://www.scholars-on-bilbao.info/list.php?var=list.
. Bertacchini E. E., Saccone D., « Toward a political economy of World heritage », Journal of cultural economics, 36, 2012, p. 327-352 ; Frey B., Steiner L., « World heritage list » in Rizzo I., Mignosa A., Handbook on the Economics of Cultural Heritage, Cheltenham, Edward Elgar, 2013, p. 171-186.
. Taalas M., « Costs of production », in Towse R. (dir.), A Handbook of Cultural Economics, Cheltenham, Edward Elgar, 2003, p. 152-160 ; Fernandez-Blanco V., Herrero L. C., Prieto-Rodiguez J., « Performance of cultural institutions » in Rizzo I., Mignosa A., Handbook on the Economics of Cultural Heritage, Cheltenham, Edward Elgar, 2013, p. 470-488.
. Ginsburgh V., « Les musées et l'État », in Actes du X e Congrès des économistes belges de langue française, Charleroi, CIFOP, 1992, vol. 1, p. 155-167 ; Mairesse F., L'inaliénabilité des collections de musée en question, Actes du colloque tenu au Musée royal de Mariemont le 28 avril 2009, Morlanwelz, Musée royal de Mariemont, 2009.
. Laclotte M., Les donateurs du Louvre, Paris, Réunion des Musées nationaux, 1989.
. Melot M., Mirabilia. Essai sur l'inventaire général du patrimoine culturel, Paris, Gallimard, 2012.
. Mairesse F., Le musée hybride, Paris, La Documentation française, 2010.
. Tobelem J.-M., Le nouvel âge des musées, Paris, Armand Colin, 2010 (2e éd.).
. Mairesse F., Le musée, temple spectaculaire, Lyon, Presses Universitaires de Lyon, 2002.
. Debord G., Commentaires sur la société du spectacle, Paris, Gérard Lebovici, 1988.
. Cornu M., Fromageau J., Poli J.-F., Taylor A.-C., L'inaliénabilité des collections, performances et limites ?, Paris, L'Harmattan, 2012.
. Jouyet J.-P., Lévy M., L'économie de l'immatériel : la croissance de demain. Rapport de la Commission sur l'économie de l'immatériel, 2006. <http://ec.europa.eu/internal_market/copyright/docs/links/immateriel_fr.pdf> ; Rigaud J., Réflexion sur la possibilité pour les opérateurs publics d'aliéner des œuvres de leurs collections, Rapport remis à Christine Albanel, ministre de la Culture et de la Communication, Paris, 20 janvier 2008. Consultable sur : http://lesrapports.ladocumentationfrancaise.fr/BRP/084000071/0000.pdf.
. Camarero C., Garrido M.J., Vicente E., « How cultural organizations' size and funding influence innovation and performance: the case of museums », Journal of Cultural Economics, 35, 2011, p. 247-266.
. Frey B., Arts & Economics, Berlin, Springer, 2000.
. Frey B., Steiner L., « World heritage list » in Rizzo I., Mignosa A., Handbook on the Economics of Cultural Heritage, Cheltenham, Edward Elgar, 2013, p. 171-186.
. Vital C., « Le Livre blanc des musées de France », Musées et collections publiques de France, numéro spécial, 260, 3, 2010, p. 1-127.
Chapitre 8
L'artiste,
les arts plastiques,
le marché de l'art
Par sa dénomination même, le marché de l'art rappelle le lien entre les plus hautes aspirations culturelles et l'interaction entre l'offre et la demande, conduisant au double portrait de l'artiste créateur mais surtout travailleur modèle, impliqué et flexible, contraint d'assurer sa subsistance par le biais de sa production. Le marché de l'art a rapidement intéressé les économistes, à commencer par Adam Smith et David Ricardo, pour les caractéristiques particulières de ces biens peu substituables et la valeur qui leur est attribuée. Les différences de qualité entre les œuvres constituent une belle illustration de la formation des coûts par l'offre et la demande, puisque le temps et le travail (ou les matériaux) peuvent être identiques pour deux œuvres dont les prix vont différer du simple au centuple. Les questions de valeur, d'expertise, d'authenticité ou de copie constituent autant de cas d'études intéressants, comme l'évolution des prix et, parallèlement, celle du goût pour certains artistes. Encore convient-il de reconnaître non pas un, mais plusieurs marchés de l'art.
Pour commencer, sans doute faut-il encore souligner qu'une grande part de l'expression artistique n'est régie par aucun marché. Qu'il s'agisse de l'exercice de calligraphie dans un monastère chrétien ou bouddhiste, des peintures ou gravures réalisées – pendant des générations – par l'élite bourgeoise, comme partie intégrante de son éducation ou du loisir que des millions de Français pratiquent de manière plus ou moins régulière, l'essentiel de la pratique artistique doit être rangé dans le rayon d'une pratique d'amateur.
Les différents marchés de l'art et leurs protagonistes
La notion de mondes de l'art, développée par Howard Becker, permet de préciser la coexistence d'univers parallèles constitués de réseaux d'artistes, de circuits de galerie, de modes de financement et de publics spécifiques. Une telle logique apparaît dans nombre de secteurs (la mode, le sport, la restauration etc.). Un marché se compose de producteurs (artistes) et de consommateurs (collectionneurs ou acquéreurs), mais surtout d'un grand nombre d'intermédiaires, qui font souvent les spécificités du marché. Dans le cas qui nous intéresse, les intermédiaires peuvent être des galeristes, des marchands en chambre (sans galerie), des lieux spécifiques (foires, expositions), mais le marché a aussi besoin d'experts et de systèmes de communication spécifiques, notamment des commissaires d'art contemporain, des journalistes spécialisés et des conservateurs. À chaque monde, ses propres spécificités, ses lieux particuliers, et ses réseaux d'échange ; les passages de l'un à l'autre de ces mondes, s'ils sont possibles, sont souvent rares.
Du marché des chromos à celui des talents consacrés
Nathalie Moureau et Dominique Sagot-Duvauroux présentent ainsi, à la suite des travaux pionniers de Raymonde Moulin, quatre marchés différents, dont celui des chromos. Par marché des chromos, on entend celui de produits artistiques « à la douzaine », qui, bien que conçus manuellement, sont largement substituables, s'inspirant d'un courant reconnu de l'histoire de l'art (impressionnisme, fauvisme, académisme), présentant des sujets peu originaux. Les circuits d'acquisition de ces biens, qui peuvent être produits à la chaîne (pour la peinture, par des spécialistes des nuages, des arbres, des maisonnettes...) transitent par des lieux de consommation plus ou moins spécialisés, soit des grands magasins ou des surfaces d'ameublement, des marchés et des lieux touristiques (la place du Tertre), parfois des galeries spécialisées dans ce genre de production. Si le critère de qualité qui préside n'est pas l'originalité, c'est plutôt le « métier » traditionnel, la technique du peintre ou du sculpteur, qui sont privilégiés, notamment la facture ou les qualités d'imitation. En tout état de cause, les producteurs de ce type d'œuvres, s'ils peuvent raisonnablement être présentés comme artistes, ne seront pas reconnus par l'institution et ont bien peu de chances de connaître un jour la possibilité d'entrer dans l'histoire de l'art. Le prix des œuvres, d'ailleurs, différant largement des règles qui seront appliquées sur les autres marchés, est fixé à partir de données classiques : prix des matériaux et temps de travail. S'il peut exister un certain nombre de collectionneurs pour ce type de biens, les particuliers ou les entreprises (on en retrouve dans la décoration de nombreux hôtels et restaurants) qui les achètent appartiennent à toutes les couches de la société.
La démarche poursuivie dans le marché des artistes en voie de légitimation, qui compose l'essentiel du monde des arts plastiques (de 20 000 à 40 000 artistes, en France) diffère largement de la logique du chromo. La question de la valeur des œuvres, qui traverse tous les marchés, y est moins fixée par des critères techniques de métier que ceux d'originalité. Les artistes qui respectent ce critère ne jouissent pas tous d'une grande notoriété, loin de là. La plupart, et notamment les plus jeunes, sortis d'une école d'art, n'ont pas encore été acceptés par les réseaux traditionnels de distribution (galeries, foires) et tentent de développer leur notoriété à partir de circuits alternatifs (internet, squats, expositions auto-organisées). Les prix des œuvres produites au sein de tels marchés demeurent relativement bas, la demande s'avérant essentiellement locale et donc restreinte.
Seul, un petit nombre d'artistes contemporains atteignent une réelle notoriété qui leur permet d'accéder à un marché plus institutionnel, celui de l'avant-garde médiatisée. Les dispositifs mis en place au sein de ce marché, accueillant un pourcentage réduit des artistes vivants issu du marché précédent, sont ceux qui constituent, en quelque sorte, le marché de l'art primaire : galeries, expositions collectives ou personnelles dans des musées ou des biennales etc. La reconnaissance par ces intermédiaires induit un autre fonctionnement, qui améliore grandement la notoriété des artistes (et donc la demande potentielle), mais aussi qui transforme les prix, lesquels vont notamment être déterminés par des galeries ou d'autres intermédiaires, ajoutant leurs marges respectives. Si, au départ, de tels prix peuvent être fixés de manière conventionnelle, la spéculation sur le marché peut augmenter de manière exponentielle les prix de certains artistes. Encore un tel marché demeure-t-il extrêmement volatil, les variations de l'offre, mais surtout de la demande pouvant fluctuer très rapidement.
Dans le marché des talents consacrés, qui s'occupe d'artistes vivants et largement établis, ou morts (et dont le stock des œuvres est, par définition, clôturé) en revanche, les œuvres et les artistes sont entrés dans l'histoire de l'art et exposés dans les musées. La place occupée par ces artistes apparaît comme nettement plus stable, bien que l'histoire de l'art elle-même connaisse des fluctuations (en témoigne la carrière des peintres académiques, ultra-célèbres à la fin du xixe siècle, discrédités jusque dans les années 1960 et largement réhabilités à partir des années 1980 ; on peut également évoquer les artistes du Seicento ou les primitifs flamands). Aux réseaux des galeries ou des musées, qui diffèrent de ceux du marché précédent, s'adjoint aussi celui des ventes aux enchères et de galeries de négoce non directement en relation avec les artistes, soit le marché secondaire dans lequel une œuvre peut se vendre plusieurs fois sur des dizaines d'années.
L'offre artistique
Comment définir l'art et l'artiste ? La question, si elle fait l'objet de réflexions en histoire de l'art ou en esthétique, intéresse forcément aussi l'économiste qu'il s'agisse de définir un marché ou d'envisager de l'encadrer (par les pouvoirs publics). Aucune réponse n'est définitive, mais chacune d'entre elles va forcément influencer la vision du marché. Pommerhene et Frey ont répertorié de nombreux critères, tels que le temps consacré à l'activité artistique, le montant des gains perçus, la réputation acquise auprès du public ou la reconnaissance par les pairs, les qualifications professionnelles (diplômes), la qualité du travail etc. Le nombre d'artistes – et le périmètre du marché qui en résulte – varie forcément en fonction de ces définitions. Le chiffre retenu en France tient compte des individus cotisant au régime de la sécurité sociale pour les artistes. Quoi qu'il en soit, ce chiffre a largement évolué à la hausse : de 14 000 en 1982, il atteint 33 000 en 2005 et 50 000 cinq ans plus tard. Les graphistes sont les plus nombreux (ce sont eux aussi qui se sont le plus développés), suivis par les peintres et les illustrateurs. Une enquête établie à partir des affiliés de la Maison des artistes permet d'en dresser le portrait. Les femmes sont minoritaires, et si le milieu artistique traditionnel (peinture, sculpture) est relativement âgé (plus de 50 ans en moyenne), la relative jeunesse des graphistes (38 ans) diminue la moyenne générale. Le secteur est majoritairement composé d'indépendants, et l'on observe de très fortes disparités au niveau du revenu. Le revenu artistique moyen est de l'ordre de 24 000 euros, mais le revenu médian est de 13 700 euros ; l'essentiel des revenus étant concentré dans les mains d'un faible pourcentage d'artistes, conséquence logique du star-system. L'une des raisons avancées pour expliquer pourquoi nombre d'artistes poursuivent dans cette voie, pratiquant plusieurs métiers ou étant aidés par leur conjoint, est qu'ils percevraient une sorte de double salaire, le premier financier, mais le second d'ordre psychologique. Il conviendrait de noter que tous les métiers pourraient à ce titre bénéficier d'une double comptabilité et que l'effort artistique peut également s'avérer extrêmement douloureux...
Si le revenu artistique est relativement faible, un certain nombre de stars – Koons ou Hirst à l'international, Boltanski ou Huyghe pour la France (et dans des proportions nettement moindres) – disposent de revenus considérables générés par le produit de leurs ventes. Mais leur organisation elle aussi est très différente et s'apparente à celle de moyennes entreprises, composées de très nombreux artistes et artisans travaillant à leurs côtés. Une telle logique n'est par ailleurs pas récente, Rubens ou Van Dijck disposant déjà d'un personnel très nombreux pour répondre à leur clientèle.
La demande ou le monde des collectionneurs
La demande pour les œuvres d'art dépend essentiellement d'un nombre relativement restreint d'acquéreurs plus ou moins réguliers : les collectionneurs. À ce groupe est adjoint un collectionnisme public, notamment en France, visant partiellement à compenser les difficultés du système de marché, mais aussi pour des raisons de préservation et de diffusion plus large de l'art, via les réseaux de musées et les fonds d'art contemporain. Les raisons qui poussent à collectionner ne sont pas toujours précises. Alma Wittlin recensait, parmi celles-ci, des considérations de thésaurisation, de prestige social, de pouvoir magique, d'expression de loyauté à un groupe, de stimulation de la curiosité ou de satisfaction esthétique. Raymonde Moulin a été l'une des premières à s'intéresser, d'un point de vue sociologique, au monde des collectionneurs d'art. Les quelques types recensés par Moulin – milliardaires magnifiques, bourgeois « comme il faut », érudits, découvreurs, spéculateurs... – confirment l'existence d'un monde relativement discret, aux contours mal définis, constitué d'artistes, d'hommes de lettres, de marchands, de professions libérales et d'hommes d'affaires, qui se situent pour la plupart « au sommet de la hiérarchie professionnelle à laquelle ils appartiennent ». Parmi ceux-ci, les « méga-collectionneurs », dont le classement des 200 premiers est établi chaque année par Art News (et dans lequel on retrouve, depuis plusieurs années, les Français Bernard Arnault et François Pinault dans le classement des 10 plus grands collectionneurs). Le recensement de l'origine géographique de ces très grands collectionneurs demeure largement corrélé avec le niveau de développement des pays auxquels ils appartiennent, et si la première place est occupée par les États-Unis, suivie (de loin) par l'Allemagne, l'Angleterre, la Suisse et la France, on note, au gré des évolutions, l'arrivée de collectionneurs issus des grandes puissances émergentes, comme la Chine, la Russie ou le Brésil. Le phénomène de concentration des revenus, déjà évoqués chez les artistes, s'observe également au niveau de la demande, qu'il s'agisse des collectionneurs privés – dont seul un très petit nombre (une centaine de collectionneurs dans le monde, selon certaines sources) seraient capables de débourser plus de 50 millions de dollars pour une œuvre.
Dans cette perspective, les musées, les centres et les fonds d'art contemporain, qu'ils soient d'initiative publique ou privée, peuvent très rarement se permettre d'intervenir à ce niveau, mis à part les quelques musées superstars dont il a été question au chapitre précédent, ces derniers eux-mêmes ne pouvant pas suivre les grands collectionneurs. Les lieux de patrimoine préfèrent dès lors pour la plupart développer une politique d'acquisition sur la longue durée, à un échelon national ou régional. Si traditionnellement, les musées apparaissent comme le réceptacle, à leur mort, des collections formées par les plus grands acteurs de ce domaine, sous la forme de legs, on assiste également, depuis quelques années, à l'émergence d'une autre logique, celle du collectionneur créant, de son vivant, la structure muséale abritant ses collections. L'idée n'est pas neuve (on peut songer aux grandes collections privées anglaises, dès le xviiie siècle, ou à la collection Thyssen-Bornemisza, aujourd'hui à Madrid), elle ne s'en est pas moins développée de manière importante ces dernières années, à l'instar des collections de François Pinault, présentées à Venise, ou à celles de la fondation de Bernard Arnault, à Paris. Ce modèle – connu sous le nom de Miami Model – est particulièrement illustré par la ville de Miami, dont les collectionneurs ont acquis une influence prépondérante dans la gestion des infrastructures dédiées à l'art contemporain. Ce dernier modèle renvoie aux caractéristiques particulières de la logique du don, évoquée plus haut.
Patronage et logique du don
Le collectionneur n'est pas simplement un spéculateur sur le marché de l'art, tant s'en faut – la plupart des collectionneurs ne rassemblent pas des œuvres ou d'autres objets pour l'argent, même si cette dernière dimension est rarement absente de leurs préoccupations. La relation du collectionneur/mécène à l'art et à l'artiste se manifeste au moins à deux moments particuliers comme partiellement liée au don : lorsque le collectionneur entre en contact avec l'artiste et lorsqu'il envisage de céder sa collection.
Dans le premier cas, la relation entre le collectionneur et l'artiste, lorsqu'elle se produit, dépasse souvent la simple logique de l'échange marchand. Depuis Alexandre le Grand et Apelle, c'est aussi bien l'œuvre d'art que la relation à l'artiste qui semblent importer, la gloire de ce dernier ou le caractère génial de sa personnalité retombant partiellement sur son protecteur. Un tel principe peut induire des comportements différents en fonction de la renommée de l'artiste, allant de l'aide spontanée à un jeune artiste prometteur à la relation privilégiée entretenue avec l'artiste confirmé. La vie de Vincent Van Gogh (l'aide de son frère, de ses amis artistes ou de certains fournisseurs et mécènes), mais aussi celle de Rubens (sa relation avec les grandes cours d'Europe), résument l'importance des relations de don et contre-don dans lesquelles les règles de l'échange diffèrent de la logique du marché. Le caractère dominateur de la puissance financière du mécène, tel que Paul Veyne a réussi à l'analyser durant l'Antiquité, influe cependant largement sur la relation à l'art et à l'artiste, comme le rappelle la logique du Miami Model évoquée plus haut : en créant son propre établissement, ce sont bien ses choix que le collectionneur entend imposer, tout en bénéficiant de l'aura particulière que l'on attribue aux donateurs. Les données sur le mécénat spécifiquement lié aux relations entre collectionneurs et artistes sont rares (mais comme nous l'avons observé, les données statistiques sur la logique du don manquent), le caractère de mécénat dans l'art, stricto sensu, n'étant pas complètement dissociable de l'achat ou du (contre-) don d'œuvres et des règles du marché. En revanche, les données liées aux dons d'œuvres par des collectionneurs sont mieux connues, du moins celles qui s'exercent au bénéfice des musées.
Dans le second cas en effet, lorsque le collectionneur songe au devenir de sa collection, l'opportunité de la donner à un musée s'avère une option souvent retenue. La construction d'un monument philanthropique (don d'une collection complète, voire construction d'un musée au nom du donateur), rappelant le geste du collectionneur, a largement permis le développement des collections publiques – de la création de la Tate Gallery aux milliers d'œuvres offertes au Louvre. Ainsi, les rapports d'activités d'un musée comme le Louvre font chaque année état de dons d'œuvres (4,2 millions d'euros en 2013) offertes par des collectionneurs aux collections publiques, mais il ne s'agit là que de la portion congrue d'un mouvement de dons autrement vaste.
L'évolution des intermédiaires
La rencontre entre l'offre et la demande passe rapidement par une organisation plus ou moins structurée, liée à l'organisation générale de la société. Durant l'Antiquité et une grande partie du Moyen Âge, la logique de marché occupe une place restreinte en regard de la Cour et de l'Église qui commandent à l'artiste, et l'organisation de la profession à partir d'un système de corporation, visant à encadrer les procédures de ventes, mais aussi à restreindre la concurrence étrangère (système qui sera aboli, en France, avec l'Ancien Régime). C'est donc moins une logique de marché qu'un système de protections, de cadeaux, de commandes et de relations de pouvoirs, fondé partiellement sur une logique publique, partiellement sur le don, qui fonde la relation entre l'artiste et son commanditaire. Il existe cependant un marché secondaire général (meubles, vêtements, objets) et organisé autour des ventes en cas de successions. Progressivement cependant, on voit se mettre en place, parallèlement à ces flux de commandes, qui sont prédominants jusqu'à la fin du Moyen Âge, un certain nombre de lieux de ventes différents de l'atelier ou des locaux de la corporation. Ce sont donc d'abord les artistes eux-mêmes, qui s'occupent des échanges. Le marché constitue l'un deux, pour les œuvres mineures, peintes « à la douzaine ». Le commerce de l'art ne se développe cependant qu'avec l'apparition des collections particulières, à la Renaissance, en Italie. Ce commerce, d'abord alimenté à partir des ruines de l'Empire byzantin, prend son essor avec la redécouverte de l'antiquité et de ses témoignages matériels : monnaies, statues, camées etc. Les tableaux ne viennent que par la suite, à partir du xvie siècle. L'essor conjoint du capitalisme, des collections, des musées et de l'histoire de l'art, durant les mêmes années, conduit à la création d'un marché pour les œuvres d'art, parfois d'expositions spécifiques, comme le pand, à Anvers au xve siècle, à l'apparition de marchands plus ou moins spécialisés, puis de ventes publiques. C'est d'abord aux Pays-Bas (Amsterdam, Leyde, Haarlem) que le commerce de l'art se développe, durant le xviie siècle, puis à Londres et à Paris, au siècle suivant. Ces marchés voient la montée de deux canaux principaux : celui des marchands, à l'image de Gersaint, dont la boutique a été immortalisée par Watteau, mais qui a également conduit des ventes publiques spécifiques, qui apparaissent au xviie siècle à Amsterdam (le mécanisme des enchères remontant à l'Antiquité), et dont les grandes maisons actuelles (Christie's et Sotheby's) apparaissent à Londres, à la fin du xviiie siècle.
De l'académie aux galeries
L'organisation du métier, longtemps régi par le système corporatif, va progressivement être remplacée par celui de l'académie – c'est le cas en France, avec la mise en place de l'Académie royale de peinture et de sculpture, fondée en 1648 – afin de mieux correspondre aux impératifs de ces nouveaux modes d'échange, qui aspirent selon une logique libérale à la suppression des corporations. C'est ainsi l'académie qui, progressivement, régule le marché, en définissant la valeur des œuvres (par la réception des nouveaux académiciens et par ses salons), transmet ses canons par le biais de son enseignement, et ouvre aux commandes royales. L'influence économique de la France, à partir du xviie siècle, va imposer la logique académique, mais aussi la tradition picturale française et la place de Paris comme lieu par excellence de la formation du goût et des valeurs artistiques, jusqu'au milieu du xxe siècle.
Jusque dans les années 1870, le système académique conditionne le marché et les valeurs, tant en France qu'à l'étranger. Comme l'ont montré les White, l'augmentation du nombre d'artistes (mais aussi le développement de nouvelles techniques, comme la photographie ou la peinture en tube, qui transforment le rapport à la peinture et ses méthodes d'enseignement) conduit le modèle académique vers une impasse et suscite la création de modèles alternatifs (des cours parallèles, puis de nouveaux salons), mais aussi la dépréciation du modèle académique, fondé sur la copie de l'ancien et la venue d'autres modes d'appréciation, qui porteront moins sur le respect des canons ou de la technique que le caractère novateur et l'authenticité. L'émergence de ces nouveaux lieux met également en valeur le rôle du marchand/galeriste, qui se charge d'exposer et d'assurer la promotion des artistes, dès lors que le rôle du Salon s'essouffle. Ainsi seront progressivement associés à l'essor de chaque nouveau mouvement des noms de marchands célèbres : Durand Ruel pour les impressionnistes ou Kahnweiler pour Picasso. Le marchand, naguère simple intermédiaire qui prenait sa commission (il en existe encore), se transforme en entrepreneur, au sens où Schumpeter l'a décrit. Il choisit ses peintres, peut tenter d'en obtenir le monopole de la production en achetant tous les tableaux ou en rémunérant l'artiste, plus sagement en les prenant en dépôt, certains galeristes, les moins aventureux se contentant de louer leurs cimaises. Cet investissement important pourra s'avérer particulièrement lucratif en cas de succès de l'artiste, mais demeure néanmoins risqué en regard du faible nombre de chances d'accès à la célébrité. Les qualités d'intuition ou de l'œil du galeriste lui permettront de faire évoluer le succès de son écurie.
Changements éco-géographiques
Si, pendant tout le xixe siècle et la première partie du xxe siècle, Paris demeure la capitale artistique et économique des arts plastiques, tant pour les marchands que pour les ventes publiques, cette situation se transforme, au sortir de la Seconde Guerre mondiale, au bénéfice de New York et de ses galeristes. Les États-Unis, sont devenus la première puissance économique mondiale depuis plus d'une génération, le nombre de ses collectionneurs ne cesse d'augmenter, tandis que l'exode des artistes et des intellectuels européens fuyant le conflit et les persécutions a dopé, en quelque sorte, le potentiel créateur du pays. La venue d'une nouvelle génération d'artistes américains (Rauschenberg, Jasper Johns...), mais aussi de galeristes comme Léo Castelli, développant des méthodes innovantes pour imposer leurs artistes dans le monde entier, conduit à l'hégémonie progressive de New York sur le reste du monde artistique.
Si la répartition du commerce de l'art évolue entre pays, elle se transforme également à l'intérieur des villes. Ainsi les nouvelles galeries se démarquent des anciennes en s'installant dans de nouveaux quartiers, souvent moins chers, qui eux-mêmes – à l'image de SoHo, puis de Chelsea, à New York, ou du quartier Rive gauche, ou près du centre Pompidou, à Paris – seront partiellement délaissés pour d'autres lieux lorsqu'ils seront devenus inabordables pour les nouveaux entrants. Il n'en reste pas moins que le marché de l'art, comme le théâtre privé, a besoin des grandes métropoles pour se développer ; aussi la plupart des galeries restent-elles cantonnées dans les capitales. Forcément, comme dans le cas du secteur privé des arts de la scène, la répartition des galeries d'art contemporain est très concentrée à Paris (qui regroupe un millier de galeries, soit près de 50 % du secteur, mais 86 % du chiffre d'affaires). Les galeries les plus importantes, sur la place de Paris, réalisent un chiffre moyen de 3 millions d'euros, contre 200 000 euros en province. Globalement, le chiffre d'affaires estimé de l'ensemble des galeries serait de l'ordre du milliard d'euros.
Deux autres types d'intermédiaires vont connaître un rôle de plus en plus important après la Seconde Guerre mondiale, les musées et les foires d'art contemporain. S'il existe quelques musées présentant de l'art vivant, durant l'entre-deux-guerres, c'est essentiellement à partir des années 1960 que ceux-ci vont se développer, l'institution se transformant : n'accueillant longtemps que les talents confirmés ou les valeurs consacrées par l'académie, elle s'investit progressivement sur la scène actuelle et joue un rôle de découvreurs, prenant parfois des risques que les galeries elles-mêmes ne souhaitent pas prendre. L'activité d'une génération de jeunes conservateurs et de commissaires d'exposition (parmi lesquels Pontus Hulten ou Harald Szeemann) va progressivement placer le musée, ou la Kunsthalle, comme l'un des intermédiaires possibles entre les artistes et le public, leur offrant, sinon la reconnaissance matérielle (qui passe par les galeries), du moins une reconnaissance symbolique (et parfois matérielle, par l'achat d'œuvres). Galeries et lieux d'exposition vont connaître, parallèlement, des mouvements de concentration, du moins sur des périodes temporaires. C'est en effet à la même époque que les biennales d'art contemporain, vastes expositions aux moyens considérables (ou organisées sur un modèle de pavillons nationaux, comme à Venise) connaissent un réel développement. À celle de Venise, inaugurée en 1895, s'adjoignent des événements de plus en plus incontournables comme la Documenta de Kassel (1955) ou la biennale de São Paulo (1951). Parallèlement, le monde des galeries se rassemble au sein de grandes foires commerciales réunissant en l'espace de quelques jours entre une centaine à près de trois cents galeries et offrant aux amateurs – plusieurs dizaines de milliers – un panorama de la création contemporaine telle que promue par les plus grandes galeries, tout en offrant à une clientèle très ciblée les avantages d'un supermarché de l'art contemporain. La répartition des plus grandes foires n'est pas sans rappeler celle des plus grands collectionneurs : Bâle (Art Basel, l'une des doyennes, créée en 1970), Paris (Fiac), Cologne, New York (Armory Show), Londres (Frieze) et Miami (Art Basel Miami). Déjà, de nouvelles foires s'organisent, en lien avec les pays émergents.
Le rôle du commissaire-priseur
L'institution des ventes publiques et l'encadrement des officiers qui en sont chargés, les commissaires priseurs, remontent au xvie siècle ; pendant longtemps, Paris demeure, en tant que capitale artistique, la plaque tournante du commerce de l'art, tant par ses galeries que par ses ventes publiques. La réglementation du métier constitue par ailleurs une barrière aux sociétés étrangères, qui ne peuvent exercer sur le territoire français. La libéralisation progressive du marché européen va radicalement transformer cette situation. Après que plainte ait été déposée pour non-respect des règles de concurrence, la France se voit ainsi contrainte par l'Union européenne, en 2001, d'ouvrir son marché aux grandes sociétés londoniennes, déjà implantées sur le continent américain et qui, en l'espace de quelques années, vont assurer une position dominante dans le monde. Paris perd ainsi rapidement sa première place au classement du chiffre d'affaires des ventes publiques au profit des États-Unis, de Londres et, à partir du début du xxie siècle, de la Chine. Les firmes Christie's et Sotheby's, qui dominent le marché, ont réussi, par le biais de leurs réseaux d'experts et de salles de ventes sur tous les continents (ainsi que grâce à l'amélioration du système de transport et de la circulation des capitaux), à atteindre les acquéreurs les plus intéressants et, par la même occasion, à obtenir les enchères les plus élevées (stimulant ainsi la décision des vendeurs de leur confier leurs meilleures œuvres). Ainsi s'est progressivement construit un duopole dans le monde des enchères artistiques, les autres maisons de ventes ne jouant plus qu'un rôle très modeste (Artcurial, seule maison française dans le top 20 des Maisons de ventes, est en 18e position ; il y a par ailleurs déjà neuf firmes chinoises dans le même classement). Après avoir été détrônée en 2010 et 2011, New York est redevenue la première place de vente dans le monde.
Le secteur des ventes publiques, qui constitue l'un des acteurs les plus importants pour le marché des talents confirmés, ne joue qu'un rôle relativement modeste en matière d'art contemporain. Certes, le marché intéresse de plus en plus Christie's et Sotheby's, qui organisent chaque année plusieurs ventes dans ce domaine, mais c'est surtout au niveau des galeries et dans les foires que se répartissent l'essentiel des transactions. Quelques artistes bénéficiant d'une notoriété déjà très importante et tentant de se passer de leurs intermédiaires traditionnels (et de leurs marges) ont parfois réussi, comme Damien Hirst en 2008, à commercialiser leur production en passant directement par les enchères. Ils n'en demeurent pas moins pour l'instant l'exception.
Un acteur public : le rôle de l'État
Le principe du marché de l'art pourrait laisser penser que l'État n'intervient que de manière très lointaine au sein du marché de l'art et si l'époque où la production artistique était, comme dans la Chine de Mao ou la Russie soviétique, totalement gérée par les pouvoirs publics, est révolue, l'État n'en joue pas moins un rôle considérable. À commencer par l'ensemble du réseau mis en œuvre pour démocratiser l'art : qu'il s'agisse de développer les musées et les lieux d'art contemporain, ou la formation artistique, même s'il ne s'agit pas directement d'une fonction d'aide du marché, mais d'éducation ou de médiation de la culture.
Interventions directes
Par ailleurs, au même titre que Louis XIV avec l'académie, l'État joue un rôle de commande visant (avec des moyens réduits, il est vrai) à soutenir ou à influencer la demande. Ainsi, bon an mal an, le Fonds national d'art contemporain et les Fonds régionaux d'art contemporain dépensent chaque année un peu plus de sept millions d'euros pour acquérir les œuvres d'un peu plus de 500 artistes, tandis que des commandes publiques sont effectuées directement pour près de trois millions d'euros. L'intervention directe auprès des galeries (les plus petites, et pour financer la promotion de jeunes artistes) demeure minime.
Contrairement aux arts de la scène, il n'existe cependant pas de statut de créateur professionnel et de régime qui pourraient être semblables à ceux de l'intermittence. Certains pays, comme les Pays-Bas, ont opté, durant les années 1970, pour des politiques de financement des artistes, avec des résultats mitigés. En revanche, outre la prise en charge des formations (académies) et des lieux de diffusion (plus d'une cinquantaine de centres d'art), un système de bourses de recherche ou de subventions sur projet, comme on le retrouve dans le secteur des arts de la scène, est également mis sur pied.
Politiques d'encadrement
De manière plus générale, l'État intervient en encadrant les transactions sur le marché, et notamment les ventes publiques (dont il convient d'assurer leur caractère non frauduleux). De la même manière que le patrimoine, les actions de mécénat bénéficient d'un système de déduction fiscale – moins développé qu'aux États-Unis – susceptible de favoriser le marché et d'enrichir à terme le patrimoine. De la même manière, les différents ministres des finances ont jusqu'ici accepté, en France, de ne pas intégrer les œuvres d'art dans le calcul de l'impôt sur le patrimoine, l'inverse étant pressenti comme une mesure très néfaste pour le marché de l'art.
De manière plus précise, l'État a mis en place un droit d'auteur spécifique, le droit de suite, qui s'applique à toutes les transactions en vente publique supérieures à 3 000 euros. Ce mécanisme agit comme une redevance et vise à assurer aux artistes ou à leurs descendants la possibilité de bénéficier d'une éventuelle gloire sur le tard ou posthume. Ce régime, pendant longtemps appliqué seulement en France, a souvent été présenté comme une incitation pour les vendeurs à préférer la vente de leurs œuvres dans d'autres pays, où le droit de suite n'aurait pas cours. Par ailleurs, la taxe rapporterait peu et surtout aux artistes déjà célèbres, tandis que les frais de redistribution du produit de la taxe s'avéreraient très élevés. Depuis 2006, une quinzaine d'États au sein de l'Union européenne ont accepté de suivre le principe de cette taxe, diminuant ainsi les irrégularités entre les marchés ; apparemment, les conséquences en termes de diminution des transactions seraient limitées.
Formation et variation des prix
La rencontre entre l'offre et la demande induit, selon la logique économique, la formation des prix. Le prix des œuvres d'art, comme nous le signalions d'emblée, constitue l'un des phénomènes qui a toujours fasciné – tant le public que les économistes. Ainsi, le marché de l'art actuel peut être en quelque sorte représenté comme l'antithèse de la valeur travail – surtout à partir de l'essor de l'art moderne et avec la suppression de la valorisation du « métier ». Cette logique – qui a notamment donné lieu à un procès retentissant (1878) entre Whistler et Ruskin, ce dernier accusant l'artiste d'avoir exigé un prix absurde pour l'une de ses œuvres – induit l'incompréhension du grand public devant les sommes pouvant être déboursées pour un tableau monochrome, ou une installation faite de feutre et de graisse.
A fortiori, les variations de l'offre et de la demande suscitent également de nombreux commentaires, à commencer par la chute radicale des grandes gloires académiques au profit des impressionnistes. La valeur des œuvres serait-elle uniquement relative et due au hasard – des goûts et des couleurs... – ou existe-t-il des règles permettant d'expliquer ces changements ou la continuité du goût à travers le temps ?
Les classements
Si l'on ne peut qu'objectivement constater des variations de prix parfois très importantes, certains économistes ont pu montrer la persistance, à travers les siècles, d'un certain nombre d'artistes : le test of time, de Hume présente certaines régularités dans l'appréciation des œuvres et des choix des générations précédentes. Néanmoins, c'est à travers un réseau de relations dense, comprenant les artistes, les collectionneurs, les marchands et les instances de légitimation (critiques et conservateurs), que le prix se forme et le pouvoir plus ou moins important de chacun de ces acteurs, bien plus qu'une offre et une demande impersonnelles, joue sur la formation des prix. Un certain nombre de paramètres, forcément, vont influencer l'offre, comme le nombre d'œuvres encore en circulation, le nombre d'expositions, la réputation de l'artiste et les prix qu'il a déjà obtenus. À l'inverse, la demande sera également influencée par l'arrivée sur le marché de nouveaux collectionneurs et l'enrichissement ou l'appauvrissement des autres, la qualité des informations dont ils disposent et, de manière générale, l'évolution de la situation économique en général (le pouvoir financier étant largement conditionné par la santé des entreprises et de la bourse).
La fluctuation de la cote des artistes et celle des montants des ventes publiques prêtent donc à la constitution de graphiques dont la ressemblance avec les cours de bourse n'est pas sans rassurer certains collectionneurs/spéculateurs. L'étude de ces graphiques permet d'évoquer des phénomènes identiques, tels qu'on les observe dans le monde de la finance (un parallèle peut être établi entre les deux et une crise économique, comme celle des subprimes, affecte rapidement l'évolution du marché de l'art). Le site Artprice, notamment, rend compte depuis une dizaine d'années du montant des transactions pour chaque artiste passé en ventes publiques. Sans surprise, c'est l'art moderne, l'art contemporain et l'art d'après-guerre qui constituent l'essentiel des transactions – le xixe siècle et l'art ancien de qualité, soit les talents consacrés, ne se présentant que de plus en plus épisodiquement sur le marché. Le classement des artistes (évoluant fortement au gré des ventes publiques) dont le « chiffre d'affaires » est le plus important comprend essentiellement des figures modernes reconnues : en 2013-2014 : Jean-Michel Basquiat, Jeff Koons, Christopher Wool, Peter Doig ou Richard Prince pour les artistes occidentaux, Fanzhi Zeng, Zhongli Luo ou Yifey Chen pour les pays asiatiques.
Si l'estimation du chiffre d'affaires peut donner lieu à un classement, d'autres estimations visant à témoigner des qualités d'un artiste ont été conçues, la plus ancienne revenant à Roger de Piles et à sa « balance des peintres », établie à la suite de son Cours de peinture par principe, en 1708. Ce tableau, notant sur 20 les qualités (dessin, coloris...) des différents artistes, sera régulièrement critiqué par les historiens de l'art, suscitant en revanche l'intérêt des économistes. Plus récemment, des classements tenant compte des expositions (personnelles, de groupe, dans des musées etc.) ont été réalisés, en Allemagne par le Kunstkompass, à partir des années 1970, et plus récemment en France par Artindex et le Journal des arts, présentant des classements parfois largement différents de ceux d'Artprice. Chacun de ces classements, s'il prétend à une certaine objectivité au niveau des statistiques présentées, peut être cependant critiqué en fonction des pondérations utilisées dans les calculs. Actuellement, Bruce Nauman, Gerhard Richter, Cindy Sherman et Ed Ruscha arrivent en tête du classement Artindex ; tandis que Gerhard Richter, Bruce Nauman, Rosemarie Trockel et Georg Baselitz s'imposent dans le Kunstkompass.
Estimer et investir dans les œuvres d'art
L'apparente variation inexpliquée des cours des œuvres d'art conduit certains à rejeter, en bloc, l'idée d'une explication quant à la formation du prix des œuvres d'art. La constitution et l'analyse (essentiellement à partir de modèles fondés sur des régressions hédoniques) de bases de données de résultats d'enchères, sur plusieurs années, ont permis depuis une trentaine d'années, de montrer la relative cohérence de la formation des prix à partir du nom des artistes, de la technique utilisée, de l'année ou de la taille des œuvres, et bien sûr des résultats précédents.
Pour autant, l'achat d'œuvres d'art constitue-t-il une opération rentable ? Il n'est guère difficile de calculer le potentiel rendement d'une œuvre acquise quelques années plus tôt et Maurice Reims, à la fin des années 1950, présentait déjà les résultats fabuleux atteints par l'investisseur avisé qui aurait, à la fin du xixe siècle, acquis des toiles impressionnistes, au contraire des collectionneurs de maîtres académiques dont la cote n'avait cessé de s'effondrer. Mais de tels choix constituent plutôt des exceptions et, apparemment, il n'est guère évident que l'investissement en œuvres d'art – mis à part quelques cas exceptionnels – soit plus intéressant que le marché des bons du Trésor. Pour l'ensemble des études qui ont porté sur l'analyse du rendement des œuvres, sur une période plus ou moins brève d'environ une génération, seules quelques-unes concluent à des rendements supérieurs à ceux qui pourraient être obtenus par des obligations classiques, et une connaissance experte, si elle permet parfois de réaliser des affaires, n'empêche pas, de manière générale, des rendements relativement moyens. Plus qu'un investissement, la seule certitude pour le collectionneur est d'apprécier réellement ce qu'il acquiert, afin de profiter du plaisir esthétique de son investissement.
. Menger M., Portrait de l'artiste en travailleur. Métamorphose du capitalisme, Paris, Le Seuil, 2002.
. Goodwin C., « Art and culture in the History of Economic Thought », in Ginsburgh V., Throsby D., Handbook of the Economics of Art and Culture, Amsterdam, Elsevier, vol. 1, 2006, p. 25-68.
. 14 % des Français ont pratiqué le dessin au cours des douze derniers mois, et 9 % ont pratiqué la peinture ou la sculpture. Donnat O., Les pratiques culturelles des Français à l'ère numérique, Paris, La Découverte / Ministère de la Culture et de la Communication, 2009, p. 201.
. Becker H. S., Arts worlds, University of California Press, 1982. Trad. fr. Les mondes de l'art, Paris, Flammarion, 1988.
. Moureau N., Sagot-Duvauroux D., Le marché de l'art contemporain, Paris, La Découverte, 2010.
. Pommerehne W. W., Frey B. S., La culture a-t-elle un prix ?, Paris, Plon, 1993.
. Chiffres clés de la culture 2013. Au total, le secteur des arts plastiques et des métiers d'art, qui regroupe aussi les photographes ou les professionnels de la mode et de la décoration, occupait 161 000 personnes en 2008.
. Gouyon M. « Peintres, graphistes, sculpteurs... Les artistes auteurs affiliés à la Maison des artistes en 2009 », Ministère de la Culture et de la Communication, Culture chiffres, 2011-2014.
. Cette hypothèse, présentée par Throsby, est discutée par Greffe X., Artistes et marchés, Paris, La Documentation française, 2007, p. 92 sq.
. Greffe X., L'artiste-entreprise, Paris, Dalloz, 2012.
. Wittlin A. S., The Museum, its History and its Task in Education, Londres, Routledge, 1949.
. Moulin R., Le marché de la peinture en France, Paris, Éd. de Minuit, 1967, p. 249.
. Esterow M., « Who Will Bid $50 million? », Art News, 9 July 2013. Disponible sur http://www.artnews.com/2013/07/09/who-will-bid-50-million/ (consulté en juillet 2013).
. Green T. « Turning a museum into a vanity space; Private collection shows are an insult to scholarship and curators », The Arts Newspaper, 207, nov. 2009.
. Martin-Fugier A., Collectionneurs, Avignon, Actes Sud, 2012.
. Veyne P., Le pain et le cirque : sociologie historique d'un pluralisme politique, Paris, Le Seuil, 1976.
. Sur l'histoire de la relation de l'artiste au marché : Greffe X., Artistes et marchés, Paris, La Documentation française, 2007.
. De Marchi N., Van Miegroet H. J., « The history of art markets », in Ginsburgh V., Throsby D., Handbook of the Economics of Art and Culture, Amsterdam, Elsevier, vol. 1, 2006, p. 69-122 ; Bertrand Dorleac L. (dir.), Le commerce de l'art de la Renaissance à nos jours, Besançon, La Manufacture, 1992.
. White H. & C., La carrière des peintres au xix e siècle, Paris, Flammarion, 1991.
. Guilbaut S., Comment New York vola l'idée d'art moderne, Nîmes, Jacqueline Chambon, 1996.
. Rouet F., « Les galeries d'art contemporain en France en 2012 », Culture études, 2013-2.
. Les premières grandes ventes commencent au xviie siècle. Voir Beurdeley M., Trois siècles de ventes publiques, Paris, Tallandier, 1988.
. Conseil des ventes volontaires de meubles, Les ventes aux enchères publiques en France, rapport d'activité 2012, Paris, 2013. Disponible sur : <http://www.conseildesventes.fr/sites/default/files/cdv-livre-rapport-activite-2012.pdf> (consultation août 2013).
. Ginsburgh V., « The economic concequences of droit de suite in the European Union », working paper, Ecares, mars 2006, disponible sur http://www.ecares.org/ecare/personal/ginsburgh/papers/143.consequences.pdf.
. Banternghansa C., Graddy K., « The impact of the Droit de Suite in the UK: an empirical analysis », Journal of Cultural Economics, 35, 2011, p. 81-100.
. Parkes A., « A sense of justice. Whistler, Ruskin, James, Impressionism », Victorian Studies, 42, 4, 1999/2000, p. 593-629.
. Ginsburgh V., Mairesse F., Weyers S., « De la narration à la consécration. L'exemple de la peinture flamande de Van Eyck à Rubens », Histoire & Mesure, 2008, XXIII-2, p. 145-176.
. Sur les questions de la valeur, voir Hutter M., Throsby D., Beyond Price. Value in Culture, Economics and the Arts, Cambridge, Cambridge University Press, 2008.
. Artprice, Le marché de l'art en 2014, publication annuelle disponible sur <http://imgpublic.artprice.com/pdf/artprice-contemporary-2013-2014-fr.pdf> (consulté en décembre 2014).
. Pour une recension des textes sur la balance des peintres : Griener P., La République de l'œil. L'expérience de l'art à l'époque des Lumières, Paris, Odile Jacob (Collège de France), 2010. Sur les aspects économiques : Ginsburgh V. et Weyers S., « De Piles, drawing and color. An essay in quantitative art history », Artibus et Historiae 45 (2002), p. 191-203.
. Le Journal des arts, 371, 8 au 21 juin 2012.
. Ginsburgh V., Mei J. P. and Moses M., « On the computation of art indices in art », in Ginsburgh V. et Throsby D. (eds.), Handbook of the Economics of Art and Culture, Amsterdam, Elsevier, 2006, p. 948-979.
. Rheims M., La vie étrange des objets, Paris, Plon, 1959.
. Pommerehne W. W., Frey B. S., La culture a-t-elle un prix ?, Paris, Plon, 1993 ; Grampp W. D., Pricing the Priceless, Art, Artists and Economics, New York, Basic books Inc., 1989 ; Ulibarri C. A., « Perpetual options: revisiting historical returns on paintings », Journal of Cultural Economics, 33, 2009, p. 135-149.
Chapitre 9
Les industries culturelles : définition et organisation
La réflexion économique ayant trait spécifiquement aux industries culturelles est somme toute relativement récente. Par un curieux renversement de l'histoire, c'est en effet le terme forgé par Theodor Adorno et Max Horkheimer qui a été utilisé pour circonscrire le domaine de l'économie de la culture le plus lié à une certaine logique de production industrielle. La connotation très péjorative du terme utilisé par les philosophes de l'École de Francfort pour analyser les effets, dans le cinéma, de l'alliance entre la culture et la logique de marché, a progressivement laissé la place à une forme de catégorisation couramment utilisée (cf. Introduction). En France, les premiers travaux en science économique remontent à l'étude d'Henri Mercillon sur le cinéma hollywoodien et de Bénédicte Reynaud-Cressent pour le livre. D'autres travaux, plus critiques ou s'inscrivant dans une perspective historique et socioéconomique, ont jalonné les années 1970 et 80, comme les travaux de Jacques Attali, de Charles-Albert Michalet, de Bernard Miège, de Mario d'Angelo ou encore de Patrice Flichy. Parallèlement, on trouve un certain nombre de travaux plus factuels, par exemple les travaux de René Bonnell sur le cinéma et ceux d'André Lange sur le disque. Depuis les années 1990, la recherche en science économique s'est intensifiée, notamment en raison des transformations provoquées par le numérique et la part croissante occupée par la musique ou les films dans les usages d'internet.
La notion d'« industries culturelles » englobe les activités fondées sur la production de biens culturels reproductibles (cf. chapitre 1), mais derrière cette appellation commune se cache en réalité une diversité de cas. Le cinéma constitue historiquement une forme entièrement inédite de création artistique qui se fonde originellement sur une reproduction industrielle et qui se confond avec son support de valorisation (le service de la projection de films en salles créé en 1895 par les frères Lumière). Le livre papier, en revanche, s'est appuyé avant sa logique de reproduction industrielle (à partir du xixe siècle) sur des formes artisanales (la presse manuelle ou la xylogravure et avant encore le codex sur parchemin) ; la numérisation du livre constitue un second renouvellement des supports. Il en va de même de la musique. À son apparition suite à l'invention du phonographe en 1877 dans les laboratoires de Thomas Edison, la musique enregistrée diversifie les modes de valorisation de la musique déjà existants (le spectacle vivant), mais surtout se substitue progressivement au marché des partitions et des instruments de musique à domicile. Par la suite, avec l'apparition de nouveaux genres musicaux comme le rock et la musique disco, la musique enregistrée devient le plus souvent le support principal de valorisation, le concert jouant un rôle de promotion des albums à travers les tournées d'artistes et de groupes de musique.
Définition et évaluation des industries culturelles
La notion d'« industries culturelles » renvoie donc à des trajectoires historiques et, on le verra, à des modes d'organisation différents (cf. chapitre 10). À ce titre, elle doit donc être utilisée avec précaution. Sa définition et l'évaluation économique de ces activités soulèvent par ailleurs des difficultés qu'il convient d'évoquer avant d'aborder leurs points communs et enfin de présenter les spécificités de chacune de ces industries culturelles.
Industries culturelles artistiques et industries créatives
En première approche, les industries culturelles peuvent être définies comme une catégorie d'activités économiques produisant et valorisant, sur une échelle de masse, des biens et des services dont le contenu artistique est significatif. Ces industries sont fondées sur une dualité : d'un côté, l'unicité d'un bien immatériel (une œuvre au sens juridique du terme, soit un bien immatériel formel et original, empreint de la personnalité de son auteur), et de l'autre, la reproductibilité industrielle d'exemplaires grâce à des technologies très différentes et évolutives dans le temps, comme l'imprimerie et les techniques de reproduction mécanique, magnétique et numérique.
Cette conception large consiste à intégrer dans la catégorie « industries culturelles » toute forme de création (d'œuvres au sens juridique du terme) dès lors que celle-ci incorpore du travail artistique, pour autant que son contenu se présente « significativement » comme artistique. Les « industries culturelles » seraient de la sorte celles qui produisent des biens culturels reproductibles à partir d'un premier exemplaire dont la production et la valorisation reposent sur la créativité. À côté du livre, de la musique et du cinéma, des activités comme le jeu vidéo, le design, la mode, l'architecture, la publicité, la production audiovisuelle, pourraient ainsi être intégrées sans problème à cette catégorie élargie par rapport à celle des seules industries culturelles. Une telle approche renvoie en fait à une catégorie analytique plus récente : celle des industries créatives. Elle nous semble poser problème. Comment en effet distinguer les industries culturelles par rapport à l'ensemble des activités recourant au travail créatif et souvent aux mêmes artistes et techniques que le cinéma ou la musique ? À quelle proportion l'expression « significativement artistique » renvoie-t-elle ? On le constate, une telle approche élargie, certes intéressante car elle permet d'établir des analyses comparées entre les différentes industries créatives, ne permet pas de délimiter avec précision et cohérence le champ des industries culturelles. Les pays recensant les catégories « industries culturelles » ou « créatives » présentent ainsi actuellement des secteurs différant parfois assez largement.
Plus fondamentalement, une telle assimilation risque de faire passer au second plan la spécificité artistique du cinéma, de la musique et de la littérature. La finalité de l'art n'est plus prise en compte. Au contraire, si l'on restreint le champ d'activités des industries culturelles au domaine de la littérature et des arts, la question de leur définition renvoie à la définition de l'art et soulève des questions d'ordre plus esthétique, certes en dehors du questionnement économique, mais qui permet de distinguer nettement les industries culturelles des autres « industries créatives » fondées sur la reproductibilité. Selon cette approche, les industries culturelles constituent une catégorie d'industries créatives produisant des biens dont la finalité n'est pas utilitaire : une œuvre d'art n'a (généralement) pas d'utilité en soi, à l'inverse d'une publicité ou d'un design, si créatifs soient-ils, ou encore d'un chef-d'œuvre de la haute couture. Une œuvre d'art se présente d'abord et avant tout comme une fin en soi, n'ayant d'autre finalité qu'elle-même. Que certaines œuvres soient transformées en bien culturel ou en bien de divertissement apparaît comme secondaire, la frontière entre les deux étant loin d'être étanche et un film d'action sera « légitime » au gré de l'évolution des conventions sociales et de la critique, notamment lorsqu'elle réévalue des œuvres passées. Mais contrairement à d'autres objets issus de l'activité créative tels qu'un design, une formule chimique ou à une équation mathématique, l'art n'a pas de vocation sociale pratique prédéterminée d'un point de vue universel.
Dans ce chapitre et le suivant, nous préférons ne pas occulter cette particularité qui fait des œuvres artistiques et littéraires des marchandises différentes des autres par leur non-vocation a priori. Nous retenons donc une approche restrictive en nous focalisant sur trois industries culturelles qui relèvent sans aucune ambiguïté du domaine de l'art, à savoir le livre, la musique et le cinéma. Le chapitre 12 revient plus longuement et dans une perspective critique sur la notion d'« industries créatives ».
Quel poids économique ?
Si la définition des industries culturelles s'avère difficile, la mesure de leur importance économique l'est sans doute plus encore. Leur poids symbolique s'avère considérable, ne serait-ce qu'à travers l'impact des stars du cinéma et de la musique sur les représentations et les comportements des individus. Ces industries sont également très présentes dans les pratiques culturelles et l'occupation du temps de loisir, mais également celui de déplacement des individus : écoute de musique, visionnage de films, lecture de romans. Pour autant, leur part dans la richesse nationale est-elle proportionnelle à leurs poids symbolique et social ? Quels indicateurs et quelles sources statistiques utiliser ? Il s'agit d'un exercice essentiel, car il est difficile de décider et de mettre en place des politiques culturelles sans en connaître les effets sur l'économie, l'emploi, et ce relativement à d'autres activités économiques.
Bon nombre d'études ont cherché à évaluer le poids économique de ce secteur (cf. chapitre 12), mais l'évaluation statistique des industries culturelles se heurte à des difficultés méthodologiques importantes. L'INSEE ne fournit pas de données spécifiques et les données sectorielles fournies par le ministère de la Culture reprennent essentiellement des données professionnelles produites par les syndicats professionnels majoritaires (le SNE dans le livre, le SNEP pour la musique enregistrée, le SEV pour la vidéo). Or, elles sont susceptibles d'être instrumentalisées par ces organismes en fonction de leur stratégie de lobbying. En revanche, les données sur le cinéma en salles et l'audience télévisuelle des films produites par le CNC et le CSA, organismes publics, nous semblent nettement plus fiables.
Par ailleurs, un certain nombre d'études ont évalué le poids des industries créatives dans l'économie. Elles considèrent ainsi l'ensemble des industries protégées par le droit d'auteur en incluant en plus des industries culturelles des activités comme les logiciels, les productions télévisuelles etc. En 2012, elles expliqueraient 6,5 % du PIB des États-Unis et sur la période 2008-2011, 4,5 % pour les 27 pays de l'Union européenne. Ce poids augmente sensiblement si l'on y ajoute les industries dépendantes des contenus protégés par le droit d'auteur (l'équipement audiovisuel, l'informatique etc.). Ainsi aux États-Unis, l'ensemble des industries dépendant directement ou indirectement de ce secteur représente 1 765 milliards de dollars, soit 11,25 % de la richesse nationale et dépassent en matière d'exportations des industries comme l'aéronautique, l'agroalimentaire ou les produits pharmaceutiques... Il faut néanmoins être prudent avec ce type d'évaluations qui servent souvent à justifier des politiques d'aides et des réglementations favorables à ces secteurs, ainsi que l'importance de l'action publique dans ces domaines (cf. chapitre 12). Cette logique poussée à son paroxysme a ainsi amené les industries du fair use (le régime juridique définissant les exceptions au copyright aux États-Unis) à quantifier leur propre poids économique. Les industries bénéficiant du droit de copie privée, de copie pour usage technique, de courte citation etc. représenteraient environ 17 % du produit national dans ce pays !
Plus récemment, le ministère de la Culture et de la Communication a publié deux évaluations du poids économique de la culture en France et en Europe. Adoptant une approche large de la culture (qui en fait rejoint les études menées dans d'autres pays sur les industries créatives, cf. chapitre 12), ces études ne fournissent pas de données permettant de mesurer précisément la part de nos trois industries culturelles. Il apparaît qu'en 2013, les branches culturelles représentent une valeur ajoutée de 44 milliards d'euros, soit 2,3 % du PIB en France. L'audiovisuel (radio, cinéma, télévision, vidéo, disque) et le livre expliquent 34 % de cette valeur ajoutée contre 16 % pour le spectacle vivant et 9 % pour le patrimoine ; le reste étant généré par la presse (12,6 %), l'architecture (6,9 %), les arts visuels (5,8 %), l'enseignement culturel (4,1 %) et les agences de publicité (11,2 %). On notera l'approche très large adoptée par le ministère de la Culture. S'agissant par exemple de la publicité, il faut admettre que le financement publicitaire joue un rôle considérable pour la production culturelle, mais peut-on légitimement assimiler le produit de ces agences publicitaires à de la culture ?
Si l'on retient l'approche restrictive des industries culturelles, telle que nous la proposons, il est néanmoins possible de comparer le poids relatif de chacune des industries culturelles. Le livre est souvent présenté comme la première industrie culturelle en raison de son chiffre d'affaires (3,9 milliards d'euros en 2013 contre 4,13 en 2012 et 4,3 en 2011). Or, si l'on retient une définition restrictive des industries culturelles ou si l'on veut plus simplement comparer les industries culturelles sur une base plus homogène, on doit déduire de ce total certains segments pour ne retenir que la littérature (26,4 %), la jeunesse (13,4 %) et la bande dessinée (9,5 %), soit une évaluation de 1,9 milliard d'euros. Or, en 2013, si la musique enregistrée représente 0,72 milliard d'euros, le cinéma (hors télévision) représente plus de 1,9 milliard d'euros (soit 1,23 milliard de recettes en salles, 0,56 pour les ventes de vidéogrammes et 156 millions d'euros pour la vidéo numérique à l'acte). Si l'on ajoute à ce chiffre les achats des films cinématographiques par les chaînes de télévision (930 millions d'euros), on obtient un total de 2,8 milliards d'euros faisant du cinéma la première industrie culturelle. Le chapitre suivant présente des données plus détaillées.
Une organisation de nature industrielle
Les industries culturelles présentent la même structure de marché dans laquelle coexistent une poignée d'acteurs (les majors) dominant essentiellement le segment de la distribution et une myriade de firmes de tailles hétérogènes opérant à tous les stades de la production et de la valorisation des biens. L'économie industrielle appréhende cette organisation à travers la notion d'oligopole avec frange concurrentielle. Cette structure s'explique par les stratégies des firmes dominantes et plus généralement, par certaines caractéristiques économiques des biens culturels reproductibles (cf. chapitre 1).
L'oligopole
En tant qu'activité industrielle et contrairement aux autres activités artistiques, le cinéma, le livre et la musique enregistrée reposent sur la production de masse de biens culturels en vue d'une distribution et d'une diffusion auprès d'un public le plus large possible. L'industrialisation concerne essentiellement la transformation d'un prototype en un bien culturel produit sur une échelle de masse. Si la production a pu être partiellement industrialisée, en particulier avec le studio system hollywoodien, elle reste marquée par une logique de singularité et de prototypage où l'écriture, la création, la fabrication des décors, la réunion d'artistes-interprètes etc. constituent des expériences uniques, non reproductibles à l'identique, même si parfois elles sont répétables et obéissent à une division du travail très poussée et à un rythme rapide à l'instar de certains types de musiques commerciales stéréotypés, de littérature populaire fondée sur les mêmes ressorts, des sequels (suites de films ayant connu le succès), de l'exploitation des mêmes personnages, décors, effets spéciaux ou encore de la production à haute fréquence de Bollywood (Inde) ou de Nollywood (Nigeria).
Toutefois, l'industrialisation concerne essentiellement la reproduction d'exemplaires et leur promotion et diffusion sur les médias de masse. Ces processus nécessitent un calibrage précis en matière de marketing et de ciblage de marché et reposent sur l'exploitation de gains de productivité permettant de dégager des marges commerciales importantes par unité vendue ou diffusée.
Cette organisation industrielle nécessite des capitaux importants, ce qui favorise la concentration des moyens de production entre les mains de quelques acteurs. Ces derniers font face à un aléa de production très fort lorsqu'ils décident de financer la production et la mise sur le marché des biens culturels. Cet aléa peut être défini par les coûts de production et de promotion multipliés par la probabilité d'échec. Il est d'autant plus élevé que ces coûts sont pour l'essentiel irrécupérables. Mais il s'explique surtout par le fait que le succès d'un film, d'un roman ou d'un album de musique est imprévisible (« nobody knows »). Ce risque est d'autant plus élevé que la demande se concentre sur quelques titres et que la période de rentabilisation est courte.
Un certain nombre de stratégies existent afin de réduire l'aléa de production. Premièrement, pour obtenir un nombre de succès commerciaux suffisant pour rentabiliser leurs investissements sur un marché de masse, les acteurs doivent multiplier les essais. Ils doivent également diversifier les modes de valorisation des biens culturels qu'ils produisent (les « fenêtres » de diffusion d'un film, les canaux de vente des livres etc.). Cela nécessite des capitaux importants, mais cela suppose également d'entretenir un réseau de partenariats et de contrats avec une hétérogénéité d'acteurs en grand nombre (les petits libraires, les salles de cinéma indépendantes...) dont certains contribuent fortement au chiffre d'affaires des producteurs tout en disposant d'un pouvoir de marché important (grande distribution, groupes de communication etc.). Deuxièmement, la réduction de l'aléa peut porter sur une différenciation du bien culturel. Celle-ci peut être « objective », notamment par le recours au vedettariat (cf. chapitre 14) et aux effets spéciaux dans le cinéma, ou « subjective » en augmentant les dépenses de promotion pour toucher une audience aussi large que possible, y compris en influençant certains modes de prescription (presse spécialisée par exemple). Troisièmement, les firmes peuvent tenter d'anticiper la demande (par exemple, en établissant des panels tests sur les scénarios dans le cinéma ou en exploitant les données internet fournies par des compagnies comme Allociné). Or, ces stratégies représentent des investissements considérables et ne sont donc pas à la portée de tous. Elles représentent des barrières à l'entrée prohibitives et favorisent la concentration du marché autour d'un oligopole (les majors).
De surcroît, ces techniques de réduction de l'aléa peuvent avoir pour effet d'alimenter mécaniquement celui-ci. En effet, pour réduire la probabilité d'échec, il faut augmenter les coûts de production et de promotion. Si toutes les firmes font de même, la rareté des ressources (stars, attention des spectateurs face à une surabondance informationnelle etc.) s'accroît et l'aléa augmente en proportion : la probabilité d'échec ne diminue pas forcément à l'échelle du marché et les coûts augmentent. Il devient ainsi de plus en plus difficile de rentabiliser les investissements. Les firmes entrent donc dans un cercle vicieux aboutissant à une augmentation chronique des coûts de production (des coûts irrécupérables), donc du risque de non-rentabilité. Cela favorise la concentration de l'offre et une baisse de la diversité culturelle, les financements et la distribution se portant sur les projets perçus comme les moins risqués et les plus conformes au goût moyen des consommateurs (cf. chapitre 11).
Enfin, l'oligopole est renforcé par l'organisation même de la distribution de détail. La grande distribution domine largement la commercialisation des biens culturels reproductibles auprès du grand public (cf. chapitre suivant). Or, son fonctionnement engendre des coûts fixes particulièrement élevés (logistique, coûts de l'immobilier en centre-ville pour les distributeurs spécialisés), ce qui la soumet à une contrainte de rentabilité. Pour cela, l'espace et le temps d'exposition sont dévolus prioritairement aux biens à fort potentiel commercial. Dans le domaine de la culture, il s'agit des livres, des films, des albums de musique qui bénéficient des budgets de promotion les plus importants ou qui ont remporté des récompenses. Certes, pour les grandes surfaces spécialisées, le nombre de références exposées peut être plus élevé que chez les libraires. Mais l'espace total d'exposition demeure limité et les distributeurs doivent alors jouer sur le temps d'exposition, très court pour un bien qui ne rencontre pas un succès quasi immédiat, beaucoup plus long pour un best-seller. Cette technique commerciale renforce ainsi l'oligopole et conduit en même temps à des inégalités très fortes de revenus entre les artistes.
La frange concurrentielle
Pour autant, ce mouvement de concentration n'empêche pas l'existence d'une « frange concurrentielle » composée d'une myriade de petites et moyennes structures de production et de distribution associée à un vaste « vivier » d'auteurs indépendants, amateurs ou professionnels. Comment expliquer cette coexistence ? D'une manière générale, les motivations des auteurs peuvent être largement intrinsèques (pulsion, plaisir d'écrire mais aussi recherche de l'estime de soi et de celle de son entourage) aboutissant à des pratiques amateurs très répandues comme le prouvent actuellement l'abondance et la diversité des contenus présents sur des plateformes d'hébergement comme YouTube. De plus, les financements de la création et de la production des œuvres sont souvent déconnectés de leur valorisation marchande et donc totalement indépendants des stratégies commerciales des acteurs dominants. Cette déconnexion s'explique par le coût relativement faible de certaines activités de création – l'écriture, la composition musicale, actuellement la réalisation et le montage de petits films grâce aux logiciels dédiés peu onéreux – et grâce à des financements publics (aides du CNC, du CNL etc. en France) ou privés (mécénat, prêts familiaux, financement participatif en ligne...) venant subventionner les coûts fixes de la création, de la production et de certaines formes de distribution indépendamment de toute contrainte marchande.
Dans le cinéma, les indépendants sont apparus historiquement avec la crise du studio system hollywoodien et la concurrence de la télévision. Durant les années 1960, la faillite du modèle classique, la possibilité de télédiffusion de créations indépendantes sur un nouveau support concurrent des salles de cinéma, mais également les midnights movies et la constitution de communautés de fans ont permis l'émergence de nombre d'indépendants tels que les sociétés de John Cassavetes et Roger Corman. Les auteurs et les éditeurs indépendants sont apparus assez tôt dans l'histoire de l'édition et de la musique en raison d'une décentralisation des lieux de valorisation, mais également d'une fragmentation plus forte de la demande favorable au développement de niches, souvent pour contourner la censure dans le livre ou s'inscrivant dans une logique de contre-culture pour la musique.
La frange concurrentielle coexiste également avec l'oligopole, car elle lui garantit un renouvellement de la « créativité » à travers les prises de risque esthétique que les majors ne peuvent bien souvent pas assumer en raison du niveau d'investissement qu'elles consacrent tant à la production qu'à la distribution et la promotion des œuvres qu'elles financent. Ces dernières distribuent également des œuvres produits par des structures de production indépendantes sur un plan juridique, mais qui en fait sont les sous-traitants des majors. La production de gros budgets cinématographiques par ces « indépendants » a lieu bien souvent pour contourner les règles juridiques et syndicales. En Europe, des sociétés comme DreamWorks et EuropaCorp ont pu jouer ce rôle avec Vivendi Universal lorsque ce groupe européen a tenté de devenir une major. Dans la musique, les labels indépendants ont longtemps joué le rôle de poissons-pilotes explorant les nouveaux courants artistiques. Les majors peuvent également trouver un intérêt à laisser subsister ou à déléguer une partie de leur activité à des sous-traitants flexibles qui sont certes indépendants sur un plan juridique, mais dont le pouvoir de négociation est faible face à des firmes intégrées qui disposent d'un accès facilité en raison de leur taille aux sources de financements, aux réseaux de distribution et de promotion.
L'existence d'une frange concurrentielle dans chacune des industries culturelles permet ainsi de garantir la diversité de l'offre. Celle-ci a tendance à s'accroître avec la baisse des barrières à l'entrée au niveau de la création et de la production de biens culturels. Les coûts de création ont ainsi diminué, notamment avec les logiciels de type « home studio », fournissant aux artistes des outils d'édition, de montage, de mixage... sans avoir à recourir à des studios et laboratoires professionnels, et les créateurs ont de nombreuses possibilités de distribution et de diffusion de leurs créations sur des plateformes numériques. Pour autant, ces artistes et ces structures n'en demeurent pas moins fragiles, souvent éphémères, bien souvent soumis aux restrictions budgétaires de l'État. Il y a loin entre le fait de publier un contenu en ligne et celui d'attirer une audience suffisante. La surabondance de contenus sur internet réduit automatiquement la visibilité de chaque création noyée dans le flot des autres contenus. Se rendre visible nécessite beaucoup de chance ou une stratégie de promotion originale qui, du reste, cesse de l'être très rapidement en étant imitée par les autres artistes et producteurs, chacun étant ainsi replongé dans un océan insondable et inaudible. Ou bien passer entre les fourches caudines des majors au gré de leurs stratégies de renouvellement de leur offre.
Dans ces conditions, le numérique peut-il changer la donne ? Les TIC ont nettement modifié les modes d'analyse des industries culturelles. Si auparavant, leur fonctionnement pouvait être décrypté à travers la notion de chaîne de valeur, chaque segment apportant des ressources et de la valeur au suivant jusqu'au marché final, le numérique bouleverse les frontières et le partage des rôles. L'arrivée de nouveaux acteurs et services issus de l'informatique et de l'internet provoque des transformations importantes : possibilités accrues d'autoédition et d'autopublication pour les auteurs, élargissement des modes de valorisation, de mise en visibilité et de recommandation des biens culturels, agrégation des avis postés en ligne par les consommateurs, innovations par l'usage, multiplication des modèles d'affaires numériques et multiplication des revenus non directement connectés à la commercialisation des contenus etc. L'ensemble de ces acteurs, anciens et nouveaux, forme un écosystème où s'entrelacent des logiques marchandes et non marchandes. Comprendre le fonctionnement des industries culturelles et décrire les modèles et stratégies économiques des acteurs nécessitent de prendre en considération ces différents liens écosystémiques qui en résultent et qui rendent souvent difficiles les recommandations en matière de politiques culturelles. Le chapitre 15 aborde plus spécifiquement ces questions.
. En France, la mise au pluriel de la notion d'industrie culturelle est notamment due à Augustin Girard : Girard A., « Industries culturelles », Futuribles, dossier « Prospective du développement culturel », no 17, septembre 1978, p. 597-605. Sur les réactions critiques en rapport à cet article, voir Martin L., L'enjeu culturel. La réflexion internationale sur les politiques culturelles, Paris, La Documentation française, 2013, p. 55 sq.
. Mercillon H., Cinéma et Monopoles. Le cinéma aux États-Unis, Paris, Armand Colin, 1953 ; Reynaud-Cressent B., « La dynamique d'un oligopole avec frange : Le cas de la branche d'édition de livres en France », Revue d'économie industrielle, vol. 22, 4e trimestre 1982, p. 61-71.
. Attali J., Bruits. Essai sur l'économie politique de la musique, Paris, Fayard/PUF, 1977.
. Michalet C.-A., Le drôle de drame du cinéma mondial, Paris, La Découverte/Centre fédéral FEN, 1987.
. En particulier, Huet A., Ion J., Lefèbvre A., Miège B., Peron R., Capitalisme et industries culturelles, Grenoble, PUG, 1978.
. D'Angelo M., La renaissance du disque. Les mutations mondiales d'une industrie culturelle, Paris, La Documentation française, 1989.
. Flichy P., Les industries de l'imaginaire, Grenoble, PUG, 1980.
. Bonnell R., Le cinéma exploité, Paris, Le Seuil, 1978.
. Lange A., Stratégies de la musique, Liège, Mardaga, 1986.
. Ainsi pour Ruth Towse : « [t]he cultural industries have been defined as consisting of firms that mass-produce goods and services with sufficient artistic content to be considered creative and culturally significative » Towse R., « Creative industries », in Towse R. (dir.), A Handbook of Cultural Economics, 2e éd., Cheltenham, Edward Elgar, 2011, p. 125.
. Bouquillon P. (dir.), Creative economy. Creative Industries, Des notions à traduire, Saint-Denis, Presses universitaires de Vincennes, 2012.
. Sources : Siwek S. E., Copyright Industries in the U.S. Economy: The 2013 Report, International Intellectual Property Alliance (IIPA), novembre 2013, disponible sur www.iipa.com ; European Patent Office, Office for Harmonization in the Internal Market, Intellectual property rights intensive industries: contribution to economic performance and employment in the European Union. Industry-Level Analysis Report, septembre 2013.
. Computer & Communications Industry Association, Fair use in the U.S. economy: Economic contribution of industries relying on fair use, Rapport établi par Rogers T., Szamosszegi A., 2011.
. Ministère de la Culture et de la Communication / DEPS Le poids économique direct de la culture en 2013, synthèse établie par Y. Jauneau et X. Niel, collection Cultures – Chiffres, mai 2014 ; Ministère de la Culture et de la Communication / DEPS, Les industries culturelles en France et en Europe. Points de repère et de comparaison, synthèse établie par R. Laurent, collection Cultures – Chiffres, juillet 2014.
. Cela s'explique notamment en raison des catégorisations et nomenclatures utilisées par l'INSEE.
. Pour cela, nous nous basons en partie sur les données statistiques fournies par le SNE pour le livre et le SNEP pour la musique enregistrée (avec toutes les limites que cela comporte), mais également l'institut Gfk et le CNC pour le cinéma et la vidéo.
. Activités produisant et valorisant la création artistique sur la base de la reproduction technique de copies à partir d'originaux.
. Les beaux livres et livres pratiques (16,7 %), l'enseignement scolaire (12,6 %), les éditions scientifiques (12,4 %), les dictionnaires, encyclopédies, cartes et atlas (4,2 %), la religion et ésotérisme (1,4 %).
. On applique ici avec une certaine marge d'erreur les clefs de répartition du chiffre d'affaires des éditeurs (Rapport du SNE, 2014, p. 65) sur le total du marché du livre (donc incluant les chiffres d'affaires des intermédiaires commerciaux).
. Reynaud-Cressent B., op. cit.
. La grande distribution résout ainsi le problème d'une capacité disponible limitée devant contenir une offre variée par la même technique que les compagnies aériennes, celle du yield management, la variable d'ajustement étant non le prix, mais le temps.
. Farchy J., Rochelandet F., « De Polygram Filmed Entertainment à Vivendi Universal : l'impossible constitution d'une major européenne », Cinémaction, Hors-Série « Quelle diversité face à Hollywood ? », 2002, p. 96-103.
Chapitre 10
Les industries culturelles : comparaisons sectorielles
Le livre, le cinéma et la musique enregistrée partagent certaines caractéristiques qui expliquent une organisation économique similaire et les distinguent d'autres activités industrielles : bien durable et période courte de rentabilisation, demande imprévisible, différenciation très forte, concentration des ventes sur une proportion faible des titres édités et distribués etc.. Pour autant, ces industries culturelles présentent chacune certaines spécificités historiques ainsi qu'au niveau de leur organisation et de leur régulation économiques. Longtemps articulées (et protégés) autour d'un dominant design – le livre papier, le cinéma en salle, le disque (vinyle puis CD) –, les industries culturelles constituent depuis l'arrivée d'internet des écosystèmes en pleine mutation. La musique puis le cinéma ont été bousculés très tôt par le numérique. Pour le livre, le choc est plus récent : l'avènement de nouveaux intermédiaires et l'arrivée des terminaux numériques (liseuses, tablettes...) contestent non seulement un modèle économique érigé au xixe siècle, mais plus fondamentalement la pratique de la lecture.
Origines et trajectoires historiques
Pour saisir les transformations en cours, il convient en premier lieu de comprendre comment ont évolué ces industries et la manière dont elles sont actuellement structurées.
Émergence des dominant designs
Le livre est historiquement la première des industries culturelles. Cette activité fondée sur la production et la valorisation d'exemplaires reproductibles devint réellement une industrie fondée sur un marché de masse à partir du dernier quart du xixe siècle. Les industries du cinéma et du disque se sont développées quant à elles à partir des années 1910. Ces activités reposent sur deux logiques complémentaires : d'une part, une logique marchande fondée sur la production et la commercialisation des biens culturels sur une échelle de masse et faisant intervenir séquentiellement l'auteur, ses partenaires économiques proches (éditeurs, producteurs, artistes-interprètes, agents), les industries techniques (imprimerie, studios d'enregistrement etc.) et, en bout de cycle, les distributeurs de gros et de détail ; d'autre part, une logique non marchande de valorisation et de prescription des œuvres dans laquelle les interactions sociales jouent un rôle essentiel.
Au cours du xixe siècle, différents obstacles au développement de l'industrie du livre sont levés. La baisse de l'analphabétisme s'accompagne de celle de l'illettrisme. La diversification progressive de l'offre de publications écrites permet de toucher un public sans cesse plus large. Mais le développement d'un marché de masse de l'écrit, en particulier celui des journaux et des revues, est rendu possible par (en même temps qu'il les provoque) des innovations fondamentales dans le domaine de l'imprimerie et plus généralement la diffusion large de la machine à vapeur. Celle-ci permet notamment de créer des conditions favorables au niveau de la demande et de l'offre. Le développement du réseau ferroviaire en France, entre 1842 et 1880, réduit les coûts de distribution des livres sur le territoire, contribuant à la disparition des colporteurs via l'acheminement plus aisé et rapide des livres plus diversifiés et en plus grand nombre. Le train permet d'intégrer l'espace territorial en favorisant le développement d'un réseau maillé de librairies et offre ainsi aux auteurs et aux éditeurs un marché national.
Du côté de l'imprimerie, la vapeur permet d'augmenter le rendement des presses et de baisser le coût unitaire des livres. Ainsi la presse mécanique à cylindre est mise au point par Friedrich Koenig autour de 1809 pour les besoins du journal The Times en Angleterre et est associée à la machine à vapeur dès 1814. Ce sont surtout quatre autres innovations mises au point initialement pour les besoins des journaux et des revues qui permettent des gains de productivité significatifs dans le livre : la rotative, mise au point par Richard Hoe en 1843 et améliorée en 1866 par Hippolyte Auguste Marinoni ; puis, en 1865, le remplacement des feuilles par des bobines de papier conduisant à une réduction importante du nombre de salariés nécessaires ; à partir de 1880, la production du papier non plus à base de chiffon, onéreux et rare, mais de cellulose permettant une baisse significative des coûts ; et enfin, la composition des textes par la linotype, brevetée par Ottmar Mergenthaler en 1885, remplaçant l'ancien procédé typographique par les caractères mobiles dont la manipulation était particulièrement chronophage.
L'ensemble de ces innovations permet l'industrialisation massive du livre et de la presse au cours du xixe siècle, aboutissant à une baisse du prix de vente moyen des livres et des revues et amplifiant ainsi la consommation de masse, elle-même motivant ces innovations. Par ailleurs, la fidélisation du public via le roman-feuilleton et l'introduction de la publicité permettent une diminution significative du prix des revues et un accroissement du lectorat. Le marché des revues entre dans une phase de maturité dans les années 1870-80, permettant alors à l'industrie du livre de prospérer et de devenir la première industrie culturelle au cours du siècle suivant.
Depuis lors, le mode d'organisation du livre a peu varié. L'origine du livre en tant que bien culturel provient de l'articulation entre les besoins d'écriture et de lecture. L'initiative peut provenir d'un éditeur qui passe commande ou plus généralement dans le domaine de la littérature, de l'écrivain qui crée l'œuvre et à ce titre, est titulaire des droits d'auteur. L'auteur peut être pluriel lorsque le livre est coécrit ou fait intervenir un illustrateur ou un photographe. L'éditeur est celui qui transforme le manuscrit (le tapuscrit) en bien culturel, c'est-à-dire qu'il porte l'œuvre sur le marché et la transforme en marchandise culturelle en lui faisant rencontrer un lectorat. Pour cela, l'éditeur mobilise un réseau d'acteurs : l'imprimeur représente l'ensemble des métiers nécessaires à la réalisation technique de l'objet, soit le travail du maquettiste, de l'infographiste, du relieur etc. ; le diffuseur prend en charge les négociations et les conditions effectives de mise sur le marché du bien culturel, en particulier la prise de commande et la négociation commerciale, le paiement et les retours ; le distributeur gère les fonctions logistiques permettant l'acheminement des livres vers leurs publics (stockage, transport vers les points de vente, paiement des factures etc.) ; enfin, le commerce de détail (librairies, grande distribution, commerçants en ligne etc.) se charge de leur vente.
Le cinéma démarre officiellement avec la première projection publique et payante (1 franc) organisée le 28 décembre 1895 à Paris par les frères Auguste et Louis Lumière. Cela étant, la nouvelle technique qui accompagne le cinématographe est issue du travail de nombreux chercheurs (Étienne-Jules Marey) et d'entrepreneurs (Thomas Edison) ayant abouti à plusieurs innovations dont le fameux kinétoscope (qui permettait un visionnage individuel avec paiement à l'unité). En outre, il faut attendre les années 1910 pour que cette industrie et cet art du spectacle se stabilisent autour d'un dominant design, lequel associe le long-métrage de fiction basé encore majoritairement de nos jours sur les conventions du classicisme cinématographique et un lieu dédié, la salle de cinéma. Si l'art du cinéma doit énormément à la créativité d'un Georges Méliès, son industrialisation débute d'emblée à l'échelle mondiale avec des entrepreneurs comme Charles Pathé et se structure avec le studio system hollywoodien.
L'industrie cinématographique étasunienne se délocalise de New York vers la Californie au cours des années 1910 et se structure progressivement autour de quelques grands studios, ancêtres pour la plupart des majors du cinéma opérant encore actuellement. Le studio system correspond à une intégration verticale très poussée par les producteurs de films en amont vers la création (salarisation et contrats d'exclusivité avec les créateurs et les artistes, financement et organisation en interne des tournages etc.) et en aval (distribution et exploitation cinématographiques). Après la Seconde Guerre mondiale, les majors vont se concentrer essentiellement sur le secteur de la distribution qui constitue le segment clé des industries culturelles (cf. chapitre 9).
L'histoire de la musique enregistrée est celle d'un bien-système composé d'un appareil de lecture, d'un support d'enregistrement et de contenus musicaux. Cette histoire fait suite à une longue préhistoire... Des réseaux d'irrigation dans les rizières indonésiennes au paléophone du poète Charles Cros, on trouve en effet un certain nombre d'exemples de reproduction mécanique du son. Il faut néanmoins attendre 1877 pour qu'un ingénieur de Thomas Edison parvienne fortuitement à la fois à enregistrer et à reproduire mécaniquement du son, en l'occurrence celui de sa propre voix, en travaillant sur des répétiteurs télégraphiques. L'histoire de la musique enregistrée se déroule de ce fait en premier lieu aux États-Unis avec le dépôt d'un brevet sur le phonographe par Edison. Elle débute de manière chaotique en raison des erreurs d'anticipation de l'entrepreneur étasunien, mais aboutit à la création de deux compagnies concurrentes et à la première guerre de standards parmi celles qui jalonneront l'histoire du disque : le phonographe (cylindres) contre le gramophone (disques). On connaît l'issue de cette guerre de standards qui ouvrira une très longue période de domination du disque jusqu'à l'avènement du compact disc (CD).
L'industrie a enchaîné des cycles de croissance rapide et de déclin, ce qui n'a pas empêché la formation et le maintien d'oligopoles à travers le jeu des rachats et des fusions-acquisitions au gré des innovations (radiodiffusion, électronique grand public) et des stratégies multimédias ou parfois de conglomérat. Si le disque demeure jusque récemment le dominant design, structurant le modèle économique et les modes de consommation de la musique enregistrée, il connaît une série d'innovations : vinyle, format court et format long, CD, qui ont permis de relancer régulièrement ce marché oligopolistique. Un autre facteur, plus fondamental, est le rôle joué par les labels indépendants qui ont également permis de relancer le marché à partir de genres musicaux nouveaux : le rock'n'roll dans les années 50 ou la musique disco dans les années 70. La numérisation des supports a totalement bouleversé ce schéma depuis la fin des années 90, en particulier avec la courte apparition de la firme d'échange de fichiers Napster en 1999.
Les industries médiatiques : concurrents et partenaires
En tant que bien culturel, le livre a connu jusqu'à sa numérisation un seul débouché commercial, constitué par la vente de livres sur support papier. À cet égard, le roman-feuilleton publié dans la presse et les revues spécialisées apparaît davantage comme une stratégie similaire au versionnage. De leur côté, le disque et le cinéma en salle ont été confrontés à la concurrence d'autres supports de valorisation. À son apparition à la fin du xixe siècle, le disque se substitue progressivement à la vente de partitions musicales, d'instruments musicomécaniques et à la pratique de la musique à domicile. Très vite, la radio devient à son tour un concurrent majeur du disque. La radiodiffusion de musique (d'abord exécutée par des musiciens en direct, puis par diffusion d'enregistrements à partir des années vingt) a ainsi concurrencé indirectement le disque via l'équipement des ménages qui au départ, en raison du prix d'achat, doivent choisir entre un récepteur radio et un gramophone. Pour autant, les radiodiffuseurs ne compensent pas les auteurs-compositeurs et leurs éditeurs en mettant en avant leur rôle de promotion. Ce n'est que par la suite que ce rapport de concurrence va se transformer en complémentarité, au départ car les puissants réseaux de stations radiophoniques comme RCA vont racheter les producteurs de disques historiques, mais surtout parce que la radiodiffusion va devenir un vecteur de promotion essentiel de la musique enregistrée. Parallèlement, les radios sont contraintes dans les années trente à verser une compensation aux producteurs de disques qui pratiquent une forme de discrimination tarifaire via un prix d'achat des phonogrammes par les stations supérieur à leur prix grand public.
Le cinéma, après avoir concurrencé largement le théâtre de boulevard et bénéficié d'un quasi-monopole dans les loisirs populaires jusqu'aux années cinquante, est confronté à la concurrence de la télévision et plus généralement aux pratiques plus individualisées (comme la sortie du week-end en voiture). Il devra se différencier, notamment à travers une programmation plus diversifiée (les multisalles dans les années 70 et les multiplexes à partir des années 90), mais également les drive-in theaters aux États-Unis qui connaîtront un certain succès entre les années 50 et 60. Pour autant, si la télévision devient un concurrent du cinéma en salle en privant ces dernières de segments importants de leur demande (hausse de l'équipement télévisuel des ménages dès la fin des années 50, entrée massive de l'audiovisuel dans les foyers dans les années 80), elle devient également une partenaire en constituant un débouché important pour les producteurs de films (jusqu'à 1 500 films diffusés à la télévision au début des années 2000) et un financeur majeur de la production cinématographique (via les pré-achats de droits télévisuels et les coproductions). Les médias audiovisuels bénéficient également pleinement des salles de cinéma comme dispositifs de promotion et de valorisation des films. Ce dernier point explique la mise en place de la chronologie des médias aux États-Unis et en Europe où cette forme de régulation permet aux salles de bénéficier d'un monopole d'exploitation des films pendant une durée jugée suffisante pour rentabiliser leurs investissements et valoriser la sortie du film comme un événement culturel.
Structure de l'offre
La structure de l'offre renvoie à la question de la concentration des activités d'édition et de distribution des biens culturels reproductibles et de ses conséquences. Cet aspect est essentiel non seulement sur le terrain de la politique de la concurrence – le niveau des prix auxquels font face les consommateurs est-il suffisamment concurrentiel ? –, mais également en matière de diversité et de qualité de biens dont la valeur est fortement symbolique et peut façonner les modes de vie, le capital culturel et les comportements des individus. En particulier, nous le verrons plus précisément dans le chapitre 11, la concentration économique soulève des enjeux en matière de diversité culturelle.
D'une manière générale, on constate actuellement une évolution à la baisse des marchés de biens culturels. Les deux biens culturels les plus affectés sont la musique enregistrée et la vidéo. En dix ans, la taille des marchés de la musique et de la vidéo physique a diminué de plus de 50 % pour atteindre en 2013 un chiffre d'affaires de 603 millions d'euros pour la musique enregistrée et de 929 millions d'euros pour la vidéo physique. Quant au cinéma et au livre, leur évolution est plus nuancée. Le marché du livre représenterait en 2013 entre 3,5 (source : Xerfi) et 3,9 milliards d'euros (source : Gfk). La littérature et la bande dessinée représentent ensemble un tiers de ce marché. Il est en augmentation de 4,2 % entre 2003 et 2013, mais on constate une baisse depuis 2009, certes à un niveau moindre que le commerce de détail dans son ensemble, laissant supposer une tendance simplement conjoncturelle. Il est en baisse continuelle depuis 2009 en France.
Tableau 10.1 : Les marchés des industries culturelles en 2013 | Livres (littérature) | Musique | Cinéma en salles | Vidéo (films)
---|---|---|---|---
Chiffre d'affaires | 1,9 | 0,79 | 1,25 | 0,56
Pic (sur les 10 dernières années) | – | 1,95 en 2003 | 1,37 en 2011 | 1,18 en 2004
Source : calcul des auteurs (à partir de données fournies par les organismes suivants : SNE, SNEP, CNC, Gfk), milliards d'euros, hors numérique.
La baisse constatée sur les différents marchés de biens culturels reproductibles affecte-t-elle la production de nouvelles œuvres ? Dans le secteur du livre, ce n'est pas le cas : l'offre de titres a presque doublé avec près de 5 % de croissance moyenne annuelle entre 2000 et 2013, passant de 51 877 à 95 483 titres (dont 50 % de nouveautés en moyenne sur cette période). De même, dans le cinéma, en 2013, 270 films ont été produits ou coproduits en France contre 203 en 2004. Au niveau de la distribution, 654 films ont été distribués en première exclusivité en 2013 (sur les 6 824 films projetés...). Dans la musique, le nombre de nouvelles références produites (album et titres) a diminué, s'agissant de la production des majors (diminution de 7 % en moyenne annuelle entre 2002 et 2012 pour atteindre 975 albums), mais a globalement augmenté sur les cinq dernières années si l'on inclut tous les acteurs (majors et indépendants) en prenant en compte le dépôt légal de phonogrammes à la Bibliothèque nationale française (10 409 références en 2013 contre 9 831 en 2005).
Cependant, cette tendance à la prolifération de l'offre rencontre une limite. Comme dans les autres industries culturelles, les capacités de distribution des livres ne permettent pas d'écouler totalement une production culturelle sans cesse diversifiée et renouvelée. Le développement de la grande distribution a certes permis de faire reculer les limites physiques des surfaces d'exposition, mais au prix d'une limitation de l'accessibilité des consommateurs à l'ensemble des biens.
Des activités très concentrées
Faire le constat d'un niveau élevé de concentration dans les industries culturelles nécessite de préciser la nature de cette concentration et les « lieux » précis où elle se concrétise. La concentration renvoie à l'idée d'une réduction du nombre de concurrents sur un marché. L'objectif pour les firmes initiant (et survivant à) ce processus de sélection est d'obtenir un pouvoir de marché, c'est-à-dire une capacité à influencer à leur avantage les prix sur le marché. La concentration peut être évaluée selon différentes méthodes (toutes imparfaites) : le nombre de firmes sur un marché donné, les parts des concurrents les plus importants dans la production totale, leurs parts de marché en termes de chiffre d'affaires etc. La concentration a un effet négatif sur le bien-être social si les consommateurs subissent de manière durable une hausse des prix par rapport à une situation de concurrence plus intense sans que cela se traduise par une hausse de la qualité des produits.
La relation entre concentration et bien-être social est cependant particulièrement difficile à prouver sur un plan empirique pour différentes raisons : données statistiques insuffisantes, évolution rapide du marché en fonction de la demande et du rythme de l'innovation (apparition de nouveaux produits) etc. Par exemple, le marché de l'édition se présente traditionnellement comme un marché très concentré (en France, il est dominé par deux groupes : Hachette et Editis), mais soumis depuis quelques années à l'arrivée de nouveaux acteurs issus du numérique remettant en cause cette position dominante. De même, le marché de la musique distribuée en flux (streaming) est concentré autour d'une poignée d'acteurs (Spotify, Deezer...), mais leur offre est soit gratuite, soit a priori moins onéreuse que le marché de la vente à l'unité.
Au niveau de la création, les barrières à l'entrée sont relativement faibles et ont été même fortement réduites avec les outils numériques d'assistance à la création. Les auteurs, les artistes-interprètes et donc les œuvres sont nombreux et les taux d'entrée et de sortie sur ce segment sont particulièrement élevés. Le nombre de titres édités chaque année donne une indication du volume d'œuvres créées (dont une très faible proportion seulement est sélectionnée par les éditeurs) : 44 678 nouveautés dans l'industrie du livre en 2012 et plus de 62 000 nouveaux albums de musique mis sur le marché en 2010. Le cas du cinéma est plus spécifique : si 209 longs métrages d'initiative française ont été produits en 2013, 500 courts métrages ont obtenu un visa d'exploitation du CNC, ce qui représente une petite partie de la production autofinancée ou en provenance des écoles et des formations de cinéma et audiovisuel, mais un vivier de création essentiel pour le cinéma. Leur valorisation se fait essentiellement lors de festivals spécialisés sur ce format (environ 336 en France), ainsi que par leur télédiffusion sur certaines chaînes comme France Télévision, Arte, Ciné Cinéma, Canal+, 13e Rue et Orange. Internet constitue à la fois une source de financement (plateformes de crowdfunding) et de diffusion massive (YouTube, DailyMotion, Vimeo etc.) rendant toute évaluation particulièrement compliquée.
Parmi ces œuvres éditées, seule une poignée permet à leurs auteurs et artistes-interprètes d'accéder au rang de star en concentrant ainsi l'essentiel des moyens financiers destinés à la production et à la promotion des biens culturels et de la sorte, les revenus artistiques (cf. chapitre 14). De même, si l'édition de livres et la production de films et de disques sont le fait d'un grand nombre de structures, la concentration des revenus autour de quelques œuvres profite essentiellement aux acteurs verticalement intégrés dans la production et la distribution de gros. Cette inégalité dans la répartition des recettes commerciales constitue une donnée récurrente dans les industries culturelles et un indicateur important de leur degré d'industrialisation. Le tableau suivant permet de comparer la concentration à tous les stades intermédiaires des filières et au niveau de la demande.
Tableau 10.2 : La concentration des ventes dans les industries culturelles | LIVRE
(supports physiques) | MUSIQUE
(supports physiques) | CINÉMA
(entrées en salle) | VIDÉO
(films et hors films)
---|---|---|---|---
Distribution de gros | 2 majors
= 75 % | 3 majors
= 76 % | 10 distributeurs (7 %) = 72 % | Données non disponibles
Distribution de détail | 18 %
(Librairies) | <1 %
(Disquaires) | 15,6 %
(Petite exploitation)
(19,2 %= moyenne) | –
42 %
(Grandes surfaces)
dont GSS = 22 % | 87 %
(Grandes surfaces)
dont GSS = 56 % | 65,3 %
(Grande exploitation)
(multiplexes = 9,3 % des établissements = 60 % des entrées) | 85,4 %
(Grandes surfaces)
dont GSS = 47 %
Distribution de détail | 18 %
(internet) | 7,7 %
(internet) | – | 13,2 %
(internet)
14,5 %
(VPC) | – | – | –
Demande
(achats d'exemplaires originaux) | 1,4 % des titres
= 45% | 5,9 % des références = 90 %23 | 1,5 % des films projetés = 73 %
|
Sources : CNC, SNE, Gfk, SNEP, DEPS ; parts de marché ; hors fichiers numériques.
Dans le livre, si les coûts de production des biens culturels sont moindres par rapport au cinéma et à la musique enregistrée (il ne nécessite pas autant de travail d'équipe, comme lors d'un tournage, d'un travail en studio etc.), ils restent très élevés au niveau de la promotion et de la distribution. Au même titre que dans les deux autres industries culturelles, la stratégie des producteurs oscille entre la recherche de gains de productivité (par la vente de titres à très gros tirage) et la mutualisation des risques (par la distribution d'une variété importante de titres). La structure de marché inhérente se présente comme un oligopole dominé par des firmes verticalement intégrées : Hachette Distribution (Hachette Livres), Interforum (Editis), Sodis (Gallimard), Union Distribution (Flammarion), Volumen (La Martinière/Le Seuil), MDS (Média Participations) et Dilisco (Magnard-Vuibert). Les deux premiers, Hachette et Editis (ex-Groupe de la Cité), forment un duopole dont le chiffre d'affaires cumulé pourrait représenter près des deux tiers du marché du livre en 2012. À cet égard, un autre indice de concentration est le rythme de rachat d'entreprises par ces grands acteurs. Les deux grands groupes leaders détiendraient ainsi chacun près de 40 maisons d'édition.
Cette concentration se retrouve dans les deux autres industries culturelles. Pour le cinéma en salles, selon le CNC, en 2013, sur 149 distributeurs de films, les 10 premiers (soit 6,7 %) distribuent 29 % des films inédits, soit 72 % du chiffre d'affaires (encaissements distributeurs). Les 5 premiers représentent près de 50 % de ces recettes. La concentration s'étend au niveau des distributeurs vidéo selon le CNC, mais son évaluation est rendue difficile par le manque de données. De plus, les comparaisons avec le cinéma en salles sont difficiles en raison de la diversité des contenus distribués sous ce format (films, séries, spectacles vivants, contenus pédagogiques etc.). L'activité de la production apparaît en revanche nettement moins concentrée : sur 188 sociétés de production ayant produit 252 films, les 6 premières en ont produit 24 % alors que 152 autres n'en ont produit qu'un seul. Le calcul de l'indice de Herfindahl-Hirschman (mesurant la concentration du marché) confirme que ce segment est concurrentiel selon ce critère. Toutefois, le CNC ne fournit pas de données permettant d'approfondir davantage : combien perçoivent les acteurs intégrés et les indépendants les plus gros en termes d'activité par rapport aux autres producteurs ? De même, les données fournies par cet organisme ne permettent pas de mesurer l'effet « entonnoir », le filtre produit par la concentration de la distribution entre les mains de quelques distributeurs.
S'agissant de la musique enregistrée, les 5 majors du disque (Universal, EMI, BMG, Warner, Sony) représentaient au début des années 2000 environ 85 % des ventes de CD audio. Toutefois, les mutations profondes ayant affecté le marché des supports physiques ont abouti à des rachats entre majors (il n'y a désormais plus que 3 firmes transnationales : Sony-BMG, Universal-EMI, Warner), mais également une diminution de leur part de marché à 75 % des ventes en 2010. Une trentaine de labels indépendants de taille moyenne (producteurs et distributeurs) ont ainsi pu développer leurs activités de distribution, notamment à travers internet, après plusieurs décennies de domination des majors. Cette évolution s'explique également par les manques de moyens pour les opérations de marketing de masse autour de stars, se traduisant notamment par une certaine déconcentration des ventes par titres au niveau de la tête de distribution. Si le marché demeure néanmoins très concentré, cela n'empêche pas l'augmentation de l'offre de titres : en termes de références de CD, on est ainsi passé de 270 259 en 2003 à 315 013 en 2010. Cela pourrait traduire à première vue la diminution des coûts de production, mais également l'étalement du risque de la part des distributeurs face à une fragmentation de la demande. Toutefois, le nombre de nouvelles références (62 487 en 2010) a diminué de 15 % par rapport à 2003, traduisant probablement une moindre prise de risque. La frange concurrentielle représenterait alors plus de 3 000 producteurs et artistes autoproduits.
La concentration se retrouve également plus en aval des filières, au niveau de la distribution de détail. On la mesure à travers la répartition des ventes entre les canaux de distribution. La grande distribution domine largement, en particulier les grandes surfaces spécialisées (la Fnac, les « espaces culturels » des grands distributeurs et les multiplexes) avec une progression importante de la distribution par internet. L'étude de ce type de concentration est essentielle pour comprendre l'accès effectif des consommateurs à la diversité culturelle. Le tableau suivant montre que pour la littérature et la bande dessinée, celle-ci peut ainsi varier sensiblement d'un canal de distribution à l'autre. Les librairies et internet constituent des vecteurs de diversité culturelle effective plus importants que la grande distribution spécialisée ou alimentaire. Qui plus est, internet répond davantage à un effet de longue traîne (cf. chapitre 15) : les références en littérature vendues à moins de 1 000 exemplaires représentent 62 % des ventes par ce canal contre 22 % en librairies et 25 % dans les grandes surfaces spécialisées (GSS).
Tableau 10.3 : Proportion des références vendues par canal de distribution du livre | Littérature | Bande dessinée
---|---|---
Ventes par internet | 84 % | 83 %
Librairies | 62 % | 85 %
GSS | 56 % | 76 %
GDA | 24 % | 50 %
Source : Syndicat de la librairie française / Gfk, 2013.
S'agissant de la musique, la grande distribution spécialisée ou non génère 89,6 % des ventes d'exemplaires. Elle a longtemps été dominée par la Fnac. Cette grande surface spécialisée est toutefois concurrencée depuis quelques années par les espaces dédiés à la culture par la grande distribution alimentaire (GDA). Dans le cinéma, si l'on assimile la grande distribution aux multiplexes, elle représente 60 % des entrées en salles. Pour la vidéo (dont les fictions cinématographiques constituent 60 % des ventes), les achats de DVD et Blu-ray s'effectuent pour l'essentiel dans la grande distribution. Si l'on considère la vidéo, les grandes surfaces représentent l'essentiel de la distribution de détail. Cependant, les données ne permettent pas de distinguer finement entre les films et les autres catégories de contenus vidéo.
Enfin, la concentration peut se mesurer du côté de la demande finale, par rapport aux dépenses des consommateurs. Elle peut être évaluée par la distribution statistique des ventes de biens culturels par titres. Ainsi pour le livre, 1,4 % des titres disponibles (673 500 au total) représentent près de 45 % des ventes, soit un écart très fort par rapport à l'offre disponible. La production est de 572 millions d'exemplaires dont 62 % de nouveautés, pour un tirage moyen par titre de près de 6 000 exemplaires. Pour la littérature, 111 millions d'exemplaires (environ 20 % du total) sont tirés, dont 26 % sont vendus. Ce dernier chiffre masque probablement des disparités très importantes entre les titres, mais aucune donnée n'est fournie directement par le Syndicat national de l'édition (SNE).
Le tableau 10.2 montre une concentration importante pour les autres biens culturels. Pour le cinéma, cette concentration peut se mesurer par rapport aux films cumulant le plus d'entrées. Ainsi sur les 6 824 films projetés en salles, les 100 films les plus performants (soit 1,5 % du total) représentent 73 % des entrées. Pour les films en vidéo, les 100 premiers titres représentent plus de la moitié du chiffre d'affaires. Si l'on reporte ce nombre aux 76 690 références consommées (sous formats DVD et Blu-ray), ces 100 premiers titres représentent 0,1 % du total.
D'une manière générale, il faut être néanmoins prudent, car ces données ne concernent que la demande finale sur le marché. Or, les consommateurs de biens culturels s'approvisionnent auprès d'autres sources, par des logiques de prêts et de partage entre individus, ainsi que par le marché de l'occasion ou l'emprunt dans les médiathèques, autant de pratiques qui peuvent modifier substantiellement cette concentration et donc aboutir à des conclusions différentes en matière d'accès effectif à la diversité culturelle.
Le numérique atténue-t-il la concentration ?
En tant que telle, la distribution électronique des biens culturels sur supports physiques ou numérisés (VOD, livre et musique numériques) apparaît comme concentrée. Cependant, le marché des fichiers numériques s'inscrit encore dans une phase d'émergence et répond à des logiques économiques différentes de celles qui régissent une chaîne de valeur traditionnelle. Cela limite la portée d'une évaluation chiffrée à ce stade.
Ainsi, les ventes pour les livres numériques (distribués numériquement, donc à ne pas confondre avec les livres papiers vendus à distance par des plateformes internet comme Amazon) représentent en 2013 une part marginale du marché de détail du livre (3 %) ou du chiffre d'affaires des éditeurs (1,1 %), même si elles progressent rapidement. Il manque également des données plus précises sur la littérature et les circuits de distribution des romans, de la poésie, de la bande dessinée etc. La firme Amazon est indéniablement l'acteur dominant des ventes en ligne de livres en France et générerait près des deux tiers du chiffre d'affaires en France. Cette position dominante pourrait devenir un facteur clé de domination de l'écosystème si le livre numérique se substituait au livre papier (cf. chapitre 15). Cela est déjà le cas dans certains pays comme les États-Unis ou le Royaume Uni où la part du livre numérique représente respectivement 25 % et 15 % du marché.
S'agissant de la musique, les stratégies de ventes par internet ont commencé beaucoup plus tôt que celles pour le livre, dès le début des années 2000. Toutefois, le modèle économique de ce marché n'est pas encore stabilisé. En luttant contre le partage illégal sur internet, les majors ont pensé pouvoir prolonger en ligne leur modèle fondé sur la vente d'exemplaires, notamment grâce au service numérique d'Apple. En 2013, si les ventes payantes par téléchargements représentent encore 50 % du marché numérique en France, elles diminuent d'année en année au profit du streaming par abonnement (43 %). Dans les deux cas, en raison d'externalités de réseaux très fortes sur internet, la distribution numérique est concentrée autour de quelques acteurs. En France, Apple et son service iTunes représentent ainsi 80 % des ventes de fichiers musicaux (Amazon et Google se partageant 10 % du marché), tandis que Deezer capte 65 % des revenus du streaming contre 12,1 % pour Spotify et 9 % pour Google. Cependant, ce type de données est à interpréter avec précaution, car la distribution de biens culturels pour des acteurs comme Apple, Google et Amazon génère essentiellement des revenus indirects particulièrement élevés, mais plus difficiles à estimer (cf. chapitre 15).
Enfin, les effets des TIC sur le cinéma sont de deux ordres, impliquant la numérisation des salles et la vidéo à la demande. S'agissant de l'équipement numérique des salles, il a transformé ce secteur en permettant de poursuivre le mouvement de différenciation du grand écran par rapport à la télévision et aux autres écrans. Dans un premier temps, il a essentiellement bénéficié aux grands circuits de salles qui avaient les capacités financières pour financer leur transition vers la projection numérique. Même si la petite et moyenne exploitation a pu obtenir par la suite des facilités pour s'équiper en numérique, on peut penser que ce processus a accéléré la concentration de l'exploitation cinématographique.
Concernant la vidéo à la demande, le secteur du cinéma en France a été jusqu'à présent relativement préservé de la prédation des géants du numérique. Certes, des plateformes comme Megaupload ou les réseaux pair-à-pair avant elle ont pu accélérer le déclin du DVD. Mais les terminaux d'Apple, le service de partage de vidéo de Google et la place de marché d'Amazon n'ont pas provoqué de transformations majeures. Jusqu'en 2014 en France, les services de vidéo à la demande offrant des films de cinéma sont essentiellement dominés par des acteurs traditionnels issus de l'audiovisuel (Canal Plus/Canal Play, ArteVod, l'INA etc.) ou des télécoms (Orange, Free...). Pour autant, leur offre a rencontré jusqu'à présent un succès mitigé et entre 2009 et 2013, la part de marché de la vidéo à la demande pour les films de cinéma est seulement passée de 2 % (61,4 millions d'euros) à 6 % (177,2). Pour le CNC, la consommation d'œuvres cinématographiques reste peu concentrée en matière de vidéo à la demande : les 30 premiers films cumulent 26,5 % du volume total des transactions en 2013 contre 25,5 en 2012. L'arrivée d'acteurs mondiaux comme Netflix et HBO pourrait transformer ce paysage. Aux États-Unis, la situation est quelque peu différente avec la forte présence d'acteurs issus du numérique, tels qu'Apple sur le marché du téléchargement payant de films et Netflix sur le visionnage à la demande, ce dernier étant concurrencé par Amazon.com (Amazon Prime). La vidéo en ligne représenterait un marché de plus de 5 milliards de dollars aux États-Unis en 2012 où chaque habitant consacre une dépense trois fois plus élevée qu'en France.
La consommation des biens culturels reproductibles
L'analyse de la demande apparaît comme un facteur clé pour comprendre l'évolution des marchés de biens culturels ainsi que la concentration des ventes de livres, de films et de musique. La production des industries culturelles est destinée à des marchés de masse et explique donc leur importance dans les pratiques culturelles des individus par rapport à d'autres formes de consommation artistique comme la fréquentation des musées ou la sortie au théâtre, pour ne citer que les plus populaires.
Tableau 10.4 : Quelques pratiques culturelles des Français (âgés de plus de 15 ans), en % | 1973 | 2008
---|---|---
Regarder la TV | 88 | 98
Écouter la radio | 89 | 87
Écouter de la musique (hors radio) | 66 | 81
Lire au moins un livre | 70 | 70
Aller au cinéma | 52 | 57
Aller au théâtre | 12 | 19
Visiter un musée ou une exposition | 33 | 37
Source : Donnat, 2009, pratiques au cours des 12 derniers mois.
Si la lecture de livres est en recul (53 % des Français liraient peu, voire aucun livre, tandis que la part des lecteurs occasionnels augmenterait au détriment des gros lecteurs), la culture de l'écran et l'écoute de musique progressent, notamment avec l'usage croissant d'internet et des terminaux mobiles. Il convient malgré tout de se méfier de ce type de comparaisons et d'interprétations très générales. S'agissant de la lecture, celle-ci peut porter sur de la littérature (classique, romans, poésie), mais également sur des livres utilitaires comme les ouvrages pratiques, scientifiques, encyclopédiques ou encore les livres d'art et d'histoire visant à la formation individuelle, à la connaissance, à des pratiques non artistiques (cuisiner, bricoler, jardiner, voyager etc.). On constate ainsi que la lecture des ouvrages relevant de cette dernière catégorie est la plus pratiquée en 2008 : 40 % des individus lisent le plus souvent des livres pratiques contre 39 % qui optent davantage pour les romans policiers et d'espionnage, 35 % pour les autres catégories de romans, 26 % pour la bande dessinée, 18 % pour la littérature classique et 9 % pour la poésie. À l'inverse, regarder la télévision ou écouter la radio peut correspondre à de la consommation de biens culturels, même si la télédiffusion de films et l'exposition médiatique de la musique tendent à se réduire ces dernières années.
La consommation des biens culturels reproductibles peut se faire par différents moyens, tels que l'achat d'exemplaires (livres papier, fichiers numériques etc.) ou d'un droit d'entrée pour le cinéma, l'abonnement à des services collectifs qui peuvent être publics et gratuits avec les bibliothèques municipales ou privés et payants à l'instar des services de streaming offerts par Deezer ou Netflix, le partage d'exemplaires ou de copies avec d'autres individus qui peuvent être des proches (prêts entre amis) ou des inconnus (réseaux pair-à-pair, déchargement et téléchargement sur des plateformes d'hébergement de contenus numériques, marché de l'occasion). De même, sur le marché des livres neufs, 426 millions d'exemplaires ont été vendus en 2013 contre 441 en 2012, 460 en 2005 et 354 en 2000. Ces données ne sont néanmoins que des indications imparfaites de la consommation de livres. Pour évaluer celle-ci, il conviendrait d'incorporer les emprunts en bibliothèque (277 millions en 2012 contre 165 en 2004), ainsi que le marché de l'occasion et le partage entre particuliers (à notre connaissance, aucune donnée n'existe pour les évaluer).
On le constate donc : le « marché » des biens culturels reproductibles est de fait sous-évalué lorsqu'il se résume à l'offre et à la demande d'exemplaires ou de droits d'accès payants. Qui plus est, pour un même bien culturel, différents modes d'approvisionnement coexistent et peuvent être tantôt concurrents (la vidéo à la demande et la location et la vente de DVD par exemple), tantôt complémentaires. Ainsi, les abonnés à Canal Plus ont été également des usagers des salles obscures et la consommation de films sur internet et la fréquentation des salles sont des pratiques cumulatives : 82,1 % des consommateurs de services payants de vidéo à la demande vont au moins une fois par an au cinéma.
La consommation de biens culturels donne lieu à différentes formes d'interactions sociales. Leur nature de biens d'expérience nécessite ainsi des échanges d'informations entre les individus confrontés à une incertitude sur leur qualité (cf. chapitre 1). Ils permettent également de tisser ou de consolider des liens sociaux, voire pour un individu de se situer par rapport à son groupe social d'appartenance. Les biens culturels reproductibles ont donné quant à eux naissance à d'autres formes de partage portant non plus uniquement sur des informations, de la connaissance sur les œuvres, mais plus directement sur les exemplaires eux-mêmes. Historiquement, le prêt de livres, puis plus proche de nous, la duplication d'albums et de titres de musique (la reproduction du contenu des 33 et 45 tours sur audiocassette) et de cassettes de films (produites légalement à partir d'enregistrement de films à la télévision ou illégalement par magnétoscopes interconnectés). Le numérique a démultiplié ces pratiques de partage, notamment en facilitant la connexion entre anonymes, en ne dégradant pas (ou moins) la qualité technique des copies obtenues et surtout en raison de la non-rivalité des copies numériques (le copieur ne se prive pas de son fichier en le partageant).
Ces multiples formes d'interactions sociales ont des conséquences très variées. Elles facilitent la sociabilité et la formation d'une culture commune. Par exemple, Burgos et al. soulignent, à travers leur étude sur la lecture et la circulation privée et informelle des livres, l'importance du prêt et de l'emprunt entre proches analysés comme échanges d'expériences s'appuyant sur des rituels de restitution. On retrouve également cette pratique d'échange à travers l'attrait du livre papier par rapport au livre numérique. Ainsi, 78 % des répondants à une enquête sur les usages de ce format déclarent préférer le livre papier pour « offrir ou partager un livre ». Cette raison devance celle du « plaisir et confort de lecture » associé au livre papier.
De même, le partage de cassettes VHS a alimenté une « culture cinématographique » très forte dans les années 80 et 90. Ces pratiques de partage ont certainement accéléré la fragmentation du marché de la musique en de multiples niches de marché, favorisant au passage le retour des labels indépendants. Elles seraient responsables de la baisse des ventes de CD de musique. On peut également soutenir la causalité inverse : le succès du partage illégal viendrait de défaillances de l'offre légale et d'un encastrement social très fort de ces usages numériques par rapport à des pratiques de partage plus anciennes. Plus fondamentalement, ces interactions favoriseraient la concentration de la demande sur les marchés de biens culturels. Le chapitre 14 traite plus spécifiquement de cet aspect.
Une autre manière d'évaluer la pratique de la lecture est le recours à l'enquête qui permet d'analyser l'évolution des goûts et des préférences des individus. Ces travaux relèvent généralement de la sociologie quantitative. Si la pratique de la lecture se développe avec les livres pratiques, la presse magasine, les blogs et autres forums, un déclin semble marquer les pratiques de lecture de romans et autres œuvres littéraires. Entre 2005 et 2014, on assiste à une baisse de 10 points des lecteurs de plus de 15 ans déclarant avoir lu au moins un livre au cours des 12 derniers mois (79 % à 69 %). Loin d'être un phénomène générationnel (les jeunes liraient moins qu'avant), cette baisse se vérifie dans presque toutes les tranches d'âge, notamment pour les lecteurs assidus (au moins 20 livres au cours des 12 derniers mois). En revanche, une constante marque ces pratiques : les non-lecteurs représentent 30 % des individus en France. Toutefois, il faut rester prudent avec les données d'enquête portant sur des pratiques de lecture se référant à un bien dont les caractéristiques évoluent rapidement actuellement : au livre papier s'ajoutent désormais le livre numérique, les blogs de BD en ligne etc. qui, s'ils ne renvoient pas à la « culture légitime », n'en demeurent pas moins culturels...
La régulation des industries culturelles
Les biens culturels ne sont pas des marchandises comme les autres en raison de leur valeur symbolique forte et de leur influence sur les représentations, les modes de vie, croyances, attitudes des individus au sein d'un groupe social ou d'un pays donnés. Les industries culturelles, tout comme les industries médiatiques (presse, télévision, internet...), ont une portée d'autant plus importante qu'elles visent des marchés grand public. La régulation uniquement par le marché et le régime du droit commun pourrait alors avoir des effets préjudiciables en matière de diversité culturelle (ou de pluralisme pour les médias) (cf. chapitre 11). En particulier, en raison de rendements croissants d'échelle aussi bien au niveau de la distribution que de la promotion des biens culturels, le libre fonctionnement du marché ne conduirait pas à une diversité suffisante au niveau de l'exposition de la production des œuvres.
Pour assurer cette diversité, les actions de l'État s'appliquent aussi bien en amont qu'en aval des filières. En amont, les aides financières (soutiens à la création, à la publication, à la distribution...) s'adressent notamment aux œuvres jugées difficiles, donc à faible potentiel commercial. En aval, l'État finance des infrastructures comme les bibliothèques, les cinémathèques, stimule la consommation des biens culturels par une TVA réduite et soutient la valorisation des œuvres françaises à l'étranger via notamment l'organisation et le financement de salons, de festivals etc. L'ensemble de ces aides et actions publiques se justifie sur un plan économique par les externalités positives liées à la consommation culturelle, à la présence de la culture française à l'étranger etc., mais également par le fait de considérer les œuvres et les modes de valorisation soutenus comme des biens sous tutelle : le marché serait défaillant et les choix de l'État, supposé plus clairvoyant, viendraient pallier cette situation. Pour autant, si certaines de ces mesures sont ciblées (aides aux œuvres ou à des lieux spécifiques de valorisation), l'objectif de diversité culturelle est plus difficile à justifier pour des interventions comme la TVA réduite ou la loi sur le prix unique s'appliquant uniformément, que l'œuvre soit de la musique contemporaine, la biographie d'un joueur de football ou un livre de cuisine.
Le droit d'auteur,
une régulation interprofessionnelle ou sociale ?
Les industries culturelles bénéficient d'une protection juridique commune : le droit d'auteur. L'évolution historique de cette forme de propriété intellectuelle et de ses moyens de mise en œuvre (société de gestion collective des droits d'auteur et voisins notamment) est notamment très liée à celle des industries culturelles et de la massification de leurs marchés au cours du xixe et xxe siècles. Les règles juridiques du droit d'auteur génèrent un régime des droits exclusifs sur la base desquels les auteurs et leurs partenaires économiques peuvent se rémunérer en contrepartie des exploitations qui sont faites de leurs œuvres. Le droit d'auteur constitue un moyen de protection des investissements particulièrement élevés dans les industries culturelles, en encadrant les relations contractuelles entre les producteurs de biens culturels et leurs exploitants, à tel point que ces dernières sont parfois regroupées sous le terme de copyright industries (cf. chapitres 11 et 12).
Cette protection légale est devenue au cours du temps une arme concurrentielle pour les majors à travers la constitution de catalogues de droits d'auteur. Plus récemment, avec le développement des usages numériques, le droit d'auteur a tendance à se transformer en une forme de contrôle non plus seulement des exploitations commerciales des œuvres, mais également des utilisations par les individus. Le déploiement de mesures techniques de protection, d'architectures informatiques privatives, mais également le recours à des licences d'utilisation permettent de restreindre l'accès et de définir des droits d'utilisation des contenus numériques créant potentiellement un déséquilibre en faveur de la protection des intérêts économiques de producteurs de biens culturels au détriment des consommateurs. En fonction des conditions d'utilisation, les consommateurs acquièrent des droits de lecture, parfois limités dans le temps (la consommation de contenus vidéo à la demande dure le temps de la location ou de l'abonnement) et ne peuvent ainsi ni prêter, ni revendre les fichiers qu'ils obtiennent. Le cas d'Amazon est éloquent. S'étant rendu compte en 2009 que l'un de ses fournisseurs ne disposait pas des droits d'exploitation pour le roman 1984 d'Orwel, cette société a procédé à l'effacement à distance des fichiers numériques correspondants sur les liseuses de ses clients lorsque ces derniers ont actualisé leur système d'exploitation. La numérisation des supports transforme ainsi fondamentalement la portée du droit d'auteur.
Des interventions asymétriques
En dehors du droit d'auteur, on constate un contraste important pour ce qui concerne les autres formes de régulation économique des industries culturelles. Si le cinéma et le livre font l'objet de mesures relativement structurantes et protectrices, ce n'est pas le cas de la musique enregistrée.
En matière fiscale, le livre et le cinéma bénéficient de taux de TVA réduits, alors que la musique et la vidéo sur support physique ou numérique sont assujetties à un taux normal de 20 %. De même, au niveau des aides à la création et à l'édition, le cinéma et la vidéo ont bénéficié en 2012 de 292,8 millions de soutiens (à travers le système du compte de soutien géré par le Centre National du Cinéma et de l'Image animée), le livre a reçu 29,3 millions d'euros dont 6 millions d'euros sous forme de subventions à l'édition versées par le Centre National du Livre, tandis que la musique enregistrée ne bénéficie d'aides récurrentes qu'à travers le Fonds pour la Création musicale (dont les aides s'élèvent à 4,2 millions d'euros en 2012 dont 1,14 pour la filière phonographique). Qui plus est, cet organisme est financé essentiellement par les sociétés civiles d'auteur, d'artistes-interprètes et de producteurs dans le domaine de la musique et seulement à hauteur de 5,2 % par le ministère de la Culture.
Plus fondamentalement, à la différence du disque, les industries du cinéma et du livre bénéficient chacune de mesures particulièrement protectrices ayant des effets structurants sur leurs modes d'organisation : pour la première, il s'agit du compte de soutien cinématographique et de la chronologie des médias et pour la seconde, de la loi sur le prix unique du livre. Ces mesures sont historiquement des leviers essentiels de l'exception culturelle française visant à protéger la production de films et de livres.
S'agissant du compte de soutien, cet instrument organise une forme de redevance prélevée sur les recettes du cinéma en salle (taxe spéciale additionnelle) et sur le chiffre d'affaires des autres exploitants d'œuvres cinématographiques et audiovisuelles (chaînes de télévision, éditeurs et distributeurs de services de télévision, édition vidéo etc.). Le produit de ces redevances alimente le compte de soutien géré par le CNC qui répartit ces sommes sous forme d'aides à l'écriture, à la production, à la distribution et à l'exploitation en salles. Ce système mis en place au lendemain de la Seconde Guerre mondiale a permis de préserver la filière cinématographique en France. Il a fait l'objet de critiques portant sur sa nature protectionniste pour les acteurs internationaux et surtout sur l'éparpillement des aides sur de nombreuses productions. Ce « saupoudrage » est jugé inefficace à la fois par les producteurs dominants, car préjudiciable à la compétitivité du cinéma français, et par les réalisateurs de films à moyen budget (« films du milieu ») qui rencontrent des difficultés de financement.
La chronologie des médias fait également l'objet de débats importants. Son objectif est de protéger l'exploitation en salle, mais également d'optimiser la rentabilisation des films en évitant la cannibalisation entre supports, et de protéger les intérêts des chaînes de télévision qui bénéficient de délais plus courts que leurs concurrents lorsqu'elles sont coproducteurs des films. En Europe, cette régulation encadrée par une directive européenne de 1997 est définie sur la base d'accords interprofessionnels. Elle définit l'ordre et les délais à partir desquels les différents distributeurs et diffuseurs de films peuvent exploiter les films. Dès lors qu'un film est distribué en premier lieu en salles, ses exploitants bénéficient d'une première fenêtre exclusive pendant 4 mois ; suivent ensuite les éditeurs de vidéo physique et les distributeurs de vidéo à l'unité, puis les chaînes de télévision payante etc. Dans cette distribution des rôles, les opérateurs de vidéo à la demande par abonnement (SVOD) doivent attendre 3 ans.
Cette chronologie est très discutée actuellement. D'une part, nombre de films ne connaissant pas de succès commercial en salles ou dont l'essentiel des recettes sur ce mode d'exploitation est dégagé en moins d'un mois, pourraient être exploités plus rapidement par le biais des autres modes d'exploitation. D'autre part, les films qui connaissent un certain succès en salles ou bénéficient de dépenses promotionnelles massives font également l'objet de téléchargements illégaux sur internet. Des services commerciaux comme la SVOD pourraient a priori contrecarrer ces usages s'ils étaient en mesure de distribuer ce type de films beaucoup plus tôt dans la chronologie des médias. Toutefois, cette « remontée » risquerait à son tour de menacer les intérêts des principaux financeurs du cinéma en France – la SVOD pouvant menacer les chaînes payantes – sans réelle garantie en matière de lutte contre le téléchargement illégal...
La loi sur le prix unique (« loi Lang ») constitue la régulation structurante du secteur du livre. Mise en place le 10 août 1980, elle encadre légalement la fixation des prix de vente au public de livres neufs dont les seuls éditeurs et importateurs ont le contrôle. Ce prix porté à la connaissance du public s'impose à tous les détaillants (librairies, grande surface spécialisée, grande distribution etc.) qui, sur cette base, ne peuvent accorder de rabais supérieurs à 5 % s'agissant des particuliers. Cette régulation vise à soutenir la diversité par la préservation d'un réseau dense de distribution de détail. Il s'agit d'une réglementation directe contraignant la fixation des prix par le commerce de détail. L'objectif est d'obtenir un prix quasi identique par livre publié sur le territoire national et donc d'empêcher les acteurs de la grande distribution d'exercer une concurrence déloyale à l'encontre des librairies qui ne pourraient riposter en offrant le même niveau de remise et verraient leur part de marché réduite pour la vente des best-sellers, source essentielle de rentabilité et de financement de la diversité de leur offre comprenant une proportion plus élevée de livres plus difficiles et dont la valorisation est plus lente. Cette régulation illustre très bien le principe de l'exception culturelle : les biens culturels étant des marchandises singulières, bénéficient de règles dérogatoires du régime de libre concurrence par la restriction des la libre fixation des prix par les firmes.
Si les aides à la lecture (notamment l'entretien de bibliothèques) et celles aux particularismes locaux (langues nationales, cultures régionales) ne font guère l'objet de critiques par les économistes, les arguments sont beaucoup plus vifs à l'encontre de la loi sur le prix unique. Pour certains auteurs, le livre est un bien privé associé à des barrières à l'entrée relativement faibles et un niveau important d'information des lecteurs (prix littéraire, critiques, salons etc.), donnant lieu à une concurrence suffisante pour assurer un niveau de production optimal. Par conséquent, la loi sur le prix unique fausserait le jeu de la concurrence. Une telle politique aboutirait d'un côté, au maintien de prix et de marges élevés au détriment de la circulation la plus large d'exemplaires publiés auprès du lectorat. À terme, cette politique empêcherait les structures de petite et moyenne taille et disposant d'une clientèle fidèle de fixer des prix plus élevés afin de financer des services plus innovants et donc de se différencier des grandes surfaces. Mais d'un autre côté, elle permettrait le financement d'un nombre plus important de titres et d'une diversité plus forte des titres distribués à travers des circuits de vente plus hétérogènes et pour certains, indépendants au niveau de leur fonction de recommandation.
Sur un plan empirique, il faut toutefois noter que la libéralisation du marché au Royaume-Uni a abouti à une réduction du nombre de librairies et une augmentation du prix des livres. Qui plus est, l'information sur le marché du livre est-elle si transparente et les mécanismes de prescription si indépendants pour assurer une valorisation suffisante des œuvres littéraires jugées difficiles en cas de libéralisation des prix ? De ce point de vue, entretenir par la réglementation un réseau maillé et hétérogène de librairies semble le meilleur garant d'un certain niveau de diversité culturelle.
. Cf. Caves R. E., Creative industries: contracts between art and commerce, Harvard University Press, 2000 ; Tremblay G., « Industries culturelles, économie créative et société de l'information », Global Media Journal, vol. 1, no 1, 2008, p. 65-88.
. Potts J., Cunningham S., Hartley J., Ormerod P., « Social network markets: a new definition of the creative industries », Journal of Cultural Economics, vol. 32, 2008, p. 167-185.
. Ces derniers disparaissent également en raison de la volonté du pouvoir à partir de 1852 de contrôler la circulation des écrits, notamment les livres censurés et les écrits politiques, soumis à l'apposition d'un timbre.
. Initialement, l'invention majeure de Johannes Gutenberg repose sur l'utilisation conjointe de la presse à bras, des caractères mobiles en plomb et d'une encre grasse. La presse à bras est alors inspirée du pressoir utilisé par les vignerons pour extraire le jus des grappes de raisin.
. Pour une description de chacune d'elle et des améliorations obtenues au cours du temps, voir la classique Histoire de l'édition française de R. Chartier et H. J. Martin.
. Pour plus de détails sur le fonctionnement de l'industrie du livre, voir Rouet F., 2013, op. cit.
. Burch N., La Lucarne de l'infini. Naissance du langage cinématographique, Paris, Nathan, 1991.
. Augros J., L'Argent d'Hollywood, Paris, L'Harmattan, 1996.
. Edison cherche en premier lieu à lancer sur le marché un ancêtre du dictaphone (il ne supporte pas la présence du petit personnel...) puis les poupées parlantes. Devant l'absence de succès, il se résout sur les conseils de ses collaborateurs à commercialiser le phonographe.
. Le versionnage (terme plus courant en anglais : versioning) est la gestion des différentes versions d'un même bien informationnel. Ce principe est d'un usage courant dans la gestion des logiciels informatiques.
. Pour approfondir, Farchy J., Rochelandet F., « La mise en place du droit d'auteur dans les industries du disque et du cinéma en France », in Marseille J., Eveno P. (dir.), Histoire des industries culturelles en France, xix e-xx e siècles, ADHE, 2002, p. 157-182.
. Farchy J., Le cinéma déchaîné. Mutation d'une industrie, Paris, Presses du CNRS, 1992.
. Creton L., Économie du cinéma. Perspectives stratégiques, (Nathan, 1994), Armand Colin, 2014.
. Source : CNC, Le marché de la vidéo, Les dossiers du CNC no 329, mars 2014. Parmi les raisons évoquées pour expliquer cette baisse : le téléchargement illégal, la disparition de certains espaces de vente, les évolutions dans les habitudes de consommation (TV de rattrapage, vidéo à la demande).
. Parmi lesquels 209 films d'initiative française dont le devis moyen de 4,8 millions d'euros. On note une certaine vitalité du cinéma avec 68 premiers films (32,5 %) et surtout 39 seconds films (18,7 %).
. La part des albums produits par les majors dans le total des références a été divisée par 2 entre 2005 et 2012, passant de 14 % à 7 %.
. Burke A., « Music business », in Towse R. (dir.), A Handbook of Cultural Economics, Cheltenham, Edward Elgar, 2011, p. 297-303.
. Source : CNC – DCTP.
. Source : Agence du Court Métrage.
. 2013 ; source : TNS-Sofres, Ministère de la Culture et de la Communication, Baromètre multi-clients – Achats de livres TNS-Sofres, panel de 3 000 personnes de 15 ans et plus). Néanmoins, les données fournies par Gfk et le Syndicat des librairies françaises sont très différentes, puisque les librairies représenteraient 38,8 % du volume des ventes pour 43,7 % du chiffre d'affaires (Le marché du livre en France, SLF/Gfk, mai 2013).
. 2013 ; source : CNC, Bilan du CNC 2013, 2014.
. 2011 ; source : Gfk/CNC/DEPS, 2012.
. En 2008.
. Le marché du livre (somme des ventes) en France représente 4,13 milliards d'euros en 2012. 36 % du chiffre d'affaires du groupe Hachette (environ 2 milliards d'euros en 2012) est réalisé en France. Quant au chiffre d'affaires du groupe Editis (filiale du groupe espagnol Planeta), il représente 705 millions d'euros. Mais aucune donnée n'est disponible sur sa répartition entre les marchés nationaux.
. Il serait ainsi intéressant de connaître le taux de distribution des films d'initiative française et leur temps moyen d'exploitation en salles.
. Observatoire de la musique / Gfk (2011), L'évolution des marchés de la musique en France 2003-2010, rapport établi par André Nicolas, Cité de la musique.
. Curien N., Moreau F., L'industrie du disque, Paris, La Découverte, coll. « Repères », 2006.
. Le top 100 en termes de volume de ventes de CD a ainsi été divisé par 2 entre 2003 et 2010 (passant de 24 à 12 millions). Mais, rapporté à l'ensemble des ventes en volume, sa part a cependant augmenté de 18 % à 21 %.
. Il serait intéressant de pouvoir distinguer les multiplexes des grands circuits de salles des multiplexes indépendants.
. Source : SLF/Gfk, 2013.
. Source : Gfk.
. Il faut faire attention aux chiffres. En évaluant la distribution sur la base des 654 films distribués en première exclusivité, les mêmes 100 films les plus performants représentent 15 % de l'offre pour 73 % de part de marché.
. Source : CNC, 2014.
. Source : Gfk, 2013.
. Source : SNEP, 2014.
. Source : Bilan du CNC, 2014. Nous avons évalué à partir des statistiques fournies par le CNC le marché des films de cinéma en agrégeant la distribution (salles, ventes de DVD et vidéo à la demande) et la diffusion : achats et préachats de droits télévisuels ; hors franchise et parts des recettes publicitaires servant aux chaînes à acheter des films.
. Cette progression s'est accompagnée de la diminution forte des ventes de DVD (près d'un tiers entre 2007 et 2013) et d'une relative stabilité des recettes en salles sur un marché du film de cinéma qui a augmenté de 1,3 % sur cette période (autour de 3 milliards d'euros en moyenne). Ces évolutions peuvent s'expliquer par le téléchargement illégal et des offres insuffisantes (catalogues peu diversifiés, services non attrayants).
. Bilan du CNC, 2014. Toutefois, pour étayer davantage ce constat, il serait intéressant de connaître le nombre total des œuvres distribuées numériquement, ainsi que la part de marché de chacun des acteurs.
. Source : Médiamerica.
. Donnat O., 2009, « Les pratiques culturelles des Français à l'ère numérique – Éléments de synthèse 1997-2008 », série Culture & Études, Ministère de la Culture et de la Communication, 12 p.
. Ibid.
. Source : www.pratiquesculturelles.culture.gouv.fr. Des comparaisons intertemporelles auraient été souhaitables pour évaluer l'évolution de la lecture de livres par catégorie. Or, la construction des questionnaires du ministère de la Culture d'une enquête à l'autre ne permet pas a priori de procéder à des analyses fiables.
. Source : SNE, 2014. On constate donc une baisse conjoncturelle sur la période récente.
. Source : MCC-SLL/Observatoire de la lecture publique.
. Source : CNC, 2014
. Di Maggio P., « Classification in Arts », American Sociological Review, vol. 52, no 4, 1987, p. 440-455.
. Burgos M., Evans C., Buch E., Sociabilité du livre et communautés de lecteurs. Trois études sur la sociabilité du livre, Paris, BPI Études et Recherche, 1996.
. Source : SOFIA/SNE/SGDL, « Baromètre des usages du livre numérique », enquête menée par OpinionWay, mars 2014.
. Guy J. M., La culture cinématographique des Français, Paris, La Documentation française, 2000.
. Liebowitz S. J., « File Sharing: Creative Destruction or Just Plain Destruction? », Journal of Law and Economics, vol. 49, no 1, 2006, p. 1-28.
. Nandi T. K., Rochelandet F., « The incentives for contributing digital contents over P2P networks: An empirical investigation », Review of Economic Research on Copyright Issues, vol. 5, no 2, 2008, p. 19-36.
. Source : DEPS/Ministère de la Culture et de la Communication.
. Farchy J., Rochelandet F., 2002, op. cit.
. Cohen J. E., « Copyright and the Perfect Curve », Vanderbilt Law Review, vol. 53, no 6, 2000, p. 1799-1819 ; Lessig L., Code, and Other Laws of Cyberspace, Basic Books, 1999.
. D'autres organismes comme la MFA accordent des aides à la musique sur des niches particulières (musique classique contemporaine, jazz de création, musiques improvisées...).
. Pour plus de détails, voir Bonnell R., op. cit. et Bilan du CNC, 2014, op. cit.
. Auparavant, leurs pratiques étaient « autorégulées » par des accords interprofessionnels sous la forme de « prix conseillés ».
. Canoy M., Van Ours J. C., Van der Ploeg F., « The Economics Of Books », in Ginsburg V. A. et Throsby D. (dir.), Handbook of the Economics of Art and Culture, vol. 1, Elsevier B.V., 2006.
. À noter que le prix unique représente un faible coût pour le contribuable par rapport à une solution alternative qui consisterait à subventionner directement les petites structures de distribution.
. Rouet F., Le livre. Une filière en danger ?, Paris, La Documentation française, 2013 (4e éd.).
. Pour ces deux domaines, voir Floch P., Sonnac N., Économie de la presse, Paris, La Découverte, coll. « Repères », 2005 et Bonnell R., La Vingt-cinquième image. Une économie de l'audiovisuel, Paris, Gallimard, 2006 (4e éd.).
Troisième Partie
Enjeux transversaux
Nous avons tenté, dans la première partie, d'évoquer les trois logiques sous-jacentes animant le monde de l'économie et leur influence, pour ce qui nous concerne, dans le secteur des arts et de la culture. Nous avons ensuite insisté sur les particularités des principaux domaines – arts de la scène, patrimoine, arts plastiques, industries culturelles – tels qu'ils nous apparaissent les plus représentatifs du monde des arts et de la culture. Il va de soi que les frontières du monde de l'art se transforment – on peut songer à l'évolution de la légitimité du cinéma et de la bande dessinée ou, actuellement, au développement du jeu vidéo qui s'éloigne de plus en plus de la logique de l'industrie du jeu pour se rapprocher de celle du cinéma – entraînant la métamorphose des frontières du champ de l'économie de la culture. Mais d'autres phénomènes induisent à leur tour des transformations plus ou moins radicales au sein de l'organisation du champ culturel. Certains sont relativement anciens, comme la logique du star-system ; d'autres sont apparus plus récemment, comme la question de la diversité culturelle.
La diversité figure parmi les grands enjeux des transformations de l'offre dans le monde. On sait que sur le plan biologique, un certain nombre d'espèces disparaissent chaque année, et l'enjeu du maintien d'une certaine diversité a été largement évoqué depuis les années 1970. La question se pose également sur le plan culturel (notamment à travers l'utilisation des langues), a fortiori à l'heure de la mondialisation des échanges et des offres mainstream produites par nombre d'oligopoles. Analysée d'un point de vue économique, la diversité l'a également été sur le plan politique, notamment dans le cadre des négociations au sein de l'Unesco où la culture et la préservation de sa diversité sont présentées comme des valeurs fondamentales pour l'avenir de notre société. Parallèlement, le domaine des arts et de la culture, longtemps associé à des enjeux radicalement éloignés du champ économique, n'a jamais été aussi étroitement associé à ce dernier, au point de s'en revendiquer comme l'un des moteurs de l'économie de demain. Une telle logique, qui repose sur les principes de l'économie de la créativité, mérite que l'on s'y attarde, même si nous ne partageons pas l'optimisme qui semble se dégager des discours revendiquant ces rapprochements.
La question de la globalité et des nouvelles temporalités – la terre comme village planétaire où la culture se crée et circule toujours plus vite – n'est pas non plus sans influences sur l'organisation de la vie artistique et de la culture en général, le permanent se substituant de plus en plus souvent à des formes brèves et événementielles, qu'il s'agisse de spectacles, de happening ou d'expositions. La même logique favorise encore un peu plus l'économie du star-system à travers l'ensemble des secteurs de la culture. Enfin, l'arrivée des nouveaux acteurs du numérique, comme nous l'avions déjà évoqué en présentant les industries culturelles, transforme radicalement l'offre, mais aussi la demande de culture, ainsi que les relations entre les deux.
Chapitre 11
La diversité culturelle
La diversité culturelle est une question récurrente en économie de la culture. Ce terme, utilisé depuis une trentaine d'années, a très largement rejoint le devant de la scène médiatique au début du xxie siècle, avec la déclaration de l'Unesco pour la diversité culturelle, s'immisçant ainsi dans le débat politique et les négociations commerciales, notamment celles touchant à la réglementation sur le cinéma. Touchant l'ensemble des secteurs de la culture, cette notion évoque particulièrement bien les enjeux politiques, sociaux et économiques majeurs liés à la culture, tels que l'accès à cette dernière et la vie en société, l'impact économique de la créativité artistique sur d'autres activités clés comme l'audiovisuel, la haute technologie, le tourisme, les effets structurants de la diversité culturelle sur l'attractivité des métropoles urbaines et la concurrence des territoires, ou encore les mesures de protection des activités artistiques locales et des identités culturelles (« exception culturelle ») dans les processus de libéralisation et de mondialisation des échanges (cf. chapitre 4).
Dès la fin des années 1990, la notion de diversité culturelle, jusqu'alors peu évoquée, s'est progressivement imposée dans les médias, notamment à travers la Déclaration universelle de l'Unesco sur la diversité culturelle (2001), puis par la préparation d'une convention évoquant cette question et la responsabilité de l'Unesco à cet égard. En affirmant sur le plan politique la nécessité de conserver une certaine diversité culturelle – et notamment les cultures les plus fragiles, nationales ou locales, menacées par l'industrie culturelle – la convention de l'Unesco semble permettre (au moins temporairement) d'éviter certaines menaces liées aux visées expansionnistes des grandes majors culturelles et de la communication. Dans un monde largement inféodé à la logique de mondialisation des échanges et de « déréglementation » des marchés, les dernières barrières (taxes, mesures de préférence ou subventions) visant à garantir le maintien d'une industrie locale ou nationale, comme l'organisation du secteur cinématographique en France, apparaissent comme autant de mesures à éradiquer. L'argument de la diversité culturelle, dans cette perspective, se présente comme le garant du maintien de politiques nationales ou régionales liées à sa préservation.
Pour autant, bien que très souvent invoquée, la notion de diversité culturelle est finalement peu conceptualisée. Dans le domaine des activités culturelles, s'agit-il de la variété des œuvres produites ou distribuées ? Ou bien encore de la diversité des biens culturels ayant retenu l'attention des consommateurs ? Cette question n'a fait l'objet de travaux d'envergure que récemment en économie. Après avoir introduit quelques éléments de définition, nous abordons trois aspects essentiels touchant à la diversité culturelle : le droit d'auteur supposé stimuler la production d'œuvres nouvelles et donc la diversité de l'offre ; les pratiques culturelles dont l'analyse des déterminants est essentielle pour évaluer l'accès effectif à la variété offerte de biens culturels ; la distribution, qui nous semble constituer la pierre d'achoppement de la diversité culturelle, car précisément elle affecte la qualité de l'appariement obtenu entre les œuvres et leur public.
Diversité culturelle : de quoi parle-t-on précisément en économie ?
Il n'existe pas de définition précise de la notion de diversité culturelle en raison notamment de la polysémie du terme culture (cf. Introduction). L'article 1 de la Déclaration universelle de l'Unesco sur la diversité culturelle illustre bien cette idée : « La culture prend des formes diverses à travers le temps et l'espace. Cette diversité s'incarne dans l'originalité et la pluralité des identités qui caractérisent les groupes et les sociétés composant l'humanité. Source d'échanges, d'innovation et de créativité, la diversité culturelle est, pour le genre humain, aussi nécessaire qu'est la biodiversité dans l'ordre du vivant. [...] ».
La notion de diversité culturelle a été mobilisée pour appréhender différents problèmes et enjeux sociaux, très souvent liés entre eux, comme la diversité des cultures locales ou nationales face au processus d'homogénéisation associé à la mondialisation et aux firmes transnationales, originaires le plus souvent des États-Unis. En économie et en sociologie, la diversité culturelle renvoie de manière plus pratique à la variété de l'offre marchande de biens culturels. Elle a ainsi été analysée, dans certains secteurs spécifiques, par rapport à la concentration de la distribution entre les mains d'une poignée d'acteurs économiques. L'objectif des travaux dans ce domaine est de déterminer l'impact de cette concentration sur la diversité culturelle. L'une des premières études sur cet aspect a été menée par Peterson et Berger en 1975 à partir du rythme de renouvellement des hits dans le Top 10 publié par le magazine Billboard. Ils montrent que, sur la période 1948-1973, la concentration dans l'industrie du disque influence négativement la diversité des titres offerts. Alexander critique cette mesure de la diversité en mettant en avant que des titres très similaires sur un plan qualitatif peuvent composer ce classement. Cet auteur obtient alors un résultat différent à partir du Top 40 et surtout, en adoptant une mesure plus qualitative de la diversité culturelle basée sur une décomposition des partitions (structure harmonique, mélodie etc.). Il conclut que des niveaux à la fois faibles et élevés de concentration sont associés à une diversité réduite et que celle-ci est plus élevée pour des niveaux intermédiaires.
D'autres études ont analysé les conséquences des politiques publiques sur la diversité culturelle. Celle-ci est en effet régulièrement invoquée pour justifier un certain nombre de politiques culturelles visant à développer cette diversité et à favoriser son accès au plus grand nombre. Ainsi les aides à la création, à la production et à la distribution de films à travers le compte de soutien du CNC, ont stimulé une offre diversifiée dans le cinéma, tandis que la loi sur le prix unique du livre a contribué à préserver un tissu de librairies en France favorable à la distribution d'une offre variée de livres. Van der Ploeg mentionne notamment trois critères mis en avant par les autorités néerlandaises pour évaluer le succès de la loi sur le prix unique du livre aux Pays-Bas : (1) une offre diversifiée de titres littéraires (nombre de titres et de genres culturels), (2) la disponibilité effective des livres (nombre de points de vente, l'importance des catalogues par point de vente...) et (3) les pratiques de lecture du public selon la catégorie sociale et les genres (général, littérature etc.). Toutefois, l'analyse empirique de cet économiste demeure assez rudimentaire. La mesure effective de la diversité culturelle constitue donc un problème fondamental essentiel à résoudre pour pouvoir mener des analyses pertinentes sur des enjeux sociaux et culturels très sensibles.
Une définition tronquée de la diversité culturelle : Stirling
Sur un plan scientifique, explorer les facteurs influençant la diversité culturelle à travers par exemple les conséquences de telle politique culturelle ou de telle stratégie industrielle, requiert une définition précise de cette notion, ne serait-ce que pour la quantifier. Or, la plupart des travaux empiriques menés depuis le travail fondateur de Peterson et Berger en 1975 ont proposé des indicateurs de mesure sans finalement définir et problématiser cette notion. Plus précisément, la nécessité d'avoir un indicateur statistique précis a de fait réduit la réflexion théorique sur la diversité culturelle en sociologie et en économie. La littérature a ainsi multiplié les indices de mesure, se heurtant à la nature multidimensionnelle de cette notion.
En économie, la diversité est généralement réduite à la notion de variété, c'est-à-dire le nombre de produits disponibles sur un marché, elle-même renvoyant à la préférence pour la diversité évoquée par Dixit et Stiglitz dans leur modèle de concurrence monopolistique de 1977, postulant qu'entre deux paniers de biens offerts au même prix, le consommateur choisira celui qui comporte le plus grand nombre de produits différents. C'est en général la définition retenue dans les analyses économiques ; néanmoins, un tel critère quantitatif n'est pas suffisant : la diversité culturelle est-elle favorisée si l'on produit 1 000 comédies sentimentales plutôt que 100 ? Il apparaît dès lors nécessaire d'introduire des différences qualitatives. Dans cette perspective, dans leur analyse de la diversité culturelle dans l'industrie du livre, Benhamou et Peltier reprennent la distinction opérée par Stirling.
Ce dernier ajoute au critère de variété, ceux plus qualitatifs de « disparité » et d'« équilibre ». Pour un nombre donné de produits, la disparité sera plus grande si les « distances » entre les produits sont importantes. Un tel critère est plus difficilement mesurable, car les différences sont justement qualitatives. On peut toutefois l'approcher au travers de grandes distinctions (culture populaire/culture savante, nationale/internationale, public/privé...) ou par la variété des sous-genres disponibles au sein d'une discipline artistique (les films documentaires, comiques, dramatiques... dans le cinéma) ou de qualités différentes au sein d'un genre (blockbusters, films d'auteur...). Tirole appréhende la diversité dans l'industrie du livre comme une forme de différenciation horizontale fondée sur l'offre combinée d'œuvres populaires (marché de masse) et plus difficiles destinées à un lectorat spécifique (marché de niches).
Le critère d'équilibre renvoie quant à lui au respect d'un certain équilibre entre les catégories. La diversité est d'autant mieux respectée que les proportions entre les catégories sont similaires. On ne pourrait ainsi pas réellement distinguer de diversité dans le cinéma si les films d'auteur étaient réduits à la portion congrue par les blockbusters. Le critère de l'équilibre est difficile à justifier, car il faudrait postuler une quasi-similarité des proportions pour conclure au respect de la diversité culturelle. Or, cela ne va pas de soi, car la proportion de films d'auteur et plus encore leur poids dans le chiffre d'affaires du cinéma ne pourront jamais être équivalents aux films à succès. Si l'on abandonne le critère des équiproportions, doit-on se replier sur un pourcentage minimal en dessous duquel on jugera la présence d'une catégorie comme non significative, ou à défaut choisir un pourcentage intermédiaire (un tiers, un quart...) ? L'« équilibre » ne peut dès lors résulter que d'une décision politique, comme en France l'établissement de quotas de chansons francophones à la radio ou de programme d'origine française ou européenne à la télévision.
La prise en compte de l'hétérogénéité des préférences individuelles
La diversité culturelle des œuvres est relative aux préférences des consommateurs. Comme le notent Peterson et Berger, « l'observation que les changements dans la concentration mènent, plutôt qu'ils ne suivent, les changements dans la diversité, contredit l'idée conventionnelle que dans un marché les consommateurs obtiennent nécessairement ce qu'ils veulent ». Ce constat est précisément intéressant parce qu'il relie la variété constatée de l'offre et les préférences des consommateurs. Or, les quelques travaux portant sur la diversité culturelle en économie de la culture ont adopté une perspective nettement plus restrictive en se concentrant essentiellement sur la variété de l'offre. La « diversité demandée » est tout aussi fondamentale que la « diversité offerte ». Aucun des trois critères (variété, disparité, équilibre) ne peut être défini indépendamment des préférences des consommateurs.
Pour Rallet et Rochelandet, « toutes choses égales par ailleurs la diversité culturelle sera d'autant plus respectée que la dispersion qualitative des œuvres augmente relativement à la dispersion des préférences ». La diversité culturelle peut ainsi être définie comme un système de relations entre la diversité des œuvres et l'hétérogénéité des préférences des consommateurs. Le nombre d'œuvres produites (la variété) ne peut s'apprécier sans prendre en compte l'étendue de la dispersion des goûts. Elle est d'autant plus grande que les consommateurs dotés de préférences spécifiques ont la possibilité de trouver les biens qui correspondent à ces préférences. Ainsi, cinq œuvres différentes introduisent a priori plus de variété s'il existe cinq goûts différents que s'il en existe dix. De même pour la disparité, les différences qualitatives entre les catégories sont relatives à l'étendue des distances entre les préférences. Enfin, cette approche relative de la diversité donne une solution au problème du critère d'équilibre qui supposerait alors que la proportion des catégories mises sur le marché soit égale à celle des préférences pour l'une ou l'autre des catégories au sein de la population.
La diversité comme relation peut être appréhendée de deux manières différentes, par le biais d'un appariement synchronique ou diachronique. Dans sa version synchronique, la diversité culturelle repose sur la qualité de l'appariement entre les caractéristiques des biens et les préférences. Il y a diversité culturelle si les individus trouvent sur le marché les œuvres qui correspondent à leurs goûts. De manière dynamique, la diversité des biens interagit avec l'hétérogénéité des préférences : une diversité accrue des biens tend à transformer les goûts et les préférences culturels, tandis que la réduction de la diversité des biens appauvrit leurs goûts. Symétriquement, l'élargissement des goûts des consommateurs incite à une diversification des biens produits.
Ce système peut être engagé dans un cercle vertueux (à une diversité croissante des biens répond une extension qualitative des préférences), auquel cas la diversité culturelle s'accroît. Mais il peut aussi fonctionner dans l'autre sens ou être bloqué lorsque le niveau de diversité des biens est trop faible pour engendrer une aspiration des consommateurs à étendre les préférences, ou lorsque l'hétérogénéité des préférences est trop pauvre pour inciter les producteurs à la diversification des biens. Cela justifie alors une action exogène du côté des biens (par exemple, l'aide à la création ou aux modes de distribution indépendants) ou du côté des préférences (une action éducative ou une aide à la découverte). L'enjeu est de déterminer si la diversité culturelle ainsi définie nécessite ou pas une intervention exogène pour enclencher une dynamique vertueuse. Pour mieux saisir cette logique, nous allons aborder la question du droit d'auteur.
Droit d'auteur et variété de l'offre
Les débats récents autour de la réforme du droit d'auteur face à internet ont rappelé que cette forme de propriété intellectuelle est souvent associée à la question de la diversité culturelle. Le projet de loi relatif au droit d'auteur et aux droits voisins dans la société de l'information déclare par exemple que « [l]a promotion de la création littéraire et artistique, condition de la diversité culturelle, constitue l'une des grandes priorités du Gouvernement ». Dans quelle mesure le droit d'auteur stimule-t-il la diversité culturelle ?
Comme toute règle juridique et institution, le droit d'auteur peut se justifier de différentes manières : par sa nature, selon une approche essentialiste, ou par ses effets sur le bien-être social, dans une démarche conséquentialiste. Or, précisément, cette deuxième approche, à dominante utilitariste, soutient que l'impact positif du droit d'auteur serait l'incitation à la création et à la production d'œuvres nouvelles qui contribueraient à nourrir la diversité culturelle à travers la variété de l'offre.
Selon cette approche, sur un marché non régulé où les copieurs d'une œuvre originale pourraient intervenir librement en reproduisant l'œuvre, une double concurrence déloyale s'exercerait à l'encontre des producteurs légitimes qui supporteraient seuls les coûts fixes de production et donc l'aléa de production. Non seulement les copieurs ne supportant pas par définition ces coûts fixes pourraient tarifer leurs exemplaires à un prix nettement inférieur, mais ils sélectionneraient uniquement les œuvres à succès pour maximiser leurs profits, bénéficiant d'un temps de recul précieux pour pouvoir observer les comportements des consommateurs au moment de la mise sur le marché des œuvres nouvelles. Les producteurs légitimes verraient alors disparaître les recettes sur les biens culturels à succès. Cela aurait pour conséquence un sous-investissement dans la production d'œuvres nouvelles et surtout un moindre subventionnement entre les œuvres à succès et les œuvres plus difficiles dont la valorisation se ferait sur des niches de marché. Un marché non régulé aboutirait à une baisse de la diversité culturelle. C'est notamment un tel argument qui a été utilisé pour renforcer les dispositifs de lutte contre le téléchargement illégal des œuvres numériques sur internet (notamment, en France, la loi Hadopi). À l'inverse, en créant artificiellement un monopole juridique sur l'exploitation de leurs œuvres, le droit d'auteur donne aux auteurs et à leurs partenaires économiques les moyens de s'approprier auprès des exploitants la valeur économique des biens culturels qu'ils créent et produisent.
Une telle approche rencontre néanmoins plusieurs limites. En premier lieu, il existe un arbitrage entre incitation et accès. Le droit d'auteur confère un monopole d'exploitation à ses bénéficiaires, susceptible de restreindre la circulation des œuvres si cela maximise leurs profits. L'appariement entre la variété de l'offre et la diversité des préférences ne serait dès lors pas optimal. Par exemple, une firme détenant des droits sur des œuvres difficilement substituables peut exiger un prix élevé pour leur utilisation (commerciale ou finale), ce qui peut exclure des individus ou des exploitants qui seraient malgré tout solvables (disposés à payer un prix supérieur à celui qui prévaudrait en situation de concurrence). De même, forts de droits exclusifs d'exploitation, les distributeurs peuvent organiser la valorisation des œuvres de manière à maximiser leurs profits, ce qui peut se traduire par un turn-over élevé et une disparition très rapide des circuits commerciaux pour les œuvres qui ne rencontrent pas rapidement une demande suffisante.
En second lieu, si le droit d'auteur protège les producteurs de biens culturels contre les copieurs, constitue-t-il pour autant une incitation à la création d'œuvres nouvelles par la protection qu'il confère aux auteurs ? On peut se poser la question inverse : sans droit d'auteur, y aurait-il de la création ?, et répondre par l'affirmative sur le plan historique, le droit d'auteur étant une notion relativement récente en regard de l'histoire de l'humanité (mais il existait d'autres moyens de protéger sa création, par une politique de secret notamment). D'un point de vue économique, si l'on supposait que les auteurs sont essentiellement guidés par des motivations extrinsèques (des récompenses comme un revenu monétaire ou une reconnaissance sociale de leur création), cet argument serait pleinement recevable. Or, nombre de travaux en psychologie ont montré que les motivations de la création sont avant tout intrinsèques. Le processus de création s'explique par de nombreux facteurs (un besoin personnel, parfois compulsif, l'inspiration...) et est partiellement marqué par le hasard, par des rencontres hypothétiques avec d'autres créateurs ou œuvres. De surcroît, l'espérance de gains monétaires s'apparente davantage à un vaste jeu de loterie à l'issue duquel seule une poignée d'auteurs sont gagnants et donc rares sont ceux qui créent des œuvres avec la quasi-certitude de percevoir des royalties (cf. chapitre 14). Le droit d'auteur soutient ainsi davantage un système extrêmement inégalitaire en matière de répartition des revenus artistiques (sans parler de l'action des sociétés gestionnaires de ces droits, cf. chapitre 12), souvent au détriment de la diversité des talents.
En revanche, le droit d'auteur constitue un instrument essentiel pour faciliter la coordination des activités de production et de distribution en régulant les relations interprofessionnelles. L'objectif de ce droit de propriété, considéré dans sa dimension pécuniaire, consiste essentiellement à créer des conditions favorables au financement de la production d'œuvres nouvelles à travers des outils permettant sa rentabilisation. Il ne s'agit pas alors de favoriser directement la variété qualitative de l'offre et la production d'œuvres de valeur esthétique élevées, donc hautement différenciées. La notion d'originalité renvoie plus à une différenciation par la signature, l'« empreinte de la personnalité de l'auteur », donc l'absence de plagiat. Le renforcement du droit d'auteur créerait ainsi des conditions plus favorables sur un plan quantitatif au financement d'un nombre accru d'œuvres, sans pour cela créer automatiquement de la distance qualitative entre elles ou une surenchère esthétique. La « diversité culturelle » serait ici définie a minima comme le nombre d'œuvres créées, ce qui peut poser un certain nombre de critiques sur un plan conceptuel, économique et politique.
Le débat peut aussi se poser en des termes symétriques : les pratiques illégales de partage et de téléchargement nuisent-elles à la diversité culturelle ? En d'autres termes, mettent-elles en danger la création culturelle et notamment les œuvres originales à petit tirage ? En fait, le maintien de la diversité culturelle au sens de la survie des auteurs s'adressant à un public restreint, dépend de financements étatiques et de mécènes privés. Il s'explique également par les reversements que leur font les producteurs d'une partie des recettes qu'ils tirent des best-sellers. Cependant, ces subventions croisées dont se targuent les producteurs pour justifier la lutte contre le téléchargement illégal ne concernent que le financement de nouvelles productions et leur lancement sur le marché. Si elles n'ont pas de succès immédiat, elles sont retirées du marché et si elles réussissent, elles vont rejoindre les rangs des best-sellers. À l'issue de ce processus de sélection, la variété des œuvres accessibles et effectivement consommées n'est pas plus grande et la loi de Pareto se maintient dans le temps. Le marché des best-sellers s'est simplement renouvelé, ce renouvellement étant au demeurant une condition de sa pérennité : les mêmes artistes ne peuvent être éternellement en haut de l'affiche.
Plus généralement, le maintien de la variété des œuvres proposées dépend du mécénat public ou privé, tant du côté de la production (subvention des revenus des auteurs) que de la distribution (loi sur le prix unique des livres en France, qui a permis le maintien des petits libraires orientant les lecteurs vers davantage de diversité). La circulation illégale des biens culturels s'avérait ici davantage une forme de valorisation à faible coût pour les auteurs ne bénéficiant pas de l'accès à la distribution et à la promotion de masse. Pour autant, nous verrons plus loin que les nouveaux modèles d'affaires numériques renouvellent les termes de ce débat.
Pour résumer, le rôle du droit d'auteur en matière de diversité culturelle doit être relativisé, car celle-ci peut s'expliquer par des motivations intrinsèques des auteurs, des artistes, de petits éditeurs ou labels passionnés qui ne placent pas la recherche de gains monétaires et la rentabilisation au cœur de leur travail ; la stratégie des producteurs qui produisent ou coproduisent beaucoup selon une logique de prototype consistant à ne pas mettre tous leurs œufs dans le même panier, à répartir le risque sur plusieurs œuvres et à utiliser les aides publiques et privées à la création qui découplent le financement et la valorisation des œuvres sur le marché. Pour autant, la diversité dont il est question ici est envisagée essentiellement du côté de l'offre. Mais qu'en est-il des pratiques de consommation culturelle ?
Les pratiques culturelles :
diversité, éclectisme et omnivorité
La diversité culturelle appréhendée uniquement au niveau de l'offre relève d'une vision réductrice (cf. supra). Pourquoi financer des œuvres difficiles ou non conformes au goût moyen si elles ne rencontrent pas un lectorat, des spectateurs, des auditeurs etc. ? Or, cette diversité du côté de la demande (demande pour une offre variée) constitue une hypothèse récurrente dans la théorie microéconomique du consommateur. Plus qu'elles ne la démontrent ou la vérifient empiriquement, les modélisations microéconomiques du consommateur postulent le plus souvent cette hypothèse. Les sociologues ont quant à eux développé de nombreux travaux sur la diversification des goûts et des pratiques culturelles.
Les économistes se sont penchés assez tôt sur la demande pour les biens culturels avec les travaux de William Stanley Jevons au xixe siècle sur la valeur de la musique et plus récemment, les travaux d'économistes comme Abbé-Decarroux et Grin sur les arts « cultivés », Lévy-Garboua et Montmarquette sur le théâtre ou encore Throsby et Withers sur les concerts de musique classique. Ces analyses soulignent notamment l'importance des effets d'apprentissage, de la recommandation sociale et l'interdépendance des choix dans la consommation de biens culturels s'avérant difficiles à assimiler à des marchandises ordinaires. Ainsi Lévy-Garboua et Montmarquette développent un modèle où la probabilité de fréquenter le théâtre augmente avec l'expérience dans ce type de pratiques dans la mesure des expériences positives passées, du prix du théâtre, de l'utilité marginale de la richesse et de la consommation de biens substituts ou complémentaires au théâtre. De leur côté, De Vany et Walls, Moul, ainsi que Beck analysent l'influence du bouche-à-oreille sur les pratiques de consommation culturelle.
Pour autant, les analyses économiques ont généralement porté sur la demande en s'adressant à un genre artistique donné (le théâtre, le cinéma, la musique). La question des goûts culturels est ainsi abordée uniquement sous l'angle d'un art en particulier, souvent en le dissociant en deux catégories opposées (la musique « classique » et populaire par exemple).
Mais peu d'études économiques se sont réellement penchées sur la diversité des pratiques culturelles et à notre connaissance, aucune sur la formation du goût et en particulier sur la demande pour une diversité d'œuvres. Celle-ci demeure simplement une hypothèse pour construire des modèles. S'agissant de la diversification des pratiques culturelles, elle s'expliquerait selon une logique d'allocation rationnelle du temps visant à optimiser l'utilité totale obtenue à travers ces activités. L'étendue et la diversification des pratiques en dehors du travail sont soumises à une contrainte temporelle, obligeant l'individu à optimiser ses choix en matière de gestion du temps de loisir.
L'économiste Gary Becker intègre cet arbitrage en envisageant l'utilité retirée par les consommateurs, non pas à partir des biens et des services qu'ils consomment, mais des activités non professionnelles liées à la combinaison des biens et des services avec du temps. L'individu subit donc deux contraintes, en l'occurrence son revenu et son temps disponible, qu'il peut réduire en investissant dans le capital humain pour augmenter le rendement du temps d'activité non professionnelle et, partant, la diversité de ses activités. Les catégories socioprofessionnelles supérieures seraient de ce fait plus « productives » et donc plus éclectiques. Gary Becker se distingue ici du sociologue Pierre Bourdieu, selon qui le capital culturel est essentiellement transmis à l'individu dès son enfance par son environnement d'origine. L'individu rationnel, au contraire, peut toujours augmenter son capital humain au cours de sa vie et améliorer sa position sociale.
De leur côté, les sociologues se sont penchés sur les questions de l'éclectisme des goûts et la diversification des pratiques de consommation culturelle. Pour quelles raisons un individu est-il amené à adopter plusieurs pratiques comme lire des romans, aller au théâtre, assister à des concerts ou regarder des films à domicile ? Depuis les travaux fondateurs de Bourdieu, de nombreux travaux ont été menés en sociologie quantitative. Bourdieu aborde ce thème sous l'angle de la légitimité culturelle et de la distinction sociale. Un individu de statut social élevé est supposé se distinguer par un goût prononcé pour les arts savants et les pratiques élevées comme la visite de musées, tout en méprisant les loisirs ou les divertissements qualifiés de « populaires ».
À la suite des travaux de Bourdieu, toute une littérature a vu le jour sous la forme d'études empiriques mettant en évidence l'éclectisme des pratiques culturelles comme facteur de distinction sociale. Cette évolution serait due à des changements sociaux majeurs comme l'allongement et l'augmentation du niveau de scolarisation, la modification des réseaux sociaux des individus, l'influence de la culture populaire sur les arts « élevés » accompagnant l'entrée dans la postmodernité, une concurrence de légitimité entre culture populaire et culture élitiste. L'invasion de l'audiovisuel et, maintenant, de l'internet dans le champ de la culture et les pratiques de loisirs, jouerait aussi un rôle en favorisant l'accès de l'élite à des formes culturelles plus populaires et inversement, l'accès des individus de condition sociale inférieure à la culture élitiste.
Identifié par différents auteurs, cet éclectisme peut s'exprimer en matière de goûts diversifiés ou de cumul des pratiques. Les individus se distinguent socialement, non par la nature même des biens culturels qu'ils consomment (arts savants, pratiques élitistes, culture légitime versus culture populaire, culture de masse, culture « indigne »), mais par la diversification (omnivorité) ou non (univorité) de leurs pratiques et préférences.
Différentes raisons ont été avancées pour expliquer la propension des individus à diversifier (omnivorité) ou non (univorité) leurs pratiques culturelles. Ces derniers auraient une prédisposition ou non à l'éclectisme, héritée de leur milieu d'origine. Pour Peterson, l'univorité peut être liée à un statut social défavorisé, mais il existe également un « univorisme de statut élevé » caractérisant des individus limitant volontairement leurs pratiques culturelles étant donné leurs croyances religieuses, une attitude sectaire voire, parfois, une forme de snobisme intellectuel. Ce déterminisme social expliquerait alors des capacités différenciées d'absorption et d'interprétation de la nouveauté. Selon Coulangeon, cette vision serait très proche des approches en termes d'habitus mettant en avant une prédisposition héritée du milieu d'origine.
Le degré de diversification des pratiques culturelles serait également une conséquence de la composition des relations sociales, de l'entourage social. En fonction de la taille de son réseau social et de la multiplicité de ses interactions, l'individu est poussé à acquérir des connaissances et à multiplier ses pratiques de loisirs, en particulier culturels, pour entretenir ses relations. De plus, si l'on considère que les interactions d'un individu donné sont plus nombreuses avec les individus situés à des échelons inférieurs de la hiérarchie sociale, la taille et la diversité des réseaux sociaux sont positivement corrélées avec le statut social. L'omnivorité culturelle serait encore une fois positivement liée au statut social. D'autres facteurs sociologiques comptent également, comme les effets générationnels et la composition du foyer. Plus l'individu est jeune, plus il serait omnivore en raison de contraintes temporelles moindres, d'interactions sociales plus développées et, éventuellement, de goûts plus ouverts, moins modelés. De même, la vie en couple, avec des enfants, peut influencer l'omnivorité soit en limitant les interactions sociales, soit en pesant sur le temps libre disponible en dehors des activités tournées vers la famille.
Distribution, appariement, prescription
La logique de la diversité culturelle vise à favoriser la rencontre avec le public. Une œuvre n'a pas de valeur dans l'absolu, elle doit être confrontée à un regard et donc être contemplée, appréciée, critiquée etc. À cet égard, dans les industries culturelles, la distribution joue un rôle fondamental puisqu'en reliant l'offre à la demande, les distributeurs remplissent les fonctions d'évaluation et de sélection des biens culturels, de promotion, d'acheminement, d'appariement etc. D'autres acteurs comme les critiques, les détaillants, les salons et les festivals, les prix littéraires, les programmateurs, les DJs etc., complètent traditionnellement ces fonctions en facilitant l'appariement entre la diversité de biens culturels et l'hétérogénéité des goûts des consommateurs.
Généralement, les producteurs de biens culturels ne distribuent en effet pas leurs contenus eux-mêmes, mais via des intermédiaires spécialisés. La distribution regroupe les différentes activités et les moyens techniques mis en œuvre pour mettre à disposition des produits (biens ou services) à un public déterminé. Pour que la relation de marché entre producteurs et consommateurs fonctionne, la distribution doit réduire certains types de « distances » les séparant, soit la distance temporelle (décalage entre le moment où la marchandise est produite et le moment des décisions d'achat et de consommation), la distance spatiale (les lieux de production et de consommation sont généralement dispersés), la distance informationnelle (en l'absence de contacts directs, le producteur ne dispose pas de moyens de collecter directement l'information sur les consommateurs) et la distance relationnelle (collecter des informations sur les consommateurs ne suffit pas toujours pour obtenir un avantage économique, il faut également entretenir des relations répétées avec les clients pour leur donner confiance et créer des habitudes).
La « gestion » de ces différentes distances par les distributeurs leur confère un pouvoir de marché susceptible de réduire la diversité culturelle effective. Les distributeurs contrôlent traditionnellement l'information sur les clients. En orientant leurs achats par le biais du marketing de masse et en bénéficiant souvent d'un contact direct avec eux, les distributeurs jouent un rôle de prescription majeur. Leur pouvoir de marché découle également de leur droit de vie ou de mort (commerciale) sur les œuvres confrontées à une contradiction entre une production abondante et des capacités limitées tant de l'exposition dans les canaux de valorisation que de l'attention des individus. Jusqu'à présent, cette contradiction a été résolue par le turn-over rapide, mais inégal, des biens dans les lieux de vente. Les biens qui rencontrent le succès bénéficient d'un temps d'exposition plus long et d'une surface d'exposition plus visible, tandis que les œuvres ayant moins de succès disparaissent rapidement des rayons. Cela favorise la concentration de la consommation sur une minorité d'œuvres. La diversité accrue de la production est ainsi sévèrement réduite par l'impossibilité pratique d'accéder au plus grand nombre de biens.
Toutefois, les distributeurs dominants ne contrôlent pas intégralement toutes les fonctions nécessaires à la rencontre entre la diversité culturelle et son public, en particulier en matière de prescription et d'accès à certains publics. D'autres acteurs entrent en ligne de compte, permettant une visibilité a minima de la variété de l'offre à la marge des circuits dominants. La nature des prescripteurs est variée, il peut s'agir de petits labels ou de majors, de critiques néo-promotionnelles et indépendantes etc. Leur rôle consiste justement à conseiller les consommateurs dans leurs choix face à une abondance d'œuvres dont la qualité ne se révèle qu'à la consommation.
Pour certains auteurs, la diversité de l'offre et son accroissement infini ne constituent pas forcément une fin en soi, car cela peut aboutir à une diminution du bien-être social en raison de l'« overchoice » inhérent. Néanmoins, ce problème se pose surtout pour des produits d'une même « ligne » (des options sur des modèles de voiture par exemple). Or, les biens culturels en tant que biens singuliers échappent à cette logique. La question se formule différemment : si l'individu peut préférer une présélection de biens culturels dans un ensemble donné d'œuvres, il est pour autant difficile de soutenir qu'il préfère moins de diversité. Remplissant une fonction de réducteur de complexité, les prescripteurs permettent aux consommateurs de sélectionner au mieux les œuvres lorsqu'ils sont confrontés à une abondance informationnelle (nombre d'œuvres offertes, messages commerciaux, grilles des programmes interminables, sorties littéraires gargantuesques...) et à une incertitude sur la qualité des biens. On peut ainsi définir le service de prescription comme la capacité d'une firme à transformer la requête potentielle de consommateurs en une demande de services spécifiques.
Mais la fonction des prescripteurs ne se limite pas à ce rôle d'appariement. Lorsque les consommateurs achètent un bien culturel, ils ne se fondent pas forcément sur leurs préférences actuelles, préformées, ne recherchant pas uniquement le film, l'album de musique ou le livre qu'ils apprécient en fonction de préférences préexistantes. Ils recherchent davantage le bien culturel qu'ils devraient apprécier en fonction de l'avis d'experts, de prescripteurs de goûts. La fonction de la prescription n'est plus alors seulement d'aider le consommateur à effectuer des choix face à un nombre important de possibilités portant sur des biens d'expérience, dont la qualité ne se dévoile qu'après la consommation. Elle consiste également à aider les individus à porter un jugement sur des biens de croyance, à faire évoluer leurs goûts et préférences en dynamique via un processus d'apprentissage et d'interactions. En d'autres termes, les prescripteurs sont avant tout prescripteurs de préférences au sens où ils aident l'individu non pas à fonder rationnellement ses choix, mais plus fondamentalement, à construire ses jugements, ses goûts culturels. C'est l'une des lacunes majeures des modèles économiques dominants actuellement sur internet, y compris celui de la longue traîne (cf. chapitre 15).
Tout l'enjeu en matière de diversité culturelle – où l'on retrouve l'opposition entre appariements synchronique et diachronique mentionnée plus haut – repose sur la nature des acteurs qui contrôlent effectivement ces deux aspects, prescription de choix et prescription de goûts. Ce qui pose problème tient à l'organisation de ce filtrage, lequel a jusqu'à présent généralement favorisé quelques auteurs, artistes et genres aboutissant de la sorte à une concentration de l'offre autour d'œuvres favorisées soit par leurs budgets promotionnels, soit par la critique de presse (cf. chapitre 14). La prescription peut alors varier de l'injonction (un seul choix prescrit) à la sélection (le consommateur décide de son choix en fonction de ses propres critères parmi une gamme de produits sélectionnés par le prescripteur) en passant par l'évaluation (le consommateur se décide en fonction d'une liste de produits recommandés et classés hiérarchiquement par le prescripteur).
Sur les marchés des biens culturels, la prescription est partagée par plusieurs agents tout au long de la chaîne de valeur. Elle répond à des finalités parfois divergentes, visant soit à accroître les ventes de biens culturels massivement promotionnés, soit à pousser certaines œuvres difficiles d'accès. La promotion commerciale peut être assurée par un distributeur, par l'auteur lui-même et par ses partenaires proches (agents, éditeurs...). L'objectif est de persuader les consommateurs d'opter pour des œuvres à gros budgets. Sa nature « invasive » lui permet de dominer toute critique négative des œuvres ainsi supportées ou indépendante d'œuvres plus marginales n'intéressant que des consommateurs déjà convaincus. La critique spécialisée peut également jouer un rôle clé, œuvrant tantôt pour les acteurs dominants – lorsqu'elle dépend financièrement trop étroitement du support médiatique sur lequel elle s'exprime (critique néo-promotionnelle) –, tantôt de manière indépendante. Elle contribue directement à façonner les préférences du public et à légitimer certains artistes à plus long terme. La critique apparaît ainsi comme un processus institutionnalisé de sélection et de filtrage des œuvres et des genres légitimes par des experts dans un environnement marqué par un flux important de nouveautés selon des logiques de prototypes. Le rôle de la critique, de même que celui des salons du livre et autres festivals de musique et de cinéma, apparaît donc ambivalent, s'agissant de diversité culturelle.
Entre ces deux catégories de prescripteurs se situent les détaillants (libraires, disquaires, petites salles de cinéma indépendantes) qui bénéficient d'une proximité relationnelle plus forte avec les consommateurs. Leur rôle est aussi plus ambigu, car si l'objectif est de vendre des biens culturels (livres...), certains passionnés peuvent, selon leurs propres goûts et culture, pousser certaines œuvres et chercher à surprendre leurs clients et ne pas se soumettre aux injonctions des éditeurs, grossistes et autres distributeurs. Historiquement, ils se présentent comme des prescripteurs essentiels à la diversité culturelle et la disparition des petits disquaires en France dans les années 1980 a probablement joué un rôle dans la crise du marché du disque une décennie plus tard. Le rôle d'autres agents comme les DJs (playlist dans les discothèques et sur les radios) peut faire l'objet d'une analyse similaire dans la musique (radios indépendantes vs. grands groupes de communication, mais aussi compromission à l'instar des payolas).
À l'autre bout de la chaîne, la recommandation peut être issue de l'action des consommateurs via le bouche-à-oreille. L'arrivée de nouvelles formes de prescriptions avec internet pourrait changer la donne. Les systèmes de recommandation, les annuaires en ligne, les moteurs de recherche, mais également les réseaux sociaux numériques, les communautés en ligne d'artistes, les blogs d'amateurs éclairés, les plates-formes de partage de vidéo etc., sont autant de nouvelles sources de conseils et d'influence potentiels sur les choix et les processus de découverte des œuvres par les consommateurs. Les effets du numérique sur la diversité culturelle sont donc potentiellement importants. Mais les TIC peuvent-elles réellement transformer les modèles économiques, par exemple en opérant une redistribution des revenus entre les artistes par la remise en question de l'économie du vedettariat et de la loi de Pareto sur la répartition des achats ? Nous traitons plus précisément cet aspect dans le chapitre 15.
. Ce chapitre reprend une réflexion et différents articles élaborés par Alain Rallet et Fabrice Rochelandet sur la question de la diversité culturelle à l'heure du numérique.
. Benhamou F., Peltier S., « How should cultural diversity be measured? An application using the French publishing industry », Journal of Cultural Economics, vol. 31, 2007, p. 85-107.
. Rallet A., Rochelandet F., « To what extent the digital revolution can enhance cultural diversity? », 17th International Conference of ACEI, Kyoto, Japon, 21 au 24 juin 2012.
. Unesco, Déclaration universelle de l'Unesco sur la diversité culturelle, Paris, 2 novembre 2001.
. Mattelart A., Diversité culturelle et mondialisation, Paris, La Découverte, coll. « Repères », 2007.
. Benhamou F., Peltier S., op. cit.
. Peterson R. A, Berger D. G., « Cycles in Symbol Production: The Case of Popular Music », American Sociological Review, vol. 40, 1975, p. 158-173.
. Alexander P. J., « Entropy and popular culture: product diversity in the popular music recording industry », American Sociological Review, vol. 61, no 1, 1996, p. 171-174.
. Van der Ploeg F., « Beyond the dogma of the fixed book price agreement », Journal of Cultural Economics, vol. 28, 2004, p. 1-20.
. Dixit A. K., Stiglitz J. E., « Monopolistic competition and optimum product diversity », American Economic Review, vol. 67, no 3, 1977, p. 297-308.
. Voir par exemple Caves R. E., Creative Industries. Contratcts between art and commerce, Cambridge, Harvard University Press, 2000.
. Op. cit., 2007.
. Stirling A., On the economics and analysis of diversity, Document de travail du SPRU no 28, 1999.
. Tirole J., Théorie de l'organisation industrielle, Paris, Economica, 1993.
. Peterson et Berger (1975), op. cit., p. 156 (notre traduction).
. Benhamou F. et Peltier S., op. cit.
. Rallet A. et Rochelandet F., op. cit.
. Ibid.
. Loi no 2006-961 du 1er août 2006 relative au droit d'auteur et aux droits voisins dans la société de l'information (ou loi DADVSI).
. Cette première approche regroupe notamment des arguments kantiens associés aux droits de la personne : une œuvre étant l'extension de la personnalité de son auteur, elle doit être protégée au même titre. Ou bien encore l'hypothèse lockéenne des droits naturels : une œuvre étant le fruit du travail de son auteur, elle lui appartient.
. Strowel A., Droit d'auteur et copyright, divergences et convergences. Étude de droit comparé, Bruxelles, Émile Bruylant – LGDJ, 1993.
. Landes W. M., Posner R. A, « An economic analysis of copyright law », The Journal of Legal Studies, vol. 18, no 2, 1989, p. 325-363.
. Cet argument général est inspiré de la théorie schumpetérienne de l'innovation selon laquelle le monopole de premier arrivé de l'entrepreneur-innovateur lui confère une rente sous la forme d'un surprofit récompensant son activité inventive. Cette rente disparaît progressivement avec l'apparition d'imitateurs et en l'absence de réaction de l'innovateur. Or, ce délai de premier arrivé peut être trop court et les biens culturels plus faciles à copier que les inventions pour permettre au créateur d'un bien culturel d'en rentabiliser les coûts fixes de production.
. Suzor N. P., « Access, progress, and fairness: rethinking exclusivity in copyright », Vanderbilt Journal of Entertainment and Technology Law, vol. 15, no 2, 2013, p. 297-342.
. Jevons W. S., On the Science and Art of Music, manuscrit non publié, conservé à la Bibliothèque universitaire John Rylands à l'Université de Manchester, 50 p.
. Abbé-Decarroux F., Grin F., « Risk, Risk Aversion and the Demand for Performing Arts », in Towse R., Khakee A. (eds), Cultural Economics, Berlin, Springer-Verlag, 1992, p. 125-140. ; Lévy-Garboua L., Montmarquette C., « A Microeconometric Study of Theater Demand », Journal of Cultural Economics, vol. 20, no 1, 1996, p. 25-50 ; Throsby D., Withers G. A., The Economics of the Performing Arts, Edward Arnold Publishers, 1979.
. De Vany A., Walls D., « Bose – Einstein dynamics and adaptive contracting in the motion picture industry », Economic Journal, vol. 106, no 439, 1996, p. 1493-1514 ; Moul C. C., « Measuring Word of Mouth's Impact on Theatrical Movie Admissions », Journal of Economics & Management Strategy, vol. 16, no 4, 2007, p. 859-892 ; Beck J., « The Sales Effect of Word of Mouth: A Model for Creative Goods and Estimates for Novels », Journal of Cultural Economics, vol. 31, no 1, 2007, p. 5-23.
. Kurabayashi Y., Ito T., « Socio-economic Characteristics of Audiences for Western Classical Music in Japan », in Towse R., Khakee A. (eds), Cultural Economics, Berlin, Springer-Verlag, 1992, p. 275-287 ; Prieto-Rodríguez J., Fernández-Blanco V., « Are Popular and Classical Music Listeners the Same People? », Journal of Cultural Economics, vol. 24, no 2, 2000, p. 147-164 ; Favaro D., Frateschi C., « A Discrete Choice Model of Consumption of Cultural Goods: the Case of Music », Journal of Cultural Economics, vol. 31, no 3, 2007, p. 205-234.
. Rochelandet F., Le Guel F., Arouri H. E. M., « L'entrelacement des pratiques culturelles et de l'usage des TIC : une analyse empirique », Économie & Prévision, no 194, 2010, p. 33-55.
. Becker G. S., Human Capital: A Theoretical and Empirical Analysis, with Special Reference to Education, New York, NBER – Columbia University Press, 1964.
. Bourdieu P., La Distinction. Critique sociale du jugement, Paris, Éd. de Minuit, 1979.
. Donnat O., Les Français face à la culture. De l'exclusion à l'éclectisme, Paris, La Découverte, 1994 ; Lahire B., La culture des individus. Dissonances culturelles et distinction de soi, Paris, La Découverte, 2004.
. Peterson R. A., « Understanding Audience Segmentation: From Elite and Mass to Omnivore and Univore », Poetics, vol. 21, no 4, 1992, p. 243-258 ; DiMaggio P., « Classification in Arts », American Sociological Review, vol. 52, no 4, 1987, p. 440-455.
. Cf. le numéro thématique de la revue Poetics, « Models of Omnivorous Cultural Consumption: New Directions in Research », coordonné par Ollivier, van Eijck et Warde en 2008.
. Peterson R. A., 1992, op. cit. ; Coulangeon P., « Classes sociales, pratiques culturelles et styles de vie – Le modèle de la distinction est-il (vraiment) obsolète ? », Sociologie et Société, vol. 36, no 1, 2004, p. 59-84.
. DiMaggio, 1987, op. cit. ; Erickson B. H., « Culture, Class, and Connections », American Journal of Sociology, vol. 102, no 1, 1996, p. 217-251 ; Relish M., « It's Not all Education: Network Measures as Sources of Cultural Competency », Poetics, no 25, 1997, p. 121-139 ; Lahire B., 2004, op. cit.
. Lin N. et Dumin M., « Access to Occupations through Social Ties », Social Networks, vol. 8, no 4, 1986, p. 365-385 ; Marsden P. V., « Core Discussion Networks of Americans », American Sociological Review, vol. 52, no 1, 1987, p. 122-131.
. Coulangeon P., « La stratification sociale des goûts musicaux. Le modèle de la légitimité culturelle en question », Revue française de sociologie, vol. 44, no 1, 2003, p. 3-33 ; Fisher T. C. G., Preece S. B., « Evolution, Extinction, or Status Quo? Canadian Performing Arts Audiences in the 1990s », Poetics, vol. 31, no 2, 2003, p. 69-86 ; Guy J. M., La culture cinématographique des Français, Paris, DEPS/Ministère de la Culture et de la Communication, La Documentation française, 2000 ; Van Eijck K., « Social Differentiation in Musical Taste Patterns », Social Forces, vol. 79, no 3, 2001, p. 1163-1184.
. Degenne A., Lebeaux M.O. et Marry C., « Les usages du temps : cumuls d'activités et rythmes de vie », Économie et Statistique, no 352-353, 2002, p. 81-99.
. Nous centrons notre propos sur les industries culturelles, mais la plupart des remarques formulées ici peuvent s'étendre aux autres activités de la culture vivante comme les beaux-arts et le spectacle vivant.
. Gourville J. T., Soman D., « Overchoice and assortment type: when and why variety backfires », Marketing Science, 24(3), 2005, p. 382-395 ; Iyengar S., Lepper M., « When choice is demotivating: can one desire too much of a good thing? », Journal of Personality and Social Psychology, 2000, 79(6), p. 995-1006.
. Benghozi P.-J., Paris T., « The economics and business models of prescription in the internet », in Brousseau E. et Curien N. (dirs.), Internet and Digital Economics, 2007, p. 291-310.
. Karpik L., L'économie des singularités, Paris, Gallimard, 2007.
. Rallet A. et Rochelandet F., 2012, op. cit.
. Creton L., « Critique et promotion dans l'univers cinématographique : distinctions, conjunctions et dysphories », Entrelacs, hors-série « Marketing du cinéma », mars 2000, p. 27-37.
. Hirsch, P. M. « Processing Fads and Fashions: An Organization-Set Analysis of Cultural Industry Systems », The American Journal of Sociology, vol. 77, no 4, 1972, p. 639-659 ; Debenedetti S., « L'impact de la critique de presse sur la consommation culturelle : un essai de synthèse dans le champ cinématographique », Recherche et Applications en Marketing, vol. 21, no 2, 2006, p. 43-59.
. La payola est un système développé par les maisons de disques (depuis au moins la fin de la Seconde Guerre mondiale) à destination des stations de radio et visant à rémunérer le passage de certains morceaux de musique afin de développer leur notoriété.
Chapitre 12
Intégrer la culture dans l'économie
Nous l'avons signalé en introduction, c'est à partir du secteur artistique – les arts de la scène, le marché de l'art ou le patrimoine – que les économistes ont progressivement jeté les fondations de l'économie de la culture. Les industries culturelles (cinéma, livre, musique enregistrée...) constituent le second jalon des délimitations de ce secteur, qui a largement été exploré depuis une trentaine d'années. Ce champ s'est cependant étendu dans deux dimensions, en fonction d'une conception plus large de la culture : d'une part, une vision anthropologique, prenant en compte les langues ou les religions ; d'autre part, une vision intégrant des secteurs plus proches des arts appliqués, comme le design, la publicité ou la cuisine. C'est ce dernier volet qui a reçu le plus d'échos, se développant essentiellement sous l'appellation d'économie créative ou de la créativité (cf. chapitre 9). Il n'est guère aisé de trouver un concept sous-jacent résumant parfaitement les enjeux des industries créatives, comme on a pu le trouver avec les notions d'expérience ou d'immatériel. « De fait, les premières définitions des industries créatives, comme de l'économie créative, sont surtout positives, c'est-à-dire que des listes d'activités sont assemblées et l'on vise surtout à mesurer leur poids économique », résume Philippe Bouquillon. On peut avec raison s'interroger sur les contours parfois élastiques de cette notion, présentant la créativité à partir d'un nombre très limité de secteurs (la mode ou le design, mais pas la recherche scientifique). On présente certes le management de la créativité au cœur de cette économie ; on pourrait aussi, comme le suggère en quelque sorte Pierre-Michel Menger, présenter cette dernière comme stade ultime de l'économie de marché, fondée sur l'hyperflexibilité de l'artiste créatif, heureux de travailler dans le domaine de la culture, et sous-payé pour cette raison.
Les raisons plaidant pour une telle extension du domaine peuvent être multiples. Sur le plan scientifique, des similitudes peuvent être observées entre le secteur traditionnel de l'économie et ces secteurs plus éloignés, par exemple parce que les arts plastiques ou les arts de la scène auraient adopté des modèles de gestion plus proches de ceux que l'on trouve dans le design ou la publicité, qui pourraient être notamment rapprochés à partir de la notion de créativité. Sur un plan plus stratégique, l'idée d'étendre le champ de l'économie de la culture permet également de montrer l'importance de son rôle au sein de l'économie générale, ce qui peut s'avérer profitable pour les acteurs de la culture, dont l'activité pourrait être mieux reconnue au regard de l'effort collectif de la société pour assurer sa croissance (dans le cadre du fonctionnement traditionnel de l'économie de marché). Sur le plan de la reconnaissance académique, un tel positionnement, par ailleurs, n'est pas non plus défavorable pour les économistes qui s'occupent de l'analyse de ce secteur spécifique, longtemps considéré comme un passe-temps agréable, mais éloigné des « vrais » enjeux de l'économie.
Ce mouvement d'extension n'est pas récent. La logique (pré-)industrielle, présente dans les ateliers d'artistes comme la Factory de Warhol ou plus récemment, les ateliers de Jeff Koons ou de Wim Delvoye, est déjà partiellement en œuvre dans les ateliers du Moyen Âge et, plus tard, chez Rubens. La logique du développement économique par le design n'est pas non plus récente, comme en témoignent les investissements de Colbert dans les grandes manufactures du luxe en France (tapisseries, porcelaine), mais surtout la création des musées d'arts industriels et décoratifs, au xixe siècle, et notamment de leur modèle à tous, le Victoria & Albert Museum de Londres.
L'évolution du contexte industriel
Il n'en reste pas moins que l'économie des sociétés occidentales a connu une évolution considérable ces dernières décennies, avec la presque disparition des secteurs primaire (agriculture) et secondaire (industrie), et une réduction drastique du secteur tertiaire (les services), notamment par le recours à la sous-traitance dans d'autres pays, comme en témoignent les activités de back-office ou des call centers, de plus en plus souvent délocalisées dans des pays où le coût de la main-d'œuvre est moins élevé. Les pays émergents – la Chine en premier lieu, au même titre que nombre d'autres pays d'Asie, mais aussi d'Afrique et d'Europe de l'Est – ont largement tiré parti de cette évolution. Un tel scénario est constitutif de l'histoire économique, dont les pays les plus avancés, sur le plan technologique, ont toujours bénéficié, privilégiant sur leur territoire les productions à plus haute valeur ajoutée et commerçant avec le reste du monde, selon la théorie des avantages comparatifs, afin d'acquérir les biens (agriculture, puis les biens manufacturés) n'étant plus produits sur place. Quels seront les biens ou les services de demain qui pourraient continuer d'assurer un niveau de production suffisamment élevé et permettraient ainsi de maintenir notre niveau de vie actuel ? Une telle logique s'inscrit au cœur du raisonnement économique et des modèles fondés sur la créativité.
Cette question est au centre d'un rapport célèbre en France, réalisé par Jean-Pierre Jouyet et Maurice Lévy sur l'économie de l'immatériel. Partant du principe que les coûts de la main-d'œuvre, s'ils peuvent être légèrement diminués, ne pourront jamais rivaliser avec ceux des pays émergents, les auteurs soulignent que les facteurs clés de la compétitivité et du leadership mondial ne seront plus seulement fondés sur des questions de coûts ou des critères purement techniques, mais à partir de caractéristiques moins tangibles, comme l'image de marque, le service après-vente ou certains critères accessoires (le développement de technologies numériques sur un véhicule, ou la sophistication d'une fibre sur un vêtement). Ainsi, le moteur de l'économie de demain, pour de nombreux auteurs, sera immatériel : « une économie physique, pas de fondement physique, mais qui place les capacités intellectuelles au cœur de la création de valeur. Désormais, c'est notre capacité à créer, à innover, à inventer qui va devenir notre principal critère de compétitivité et notre première source de croissance ». On retrouve partiellement ce principe dans la notion d'économie de l'expérience : ce que le consommateur décide d'acquérir est moins un produit ou un service qu'une expérience spécifique, ou plus précisément, ce qui distingue deux produits entre eux n'est plus seulement la qualité du produit (un café), ni celui du service (le sourire ou la compétence du serveur), mais un ensemble plus diffus, qui procure au consommateur une expérience plus ou moins totale, intégrant le lieu et son atmosphère, ou le conditionnement par la publicité, comme de nombreuses chaînes de restauration – Hard Rock Café ou Starbucks – l'ont particulièrement bien compris. L'économie de l'expérience repose donc sur un ensemble tout aussi bien matériel qu'immatériel, et l'investissement le plus important, pour se différencier dans les produits reflète cette logique, étant majoritairement consacré au marketing, à l'image, au design, bien plus qu'à la seule qualité du produit ou à ses caractéristiques techniques. Dans une telle perspective, les investissements immatériels deviennent probablement aussi importants (sinon plus) que les matériels : ce sont la marque, les brevets, les savoir-faire, les logiciels, et plus encore la manière de les produire qui deviennent facteurs de succès.
Les politiques économiques visant à améliorer la croissance, dans cette perspective, tentent de stimuler les efforts dans ces domaines immatériels, soit les techniques de marketing et de communication, les technologies de l'information et de la communication, la protection des actifs immatériels (marques, brevets, droit d'auteur), mais surtout le développement de l'innovation et des moyens pour stimuler cette dernière. C'est dans cette perspective que déjà en 2000, à Lisbonne, l'Union européenne avait formulé des objectifs pour 2010 visant à investir dans « la société de la connaissance » (soit les systèmes éducatifs et les systèmes d'information et de communication), de manière à assurer l'économie la plus compétitive et la plus dynamique du monde. Ces objectifs n'ont pas été atteints, mais ont fait l'objet de mesures visant à assurer, pour les années qui viennent, les conditions nécessaires à produire une croissance fondée sur ces actifs essentiellement immatériels. Dès 2007, le commissariat à la culture présentait un Agenda européen de la culture, dans lequel il présentait cette dernière en tant que catalyseur de la créativité dans le cadre de la stratégie de Lisbonne pour la croissance et l'emploi. Dans cette perspective, la culture est présentée, selon cette rhétorique discutable, comme un facteur de développement économique majeur, et investir dans la culture revient, selon cette logique, à investir dans ce qui apparaît comme le cœur de la politique économique (l'emploi et la croissance).
Logique des industries culturelles et créatives
Le financement public de la culture, largement critiqué par les partisans d'une logique de marché, a toujours été contraint de se justifier pour démontrer son importance. On sait combien les études d'impact économique, dans cette perspective, ont joué un tel rôle, visant à montrer qu'investir dans la culture ne présentait pas une dépense improductive, sinon symbolique, mais pouvait avoir des répercussions concrètes et directement profitables pour l'emploi et la richesse nationale. C'est un raisonnement similaire qu'emploient les promoteurs de l'économie de la créativité, présentant cette dernière comme le moteur essentiel de la nouvelle économie, et la culture comme l'un des vecteurs nécessaires pour faire apparaître les conditions de son développement. Un tel argument laisse augurer de possibles investissements dans le domaine de la culture, donc de possibles subventions ; on peut comprendre qu'une partie du secteur culturel ait considéré, à l'aune du Commissaire de l'Union européenne chargé de ces matières, l'argument des industries créatives de manière très positive.
L'impact de la culture sur la créativité
Parmi les différentes stratégies qu'une entreprise peut développer afin de préserver sa position ou devancer ses concurrents, la création de nouveaux produits, ou le lancement de nouveaux modes d'organisation ou de production, est souvent envisagée. Une telle logique repose sur l'innovation perpétuelle, qui vise à développer sans cesse de nouvelles versions ou gammes de produits, qu'il s'agisse de la mode (par définition), de voitures ou de téléphones portables. Un tel mouvement demeure néanmoins limité : si l'innovation permet d'améliorer un produit existant, il en faut plus pour créer des produits résolument différents, comme les premiers téléphones, les ordinateurs personnels ou les tablettes. Cette logique, qui repose sur une vision différente, est celle de la créativité, à la base de nombreuses fortunes, notamment celles liées aux technologies numériques – d'Apple à Google, en passant par Facebook, mais aussi celles des financiers et des nouveaux produits – parfois bien critiquables – inventés pour le marché boursier. La notion de créativité a fait l'objet de recherches de plus en plus précises dès la fin des années 90, au même moment que le développement de la notion d'industries créatives. Globalement, la notion de créativité est utilisée de manière spécifique en regard des procédures générales d'innovation, tel qu'elles sont utilisées dans les entreprises en recherche et développement : « La créativité peut être comparée avec l'intelligence dans la mesure où elle se caractérise par une pensée heuristique, ouverte ou divergente, plutôt que par un processus de pensée algorithmique ou convergent ».
Si la créativité apparaît à la source de la valeur ajoutée et, souvent, des plus grandes fortunes actuelles, elle participe aussi à tous les développements économiques, qu'ils soient financiers, technologiques ou immatériels. Aussi, forcément, l'économie s'est-elle intéressée aux facteurs conditionnant la créativité. Certains individus semblent naître avec des facultés créatives hors du commun, comme les génies artistiques – de Léonard de Vinci à Mozart – en témoignent. Il n'empêche que si la créativité peut varier d'un individu à l'autre, il peut sembler possible de développer cette capacité si remarquable. La grande complexité du phénomène créatif et l'absence de méthodes fiables pour déterminer les conditions nécessaires à son développement, qui apparaissent comme l'interaction entre l'individu et son contexte socioculturel – on ne la cultive pas comme les plantes en serre – n'en ont pas pour autant empêché certains, comme Richard Florida (cf. infra), de présenter plusieurs facteurs comme ceux qui participent à son éclosion. C'est dans cette perspective que la culture est évoquée comme le terreau induisant un sens plus ou moins développé de qualités comme l'intuition, la spontanéité, la mémoire, l'imagination ou le sens de l'esthétique, autant de caractéristiques permettant d'influer sur le développement de nouvelles visions dans tous les domaines d'activité de la société, et notamment dans l'industrie.
Ainsi existerait-il un sens de la créativité pouvant être influencé par la culture (il peut en exister d'autres), fondé à partir de compétences techniques personnelles.
La « créativité basée sur la culture » dépendrait ainsi d'aptitudes personnelles (comme l'imagination ou la capacité de penser de manière non linéaire), de compétences techniques (un savoir-faire ou une intelligence manuelle), mais aussi d'un environnement social particulier. Si les politiques peuvent avoir une influence indirecte sur le développement des deux premiers facteurs, elles peuvent en revanche directement conditionner l'environnement social, via l'éducation et la culture. C'est dans une telle perspective que s'est développée la notion de « classe créative » regroupant un certain nombre de professions, comme les publicitaires, les spécialistes des technologies numériques, les architectes etc., considérée comme un élément essentiel de la société pour améliorer l'économie. Richard Florida, dans un ouvrage célèbre, mais contesté, tente de montrer les conditions nécessaires pour attirer ces créatifs, comme on a longtemps spéculé sur la manière d'attirer les investisseurs, afin de faire bénéficier l'économie du dynamisme de cette classe particulière. Il demeure cependant difficile de savoir si la créativité (et donc selon la logique des industries créative, l'économie) d'une région peut se développer proportionnellement, par l'attraction de nouveaux talents, ou si le phénomène ne fonctionne pas selon une logique du winner-take-all (le gagnant remporte la mise, cf. chapitre 14) où la richesse se développe essentiellement à partir du succès de quelques-uns.
Le secteur des industries créatives
La notion d'industrie créative est relativement récente. Si on n'en trouve pas vraiment de trace dans le développement de la notion d'industrie culturelle, au cours des années 1980, elle s'impose en filigrane, comme dans cet article de Barbara Kibbe sur les artistes créateurs et les industries culturelles, paru en 1982. C'est cependant au milieu des années 1990 qu'elle apparaît dans le monde anglo-saxon. On en trouve ainsi des traces dans la politique nationale australienne en 1994, et quatre années plus tard au Royaume-Uni. L'un des premiers ouvrages à faire le point sur ce nouveau domaine, présentant les industries créatives comme la conjonction des secteurs de la culture et du divertissement (entertainment), est l'ouvrage de Richard Cave, paraissant en 2000. Ce secteur lui-même n'est pas délimité de la même manière dans les différents pays, mais il repose sur une logique relativement identique, où l'art apparaît comme une sorte de matière première, utilisée dans la production de biens culturels ou non. En quelque sorte, de la même manière que la recherche fondamentale développée par les scientifiques trouve des utilisations par le biais de la recherche appliquée, les idées ou les formes conçues pour le marché de la culture participeraient de la conception de nouveaux produits.
Selon cette logique un peu réductrice (car on peut également développer des produits très novateurs à partir d'activités standards), Steve Jobs n'aurait pas pu développer ses produits sans l'art minimal et le white cube. Les créateurs se nourrissent de la création des autres, dans de nombreux domaines, à tel point que dès l'entre-deux-guerres, il apparaît possible d'enseigner dans une même école les arts plastiques et l'architecture (c'est le cas du Bauhaus ou du Wiener Werkstätte), et que le modèle du musée d'art moderne va associer (avec le Landesmuseum de Hanovre, puis le MoMA de New York) les arts traditionnels à l'architecture, les arts décoratifs et le cinéma. Une telle logique d'inspiration est par ailleurs ancienne : l'industrie de céramique de Wedgwood, qui a fait fortune en Grande Bretagne au xixe siècle, n'aurait pu se développer sans la céramique antique et le vase de Portland, et c'est sur un tel modèle que le Victoria & Albert Museum est conçu dans les années 1850.
Tandis que la France continue de restreindre son champ d'intervention politique à la culture et aux industries culturelles, la Grande-Bretagne adopte, dès la fin des années 90, une définition relativement extensive des industries créatives, le Department of Culture, media and sport (DCMS) intégrant, sous cette appellation, la publicité, l'architecture, le marché de l'art, l'artisanat, le design, la mode, le cinéma, les logiciels de loisir, la musique, les arts de la scène, l'édition, les services informatiques, la radio et la télévision, mais pas le patrimoine. C'est cette double vision, à laquelle s'ajoute celle de l'économie de l'expérience (notamment suivie dans les pays scandinaves), qui amène la société de consultance KEA à proposer à l'Union européenne, comme avait pu le faire David Throsby, une vision sous forme concentrique, à partir du secteur artistique, se développant aux industries culturelles, puis créatives. Malgré un tel essai de synthèse, la définition du secteur continue de susciter interrogations et critiques, notamment de la part de Philippe Bouquillion, Bernard Miège ou Yann Nicolas.
De telles discussions sur la définition du champ sont importantes, dès lors qu'il s'agit de quantifier l'activité du secteur : forcément, au plus celui-ci sera défini de manière extensive, au plus il présentera un chiffre d'affaires élevé, mais également une plus grande disparité dans ses modes de fonctionnement.
De nombreuses études, nationales ou internationales, ont ainsi tenté de mesurer la place de la culture au sein de l'économie. On peut à juste raison s'interroger sur la méthode envisagée pour ces calculs (choix des secteurs) dont on pressent qu'ils cherchent le plus souvent à démontrer l'importance de la culture dans l'économie, et donc à justifier les investissements publics qui lui sont consacrés. Ainsi le bilan présenté par KEA, en 2006, apparaît-il particulièrement impressionnant : le chiffre d'affaires de l'ensemble du secteur, de 654 milliards d'euros, participe à concurrence de 2,6 % au PIB de l'Union européenne, dépassant souvent largement certains secteurs industriels classiques, comme la chimie ou le textile. La croissance de ce secteur est présentée comme plus forte que le reste de l'économie, regroupant 5,8 millions d'emplois, soit plus de 3 % de l'emploi européen (les chiffres datent d'avant la crise). Les chiffres publiés en 2014 par le bureau d'étude Ernst & Young, tout aussi édifiants, présentent le même constat optimiste (536 milliards de CA, 7,1 millions d'emplois) sur ces secteurs rassemblant les arts, mais aussi la publicité etc.. C'est une logique similaire que l'on retrouve dans d'autres cénacles internationaux, comme les Nations unies et l'Unesco. Ainsi, le secteur des industries créatives représenterait en 2005, selon l'UNCTAD (United nation Conference on Trade and Development, ou Cnused en français), 3,4 % du commerce mondial, et des exportations de plus de 400 milliards de dollars. On retrouve les mêmes principes dans la rhétorique utilisée par l'Unesco pour promouvoir la diversité culturelle : si cette dernière apparaît comme une réponse visant à contrecarrer l'impérialisme des industries culturelles dominantes, et principalement le cinéma américain, le maintien de la diversité est présenté à son tour comme un investissement porteur d'avenir, bénéficiant au développement de tous les pays. Récemment, le ministère de la Culture, en France, présentait de la même manière une étude visant à démontrer l'importance du poids de la culture dans la vie économique du pays.
Développer la créativité
La première Exposition universelle de 1851 constitua, pour beaucoup, un révélateur pour bien des nations. À l'heure de l'élargissement du commerce mondial, la comparaison entre le niveau de qualité des produits, entre les nations, s'avérant une source d'enseignement extrêmement précieuse. On sait que c'est dans cette perspective que la Grande-Bretagne développa, la première, un réseau d'écoles d'art appliqué et de musées d'art industriel, afin d'améliorer la qualité de ses produits manufacturés. Une telle vision s'est poursuivie tout au long des années, notamment en Grande-Bretagne et aux États-Unis, à travers des départements de musée ou des maisons du design, et c'est dans le fil de cette tradition (que l'on retrouve aussi très tôt en France, au début du xixe siècle, avec des expositions nationales de l'industrie) que l'effort britannique pour les industries créatives peut être perçu.
Les villes créatives. La notion de villes créatives est apparue dans la foulée de l'ouvrage de Richard Florida, afin de décrire, mais aussi de tenter d'attirer la classe dite créative, vivant dans certains quartiers spécifiques, comme à San Francisco, et censée participer plus que d'autres au développement économique. Cette logique n'est pas neuve : dès les années 1990, la notion de qualité de vie d'un site est régulièrement mise en avant afin d'attirer les contribuables les plus dynamiques ou les plus importants ; les infrastructures culturelles participant à cet effort d'attractivité. Si l'on retient souvent de Bilbao l'impact économique important créé par l'afflux touristique, dû au Guggenheim Museum, c'est l'ensemble de la ville qui a été transformé et a permis d'attirer une nouvelle population, notamment des galeries et des créateurs. Ainsi voit-on par exemple, à partir de 2004, se mettre en place, à Londres, une plate-forme Creative London, afin de montrer les atouts de la ville en matière d'offre d'infrastructures et de supports pour faciliter l'implantation des entreprises actives dans les secteurs de la créativité. Cette logique, visant à créer des sortes de pépinières de nouveaux talents, offrant des supports en matière de promotion ou d'assistance administrative, mais aussi d'incitants fiscaux, se retrouve rapidement dans d'autres villes, notamment à Berlin, en Westphalie du Nord ou à Vienne. Une certaine logique de spécialisation a également vu le jour, comme à Montréal, qui a développé une stratégie visant à attirer les entreprises spécialisées dans le secteur du jeu vidéo par le biais d'incitations fiscales et d'infrastructures logistiques ou éducatives liées à ce projet. L'Unesco, pour sa part, a lancé dès 2004 un réseau de villes créatives, fédérées autour de thématiques culturelles comme le cinéma, le design ou la gastronomie. À ce jour, une trentaine de villes dans le monde ont rejoint ce réseau, dont Lyon (arts numériques) et Saint-Étienne (design).
Les capitales culturelles. C'est dans une telle perspective que la notion de capitale culturelle est pressentie comme un potentiel levier économique, tant pour le tourisme (cf. chapitre 13) que pour l'attraction du potentiel créatif. La logique des capitales culturelles européennes, si elle prend sa source dans un projet politique, a permis de montrer comment l'investissement dans la culture peut transformer la physionomie d'une ville – l'exemple de Glasgow est souvent cité, mais on peut également mentionner, en France, Lille ou Marseille – et lui permettre d'attirer de nouveaux habitants. Il n'empêche qu'apparemment, les résultats de telles politiques se voient plutôt à court terme. Cette même logique conduit actuellement les grandes métropoles à investir massivement dans leurs infrastructures culturelles et à se comparer afin d'espérer attirer le potentiel créateur de demain. Il n'est pas étonnant, dans ce contexte, de voir apparaître des publications comme celle lancée par le Maire de Londres, à la suite des Jeux Olympiques, comparant les grandes capitales en fonction de leur offre culturelle et de leur vie sociale.
Le Livre vert de l'union européenne. C'est dans cette même perspective qu'a été publié, en 2010, le livre vert de l'Union européenne, intitulé « libérer le potentiel des industries culturelles et créatives ». Les pistes suggérées dans le rapport visent, selon le même schéma, à investir dans les industries créatives, qu'elles soient locales, régionales ou nationales, afin de développer ce secteur en Europe, notamment par la création de nouveaux espaces d'expérimentation, la mobilité des acteurs culturels et des œuvres, la promotion des échanges culturels et leur commerce.
La logique du don au sein du processus de créativité. Il convient par ailleurs de noter l'importance des relations que l'on pourrait faire entrer dans la logique du don, au bénéfice du processus de créativité. Le principe est simple, que l'on retrouve dans la logique de l'atelier ou d'ensemble d'ateliers partagés par plusieurs artistes – on peut songer au Bateau-lavoir ou à la Ruche à Paris – dont les moyens sont limités et où l'échange gratuit apparaît aussi bien pour les biens matériels que dans le processus de créativité (le travail quasi collectif d'un Picasso et d'un Braque). La circulation du don et notamment celle des idées créatives, artistiques, à travers la communauté artistique, mais aussi scientifique, apparaît comme un processus favorisant ainsi le développement de la créativité. C'est la même logique que l'on retrouve sur internet, à travers une certaine idée du gratuit visant la circulation rapide des idées et leur amélioration, par le biais notamment de licences copyleft ou par les processus de crowdsourcing dans les communautés d'internautes, évoquées au chapitre 5.
La créativité, une nouvelle formule magique ?
Si le processus de créativité apparaît comme fondamental pour le développement d'une société – tant au niveau de son industrie que de ses productions artistiques et culturelles – il n'empêche que l'on peut s'interroger sur les raisons de l'engouement pour ce qui pourrait presque apparaître comme le nouveau Graal des sociétés occidentales et se répercute aussi bien via l'Union européenne que l'Unesco. La culture contribue-t-elle réellement à l'épanouissement de la créativité ? On le suppose, mais aucune expérience n'a jamais pu démontrer que quelques musées et autres centres culturels, un système fiscal avantageux et une certaine tolérance en matière sociale pouvaient constituer les conditions nécessaires et suffisantes pour attirer les créateurs et développer l'économie. On peut voir dans cette formule un nouvel effet de mode, auquel souscrivent bon nombre de politiques de villes de toutes tailles (car peu de chose est évoqué sur l'importance des moyens à mettre en œuvre pour déclencher le supposé phénomène) et auquel le processus de mondialisation apporte une ampleur particulière. On peut également comprendre l'alliance objective qui se présente entre, d'une part, le monde de la culture qui peut tirer parti de cette logique pour espérer obtenir plus de subventions ou, au moins, justifier ces dernières, et, d'autre part, certains économistes qui voient dans l'extension du domaine auquel ils consacrent leur carrière une potentielle reconnaissance académique. Quoi qu'il en soit, si l'on doit bien prendre en compte ce phénomène lié à la créativité tel qu'il se développe à l'heure actuelle, beaucoup de chemin reste à parcourir avant de pouvoir en définir clairement les dimensions, mais aussi pour comprendre plus précisément l'impact de la culture sur le développement de l'économie.
Protéger la créativité :
le droit d'auteur et le copyright
Si la question de l'investissement et de la promotion s'inscrit au cœur des industries créatives, les notions de protection de la créativité s'avèrent tout aussi cruciales. Il n'est guère étonnant, dans ce contexte, que les industries culturelles et créatives soient également dénommées copyright industries, tant cette notion participe au modèle économique qui prévaut dans ce secteur. L'ensemble des secteurs industriels s'est toujours reposé sur une logique privative, au cœur du système capitaliste : au même titre que la propriété privée est reconnue par un titre de propriété, l'invention appartient à son inventeur pour autant que ce dernier ait déposé un brevet montrant le caractère original de son procédé technique. Cette logique s'est trouvée renforcée, dans le monde de la culture, à travers la notion de droit d'auteur, en France, et de copyright, dans les pays anglo-saxons. Faut-il le souligner ? L'avènement de la notion d'originalité, qui caractérise notre système artistique à partir du xixe siècle, vient en parallèle avec le développement du droit d'auteur : pour qu'il y ait droit d'auteur, il convient de montrer le caractère original d'une œuvre (soit après un litige, et donc de façon ex post, soit en le déclarant auprès d'une société de droit d'auteur, afin de le protéger automatiquement), et c'est ce principe qui garantit, en quelque sorte, à l'artiste (qu'il soit plasticien, écrivain ou musicien) un monopole sur sa production, lui permettant de tirer pleinement profit de sa commercialisation. Le plagiat, dans cette perspective, est condamnable devant les tribunaux. La copie, si elle peut être envisagée – elle est même indispensable pour le marché de l'édition littéraire ou musicale et pour le cinéma – est sévèrement réglementée, au bénéfice du propriétaire de l'œuvre originale (certains de ces droits étant inaliénables dans le droit d'auteur, comme la paternité d'une œuvre, tandis qu'ils peuvent être cédés dans le cas du copyright mais avec des conditions très spécifiques). De manière générale, le copyright ou le droit d'auteur permettent de lier le secteur des arts, des industries culturelles et créatives, comme la mode ou le design. C'est sur base de la logique du copyright que le secteur du luxe (la mode et ses accessoires, comme les sacs Louis Vuitton ou les vêtements Lacoste) a entamé, depuis de nombreuses années, une guerre à la contrefaçon, comme l'industrie du film et de la musique a tenté de préserver son modèle économique largement remis en cause depuis l'avènement d'internet.
Économie et légitimité du droit d'auteur
S'il est un secteur qui s'est extrêmement développé ces dernières années, c'est bien celui de l'industrie de la protection du droit des auteurs. Car il existe bien une économie du copyright, qui peut être appréhendée pour elle-même, se développant par le biais des sociétés de gestion des droits (soit des sociétés visant à regrouper les auteurs ou détenteurs de droit et à assurer la perception collective de leurs droits) et des avocats chargés de les faire respecter. Le prélèvement de droits au bénéfice des auteurs sur des photocopies ou sur des photos de monuments, l'instauration de droits voisins (les interprètes d'œuvres musicales, certains techniciens) ou du droit de suite (cf. chapitre 8), représente une économie particulière dont les enjeux financiers sont considérables.
La question se pose immédiatement à partir des débuts de l'industrie du livre, lorsque les premiers imprimeurs affinent leur technologie alors révolutionnaire... mais dont le procédé est reproductible, obtenant pour leur implantation des privilèges de monopole, durant une durée plus ou moins longue. Le droit des auteurs se développe parallèlement en Grande-Bretagne (un premier copyright de 14 ans est octroyé pour les auteurs, en 1709) et en France, au xviiie siècle, Beaumarchais fondant la première société d'auteurs en 1777, la Révolution française entérinant le principe d'une propriété littéraire et artistique. Dès cette époque, cependant, les positions divergentes s'affrontent, entre les partisans d'une propriété perpétuelle, transmise à la famille, et ceux d'une propriété publique totale. C'est donc un compromis qui est envisagé, garantissant la propriété d'une œuvre à son auteur, durant sa vie et quelques années après sa mort, avant son entrée dans le domaine public. Quelques exceptions au droit d'auteur existent également, comme le droit de citation et les cas pour lesquels la recherche des ayants droit s'avérerait trop coûteuse par rapport au bénéfice escompté (fair use). Cette propriété de l'œuvre par les ayants droit, après la mort de l'auteur, sera progressivement étendue : vers la fin du xixe siècle, elle est amenée à 50 ans après la mort, pour atteindre 70 ans dans la majorité des pays. La convention de Berne, initiée en 1886, étend ce droit aux auteurs des États signataires. Ces accords sont actuellement gérés sur un plan mondial, au sein de l'ADPIC (Accords sur les aspects du droit intellectuel qui touchent au commerce) et de l'OMPI (Organisation mondiale de la propriété intellectuelle, fondée en 1967).
Le raisonnement économique favorable au droit d'auteur repose sur le principe que la création artistique, industrielle ou non, présente un investissement considérable en temps et en argent (le budget d'un film de cinéma ou d'un jeu vidé), qu'il est nécessaire de pouvoir rentabiliser. S'il n'existait pas de possibilité pour un investisseur de se prémunir du risque de se voir copier, celui-ci n'aurait aucune incitation à investir, puisqu'il perdrait à coup sûr sa mise. Cette logique doit cependant être nuancée par la notion même de propriété de l'auteur, qui est très relative. Celui-ci a en effet souvent largement été influencé par d'autres auteurs (Manet s'inspirant de Raphaël ou Disney de Victor Hugo), alors que ces derniers ou leurs descendants n'en touchent aucun bénéfice. Par ailleurs, si certains auteurs – Victor Hugo, Michael Jackson ou Jean Nouvel – peuvent bénéficier de droits considérables, dus à leur statut de star (cf. chapitre 14), la rémunération de la plupart des autres demeure très modeste, du moins pour ce qui concerne les droits versés. Ainsi, de nombreux auteurs (artistes travaillant pour l'administration ou scientifiques universitaires) bénéficiant déjà d'un traitement ne dépendent nullement du droit d'auteur pour leur subsistance. C'est ainsi un système essentiellement fondé sur une logique bénéficiant aux auteurs déjà largement rétribués, que vise à protéger ce type de droits, au détriment d'une diffusion plus importante de leur œuvre.
Dans cette perspective, d'autres logiques de rémunération pourraient être envisagées, comme la prise en charge complète des artistes par les pouvoirs publics (qui a été largement appliquée du temps de l'Union soviétique ou dans la Chine de Mao), considérés comme des fonctionnaires de l'État et qui, moyennant un système de récompenses symboliques, voient leur production tomber immédiatement dans le domaine public.
Ce débat a bénéficié d'un regain d'intérêt dans le cas du développement d'internet, la diffusion des œuvres se multipliant de manière exponentielle, tandis que les coûts de copie et de reproduction s'avèrent quasiment nuls. Les secteurs les plus touchés – la musique et le cinéma – ont immédiatement songé à des ripostes plus ou moins radicales, comme le système Hadopi en France, avec des résultats mitigés. C'est dans cette perspective que le modèle de la gratuité des droits est revenu à l'avant de la scène. Ainsi, de nouveaux modèles économiques ont vu progressivement le jour, fondés – comme Google ou YouTube – sur un financement par la publicité, ou comme Deezer par un mixte de gratuité et d'abonnement. La culture de la gratuité, ainsi, s'est opposée frontalement à la logique du droit d'auteur. Pour les uns, partisans de la logique de Friedman (There is no free lunch), « la gratuité, c'est le vol », et toute contravention aux règles du copyright doit être sévèrement sanctionnée. Pour les autres, au contraire, la gratuité stimulerait elle-même les ventes, les téléchargeurs illégaux s'avérant aussi être de grands consommateurs, tandis qu'elle serait largement profitable au développement de la créativité. C'est dans cette même logique que l'on a vu se développer des mouvements sur internet en faveur du copyleft, un droit reconnaissant la paternité et le droit de citation d'une œuvre, mais dont la cession est gratuite. C'est un tel principe qui anime des communautés autour de projets comme Wikipedia ou Linux.
Organisation actuelle du droit d'auteur
Si le droit d'auteur est parfois critiqué, c'est peut-être moins pour son principe que pour son organisation pratique, reposant essentiellement sur l'existence de sociétés chargées de percevoir ces droits, dont le fonctionnement n'apparaît pas toujours comme optimal. Théoriquement, bien sûr, chaque auteur peut veiller seul à l'exploitation de ses droits. Pratiquement, seuls les ayants droit de quelques artistes très célèbres (les héritiers Matisse ou Picasso) ont les moyens nécessaires pour rémunérer une équipe suffisante afin de faire respecter leurs droits dans le monde. Le recours à un prestataire de service tiers s'avère dès lors la solution la plus simple. Dans le cas du cinéma ou du livre, c'est le producteur ou l'éditeur qui se charge de conclure un contrat avec l'auteur et de lui reverser les droits. Pour les autres domaines artistiques – musique, photo, graphisme, théâtre etc. – ce sont des entreprises spécialisées qui se chargent de ces transactions. Ainsi, en France, une vingtaine de sociétés se partagent ce marché, notamment la SACD (société des auteurs et compositeurs dramatiques), la SCAM (société des auteurs multimédia) ou la SACEM (société des auteurs, compositeurs et éditeurs de musique).
La gestion de telles sociétés a fait l'objet de nombreuses réactions négatives, critiquant le peu d'explicitation des méthodes de répartition et l'importance des frais de fonctionnement des sociétés (de l'ordre de 20 %). Leur situation de monopole leur permet ainsi d'imposer à la fois des droits relativement élevés auprès des exploitants des œuvres figurant à leurs répertoires et des frais de gestion importants à leurs adhérents, tout en les contraignant peu à améliorer leurs méthodes de gestion.
. L'économie de l'immatériel et l'économie de l'expérience sont évoquées plus bas.
. Bouquillon P., Miège B et Moeglin P., L'industrialisation des biens symboliques. Les industries créatives en regard des industries culturelles, Grenoble, Presses universitaires de Grenoble, 2013, p. 24.
. Menger M., Portrait de l'artiste en travailleur. Métamorphose du capitalisme, Paris, Le Seuil, 2002.
. Greffe X., L'artiste-entreprise, Paris, Dalloz, 2012.
. Jouyet J.-P., Lévy M., L'économie de l'immatériel : la croissance de demain. Rapport de la Commission sur l'économie de l'immatériel, 2006, p. 7. Disponible sur : <http://ec.europa.eu/internal_market/copyright/docs/links/immateriel_fr.pdf> (consulté en juillet 2013).
. Pine II B. Joseph, Gilmore J. H, The experience economy: work is Theatre & every Business a Stage, Boston, Harvard Business School Press, 1999.
. On songe aux études présentées dans le cadre de l'évaluation des retombées sur Bilbao, très largement utilisées pour justifier la création d'autres musées ou autres infrastructures culturelles. Voir le chapitre 4.
. Brabandere L. de, La Valeur des idées, Paris, Dunod, 2007.
. Sternberg R.J., Handbook of Creativity, Cambridge, Cambridge University Press, 1999.
. Bryant, W. D. A. et Throsby D., « Creativity and the Behaviour of Artists », in Ginsburgh V. A. & Throsby D, Handbook of the economics of art and culture, vol. 1, North-Holland, 2006, p. 507-529. Voir aussi Brabandère L. de, op. cit.
. Csikszentmihalyi M., Creativity: Flow and the Psychology of Discovery and Invention, New York, Harper Perennia, 1996.
. Throsby D., The Economics of Cultural Policy, Cambridge, Cambridge University Press, 2010, p. 95 sq. ; Flew T., The global creative industries, Cambridge, Polity Press, 2013.
. Voir l'étude produite pour l'Union européenne : KEA, The Impact on culture on creativity, 2009. Étude conduite pour la Commission européenne. Disponible sur : <http://ec.europa.eu/culture/key-documents/doc/study_impact_cult_creativity_06_09.pdf> (consulté en décembre 2011).
. Florida R., The Rise of the Creative Class : and How it's Transforming Work, Leisure, Community and Everyday Life, New York, Basic Books, 2002. Voir Vivant E., Qu'est-ce que la ville créative ?, Paris, PUF, coll. « La ville en débat », 2009 ; Greffe X., Artistes et marchés, Paris, La Documentation française, 2007, p. 280 sq.
. Kibbe B., « Les artistes créateurs, les industries culturelles et la technologie aux États-Unis d'Amérique », in Unesco (Collectif), Les industries culturelles. Un enjeu pour l'avenir de la culture, Paris, Unesco, 1982, p. 107-124.
. Throsby D., « Public funding of the Arts in Australia. 1900-2000 », in Australian Bureau of Statistics, Australian Yearbooks 2001, p. 548-561.
. Caves R., Creative Industries. Contratcts between art and commerce, Cambridge, Harvard University Press, 2000.
. Bouquillion P. (dir.), Creative economy. Creative Industries, Des notions à traduire, Saint-Denis, Presses universitaires de Vincennes, 2012.
. KEA, Study on the economy of culture in Europe, Bruxelles, 2006, Étude conduite pour la Commission européenne. Disponible sur : <http://ec.europa.eu/culture/key-documents/doc873_en.htm> (consulté en juillet 2013).
. Ernst & Young, Les secteurs culturels et créatifs européens, générateurs de croissance, décembre 2014. Disponible sur : <http://www.ey.com/FR/fr/Newsroom/News-releases/communique-de-presse---ey--secteurs-culturels-et-creatifs-europeens> (consulté en décembre 2014). De telles études (autant celle de KEA que celle d'E&Y) ne peuvent être qualifiées de totalement objectives, ayant notamment pour ambition première de montrer l'importance et la dynamique du secteur...
. UNCTAD (United Nations Conference on Trade and Development), Creative Economy. Report 2008, United Nations, 2008. Disponible sur : <http://www.unctad.org/en/docs/ditc20082cer_en.pdf> (consulté en août 2013).
. Unesco (Collectif), Politiques pour la créativité. Guide pour le développement des industries culturelles et créatives, Paris, Unesco, 2011. Disponible sur : http://www.unesco.org/new/fr/culture/themes/cultural-diversity/diversity-of-cultural-expressions/tools/policy-guide/ (consulté en juillet 2013).
. Kancel S. et al., L'apport de la culture à l'économie en France, Paris, Inspection générale des Finances et Inspection générale des affaires culturelles, décembre 2013. Disponible sur : http://www.ladocumentationfrancaise.fr/rapports-publics/144000006.
. Greffe X., Artistes et marchés, Paris, La Documentation française, 2007, p. 157-217. C'est un rôle similaire que l'on retrouve dans les grandes écoles allemandes, comme celle du Bauhaus à Weimar et Dessau, durant l'entre-deux-guerres, puis celle d'Ulm à partir de 1953.
. Audit Commission, The Road to Wigan Pier? Managing Local Authority Museums and Art Galleries, Londres, HMSO, 1991. Cf. également les travaux de Allen J. Scott sur la localisation des industries culturelles et créatives et les effets bénéfiques de la proximité géographique [Scott A. J., « Creative cities: the role of culture », Revue d'économie politique, vol. 120, 2010, p. 181-204] ou ceux de l'équipe de Patrick Cohendet sur l'industrie du jeu video et la ville de Montréal [Cohendet P, Granddadam D., Simon L., « The anatomy of the creative cities », Industry and Innovation, vol. 17, 2010, p. 91-111].
. Voir les articles présentés sur le site internet Scholars on Bilbao, qui répertorie tous les articles scientifiques sur ce sujet : <http://www.scholars-on-bilbao.info/list.php?var=list> (consulté en juillet 2013).
. Cohendet P., Simon L., « Playing across the playground: paradoxes of knowledge creation in the videogame firm », Journal of Organizational Behavior, vol. 28, no 5, juillet 2007, p. 587-605.
. Richards G., « The European Cultural Capital Event: Strategic Weapon in the Cultural Arms Race? », Journal of Cultural Policy 6(2), p. 159-181; Palmer/Rae Associates, European Cities and Capitals of Culture. Study prepared for the European Commission, Bruxelles, 2004. Disponible sur : <http://ec.europa.eu/culture/pdf/doc654_en.pdf> (consulté en juillet 2013).
. Mayor of London, World Cities Culture Report, Londres, 2012. Disponible sur : <http://www.london.gov.uk/sites/default/files/WorldCitiesCultureReport.pdf> (consulté en juillet 2013).
. Commission européenne, Livre vert. Libérer le potentiel des industries culturelles et créatives, Bruxelles, 2010. Disponible sur : <http://ec.europa.eu/culture/our-policy-development/doc/GreenPaper_creative_industries_fr.pdf> (consulté en décembre 2010).
. Sur la communauté scientifique et artistique, voir les articles de Lewis Hyde et Jacques Godbout dans Chanial P. (dir.), La société vue du don. Manuel de sociologie anti-utilitariste appliquée, Paris, La Découverte, 2008.
. Anderson C., Free ! Entrez dans l'économie du gratuit, Paris, Pearson, 2009.
. Voir Gordon W., Watt R. (dir.), The Economics of Copyrigth, Northampton, Edwar Elgar, 2003.
. Pour une étude générale sur cette question : Greffe X., Économie de la propriété artistique, Paris, Economica, 2005.
. Ainsi pour Venise, qui octroie un tel privilège à l'imprimeur Johan von Spreyer lorsqu'il s'installe dans la ville. Voir Benhamou F., Farchy J., Droit d'auteur et copyright, Paris, La Découverte, 2009 (nouv. éd.).
. Olivennes D., La gratuité, c'est le vol, Paris, Grasset & Fasquelle, 2007.
. Voir par exemple Collectif, La bataille Hadopi, Paris, In Libro Veritas, 2009.
. Rochelandet F., « Are Copyright Collecting Societies Efficient Organisations? An Evaluation of collective Administration of Copyright in Europe », in Gordon W.J., Watt R. (eds), The economics of copyright, Cheltenham, Edward Elgar, 2003, p. 176-197 ; Jouyet J.-P., Lévy M., op. cit. ; Greffe X., op. cit., p. 99 sq.
Chapitre 13
Temporalité, spatialité
Nous sommes conditionnés par notre rapport au temps et à l'espace, deux dimensions apparemment objectives, quantifiables, mais dont le fondement est conditionné par les civilisations. La question du temps influe immédiatement sur notre rapport à la vie : temps de travail ou de loisir qui augmente ou diminue, celui-ci conditionne aussi l'économie et notamment celle des arts et de la culture. Comme notre rapport au temps, celui à l'espace a radicalement évolué au cours des dernières décennies. Ce qui nous paraissait infiniment loin s'est rapproché de manière étonnante ; en même temps, il semble parfois plus rapide de parcourir quelques milliers de kilomètres que d'atteindre un lieu proche dont nous connaissons mal le chemin.
La phrase d'Andy Warhol, prononcée en 1968, est restée célèbre : « In the future, everybody will be world famous for 15 minutes ». À l'aune de la téléréalité et du buzz sur internet, une telle formule ne peut manquer de faire réfléchir. Bien sûr, une telle prédiction est forcément liée au développement des nouvelles technologies, mais aussi au temps et à l'espace, au rétrécissement, en quelque sorte, d'un certain type de temporalité et à l'allongement des zones de couverture médiatique. L'économie de la carrière artistique qui en découle ne peut manquer de se transformer au gré des processus de starification (cf. chapitre 14), comme le montrent les carrières de Loana, première star du Loft, ou celle de Susan Boyle, championne de Britain's got talent. Mais plus encore, c'est l'ensemble des modes opératoires de la diffusion de l'art et de notre appréciation ou nos modes de consommation de l'art qui se conjugue sur le mode de l'immédiateté et des longues distances.
Temps, espace, économie
La conception d'un temps linéaire, faut-il le rappeler, est occidentale et s'oppose au temps cyclique de l'éternel retour. C'est cette linéarité qui permet l'Histoire, telle que nous l'envisageons : une histoire avec un commencement (le big bang, mais aussi, en Europe, la naissance du Christ) et qui suppose une fin du monde (que nous espérons la plus éloignée possible). C'est cette même linéarité qui permet de développer la notion de patrimoine et la valeur d'ancienneté, tel qu'elle s'est imposée essentiellement à partir du xixe siècle, laquelle influence largement l'économie de la culture. Cette linéarité du temps a pendant longtemps été vécue parallèlement au temps cyclique : cycle des saisons, de la vie et de la religion (de la naissance à la résurrection du Christ). Ce temps cyclique est celui de la culture et du sacré, et pendant longtemps (jusqu'à la Première Guerre mondiale), il prédomine sur la linéarité, notamment dans les campagnes. Cette société « sans âge » s'efface progressivement face à la modernité, au bénéfice de celle que nous connaissons de nos jours, l'effacement des religions, la maîtrise des saisons agricoles et les avancées technologiques ont raison de ce cycle lent, donnant à notre vie une dimension bien plus directement linéaire. Une linéarité qui n'en demeure pas moins, au début, relativement lente, au gré des voyages à pied, en cheval ou dans les premiers trains, mais qui va s'accélérer progressivement, donnant de l'espace une nouvelle représentation. Il faut actuellement trois heures pour joindre Paris et Marseille, en TGV, alors qu'il en fallait plus de 16 à la fin du xixe siècle et que le même trajet nécessitait une quinzaine de jours un siècle plus tôt, à une époque où les limites du monde lui-même n'étaient pas encore définies. Le processus de mondialisation, qui se met en œuvre parallèlement au développement du capitalisme et de la révolution industrielle, contribuera largement à refaçonner totalement notre rapport au temps et à l'espace.
Le tour du monde en 80 jours, de Jules Vernes (1872), constitue une parfaite illustration de la volonté occidentale de maîtrise du monde et du temps, sur fond de colonialisme. Le tour de force de Phileas Fogg, traversant les continents en à peine plus de douze semaines, marque la domination technologique européenne des transports et bouleverse notre rapport aux distances, mais il présente aussi la maîtrise du temps comme une performance remarquable. Le temps, le capitaliste investisseur et prêteur le sait bien, c'est de l'argent ; les distances, c'est aussi de l'argent, et la maîtrise de l'un et de l'autre facilite forcément l'enrichissement, tandis que la découverte de nouveaux territoires permet, elle aussi, d'augmenter la richesse. Le rapport de notre économie occidentale sera ainsi marqué par ce rapport aux temps et à l'espace, se transformant au gré des explorations de nouveaux marchés, en Amérique, en Russie ou en Chine. Une telle maîtrise du temps se retrouve non seulement au programme de Fogg et de Passepartout, mais aussi des ouvriers d'usine, dont les journées sont cadencées de manière optimale. Aussi l'émancipation ouvrière passe-t-elle par la réduction du temps de travail – l'obtention des « trois huit », soit huit heures de travail, huit heures de sommeil et huit heures de loisir, alors que la journée, à la fin du xixe siècle, tourne autour des 12 à 15 h. L'obtention de la journée de 10 h, en 1900 en France, constitue une première victoire. Ce sera cependant à ce moment que le gestionnaire concentrera son effort, dans une optique tayloriste (séparation des tâches et chronométrage) pour que le temps investi à l'usine soit le plus efficace possible.
Les temps modernes, le film de Chaplin (1936), présente un monde ayant intégré jusque dans ses pires excès la logique tayloriste. Cette époque voit s'annoncer en France les congés payés et la semaine de 40 h, qui constitue une émancipation notoire et donne la possibilité d'un temps de loisir, mais suscite la critique d'Adorno et Horkheimer, qui voient dans la « culture » proposée en guise de loisir, le jazz ou le cinéma de l'entre-deux-guerres, le même conditionnement des masses que celui des usines capitalistes. Ce moment d'ouverture progressive à un possible temps de loisir se poursuit durant les trente glorieuses, qui voient s'établir progressivement, au gré de la réduction du temps de travail, ce qui apparaît comme une époque de productivité et de mutations profondes.
Nous nous situons certes dans le prolongement de cette logique de loisir, dans un univers mondialisé où sur chaque continent, nous pouvons trouver les éléments d'une même culture mainstream, pimentée de particularités locales. Le temps de loisir, incontestablement, s'est allongé, d'abord par la diminution du temps de travail (de 40 à 35 h), ensuite par l'allongement du temps de retraite conjugué à l'augmentation de notre espérance de vie. C'est du moins, bien sûr, un tel constat que l'on peut tirer pour les pays anciennement industrialisés, les conceptions spatio-temporelles s'avérant encore largement différentes en Chine ou en Afrique du Sud.
La question de l'espace
Notre vision subjective de l'espace n'a plus grand-chose à voir avec celle de nos ancêtres. Non seulement le franchissement des distances est plus rapide, mais il est aussi devenu bon marché, alors qu'il n'était réservé qu'à l'élite. La révolution des transports low cost a induit des changements de pratiques culturelles considérables, nous pouvons ainsi nous déplacer, pour un week-end, dans une capitale européenne, sans considérer une telle action comme déraisonnable. Le monde entier semble entre nos mains, l'impression que nous pouvons en ressentir, à travers l'utilisation de Google earth, n'a jamais autant donné l'impression d'un village planétaire.
La diminution du coût des transports, la rapidité des interconnexions et la connaissance de ce que font nos voisins aux quatre coins du monde, induit au moins deux conséquences majeures : d'une part, le principe d'un marché de débouchés mondial et une logique de produits mainstream, d'autre part, un développement des flux touristiques sans précédent. L'idée de produits généraux – qu'il s'agisse d'ordinateurs ou de chaussures de sport, mais aussi de musique ou de films de cinéma, voire d'œuvres d'art – destinés à un marché mondial a révolutionné les modèles économiques de l'économie de la culture. Le phénomène Psy, dont la vidéo Gangnam Style a été la première à être visionnée plus d'un milliard de fois sur YouTube, s'explique non seulement par l'existence d'internet, mais aussi par la possibilité d'acheminement d'une offre dématérialisée aux quatre coins du monde, et par le fait que le chanteur, lui aussi, bien qu'un peu moins rapidement qu'internet, a parcouru le monde. C'est la même logique qui permet à Christie's et Sotheby's d'envoyer les œuvres à l'endroit de la planète où elles se vendront le mieux, et aux collectionneurs du monde entier de suivre les enchères en direct, sur place ou par téléphone. Si le marché est le monde, il faut bien des compagnies de taille mondiale pour tenter de les conquérir, et il n'est guère étonnant, dans cette perspective, que le développement d'oligopoles mondiaux, dans le secteur de la musique, du film, du livre ou de la télévision, n'ait cessé de se préciser au fil des années. Le regroupement auquel on assiste, intégrant ces différents secteurs (les américains Disney, Time Warner, News corps, Viacom, NBC et le japonais Sony), laisse penser à une concentration encore plus forte dans les années à venir.
L'influence de la réduction spatiale du monde est manifeste pour la fréquentation des lieux de patrimoine, comme nous le présenterons plus loin, et les villes d'art et capitales culturelles profitent de ce changement reflété partiellement par les études d'impact économique. En revanche, certains secteurs de la culture, comme une partie de la littérature et de la poésie, semblent nettement plus imperméables à ces changements spatiaux, leur marché pouvant plus difficilement, pour des raisons techniques (de traduction et de particularismes) être adaptés à un goût universel.
De manière générale cependant, contrairement aux secteurs de l'industrie classique, le monde de la culture, comme industrie de prototype, est relativement éloigné de problèmes de délocalisation que l'on observe dans l'automobile, mais aussi dans les services. Certes, à la marge, quelques services peuvent être sous-traités, comme les questions de réservation ou de service après-vente, mais ils sont rares.
La question du temps
Plus que l'espace encore, la transformation de notre notion du temps a conditionné notre rythme de travail, de production, mais aussi de consommation. Si l'on parle de slow et de fast food pour la nourriture, il existe aussi un mode de consommation rapide pour la culture, peut-être avec les mêmes conséquences.
Le raccourcissement du temps conduit à la notion de quasi-instantanéité, qui a pu être expérimentée à partir du télégraphe, puis du téléphone et du fax, et que l'on exige maintenant de sa connexion internet. Les méthodes de production, elles aussi, n'ont cessé de chasser le « gaspillage temporel », privilégiant le respect des délais et l'accélération des livraisons et la production « minute », just on time, sans stocks trop coûteux. Une grande partie des métiers de la culture est depuis longtemps confrontée à la pression des dates de livraison, qu'il s'agisse de l'inauguration d'une exposition ou de la première d'une pièce de théâtre. Il n'en reste pas moins que les cadences, au fil des années, se sont accélérées. À l'image de l'intermittence, la carrière de l'artiste en travailleur est de plus en plus flexible, et celui-ci, qui pouvait naguère espérer passer sa vie dans une même entreprise, sera de plus en plus souvent confronté à une quinzaine d'emplois différents au cours de sa vie, avec des perspectives d'avenir forcément plus limitées.
On le sait, l'organisation de la productivité, comme dans le secteur des arts de la scène, si elle peut être parfois améliorée, possède des limites bien balisées : on ne peut augmenter le tempo d'un quatuor de Beethoven ni réduire le nombre de ses interprètes (cf. chapitre 6). Ce principe, qui a fait la renommée de Baumol, impose certaines limites aux réductions du temps de préparation d'une œuvre. Il n'en demeure pas moins que si, sur scène, l'artiste demeure dans un temps – partiellement sacré – qui lui appartient ou appartient à l'œuvre, le temps de répétition, lui-même, a tendance à diminuer, tant pour les arts de la scène que pour la préparation d'une exposition.
Le temps du loisir
L'accélération des temps de production se poursuit, provoquant une frénésie dont Charlot montrait, de manière caricaturale, les répercussions potentielles. On pourra rétorquer qu'en revanche, le temps de loisir a justement augmenté, permettant à chacun de se reposer comme aucune génération n'en a eu la possibilité. Ce temps de loisir constitue, pour le monde de la culture, le moment pour apprécier ou consommer des produits relevant de ce secteur. On peut distinguer, à cet égard, deux secteurs différents, selon la possibilité que le consommateur demeure sur place ou se déplace en dehors de son lieu de vie.
Le temps du loisir sur place
Après le travail, le repos. La période la plus régulière du loisir est quotidienne, mais très limitée. Une fois les heures de travail terminées, les tâches ménagères effectuées, quelques heures au plus s'offrent à ceux qui se destinent, avant de dormir, à une activité de loisir. Nombreux sont ceux qui occupent cette tranche quotidienne avec la télévision, pendant que certains continuent de lire, d'aller au théâtre, au musée ou au cinéma.
On doit à McLuhan et à son maître, Harold Innis, une réflexion majeure quant à l'influence de la structure des médias sur leur contenu (The medium is the message, ou le médium structure le message). La structure du médium lui-même peut être envisagée comme conditionnée par la structure économique. Le passage de l'oralité au monde de l'écrit plonge l'humanité dans une nouvelle vision du monde, orientée par le livre. La Galaxie Gutenberg, pour reprendre le titre de l'un des ouvrages de McLuhan, détermine son mode de fonctionnement : une structure linéaire (de gauche à droite, de haut en bas) et continue, favorisant la vision et fondée sur l'intellect, mais également située dans la temporalité de la lecture. Lire un livre requiert souvent plusieurs heures, et cette activité constituera l'un des loisirs par excellence, qu'il s'agisse de la bible (notamment chez les protestants) ou de romans. Le temps du loisir, dans cette perspective, peut encore s'envisager comme un moment permettant de se délasser, de se divertir, mais aussi de se former, et l'éducation populaire ou permanente, dans cette perspective, constitue la possibilité, à partir du temps de loisir, d'une formation à la citoyenneté.
Peut-être une telle réflexion eut-elle été possible à une époque sans télévision, vue pourtant, à son origine, comme un puissant vecteur d'émancipation. McLuhan souligne, à juste titre, la révolution que constitue cette technologie fondée sur l'image, dont la structure n'est pas linéaire (un journal télévisé, par exemple) et dont le rythme diffère fondamentalement de celui de la lecture. C'est par la télévision que, progressivement, un sentiment de monde global émerge, mais aussi qu'une autre logique s'installe dans le temps du loisir. McLuhan, optimiste, voyait dans l'avènement de cette révolution médiatique une transformation radicale de notre manière de penser la société. Car le médium influençant à son tour notre manière de voir le monde, c'est non plus conditionné par l'écrit, mais par l'image mouvante et non linéaire que nous voyons le monde. Quelques années plus tard, le constat de Neil Postman, théoricien des médias, s'avère quant à lui nettement plus pessimiste, voyant dans la structure télévisuelle, et notamment à travers les changements de temporalité, un nivellement radical par le bas. Ainsi, le débat politique qui, jusque durant l'entre-deux-guerres, pouvait durer plusieurs heures et présenter les traits d'une argumentation structurée, a-t-il laissé la place, lorsqu'il a investi la petite lucarne, à un show alternant les courtes séquences, donnant la prééminence aux effets de manche sur l'argumentation. Est-ce la cadence du travail qui progressivement a déteint sur les rythmes de la télévision, ou son rythme propre ? Toujours est-il que la temporalité infligée par cette dernière renforce nos modes de consommation de micro-séquences, tout en influant sur nos capacités de concentration. On sait la place qu'a prise la télévision, comme première pratique culturelle – et de loin – des Occidentaux. Les usages résultant d'internet, unissant à nouveau texte et image, conduiraient-ils à une autre temporalité ? On pourrait en douter, lorsque l'on constate les modes de fonctionnement des réseaux sociaux comme Facebook et Twitter, privilégiant des temps de réponse toujours plus courts, construits de manière simpliste, leur histoire semblant s'évanouir aussitôt publiée.
Ainsi, conditionnés et aidés par des médias se déclinant de manière toujours plus rapide, semblons-nous consommer la culture toujours plus rapidement. La télévision n'est pas la seule à avoir vu son rythme se transformer : les rythmes musicaux (la musique électronique notamment) ont pu atteindre des cadences qui laisseraient rêveur un entrepreneur tayloriste, tandis que le montage des films de cinéma (le nombre de plans-séquences), lui aussi, s'est accéléré – à tel point qu'un cinéphile des années trente pourrait être passablement désorienté face à un film d'action actuel. Une telle logique se retrouve dans les jeux vidéo dont ils constituent l'un des principes de base (l'accélération des épreuves, au point qu'il ne devient plus possible de jouer). Certes, il existe encore bon nombre de moments dont la cadence n'est guère différente de celle qui était connue il y a deux siècles, comme l'écoute d'un concerto de Mozart ou un passage chez le coiffeur ; il n'en reste pas moins que les questions de rapidité semblent conditionner une part toujours plus grande de notre existence, allant jusqu'à se présenter dans notre expérience de travail (nous en changeons beaucoup plus souvent qu'il y a deux générations) ou la vie de couple. Par-delà la consommation, la logique d'exploitation, elle aussi, apparaît comme toujours plus rapide. S'agit-il d'une impression du temps qui s'accélère, ou d'un phénomène découlant d'une offre trop importante multipliant de manière exponentielle les possibilités de choix, et donc diminuant d'autant l'attention qui pourrait être consacrée à l'ensemble des biens ? Toujours est-il qu'un film, s'il ne répond pas à la demande après deux semaines, quittera l'affiche, comme la plupart des livres et des disques quitteront leurs rayons et leurs bacs (il semble pouvoir rester plus longtemps sur internet, pour autant que l'évolution de ce médium ne transforme la situation). Le remplacement systématique, dès les premiers signes d'obsolescence, semble produire une production de la nouveauté perpétuelle, où les produits classiques, sauf s'ils sont encore largement rentables (comme les films de Disney), disparaissent des présentoirs. Dans cette perspective, bien des ouvrages et des expositions, mais aussi des films – à commencer par Citizen Kane (Orson Welles) – risqueraient de disparaître rapidement.
Même des lieux tournés vers le passé, comme les musées, sont marqués par de tels modes de consommation. Institutions de la permanence par excellence, les voici devenus de plus en plus temporaires. Après tout, le monde des arts de la scène fonctionne de manière identique depuis des siècles, tandis que les foires commerciales constituent, depuis l'Antiquité, un moment de rupture et de nouveauté en regard des marchés traditionnels. L'un n'excluait pas l'autre, ce qui a tendance à devenir le cas de nos jours. Le phénomène de la disparition du musée permanent inquiète depuis les années 1950. À l'époque, pourtant, le phénomène n'est qu'embryonnaire, et le musée demeure encore relativement peu populaire. C'est à partir des années 1980, lorsqu'il développe de grandes expositions blockbusters, que son succès s'accroît. Car l'exposition temporaire, avec une date de début et une fin, incite à la fréquentation, contrairement au musée permanent, censé demeurer immobile. Aujourd'hui, le musée sans événements temporaires ne trouvera plus d'écho médiatique, ce mode de communication passant par l'actualité.
Le temps du loisir d'escapade
La conquête des congés payés a constitué non seulement une grande victoire pour les travailleurs, mais a aussi donné la possibilité d'envisager d'autres pratiques culturelles. Par-delà la période des congés traditionnels, en juillet et août, l'éventualité d'une escapade de quelques jours ou d'un week-end s'est trouvée renforcée par la réduction du temps et des coûts de transports. Cette temporalité est utilisée de la même manière que les autres, pour se détendre et se délasser, mais aussi pour s'instruire. Ces deux dernières possibilités ont induit deux phénomènes importants, qui ne cessent de se développer au sein de la culture : le tourisme culturel et les festivals.
Le temps des festivals. Contrairement à la foire ou à l'exposition temporaire et à la pièce de théâtre, le festival constitue une offre temporaire, mais dans un emplacement qui, au départ, n'est pas spécialement lié au lieu de production : église, prairie, théâtre antique, il s'agit moins de poursuivre une activité entamée sur l'année que de proposer, à un public provenant généralement de l'extérieur, une offre spéciale sur un temps réduit. L'histoire des festivals remonte au xviiie siècle (mais on pourrait lui trouver des racines plus anciennes), avec le Three choirs festival (1724, Gloucester, Hereford, Worcester) et le Händel Festival à Westminster Abbey. Elle concerne les arts de la scène, comme l'opéra à Bayreuth (1876) et Salzbourg (1920), ou le théâtre à Avignon (1947), mais aussi les arts plastiques, comme la Biennale de Venise (1895) et le cinéma, comme la Mostra de Venise (1932) ou le Festival de Cannes (1946). En l'espace de quelques décennies cependant, leur nombre s'est accru de manière spectaculaire. Une étude de 2001 en dénombrait près de 700 rien qu'en France, et leur nombre n'a cessé de croître. Leur fréquentation est souvent remarquable : en l'espace de quelques jours ou au plus de quelques semaines, ils parviennent à attirer plusieurs dizaines de milliers de spectateurs voire plusieurs centaines de milliers (jusque 800 000 visiteurs pour le Festival interceltique de Lorient). Si leur nombre ne cesse d'augmenter, c'est aussi parce qu'ils constituent un mode de participation particulier, remplaçant certains grands événements de socialisation, comme les pèlerinages et les processions. Ce n'est peut-être pas un hasard si Woodstock (1969), festival mythique par excellence, se produit à une époque de plein déclin du phénomène religieux.
Le festival, en quelque sorte, constitue avec les foires ou les compétitions l'un des éléments moteurs et particulièrement représentatifs de l'économie de la créativité. Très rapidement, il a fait l'objet d'études économiques visant à montrer l'intérêt de son financement en regard des bénéfices directs, indirects et induits qui en découlent. Bruno Frey a répertorié les facteurs déterminant la demande et l'offre de festivals. La demande dépend forcément de l'augmentation du revenu des festivaliers, des coûts de fréquentation et des coûts de transaction (qui doivent être faibles), ainsi que de l'existence de groupes et de représentants politiques intéressés par le festival (pour des raisons de promotion, comme les firmes de disque, ou de visibilité, comme les responsables politiques). L'offre, quant à elle, augmentera si les coûts de location et d'implantation sont faibles (ce qui est le cas durant les vacances), s'il y a peu de contraintes organisationnelles (peu de syndicats) et une grande souplesse en matière d'innovation (ce que permettent les événements temporaires). Ces principes expliquent le développement des festivals durant les vacances, mais aussi tout au long de l'année, en raison de la souplesse de leur structure. Au même titre que l'artiste présenté par Pierre-Michel Menger comme le travailleur par excellence, réputé pour sa souplesse, son investissement au travail et son coût relativement faible, on pourrait ainsi présenter le festival comme la structure culturelle par excellence du xxie siècle, sans infrastructure – car empruntant celle des autres – sans contraintes syndicales et sans risques trop élevés, puisque temporaire par définition. Le risque de l'institutionnalisation guette cependant les festivals les plus établis, comme celui de Salzbourg, engoncé durant les années 1980 dans une structure de plus en plus coûteuse et inféodée au personnel politique.
Le tourisme culturel. C'est une logique relativement similaire qui conduit au tourisme culturel. Le temps, comme celui des événements, est limité pour le touriste, qui n'a qu'un certain nombre de jours à consacrer à la visite de monuments. En trois jours, le programme de visite, à Paris, ne peut comprendre qu'un nombre limité de musées ou de lieux de patrimoine, si l'on décompte le temps de promenade, les repas et le shopping, parfois quelques sorties au théâtre. C'est ce même temps limité qui conduit cependant le touriste à fréquenter des lieux – des musées et monuments – qu'il prend rarement le temps de visiter dans sa propre ville. C'est le même type d'analyse d'impact qui, par ailleurs, est utilisé pour le tourisme culturel et pour les festivals.
Faut-il le rappeler ? Une partie seulement du tourisme peut être qualifiée de « culturel », en regard des vacances à la mer ou en montagne. Forcément, cette pratique est conditionnée, comme les pratiques culturelles des Français, par le niveau d'éducation, mais aussi par le rythme de travail tout au long de l'année – qui induit l'envie d'un repos plus ou moins important. Le touriste, pour les statistiques, est celui qui passe au moins une nuit (et au plus un an) en dehors de son environnement habituel. Il n'empêche que, naguère considéré comme relativement peu important, le tourisme culturel est de plus souvent présenté comme un « gisement » particulièrement rentable et porteur pour l'avenir.
La France demeure la première destination touristique au monde, avec plus de 80 millions de touristes internationaux, mais seulement la troisième destination au niveau du chiffre d'affaires (derrière les États-Unis et l'Espagne). En tant qu'industrie, la contribution du secteur du tourisme est évaluée à près de 8 % du PIB, plus de 235 000 entreprises en France en dépendant. Lorsque l'on estime que, de manière générale, le milliard de touristes, dans le monde a dû être atteint en 2012, et qu'il devrait être de 1,8 d'ici une quinzaine d'années, le tourisme apparaît comme l'un des moteurs de l'économie actuelle, et la culture est envisagée, dans cette perspective, comme l'un de ses principaux vecteurs d'attraction, en témoigne la présence des statistiques de fréquentation des sites patrimoniaux ou des grandes expositions parisiennes dans les chiffres clés du tourisme français. Il est vrai que dans les vingt principales destinations et attractions fréquentées par les touristes lors d'une visite à Paris, on en dénombre 17 qui sont des musées ou des lieux de patrimoine. Ainsi, la fréquentation exponentielle des musées superstars, ces dernières années, est-elle largement expliquée par le développement touristique mondial, et la relative stabilité des lieux sélectionnés lors d'une première visite à Paris.
Tendances
Toujours plus vite, toujours plus proche. A priori, les tendances qui se sont manifestées ces dernières années ne sont pas sur le point de s'inverser, de même que leur influence sur les pratiques culturelles. Le temps long de la permanence semble définitivement laisser la place à l'événement, à tel point qu'une typologie des actions culturelles pourrait être mise en place à partir de ce principe. La mondialisation implique le développement des échanges et des flux, de plus en plus denses et de plus en plus rapides. Le déclin du monde industriel en Europe pourrait-il être compensé par l'économie de la créativité et le tourisme, les deux coïncidant partiellement dans leur utilisation de la culture comme matière première ? En tout état de cause, le comportement du visiteur ou du spectateur, de plus en plus radicalement soumis à la pression de la production (cf. conclusion), apparaît bien comme celui d'un consommateur à part entière, souhaitant être traité comme tel. Les quelques millions de touristes supplémentaires du Louvre n'ont plus les mêmes comportements que les visiteurs des années 1970, n'ayant la plupart du temps pas été imprégnés par l'habitus du visiteur classique de musée. C'est en consommateur qu'ils entrent et vont parfois aussi visiter Euro Disney à la suite. Une telle attitude est-elle pour autant condamnable ? De la même manière, les transformations de la temporalité que l'on observe sont-elles blâmables ? Il est fort probable que l'accélération des méthodes de consommation risque d'influer, à son tour, sur les pratiques de lecture et de visite ou d'écoute, réduisant peut-être le niveau de concentration requis (condition presque nécessaire) pour assister à un opéra de Wagner ou un film de Tarkovski.
Mais nous ne pouvons observer de telles répercussions qu'à travers nos yeux et notre mémoire d'Occidentaux, à partir d'une vision relativement formatée du patrimoine, finalement bien peu mondiale. Car la mondialisation est aussi susceptible d'influences plus radicales. Déjà, la bande dessinée occidentale n'est plus la même, à l'aune du manga. L'influence de la culture asiatique semble conditionner notre vision du patrimoine, qui s'est très bien accommodée de la notion de patrimoine immatériel. Quant au tourisme, pour combien de temps la France conservera-t-elle encore la première place du palmarès des arrivées ? Car nombreuses sont les nations qui ont compris l'avantage de cette industrie particulière, à commencer par les pays du Moyen-Orient, dont les projets de développement culturel (les musées du Qatar ou d'Abou Dhabi) n'ambitionnent pas de jouer un rôle de figuration. Partant, en rapprochant les distances, c'est toujours un marché plus unique et plus cohérent qui se forme, contribuant à la logique du star-system, si importante dans le monde de la culture.
. Adorno T. W., Horkeimer M., (1944) Dialectique de la raison, Paris, Gallimard, 1974 (pour la trad. fr.).
. Fourastié J., Les trente glorieuses, Paris, Fayard, 1979.
. Martel F., Mainstream. Enquête sur cette culture qui plaît à tout le monde, Paris, Flammarion, 2010.
. Menger M., Portrait de l'artiste en travailleur. Métamorphose du capitalisme, Paris, Le Seuil, 2002.
. Institute of Museum and Library Services, Museums, Libraries and 21st Century skills, Washington, Institute of Museum and Library Services, 2009. Disponible sur : <http://www.imls.gov/assets/1/workflow_staging/AssetManager/293.PDF> (consulté en août 2013).
. McLuhan M., Pour comprendre les médias, Paris, Le Seuil, 1968.
. Dumazedier J., Vers une civilisation de loisirs ?, Paris, Le Seuil, 1962. Voir Chaumier S., Mairesse F., La médiation culturelle, Paris, Armand Colin, 2013.
. Postman N., Se distraire à en mourir, Paris, Nova édition [1985], 2010.
. Pour autant, internet dispose d'archives particulièrement vastes, mais ceux qui gèrent cette mémoire immense sont rarement les mêmes que ceux qui produisent de tels discours jetables.
. Triclot M., Philosophie du jeu vidéo, Paris, Zones, 2011.
. Wildestein G., « Le Musée permanent en France », La Gazette des Beaux-Arts, supplément, 1055, déc. 1956.
. Benito L., Les festivals en France. Marchés, enjeux et alchimie, Paris, L'Harmattan, 2001.
. Sur les festivals et événements sociaux actuels, voir Bénard N. (dir.), Festivals, raves parties, free parties, Histoire des rencontres musicales actuelles, en France et à l'étranger, sl, Camion blanc, 2011.
. Moeran B., Strandgaard Petersen J. (dir.), Negociating Values in the Creative industries, Fairs, Festivals and Competitive Events, Cambridge, Cambridge University Press, 2011.
. Pflieger S., Les retombées économiques du festival d'Avignon, rapport pour Avignon Emploi Développement, BIPE, 1986, 106 p.
. Frey B., « Festivals » in Towse R. (dir.), A Handbook of Cultural Economics, Cheltenham, Edward Elgar, 2003, p. 232-236 ; Frey B., Busenhart I., « Special exhibitions and festivals », in Ginsburgh V., Menger P.-M., Economics of the Arts. Selected Essays, Amsterdam, Elsevier, p. 275-302.
. Pommerehne W. W., Frey B. S., La culture a-t-elle un prix ?, Paris, Plon, 1993.
. Selon les préconisations de l'Organisation mondiale du tourisme. Les définitions et le cadre statistique dont se sert notamment la France peuvent être téléchargés sur internet : <http://www.dgcis.gouv.fr/files/files/archive/www.tourisme.gouv.fr/stat_etudes/definitions_tourisme.pdf> (consulté en juillet 2013).
. Origet du Cluzeau C., Le tourisme culturel. Dynamique et prospective d'une passion durable, Bruxelles, De Boeck, 2013.
. Ministère de l'Artisanat, du Commerce et du Tourisme, Chiffres clés du tourisme, édition 2012. Disponible sur : http://www.dgcis.gouv.fr/files/files/directions_services/etudes-et-statistiques/stats-tourisme/chiffres-cles/chiffres_Cles_Tourisme_2012web.pdf.
. UNWTO (United Nations World Tourism Organization), Tourism Highlights, 2012 Edition. Disponible sur : http://mkt.unwto.org/en/publication/unwto-tourism-highlights-2012-edition.
. Les trois autres sont Eurodisney (première destination, avec 16 millions de visiteurs), La Vallée Village et la Tour Montparnasse.
. Vauclare C., « Les événements culturels, essais de typologie », Paris, Cultures études, 2009-3, 8 p.
. Desvallées A., Mairesse F., Deloche B., 2011, « Patrimoine », in Desvallées A., Mairesse F. (dir.), Dictionnaire encyclopédique de muséologie, Paris, Armand Colin, p. 421-452.
Chapitre 14
Globalité :
l'économie du star-system
Pour Edgar Morin, la star est à la fois un mythe et une marchandise. Mythe assimilé à une divinité ou à un héros grec, la star est créatrice de lien social (de « communautés de fans »). Et marchandise associée à des œuvres, elle est un vecteur essentiel de leur valorisation sur des marchés de masse. Si l'économie du « star-system » renvoie immanquablement aux incarnations charnelles du vedettariat : acteurs, chanteurs, écrivains etc., le processus de « vedettarisation » touche également de nombreux autres domaines : des institutions (des musées comme le Louvre et le Musée d'Orsay), aux événements artistiques (le canard géant de Florentijn Hofman) et, au-delà du seul domaine des arts, tout champ pouvant être couvert par les médias et donc attirer et entretenir une audience ou un public significatifs : le sport, la mode, la médecine, l'humanitaire, les « experts » de tous poils, les chefs d'entreprise etc. jusqu'aux quidams propulsés par la téléréalité. Dans ce chapitre, nous nous concentrons sur le domaine des arts où les exemples d'application des fameuses lois de puissance (loi de Pareto, loi de Zipf...) ne manquent pas et contribuent à façonner la structure des marchés artistiques.
Production de la star
Le phénomène du vedettariat traduit un engouement, une fascination, une attirance se déclinant par une concentration de la demande sur une part très faible de l'offre de biens et de services culturels et artistiques. L'essentiel des ventes d'albums de musique ou de livres, de la fréquentation des musées ou cinématographique etc., se dirige vers un petit nombre d'artistes, d'œuvres ou d'établissements. Cette concentration de la demande engendre à son tour une distribution inégalitaire des revenus, de l'exposition, des collaborations artistiques, qui renforcent à leur tour le processus de starification. C'est cette logique qui est résumée par la formule « the winner-take-all » (le gagnant remporte la mise), évoquant, comme pour le gagnant d'un tournoi, que les stars (qu'il s'agisse d'acteurs, d'écrivains ou de musées) bénéficient de la plus grande partie de la redistribution des gains sur le marché, tandis que les autres se contentent des miettes...
Il n'existe pas d'explication univoque à ce phénomène, mais une confluence de logiques touchant à la fois aux conditions d'offre et aux mécanismes de formation de la demande. Cela tient à l'incertitude qui entoure ces processus : si le vedettariat joue un rôle structurant dans nombre d'activités, on peut dire qu'il est endémique à l'économie des arts et de la culture. En effet, faire face à l'incertitude revient à tenter de réduire l'aléa de production qui peut se définir ex post comme la somme des ressources consacrées à une production (le budget d'un film, les contributions bénévoles à un événement culturel...) multipliée par le risque d'échec. Une telle stratégie conduit bien souvent les acteurs de ces filières à recourir au vedettariat afin de capter plus aisément une part du public et ce faisant, paradoxalement, à entretenir pleinement l'aléa... Par exemple, un festival de musique nécessite, pour attirer du public, et bien plus encore les faveurs de ses financeurs, la présence d'un chanteur, d'un musicien ou d'un groupe nationalement ou mondialement connu. La présence d'un comédien connu à l'affiche d'un film peut rassurer les financeurs d'un film et réduire le risque en singularisant cette œuvre auprès de son public potentiel. Paradoxalement, dans ces deux exemples, la recherche de stars alimente mécaniquement l'aléa de production en concentrant la demande professionnelle sur quelques artistes, ce qui augmente leurs exigences financières et donc les budgets, ce qui in fine alourdit l'aléa de production. Le principe de la main invisible (cf. chapitre 3) semble donc ici mis en échec, car la recherche par un producteur de son intérêt individuel (lorsqu'il cherche à réduire l'aléa de production et à accroître la rentabilité de ses choix) ne conduit pas à une amélioration de l'intérêt collectif dès lors que cela nourrit l'incertitude pour tous les autres acteurs !
Le vedettariat peut néanmoins trouver sa raison d'être comme un moyen de pallier l'incertitude sur la qualité de biens culturels analysés ici comme des biens d'expérience (cf. chapitre 1). La présence de stars permet ainsi d'établir un niveau de confiance entre les offreurs et les demandeurs de biens culturels, jouant un rôle analogue à un label certifiant la qualité d'un produit. Toutefois, si un tel mécanisme permet de comprendre le besoin d'artistes connus susceptibles d'influencer la décision des consommateurs, il n'explique pas complètement le système du vedettariat et en particulier, la concentration des revenus artistiques.
Une différence de talent entre les stars et les autres artistes ?
Les analyses portant sur le système du vedettariat relèvent de champs disciplinaires très différents. Pour leur part, les économistes se sont concentrés sur l'analyse du « marché » des stars, définies comme des « individus qui ont obtenu une notoriété et un succès considérables dans leur domaine et dont les revenus inhérents sont significativement plus élevés que ceux de leurs concurrents ». En d'autres termes, la répartition des revenus entre les artistes suit une loi de puissance : une faible proportion d'entre eux (les « stars ») concentre l'essentiel des revenus artistiques.
Adam Smith, dans la Richesse des Nations (1776), est déjà frappé par le niveau démesuré (« exorbitant ») des récompenses touchées par les artistes (il cite notamment les comédiens, les danseurs et chanteurs d'opéra) en contrepartie de leurs prestations. Il l'explique par la « rareté » et la « beauté des talents », mais également « the discredit of employing them in this manner ». En effet, pour Adam Smith, employer ses talents pour en tirer un gain monétaire constitue une sorte de dévoiement de son art, une « prostitution publique ». Sachant que l'existence des stars est de nos jours étroitement liée à leur présence sur des médias de masse, le niveau de « prostitution » est tel que, finalement, leur rémunération serait sans commune mesure avec celle des autres artistes, ceux qui se « livrent » à un niveau plus local et donc ne bénéficient par de la caisse de résonance fantastique des médias.
Le débat entre les économistes de la culture va véritablement s'établir suite à la publication en 1981 d'un article par l'économiste Sherwin Rosen dans l'American Economic Review. Deux approches vont alors s'opposer. D'un côté, Rosen et MacDonald expliquent le phénomène des superstars par des différences (mineures) de talent entre les artistes. De l'autre, Adler et Chung & Cox rejettent cette explication pour mettre l'accent sur les mécanismes de formation de la demande et les effets boule de neige. Selon la première explication, l'existence de stars et les asymétries très fortes dans la distribution des revenus artistiques tiendraient à des différences de talent entre les artistes. Or, la distribution des revenus est fortement asymétrique. Sur un marché classique où la rémunération des travailleurs est proportionnelle à leur productivité marginale ou à la qualification, cela supposerait des différences de talents extrêmement élevées. Or, même en l'absence de critères objectifs pour les mesurer, de telles disparités de talent n'apparaissent pas vraiment dans la réalité.
Rosen propose une explication différente. En l'absence de données quantifiables sur le talent, cet auteur suggère qu'une différence minime de talent peut engendrer des écarts disproportionnés de revenus entre les artistes. Il appuie son raisonnement sur deux grandes hypothèses. Selon lui, le talent est hiérarchisé, mais il est aussi inégalement distribué dans les populations d'artistes (comédiens, chanteurs etc.), il est observable sans coûts par les consommateurs et surtout il s'avère imparfaitement substituable : un consommateur arbitrera toujours en faveur d'une « petite quantité » de talent (objectivement) supérieure, au détriment d'une grande quantité de moindre talent. Deuxième hypothèse clé de son raisonnement, les biens culturels font l'objet d'une « consommation jointe », à savoir qu'un réalisateur aura fourni le même effort si son film est vu par une personne (lui-même...) ou fait un million d'entrées en salles. Le coût total de production du film est fixe et son coût unitaire diminue donc avec le niveau de fréquentation (le nombre d'entrées en salles).
La première hypothèse explique pourquoi les revenus sont fortement concentrés sur les personnes les plus talentueuses. En d'autres termes, leur demande sur le marché du travail, et donc leurs revenus, augmente plus que proportionnellement à leur niveau de talent. Néanmoins, cela n'explique pas le petit nombre de stars présentes sur chaque marché. Sherwin Rosen mobilise pour cela la deuxième hypothèse basée sur la fonction de production : la taille du marché pour un bien culturel s'accroît plus vite que le talent. En raison des économies d'échelle inhérentes à certains marchés (et notamment celui du cinéma ou de la musique enregistrée), un seul artiste peut desservir de manière viable un marché donné : « fewer are needed to serve it the more capable they are ».
Explicitons un peu. Dans un premier cas de figure, un seul artiste surpasse tous les autres, et comme les consommateurs privilégient le meilleur talent, il se trouve ainsi en situation de monopole et peut fixer son prix en fonction de la réactivité des demandeurs. Une faible élasticité-prix de leur part lui permettra alors d'exiger un prix élevé et limitera le nombre de demandeurs de ses services. Le deuxième cas de figure envisage la coexistence de plusieurs artistes disposant d'un niveau de talent similaire et supérieur à tout autre artiste présent sur le marché. En raison du coût unitaire décroissant, un seul artiste devrait survivre à la concurrence, mais il serait alors pauvre, puisqu'à l'équilibre de marché, il aura dû diminuer ses exigences tarifaires pour s'imposer et donc fixer un prix égal au minimum du coût unitaire. Or, ce deuxième cas de figure n'explique en rien l'existence constatée de stars dont les revenus sont très élevés. Et Rosen de conclure : il existe forcément une star plus talentueuse que les autres, l'écart peut être théoriquement infime, mais perceptible pour les consommateurs.
Pour autant, le modèle de Rosen rencontre un certain nombre de limites. Il repose sur l'hypothèse de marchés monopolistiques, alors que, le plus souvent, les marchés artistiques sont des marchés de biens différenciés, s'assimilant davantage au modèle de la concurrence monopolistique selon laquelle l'hétérogénéité des préférences des consommateurs se traduit par une offre d'un nombre d'artistes nettement plus important qu'en situation de monopole. Rosen explique davantage la constitution de monopoles « locaux », présentant une star par genre littéraire, musical, cinématographique etc. Pour autant, les marchés des biens culturels reposent le plus souvent sur la coexistence de plusieurs stars sur des genres spécifiques, ce qui nécessite de prendre en compte d'autres facteurs d'explication comme la diversité des goûts et le goût pour la diversité de la part des consommateurs.
En outre, Rosen postule plus qu'il ne démontre la substituabilité imparfaite (tout consommateur préférerait systématiquement une prestation artistique d'une superstar à un ensemble de prestations d'artistes de moindre talent). Du côté de l'offre, il n'explique pas non plus la répartition inégale du talent entre les artistes, mais encore une fois la considère comme exogène à son modèle.
Toutefois, on peut s'interroger sur l'origine des différences de talents et de leur appréciation par les individus. MacDonald propose une explication du vedettariat à partir de l'évaluation des consommateurs confrontés à une incertitude sur la qualité des biens culturels. Envisageant le spectacle vivant, il fait l'hypothèse qu'un artiste fait toujours des prestations de même niveau de qualité. Toute interprétation donne une information aux spectateurs sur la qualité. Le marché opère alors une fonction de tri et, dans un premier temps, les mauvaises prestations provoquent la « sortie » du marché des artistes concernés, tandis que les artistes les plus talentueux s'y maintiennent et peuvent ainsi réitérer d'autres prestations en attirant toujours plus de spectateurs et en augmentant le prix de leurs interprétations. En effet, les consommateurs sont prêts à payer davantage pour les artistes qui réduisent leur risque de déception et dont ils connaissent la qualité grâce à leurs prestations passées. Les revenus sont alors proportionnels à la probabilité d'effectuer une prestation de qualité. Le processus se poursuit avec des effets cumulatifs aboutissant à la domination du marché par quelques stars.
Adoptant la même perspective, Borghans et Groot estiment que l'impact de ce différentiel de talents sur les écarts de revenus est amplifié par les médias de masse. Les stars bénéficient ainsi d'une rente, car les médias renforcent l'imparfaite substitution entre les artistes auprès du public, lequel préfère bénéficier des meilleures performances. « En raison de la production des médias, une seule personne est nécessaire pour servir l'ensemble du marché pour lequel, sans cette technologie, de nombreux producteurs seraient nécessaires. L'allocation efficace suppose que le producteur le plus talentueux soit affecté à cette tâche, mais dans la pratique, la situation réelle fournit cette personne avec la possibilité d'exploiter la position de numéro un ».
Pour autant, ces améliorations du modèle proposé par Rosen postulent plus qu'elles n'expliquent les inégalités de talents et surtout l'adéquation des préférences des consommateurs à ces inégalités. Qui plus est, ces approches présentent un caractère idéologique assez marqué, sous-entendant que ces inégalités fortes de revenus entre les artistes seraient socialement acceptables, car elles résulteraient principalement d'écarts de talents. Le marché récompenserait ainsi certains individus, les stars, en raison de leurs dons ou de leur travail antérieur pour obtenir un talent supérieur aux autres.
Le rôle de la demande et des interactions sociales
Dans les approches comme celle de Rosen, si les différences de talent expliquent le vedettariat, aucun éclaircissement n'est donné à ces écarts talentueux qui demeurent donc exogènes à son analyse. Or, le comportement des consommateurs peut jouer un rôle significatif en déterminant de manière ex post les écarts de talent.
Se fondant sur l'article fondateur de Stigler & Becker sur la question du goût, Adler part du constat que la consommation de biens culturels nécessite de l'information : au plus un individu va au cinéma, lit ou écoute de la musique, au plus il est capable d'apprécier les œuvres qu'il consomme par la suite dans le même registre. Or, précisément, cet apprentissage du goût, le développement de cette capacité d'appréciation des œuvres, constitue un processus social fondé sur des interactions avec d'autres individus (qui est au cœur de l'habitus de Bourdieu), que ce soit directement avec l'entourage social (interactions locales) ou à travers les médias (interactions globales). Or, les individus possèdent des capacités cognitives limitées. Il est difficile d'accumuler des connaissances, même minimes, sur toutes les activités et les champs de connaissance et en moyenne, un individu doit renoncer à nombre d'activités et se concentrer sur quelques activités ou, en matière culturelle, sur peu d'artistes dans un nombre restreint de champs artistiques. Le fait que la majorité des individus se concentrent sur les mêmes artistes, les stars, s'explique alors par le besoin d'échanger, d'interagir, de discuter avec les autres. Adoptant une approche sociologique somme toute rudimentaire, Adler montre que l'appariement social nécessite de minimiser le coût de connaissance et de recherche d'interlocuteurs partageant les mêmes centres d'intérêt. Le vedettariat peut ainsi être perçu comme un mécanisme de marché facilitant les interactions.
Sous un angle purement économique, les coûts d'information et la situation d'incertitude radicale dans laquelle le consommateur prend ses décisions peuvent également expliquer l'émergence des stars. Contrairement à une entreprise, le consommateur n'a pas les capacités à réunir et à traiter un nombre trop important d'informations pour déterminer la qualité d'un bien d'expérience. Le coût d'opportunité du temps consacré à une telle activité est rédhibitoire et amène donc les individus à se fier à des signaux, à des méta-informations produites par des agents tiers (des certificateurs, des experts, des classements comme les palmarès etc., cf. chapitre 2). La star a ainsi longtemps joué ce rôle dans le cinéma, supplantant au cours des années 1910 la marque des studios. Qui plus est, la vérification de ces méta-informations s'avère coûteuse et sa qualité aléatoire : suspicion sur les jurys de prix littéraire, critique néo-promotionnelle. L'individu peut alors adopter un comportement conformiste en fondant rationnellement ses décisions sur les comportements des autres. D'autant plus que l'individu peut ne pas préférer prendre de risques (« adverse » au risque) : il se dirigera plus volontiers vers les best-sellers et donc il négligera tous les signaux négatifs quant à la qualité des œuvres qu'il sélectionnera.
Quelle que soit la perspective retenue, la différence de talents s'établit essentiellement comme le résultat du jugement a posteriori des consommateurs et des médias. La frustration des artistes, a priori talentueux, mais ne parvenant à devenir des stars est double, car ils n'ont ni l'audience, ni la reconnaissance sociale qui viendrait couronner leur carrière. Or, la différence d'audience façonne in fine la différence faussement perçue entre les talents. Cette analyse peut être par ailleurs étendue aux réseaux de collaborations artistiques où les jeunes artistes peuvent préférer travailler avec des artistes déjà connus afin d'améliorer leurs perspectives professionnelles. Ces liens préférentiels alimenteraient un « effet Matthieu » selon lequel les artistes les plus connus renforceraient leur position sur les marchés artistiques en bénéficiant ainsi régulièrement d'apports créatifs.
Pourquoi seulement quelques artistes deviennent-ils des stars si leur talent initial est identique ou bien impossible à hiérarchiser a priori de manière objective ? À la manière des modèles de compétition technologique où un standard est vainqueur en raison d'un petit événement, les premiers consommateurs peuvent procéder aléatoirement lorsqu'ils optent pour un nouvel artiste. Dans un tel processus, l'avantage initial, créé de manière purement hasardeuse, consiste pour un artiste chanceux à attirer vers lui un public initial plus large que ses concurrents. Ces effets s'avèrent auto-renforçants (« effets boule de neige »). Toutefois, cet avantage initial peut être stimulé, à l'image d'une firme annonçant des chiffres extravagants sur les ventes d'un nouveau produit pour entraîner des ventes supplémentaires et concrétiser ses annonces mensongères... Dans les années cinquante, les pratiques des « payolas » (illégales par la suite) par les majors du disque ont consisté à verser des dessous-de-table à des animateurs radios en vue pour diffuser plus fréquemment leurs 45 tours et ainsi favoriser leurs ventes au détriment de la concurrence. La mise aux enchères par Google de mots clés peut largement être instrumentalisée et s'apparenter à cette vieille pratique... comme l'achat par un auteur d'exemplaires de son livre, la présence d'éditeurs dans certains prix littéraires etc. Parfois, un pur hasard peut s'avérer suffisant, comme l'atteste l'exemple du groupe suédois Roxette ayant connu le succès en 1986 aux États-Unis par l'entremise d'un fan, étudiant en Suède, qui, à son retour à Minneapolis sut convaincre des DJs de radiodiffuser sur des stations étudiantes un des morceaux de leur premier album. Le bouche-à-oreille fit le reste.
Dans tous ces cas, aucune différence de talent initial ne peut être retenue comme une condition nécessaire et suffisante pour expliquer l'émergence de superstars. On retrouve ces phénomènes de small events dans d'autres domaines comme la science. Ainsi, lorsqu'Albert Einstein qui vint en 1921 à New York dans le cadre d'une délégation sioniste menée par Chaim Weizman et accueillie par des milliers de Juifs sur place, les grands journaux de l'époque rapportèrent que cette ferveur s'adressait au père de la relativité générale, scientifique inconnu du grand public et ayant fait des contributions ni plus, ni moins importantes que celle de Niels Bohr et de Werner Heisenberg, ce qui contribua fortement à la renommée du savant sur le continent américain.
Dans les modèles de cascades informationnelles et de comportement de troupeau, non seulement les écarts de talent entre artistes ne jouent aucun rôle pour expliquer l'apparition des stars, mais, contrairement à l'hypothèse formulée par Adler, les individus n'ont pas à supporter de coûts d'information puisqu'il leur suffit d'observer et de répliquer les décisions des autres consommateurs et donc rationnellement ne pas intégrer leurs propres informations incomplètes et menant à des décisions incertaines. L'explication proposée par Adler semble séduisante parce qu'elle intègre l'importance des processus d'interaction sociale pour expliquer le vedettariat. Ses hypothèses n'en demeurent pas moins réductrices quant aux comportements de consommation culturelle. Ainsi la formation du lien social y est conçue comme un processus rationnel, fondé sur un principe d'optimisation. Mais surtout, il ne peut s'établir qu'à travers des ressemblances, des similarités de goûts. Or, la sociologie des réseaux sociaux et avant elle, Georg Simmel, ont bien illustré le fait qu'un individu crée du lien social, certes en s'assimilant au groupe, mais également en cherchant à se différencier des autres. Cette dualité permet notamment d'expliquer les changements de mode et le renouvellement plus ou moins forts dans les composantes du star-system. Il n'en demeure pas moins que le vedettariat peut s'expliquer par le besoin d'une culture commune entre les individus.
Les analyses empiriques
Au-delà de ses connotations idéologiques, ce débat a des implications dans un certain nombre de domaines. Par exemple, le droit à l'image d'une star est-il justifié ? Oui, si l'on admet la thèse de Rosen, pour lequel la star ne fait que s'approprier une partie de la valeur sociale des utilisations faites de son image, elle-même créée par une différence initiale de talent. En revanche, l'approche d'Adler remet en cause la légitimité d'un tel droit, puisque ce sont alors de petits événements amplifiés par des effets boule de neige qui propulsent au-devant de la scène une poignée d'artistes. De ce point de vue, les cachets touchés par les vedettes semblent probablement trop élevés. Un certain nombre de travaux empiriques ont été menés pour tenter de départager ces deux thèses et leurs conséquences économiques.
Le talent, cause ou conséquence du vedettariat ?
Les inégalités habituellement observées en matière de taux de rémunération entre les artistes s'expliquent assez bien : les stars étant rares, la loi de l'offre et de la demande s'applique ici parfaitement, expliquant une surenchère des demandeurs (les producteurs de biens culturels, les organisateurs de festivals etc.) conduisant à une inflation des cachets et des droits d'auteur perçus par les stars dont l'offre (le nombre d'individus entrant ou opérant sur le marché) est très rigide au prix.
Hamlen teste cet effet superstar à partir d'une mesure a priori objective de la qualité de la voix de 107 interprètes de variété, à savoir une harmonique élevée lorsque les interprètes chantent le mot « love ». Certes, cette quantification ne renvoie qu'à une dimension de la qualité perçue et somme toute conventionnelle. Pour autant, l'élasticité des ventes de disques par rapport à cet indicateur s'avère positive, mais faible (0,14). En d'autres termes, les écarts de talents ainsi évalués peuvent expliquer le succès commercial des disques, mais ils sont largement supérieurs aux différences de ventes, contredisant ainsi l'hypothèse centrale du modèle de Rosen. Toutefois, la méthodologie utilisée par cette étude exploratoire comme par d'autres analyses similaires est contestable, tant du point de vue des variables utilisées pour estimer leur talent que par le fait qu'elles n'intègrent pas simultanément de facteurs relatifs aux effets de demande (bouche-à-oreille, exposition dans les médias etc.).
D'autres études contestent les hypothèses de Rosen, suggérant que le phénomène des superstars ne serait pas dû à des écarts de talents, mais s'expliquerait plutôt par des éléments de hasard. Se basant sur le nombre de disques d'or sur le marché étasunien de la musique populaire, Chung et Cox montrent que l'émergence des stars s'explique par des effets boule de neige, car un consommateur aura une probabilité plus faible d'acheter un album de musique si aucun autre acheteur ne l'a déjà acheté. Ces petits avantages initiaux (des boules de neige) qui bénéficient à quelques titres et à une poignée d'artistes se transforment en succès (avalanches) par des processus d'auto-renforcement. Pour autant, ces résultats n'intègrent pas de variables pour tester simultanément les écarts de talent. De même, l'élément aléatoire sur lequel repose l'avantage initial est postulé, alors qu'en fait, il peut être provoqué par des stratégies promotionnelles allant jusqu'à la provocation délibérée. Une étude plus systématique des biographies d'artistes au début de leur carrière permettrait de mettre en évidence le poids de ces stratégies, mais il faudrait pour cela des informations sur les artistes non-stars... À l'inverse, Ginsburgh et van Ours, montrent qu'un avantage initial, non lié au talent, mais à l'ordre d'apparition des artistes lors du concours musical international Reine Élisabeth de Belgique (CMIREB), peut déterminer le succès commercial des artistes par la suite. En effet, cet ordre d'apparition est aléatoire et donc a priori non directement lié au talent des artistes, mais influe sur le classement final et sur la carrière des musiciens.
Ce résultat est conforté expérimentalement par Sagalnik, Dodds et Watts à travers une expérimentation originale permettant de tester en l'isolant d'autres facteurs, l'influence des proches sur les choix des consommateurs et l'émergence de phénomènes de winner-take-all. Pour cela, ces économistes ont créé un marché « artificiel » (une plateforme de distribution numérique) sur lequel sont proposées des œuvres musicales inconnues (sélectionnées à partir d'un site de musiciens, purevolume.com) à des individus recrutés à partir du site bolt.com (14 341 participants au total). Les sujets ont été répartis aléatoirement entre deux grandes spécifications, selon que le nombre de téléchargements ou les notes des utilisateurs précédents figurent ou non à côté de chacun des 48 morceaux proposés (eux-mêmes étant proposés soit aléatoirement, soit dans l'ordre décroissant du nombre de téléchargements). Par conséquent, il s'agit de tester les choix de consommateurs face à des biens d'expérience dont ils ne connaissent pas la qualité et avec connaissance ou non des choix des consommateurs précédents. Cette expérimentation in vivo, menée à la manière de toute autre science expérimentale, montre que l'influence sociale joue un rôle significatif par rapport à une situation où les décisions sont prises de manière indépendante et donc déterminées a priori essentiellement par la « qualité » des œuvres. Dès lors, « les experts ne parviennent pas à prédire le succès, non pas parce qu'ils sont incompétents ou mal informés sur les préférences des autres, mais parce que les décisions individuelles sont soumises à l'influence sociale ». Cette étude montre également que la théorie économique doit prendre en compte les interactions sociales entre une multiplicité d'agents et que les marchés ne sont pas de simples mécanismes agrégeant des préférences préétablies des consommateurs, mais des lieux où les interactions entre une multiplication d'agents expliquent les résultats (prix, choix etc.) et surtout leur imprévisibilité.
L'ambivalence des réseaux de collaboration artistiques
Le vedettariat peut également s'expliquer en amont, sur les marchés du travail où se nouent des relations verticales entre artistes et producteurs, mais également horizontales entre les artistes eux-mêmes, lorsqu'ils coopèrent sur des projets artistiques communs.
Sans expliquer l'émergence des stars, certains économistes ont essayé d'expliquer la probabilité de succès dans le domaine de la musique en examinant l'organisation en interne de 151 groupes de rock, soit 1 494 albums sortis entre 1970 et 2004. Ils montrent notamment qu'une rivalité élevée entre les membres d'un groupe influence positivement ses chances de succès (évaluées imparfaitement par les certifications de la Recording Industry Association of America ou RIAA) et donc implicitement la concentration du marché. La probabilité de succès est moindre en cas d'instabilité du groupe (changement dans la composition) et de recours important à des musiciens extérieurs au groupe pour les compositions.
D'autres études ont analysé les réseaux collaboratifs sur les marchés du travail artistique, les mondes de la création artistique peuvent être décrits comme des structures sociales spécifiques à travers lesquelles des acteurs de nature variée (les artistes, les organisations, les différents acteurs du monde artistiques) interagissent de différentes manières et à travers de multiples canaux et outils de communication (collaborations directes ou influences artistiques, lieux de rencontres et de discussions physiques ou numériques etc.). La littérature, essentiellement sociologique, envisage en particulier ces liens sur le plan du travail et des collaborations artistiques. S'inspirant des travaux de Milgram, ces travaux distinguent différents types de réseaux sociaux. On trouve notamment les réseaux structurés par des liens préférentiels (les « scale-free networks »), inégalitaires, au sein desquels un artiste préférera collaborer avec des artistes déjà connus et qui peuvent donc représenter la structure sous-jacente au best-seller. D'autres types de réseaux sont marqués par des effets « petit monde » ou à structure communautaire, ils renvoient alors à la structure collaborative en matière de création artistique.
Dans le premier cas, des liens privilégiés s'établissent et chaque nouvel artiste (nouveau sommet ajouté au graphe) a tendance à préférer une collaboration avec une star dès lors que la réputation et l'influence qu'exerce celle-ci peut lui permettre d'améliorer son statut et de créer des opportunités nouvelles en matière de financement et de valorisation. En dynamique, cette position centrale des stars dans le réseau de collaboration est auto-renforçante, car chaque nouveau lien établi augmente l'attractivité des stars selon une logique de preferential attachment. Cette logique de type « winner-take-all » ou effet Matthieu s'ajoute à celles déjà mentionnées plus haut pour renforcer la distribution inégalitaire des revenus dans le modèle du best-seller.
Dans le second cas, les réseaux à structure communautaire, les artistes collaborent entre eux pour créer de nouvelles œuvres et manières d'interpréter des œuvres, pour explorer et mettre au point de nouvelles formes d'expression artistique en combinant leurs ressources et potentiels créatifs. Ce travail collectif s'exerce à travers des petits groupes sociaux au sein desquels interagissent étroitement et intensément des artistes poursuivant un projet artistique commun. La structure de ces réseaux artistiques répond alors à une logique de communautés, car les nœuds d'un tel réseau social (les artistes au sein des mondes de l'art) sont liés ensemble dans des petits groupes densément connectés en interne, mais peu reliés avec le reste du réseau social. En d'autres termes, les liens sociaux entre les individus composant un groupe artistique donné sont très forts entre eux (densité locale forte) et plus faibles avec des individus situés en dehors du groupe. L'ensemble forme ce que l'on peut appeler des sous-réseaux artistiques locaux, souvent localisés géographiquement, reliés dans un réseau plus global.
Les travaux dans ce domaine explorent les liens les plus visibles, comme les collaborations sur des albums de musique ou les liens établis à travers les sites de fans. Pour autant, les mondes de l'art fonctionnent sur des bases plus complexes. D'une part, des catégories de liens autres que les partenariats de travail structurent également les mondes de la création artistique comme les liens amicaux, culturels, de connaissances etc. Des rencontres lors de festivals, le fait de partager certaines caractéristiques sociales (genre artistique, région d'origine, expériences politiques etc.), appartenir à un même « cercle social », plus simplement d'apprécier les œuvres d'un autre artiste... peuvent générer et entretenir des liens et ainsi concourir à structurer les réseaux sociaux. Le site internet MySpace fournit un bon exemple de relevé numérique en temps réel des liens qui se tissent entre les artistes à travers leurs pages. D'autre part, les artistes ne constituent pas les seuls acteurs de ces réseaux sociaux, mais ils sont liés à d'autres catégories d'acteurs comme les consommateurs et les prescripteurs qui favorisent par leurs pratiques les connexions entre les artistes, mais également avec les acteurs économiques selon une logique « petit monde », souvent par des hasards, des rencontres fortuites entre personnes ou entre des personnes et des œuvres. De tels petits événements peuvent alors favoriser des effets croissants de diffusion et permettre à certains artistes et projets artistiques de dépasser leur sous-réseau social initial (local) pour être davantage connecté au reste du réseau (global).
Les conséquences du vedettariat :
une garantie de succès ?
L'existence de stars a différentes conséquences. La plupart sont en fait difficilement évaluables. Par exemple, pour Frank & Cook, les stars susciteraient des vocations artistiques en trop grand nombre. En d'autres termes, un nombre excessif (« sur-optimal ») de candidats s'engageraient à plein temps dans une activité artistique, dans l'espoir de figurer parmi la poignée de vainqueurs d'un vaste jeu de loterie. Or, trop de ressources et de temps seraient gaspillés en raison du nombre de perdants dont la formation serait in fine inadaptée aux besoins du marché du travail et la rémunération inférieure au niveau espéré en l'absence du signal trompeur provoqué par les cachets excessifs des stars. Face à cette situation favorisant le détournement de ressources productives et l'accroissement de la pauvreté, le gouvernement devrait-il limiter les cachets des stars pour rendre la carrière artistique moins attractive ? Les artistes sont-ils si naïfs qu'ils ne se rendent pas compte de leurs très faibles chances de devenir des stars (ce qu'évoquait déjà Adam Smith) ? Certains peuvent être certes victimes d'un biais de sur-optimisme, mais beaucoup exercent un double emploi pour subvenir à leurs besoins. Les compensations sont plus souvent de nature psychologique ou symbolique. Un tel raisonnement repose en fait sur une hypothèse forte, à savoir que les motivations sous-jacentes à la création et à la carrière artistiques seraient essentiellement extrinsèques, monétaires.
Pour autant, une fois le processus de sélection des stars réalisé, qu'en est-il de leurs « performances » ? Celles-ci peuvent se décliner en plusieurs variables : le succès au box-office (classement dans les ventes, en matière d'audience, de fréquentation etc.) ou la profitabilité liée à l'emploi d'une star dans une œuvre ou un festival.
Le cinéma hollywoodien est l'industrie qui produit le plus de statistiques sur ses résultats et a ainsi donné lieu à la plupart des travaux empiriques, essentiellement économétriques, pour vérifier ces relations. Le principe est de tester l'influence du vedettariat sur le box-office par rapport à d'autres facteurs comme le genre, le budget du film et les dépenses marketing, la durée et la surface d'exploitation (nombre de copies et d'écrans), les critiques (positives ou négatives), les récompenses, la taille des firmes (producteurs, distributeurs) et le bouche-à-oreille. Différents travaux montrent que la présence d'une star au générique provoquerait un accroissement des recettes en salles. Quant à la rentabilité des films, la popularité d'une actrice ou d'un acteur permet d'atténuer l'impact négatif de mauvaises critiques jouant le rôle d'une « police d'assurance » contre l'échec. En revanche, la présence de stars n'a pas d'impact lorsque les critiques sont positives. Le succès et la teneur des critiques étant des phénomènes impossibles à prévoir, l'emploi de stars aurait les mêmes effets positifs que les effets spéciaux. Toutefois, si cette recette magique permet aux exécutifs de se maintenir en évitant des échecs cuisants elle n'est pas neutre en matière de coûts et pèse sur la rentabilité des films. Les cachets excessifs augmentent l'aléa de production et surtout le risque de non-rentabilisation des films dont le budget est largement alourdi par la présence de stars. Si les stars peuvent s'avérer une garantie contre l'échec commercial, elles captent l'essentiel de la rente qu'elles génèrent à travers leur rémunération.
De Vany et Walls soulignent également l'impact positif du vedettariat sur le succès commercial des films en salles. Mais envisageant l'impact de chaque star sur les films composant leur échantillon (assez large), ces économistes montrent que seulement une poignée de stars (19 stars sur un échantillon total de 2015 films sur la période 1984-1996) ont un impact significatif sur le box-office. Et les stars les plus médiatisées et donc supposées avoir un tel impact ne figurent pas dans cette liste. Qui plus est, aucune star ne peut garantir un résultat positif. De manière intéressante, ces auteurs soulignent que s'il y a corrélation entre la présence d'une star et le succès d'un film, la causalité sur un plan économique n'est pas démontrable par les seuls résultats statistiques : « Une star est peut-être quelqu'un qui a la chance de livrer une belle performance dans un excellent film. Une fois que quelqu'un est béni avec le manteau de la célébrité, il est clair que l'amélioration des projets et des budgets plus importants lui sont présentés. Par conséquent, ses chances d'apparaître dans de grosses productions montent et ses chances d'être considéré comme une star demeurent plus élevées que la moyenne ».
Plus généralement, ces études présentent un certain nombre de limites. Elles se fondent parfois sur des échantillons faibles et surtout n'expliquent que les recettes en salles. Or, certains acteurs non profitables dans les salles obscures, comme Bruce Willis ou Sylvester Stallone, le deviennent probablement si l'on agrège tous les revenus générés par leur présence à l'affiche. Ces études postulent implicitement que la valorisation de la star se décline uniquement autour du support premier, l'exploitation en salles (rejoignant l'idée que l'aura d'un film se crée à l'occasion de sa sortie dans les salles obscures), alors qu'il s'agit d'un processus a priori multi-supports (salles, éditions vidéo, vidéo à la demande, télédiffusion) et intertemporel. Par exemple, l'apport d'une star semble essentiel en amont, au moment du financement d'un film (cf. chapitre 9) et, en aval, sur l'audience télévisuelle et l'exploitation des films de catalogue sur les plateformes numériques. Mais à notre connaissance, aucune étude ne vient étayer ou démentir ces hypothèses. Un autre problème fondamental réside dans la définition d'une star. La star se définit à partir d'un succès commercial passé ou des récompenses, des critiques positives et donc une légitimation, une consécration par les dispositifs de jugement tels que les festivals ou les grandes messes télévisuelles. Il conviendrait de distinguer ces effets dans les études. Or, considérer ces variables ensemble peut poser des problèmes, car elles sont souvent mutuellement corrélées : les dépenses marketing et l'image de marque d'une star par exemple. Enfin, les résultats obtenus pour le cinéma peuvent-ils être étendus à d'autres secteurs comme la musique ou le livre ? Le manque de données dans ces secteurs empêche de généraliser ou de relativiser les résultats obtenus pour le cinéma en salles.
Un processus global à l'encontre de la diversité culturelle et des cultures « locales » ?
En France, la question du cachet des stars a fait l'objet de débats assez vifs dans le milieu du cinéma après la publication le 28 décembre 2012 d'une tribune de Vincent Maraval dénonçant le niveau jugé exorbitant des rémunérations des stars françaises en relation avec leurs performances. Ce débat a surtout mis en évidence le problème du financement du cinéma (cf. chapitre 10) et les menaces pesant sur les « films » ou « cinéma du milieu » selon l'expression médiatisée par Pascale Ferran lors de la cérémonie des César en 2007, soit « des films populaires à vocation artistique et dont le budget est moyen ». Or, ces films du milieu seraient menacés par la « ponction » exercée par les stars en France sur les cachets qui pèsent directement sur le financement du cinéma, notamment par les chaînes de télévision, et alors même que leurs résultats en termes de recettes en salles sont souvent jugés insuffisants (donc potentiellement non rentables). Par ricochet, ils alimentent à un niveau non optimal le compte de soutien cinématographique, autre source de financement du cinéma du milieu.
Or, par leur prise de risque artistique (même si celle-ci est difficile à mesurer sur une base objective) et leur rôle de captation de la créativité, les films du milieu jouent un rôle crucial dans la dynamique et le renouvellement du cinéma français. Les stars et à travers elles, le manque de risque des grands producteurs, distributeurs et financeurs du cinéma, menaceraient actuellement cette dynamique. Néanmoins, des études empiriques seraient nécessaires pour évaluer sur un plan scientifique ces évolutions et leurs conséquences.
Comme le note Adler, la mondialisation intensifie les conséquences économiques liées à la substitution des stars locales par des superstars mondiales, essentiellement étasuniennes ou valorisées par des multinationales de la culture. Or, on retrouve ici les termes du débat opposant Rosen à Adler : d'un côté, si l'on suppose que cette domination progressive des superstars est le fait de leur supériorité artistique (leur talent supérieur), alors toute condamnation et mesure protectionniste (à l'instar de l'exception culturelle française) irait contre les intérêts des consommateurs, jugés responsables et aptes à évaluer et à décider en fonction de leurs préférences et de la qualité de l'offre. D'un autre côté, en admettant la thèse défendue par Adler, une culture « globalisée » et portée par des superstars peut détruire ou tout du moins marginaliser les cultures locales, « non pas parce qu'elle est meilleure, mais simplement parce qu'elle est globale ». Et prenant acte que ce mouvement de mondialisation de la culture (cette culture globale) est un processus inéluctable (en raison de la puissance des acteurs économiques qui le portent, mais également de l'ouverture des marchés et des mécanismes propre à la demande de biens culturels), l'enjeu de politique culturelle est alors de chercher comment abaisser les barrières à l'entrée au marché des « superstars » et d'ainsi permettre une diversité culturelle plus importante.
L'entrée en scène depuis une dizaine d'années des « géants du numérique » (cf. chapitre 15) intensifie ce débat, mais également le complexifie. En effet, les opérateurs mondiaux de plateformes comme Apple, Google, Amazon, Netflix, Facebook etc. pourraient amplifier ce processus négatif lié aux superstars à travers des stratégies numériques fondées sur l'exploitation d'effets de réseaux et plus encore, par leurs tentatives d'instrumentalisation des réseaux sociaux numériques. Pour autant, l'impact de leurs stratégies et de leurs modèles économiques sur les écosystèmes de la culture n'est pas si univoque, comme le montre le chapitre suivant.
. Morin E., Les Stars, Paris, Le Seuil, 1957.
. Benhamou F., L'économie du Star-System, Paris, Odile Jacob, 2002.
. La loi de Pareto ou principe de Pareto, encore intitulée loi des 80/20, vise à expliquer un phénomène constaté empiriquement dans de nombreux domaines, à savoir qu'environ 20 % des causes expliquent 80 % des conséquences. Par exemple, 20 % des livres rapportent 80 % du chiffre d'affaires, ou 80 % du chiffre d'affaires d'une organisation est représenté par 20 % des clients. La loi de Zipf, qui part d'une observation empirique, s'intéresse à la fréquence des mots dans un texte.
. Kretschmer M., Klimis G. M. et Ju Choi C., « Increasing Returns and Social Contagion in Cultural Industries », British Journal of Management, vol. 10, 1999, p. 61-72.
. En fait, contrairement au risque, l'incertitude ne peut pas être probabilisée a priori (ex ante) et sur une base objective. Un producteur de biens culturels estimera le risque de son projet par rapport aux données passées sur des projets similaires à partir desquelles il fondera sa décision sur des probabilités subjectives, elles-mêmes pouvant être biaisées par une surestimation des chances de succès (syndrome des entrepreneurs-innovateurs !).
. Menger P.-M., Le travail créateur. S'accomplir dans l'incertain, Paris, Gallimard-Le Seuil, 2009.
. Morin E., op. cit. ; Dyer R., Stars, Londres, British Film Institute, 1979 ; Menger P.-M., « Artistic Labor Markets and Careers », Annual Review of Sociology, 25, 1999, p. 541-574.
. Adler M., « Stardom and Talent », in Ginsburgh V., Throsby D., Handbook of the Economics of Art and Culture, Amsterdam, Elsevier, vol. 1, 2006, p. 895-906, p. 897.
. Borghans L., Groot L., « Superstardom and monopolistic power: why media stars earn more than their marginal contribution to welfare », Journal of Institutional and Theoretical Economics, 54, 1998, p. 546-571.
. Rosen S., « The economics of superstars », American economic review, 71, 1981, p. 845-858 ; Mac Donald G. M., « The economics of rising stars », American economic review, 78, 1988, p. 155-166.
. Adler M., « Stardom and talent », American Economic Review, 75, 1985, p. 208-212 ; Chung K. H., Cox R. A. K., « A stochastic model of superstardom: an application of the Yule distribution », Review of Economics and Statistics 76, 1994, p. 771-775.
. Ce problème semble a priori plus explicite dans le domaine du sport où les performances sont quantifiables.
. En simplifiant, si un consommateur estime que Brad Pitt est dix fois plus talentueux qu'un acteur moins connu, il lui faudra au moins 10 films de ce dernier pour obtenir la même satisfaction tirée d'un seul film de la star étasunienne. Partant, un producteur sera prêt à payer cette star 10 fois plus cher pour limiter les risques d'échec ou augmenter les chances de succès.
. Rosen S., op. cit., p. 847.
. Schulze G. G., « Superstars », in Towse R. (dir.), A Handbook of Cultural Economics, Cheltenham, Edward Elgar, 2011 (2e éd.), p. 401-407.
. « The distribution of talent is assumed to be fixed in the population of potential sellers and costlessly observable to all economic agents », Rosen S., op. cit., p. 856.
. MacDonald G. M., « The economics of rising stars », American Economic Review, 78 (1), 1988, p. 155-166.
. Borghans L., Groot L., op. cit.
. Adler M., « Stardom and talent », American Economic Review, 75 (1), 1985, p. 208-212 ; Stigler G., Becker G., « De gustibus non est disputandum », American economic review, 67 (2), 1977, p. 76-90.
. Stigler G., « The economics of information », The Journal of Political Economy, 69 (3), 1961, p. 213-225.
. Morin E., op. cit.
. Creton L., Économie du cinéma. Perspectives stratégiques, Paris, Armand Colin, 2014 (5e ed).
. Adler M., 2006, op. cit.
. L'effet Matthieu est une formule adoptée par Robert Merton, à partir du Nouveau Testament (« Car on donnera à celui qui a, et il sera dans l'abondance, mais à celui qui n'a pas on ôtera même ce qu'il a »), et utilisée notamment par Françoise Benhamou (op. cit.) pour évoquer les principes du star-system.
. Arthur W. B., « Competing technologies and lock-in by historical small events: the dynamics of allocation under increasing returns », International Institute for Applied Systems Analysis Paper WP-83-92, 1983.
. Peterson R. A., Berger D. G., « Cycles in Symbol Production: The Case of Popular Music », American Sociological Review, vol. 40, 1975, p. 158-173.
. Kretschmer K. et Ju C., (1999), op. cit.
. Missner M., « Why Einstein became famous in America », Social Studies of Science, vol. 15, no 2, 1985, p. 267-291.
. Banerjee A. V., « A simple model of herd behavior », Quarterly Journal of Economics, 107 (3) août 1992, p. 797-817. Bikhchandani S., Hirshleifer D. et Welch I., « A Theory of Fads, Fashion, Custom, and Cultural Change as Informational Cascades », Journal of Political Economy, vol. 100, no 5 (oct. 1992), p. 992-1026.
. Simmel G., « Fashion », International Quarterley, 10, 1904, p. 130-155.
. Hamlen W. A., « Superstardom in popular music: empirical evidences », Review of Economics and Statistics, 73, 4, 1991, p. 729-733.
. Lucifora C, Simmons R., « Superstar effects in sport: evidence from Italian soccer », Journal of Sports Economics, vol. 4, no 1, 2003, p. 35-55 ; Krueger A. B., « The Economics of Real Superstars: The Market for Concerts in the Material World », Journal of Labor Economics, 23(1), 2005, p. 1-30. D'autres études testent à la fois le talent et la popularité, mais en se focalisant sur un domaine non artistique, comme le football (Lehmann E. E. et Schulze G. G., « What does it take to be a star? The role of performance and the media for German soccer players », Discussion Paper Series 1, Department of International Economic Policy, University of Freiburg, 2007, revised Mar. 2008 ; Franck E. et Nüesch S., « The Effect of Talent Disparity on Team Performance in Soccer », Working Papers 0087, University of Zurich, Institute for Strategy and Business Economics (ISU), 2008, revised 2009. Elles cherchent à expliquer l'impact respectif des performances et de l'exposition médiatique des joueurs sur leurs revenus. Mais leurs résultats sont contradictoires, l'une montrant qu'aucune des deux variables n'est significative et l'autre, le résultat inverse...
. Chung K.H., Cox R.A.K., « A stochastic model of superstardom: An application of the Yule distribution », The Review of Economics and Statistics, 76 (4), 1994, p. 771-775.
. À l'instar d'une Britney Spears se vantant d'être chaste ou d'une Madonna attirant l'attention de la presse grâce au comportement agressif de son mari à l'endroit des photographes (cité par Adler, 2006).
. Ginsburgh V., van Ours J., « Expert opinion and compensation: Evidence from a musical competition », American Economic Review, 93, 2003, p. 289-296.
. Salganik M. J., Dodds P. S. et Watts D. J., « Experimental Study of Inequality and Unpredictability in an Artificial Cultural Market », Science, 311, 2006, p. 854-856.
. Ibid., p. 856.
. Ceulemans C., Ginsburgh V., Legros P., « Rock and Roll Bands, (In)complete Contracts, and Creativity », American Economic Review, vol. 101, no 3, 2011, p. 217-21.
. Gleiser P. M., Danon L., « Community Structure in Jazz », Advances in Complex Systems, vol. 6, 2003 ; p. 565-573 ; Smith R. D., « The Network of Collaboration Among Rappers and Its Community Structure », Journal of Statistical Mechanics: Theory and Experiment, février 2006 ; Grandadam D., « Networks, creativity and the finest in jazz 1939-1979 », Document de travail BETA, Université de Strasbourg, 2009.
. Milgram S., « The small-world problem », Psychology Today, vol. 1, no 1, 1967, p. 61-67 ; Merton R. K., The Sociology of Science, University of Chicago Press, 1973 ; Barabasi A.-L., Albert R., « Emergence of Scaling in Random Networks », Science, vol. 286, 1999, p. 509-512 ; Newman M. E. J., Girvan M., « Finding and evaluating community structure in networks », Physical Review E, vol. 69, no 2, 2004.
. Kretshmer et al., op. cit.
. Arthur W. B., « Increasing Returns and The New World of Business », Harvard Business Review, juillet-août, 1996, p. 100-109.
. Frank R. H., Cook P. J., The Winner-Take-All Society, New York, The Free Press, 1995.
. Menger P.-M., Le travail créateur. S'accomplir dans l'incertain, Paris, Gallimard-Le Seuil, 2009.
. Bagella M., Becchetti L., « The Determinants of Motion Picture Box Office Performance: Evidence from Movies Produced in Italy », Journal of Cultural Economics vol. 23, 1999, p. 237-256. Jansen C., « The Performance of German Motion Pictures, Profits and Subsidies: Some Empirical Evidence », Journal of Cultural Economics, 29, 2005, p. 191-212 ; Albert S., « Movie Stars and the Distribution of Financially Successful Films in the Motion Picture Industry », Journal of Cultural Economics, vol. 22, 1998, p. 249-270.
. Basuroy S., Chatterjee S., Ravid S. A., « How Critical Are Critical Reviews? The Box Office Effects of Film Critics, Star Power, and Budgets », Journal of Marketing, vol. 67, no 4, 2003, p. 103-117.
. Ibid.
. De Vany A., Walls W. D., « Uncertainty in the Movies: Does Star Power Reduce the Terror of the Box Office? », Journal of Cultural Economics, 1999, 23, p. 285-318.
. Ibid., p. 310 (notre traduction).
. Jansen C., « The Performance of German Motion Pictures, Profits and Subsidies: Some Empirical Evidence », Journal of Cultural Economics, 29, 2005, p. 191-212.
. Adler M., op. cit. (2006), p. 905.
. Voir également sur ces débats Mattelart A., Diversité culturelle et mondialisation, Paris, La Découverte, coll. « Repères », 2007.
Chapitre 15
L'arrivée des nouveaux acteurs du numérique
Un constat s'impose d'emblée : le numérique est devenu omniprésent et cette pénétration massive (pervaniveness) se retrouve jusque dans la vie intime des individus avec les usages banalisés de l'internet, des réseaux sociaux numériques (RSN) et des applications mobiles. Les activités culturelles constituent un terrain particulièrement propice à (et révélateur de) ces transformations. En l'espace d'une vingtaine d'années, ces usages massifs des TIC ont fait évoluer les pratiques culturelles : l'information et la discussion sur les œuvres et les artistes, la consommation culturelle, l'organisation des sorties etc. Le recours à internet est en effet devenu un réflexe pour s'informer sur un livre, les horaires des salles pour un film ou l'agenda d'un artiste etc. Cette pratique s'est affirmée ainsi comme un passage obligé pour organiser les pratiques culturelles. Ces transformations ont mis sur le devant de la scène des acteurs nouveaux, la plupart du temps qui ne sont pas issus des secteurs culturels et dont les modèles économiques ont commencé à remodeler sérieusement les écosystèmes de la culture.
La transformation du paysage
Ce n'est pas simplement une révolution technique qui explique les bouleversements provoqués par l'arrivée du numérique dans le monde des arts et de la culture, mais un ensemble nettement plus vaste et complexe, fondé d'abord sur un renouveau des relations sociales conditionnées par la technique, mais surtout aussi sur l'arrivée de nouveaux acteurs économiques, de nouveaux modes de consommation, et enfin de nouveaux types d'intermédiaires (les infomédiaires) mettant en relation des groupes d'utilisateurs et exploitant de manière novatrice les systèmes d'échange au sein de la société.
Le numérique, un nouveau paradigme sociotechnique
L'expression de « révolution technologique » est trompeuse, voire erronée, car les innovations qui portent une telle révolution ne sont pas tant technologiques que sociales, politiques, organisationnelles et culturelles. Avant le numérique, la machine à vapeur et l'électricité ont accompagné un ensemble de transformations dans les mentalités, les pratiques sociales, les modes d'organisation des entreprises et des marchés. Mais si la machine à vapeur a par exemple permis un maillage du territoire au niveau de la distribution des livres et la massification de ce marché, c'est surtout la volonté à la fois des éditeurs et de l'État qui a été prépondérante pour massifier le marché du livre et pousser cette pratique sociale.
Il ne faut donc pas se tromper : les technologies numériques ne suffisent pas à expliquer les évolutions en cours. Certaines techniques existaient bien avant l'apparition de l'internet, comme la numérisation des signaux analogiques et du son dans les années 1960 et celle de la transmission électronique d'informations entre serveurs (le Minitel). Mais celles-ci n'ont pas engendré les mêmes changements que ceux qui sont en œuvre depuis une vingtaine d'années. En fait, la révolution numérique correspond davantage à une conjonction d'éléments dont plusieurs ont été évoqués dans les chapitres précédents, comme l'évolution des représentations sociales, l'affirmation de l'individualisme, la montée du temps libre et des loisirs, l'allongement des temps de déplacement et la mobilité plus forte des individus, la libéralisation des marchés et la convergence des télécoms et de l'informatique, la globalisation financière et les changements organisationnels des entreprises. Dans ce contexte spécifique, l'utilisation, l'appropriation et finalement l'usage des TIC par les individus et les organisations permettent la construction de nouveaux services, font évoluer les pratiques sociales et finalement bouleversent les régulations traditionnelles de l'économie.
L'évolution technologique n'est pas linéaire. Il existe ainsi un processus relativement complexe entre la recherche scientifique et la croissance du système productif (recherche, découverte, expérimentation, développement, imitation, adoption de nouveaux produits ou procédés de production). Une longue période s'est ainsi écoulée entre la découverte de la télédiffusion d'images en mouvement (début du xxe siècle) et le développement du marché de la télévision aux États-Unis, à partir des années 1950. L'innovation technique est tributaire à la fois de la recherche scientifique et des inventions, du degré de réceptivité du système productif et de l'adoption des biens et services par le marché. Les choses se compliquent de nos jours avec le rôle croissant de l'innovation ascendante : les utilisateurs ont un rôle croissant dans le façonnage des innovations, en particulier des innovations de service, ainsi que dans les processus de diffusion des technologies et des produits.
L'économie numérique
Il n'en reste pas moins que le système internet, conçu au début des années 1960, entraîne une révolution des usages à partir du milieu des années 1990, avec l'avènement de l'internet Society et le développement exponentiel des sites internet (le moteur de recherche Google est lancé en 1998). Dix ans plus tard, au milieu des années 2000, une autre révolution technique conduit à l'avènement de logiciels plus simples d'utilisation, permettant une réactivité inédite et la participation des internautes. Ce mouvement induira, à son tour, le développement considérable des blogs puis des réseaux sociaux (MySpace, puis Facebook etc.).
Le numérique bouscule profondément les technologies de l'information et de la communication et parmi ces changements majeurs figure en première place le réseau mondial internet. L'économie numérique (digital economy) désigne les transformations des activités économiques et sociales portées par la diffusion massive d'une technologie « générique », le numérique, qui engendre un ensemble d'opportunités nouvelles dont peuvent s'emparer avec plus ou moins de succès les individus et les organisations. L'utilité d'internet repose sur ses nombreux usages : chercher ou mettre à disposition des informations, communiquer, développer des interactions sociales et effectuer des transactions sur des marchandises, des services etc.
L'arrivée des premiers pure players, prestataires de services nés avec internet (moteurs de recherche, portails et annuaires web), a favorisé l'émergence de nouveaux services en ligne, comme les portails et annuaires, moteurs, messagerie, agrégateurs, blogs, forums, commerce électronique, comparateurs, wiki... et plus récemment, réseaux sociaux numériques. L'un des premiers usages massifs de ces services a par exemple consisté en la recherche et le partage de contenus protégés par le droit d'auteur, élargissant considérablement l'accès des internautes aux biens culturels mais bousculant les modèles classiques de distribution.
Deux grands modèles économiques organisent l'ensemble de ces services : d'une part, le commerce électronique dont Amazon et eBay ont longtemps représenté l'archétype et d'autre part, l'infomédiation (cf. infra) et ses multiples variantes, soit dérivées de médias classiques (les journaux ou chaînes de télévision existantes), soit entièrement nouvelles (réseaux de partages de données, sites de rencontres, réseaux sociaux etc.).
Derrière les nombreux sites de commerce électronique, une croyance alimente à la fin des années 1990 une bulle spéculative autour du potentiel de la vente en ligne, supposée se substituer ou marginaliser à terme les formes traditionnelles de la distribution en libérant les acheteurs et les vendeurs des contraintes géographiques. Ces croyances se sont révélées inexactes, et le tout-numérique ne s'est pas imposé et a davantage laissé la place à une hybridation de type click and mortar (commerce en ligne associé au commerce classique) où seules certaines fonctions commerciales sont numérisées (comme la sélection et le paiement des produits en ligne) et s'hybrident avec des fonctions commerciales classiques. Par ailleurs, les TIC allaient permettre une désintermédiation et faire tendre les marchés vers les conditions idéales de la concurrence parfaite. Les comparateurs de prix et les forums de discussion réduiraient significativement les coûts d'information et de transactions supportés par les consommateurs qui pourraient être atteints directement par les producteurs, ce qui éliminerait les marges d'intermédiation.
Or, les pratiques des consommateurs et des entreprises sur internet n'ont pas eu les effets vertueux escomptés. Les comparateurs de prix n'ont pas éliminé les dispersions de prix pour un même produit, tandis que les intermédiaires se sont multipliés. Pour les biens culturels, une analyse des prix de 125 livres, 108 albums de musique et 104 logiciels en 1996 et 1997 à travers 52 sites internet et magasins physiques a montré que la dispersion des prix était similaire entre les deux canaux de vente et que les prix en ligne étaient (à l'époque) supérieurs en moyenne. Pour autant, ces résultats ont été contestés en raison de la nature très émergente du marché observé. Brynjolfsson et Smith ont ainsi étudié le marché en ligne plus développé et relevé les prix de 20 livres et 20 cd de musique vendus dans 41 lieux de vente en ligne et hors ligne de février 1998 à mai 1999, observant que la dispersion des prix en ligne subsiste, mais que cette dispersion et la moyenne des prix en ligne sont inférieures à celles observées dans les magasins physiques. Différentes explications ont été avancées par expliquer cette dispersion : le boycott fréquent des producteurs, les stratégies de différenciation extrêmes et l'information incomplète produite par les logiciels de collecte automatisée de prix en ligne, le rachat des comparateurs de prix par certains distributeurs, le manque de confiance de consommateurs permettant aux vendeurs jouissant d'une bonne réputation de fixer des prix plus élevés et finalement l'entrée en scène des infomédiaires.
Les infomédiaires
La montée en puissance des acteurs du numérique s'est davantage manifestée à travers les services de mise en relation entre les utilisateurs d'internet. Les réseaux sociaux numériques (réseaux de partage, communautés en ligne, réseautage social, sites de rencontre etc.) se sont ainsi largement imposés au niveau des usages numériques. Dans le domaine des biens culturels, ces réseaux sont à la base du succès de certains services en ligne basés sur l'exploitation de la longue traîne : les interactions sociales et la prescription en ligne peuvent ainsi canaliser l'attention des consommateurs sur des œuvres jugées difficiles, oubliées ou n'ayant pas connu de succès commercial.
Plus généralement, au-delà des interactions entre les individus, l'explosion d'informations sur internet permise par la réduction du coût de l'information numérisée (collecte, traitement et diffusion) a favorisé l'émergence de nouveaux acteurs. Les flux d'informations se sont diversifiés, soit verticalement entre les vendeurs et les acheteurs pour surmonter des problèmes de confiance en ligne, soit horizontalement entre les consommateurs eux-mêmes (communautés, forums...). Cette surabondance informationnelle a nécessité un renouvellement des fonctions d'intermédiation et des services de traitement, de sélection et de production d'informations pertinentes qui a conduit à l'apparition de nouveaux métiers et acteurs : les « infomédiaires », soit les compagnies qui constituent les plus grands succès ayant jalonné l'histoire d'internet, comme Yahoo!, Napster, Google, Meetic, Amazon, Facebook, Twitter...
L'infomédiation (néologisme anglais issu de la contraction des mots information et intermediation) s'est imposée comme le modèle dominant sur internet. Les infomédiaires opèrent des plateformes mettant en relation des groupes d'utilisateurs – réduisant ainsi les coûts de transaction – et exploitent les effets de réseaux qui en résultent. À la différence des commerçants, ils ne vendent pas de biens directement et ne disposent pas de droits de propriété sur les ressources qui font l'objet de transactions. Ils produisent des méta-informations nécessaires à la réalisation de ces transactions. Ils se distinguent selon la nature des méta-informations qu'ils exploitent : données commerciales pour organiser et établir des transactions (informations sur les vendeurs, les prix ou les caractéristiques du produit, tests...), données relationnelles facilitant la mise en relation (exposition de soi, avis, notations, commentaires, résultats de requêtes sur les moteurs de recherche etc.).
À l'instar des intermédiaires traditionnels, les infomédiaires remplissent trois fonctions essentielles : l'appariement (matching), l'agrégation et l'authentification. Celles-ci permettent de réduire un certain nombre de « distances » entre les offreurs et les demandeurs et plus généralement, avec l'avènement des réseaux sociaux numériques, entre les internautes. Elles étaient déjà réalisées par les intermédiaires traditionnels (associations de consommateurs, revues spécialisées etc.), mais internet renforce leur efficacité et surtout leur utilité, car le contenu informationnel est devenu un trait essentiel des transactions en ligne.
Les infomédiaires occupent une position centrale en minimisant les coûts de transaction entre les acteurs (fonction d'appariement) et surtout en exploitant les effets de réseaux réciproques (fonction d'agrégation) : plus il y a d'offreurs, plus la probabilité que le demandeur trouve un bien ou un service ou une personne satisfaisant ses préférences augmente, plus la plateforme attire de demandeurs, ce qui renforce son attrait pour les offreurs et ainsi de suite... L'appariement et l'agrégation renvoient à une poignée de sites, voire un seul, face à des marchés fragmentés où l'information est non transparente et conduirait en l'absence d'intermédiaires à un nombre de transactions très limitées. Leur pouvoir de marché est renforcé par leur rôle d'authentification ou de certification en ligne. L'environnement numérique où nul ne se connaît, ne se rencontre physiquement, n'établit de relations répétées, est en effet marqué par des asymétries informationnelles fortes et des risques très élevés de comportements opportunistes. La certification joue donc un rôle essentiel.
Dans le domaine de la culture, les infomédiaires se sont très tôt développés sous forme de plateformes d'échange de contenus numérisés (les réseaux pair-à-pair), mais également d'agrégation et de transaction (sites recensant les expositions, les festivals... et permettant l'acquisition de billets d'entrée). Certains se spécialisant sur des fonctions très précises, d'autres diversifient leurs offres de services. Dans le premier cas figurent des services commerciaux comme l'achat de tickets en ligne (Ticketnet, Digitick, Francebillet...), des bases de données plus orientées vers la recherche d'informations sur les biens culturels (Imdb, Discogs, Allmusic, Worldcat, LibraryThing, evene.fr, lechoixdeslibraires...), des sites d'agrégation de critiques (Rotten Tomatoes, iDreamBooks, Metacritic, Allociné), des communautés de pratiques (DeviantArt, Goodreads, SensCritique, Vodkaster...). Dans le second cas, on trouve des sites et plateformes thématiques (Allociné) ou généralistes (Facebook, Google/Youtube, Amazon, Dailymotion, Twitter, Wordpress, Scribd etc.).
Pour autant, au-delà de cette diversité d'acteurs, une poignée d'entre eux seulement dominent actuellement le marché, que ce soit en matière d'audience, de levées de fonds, de fourniture de services et de données, de revenus publicitaires etc. Ces opérateurs de plateformes numériques se sont imposés comme intermédiaires obligés au sein de nombreux secteurs traditionnels, en particulier le monde de la culture. Cela leur permet notamment de capter directement ou le plus souvent, indirectement la valeur inhérente aux transactions réalisées par les utilisateurs professionnels ou finaux de leurs services.
De nouveaux modèles numériques :
longue traîne et crowdfunding
Les acteurs numériques ont développé de nouveaux modèles économiques. Sur les marchés de la culture, certains portent sur la valorisation des biens culturels, d'autres, plus récemment, sur leur financement.
À l'origine, l'hébergement et le partage de fichiers en ligne introduisent une rupture dans l'histoire des pratiques culturelles, en démocratisant massivement l'accès à tout type de contenus numérisables – à commencer par la musique et les films. Malgré des moyens légaux et techniques très importants pour les empêcher ou les dissuader, ces pratiques illégales du point de vue du droit d'auteur se sont largement répandues et diversifiées avec internet. Elles ont ainsi favorisé une dissémination très large des œuvres sans pour autant contribuer au financement des biens numériques ainsi téléchargés et partagés. Pour autant, très tôt, une plateforme pionnière comme Napster (1999-2001) a tenté de construire un modèle économique permettant de générer des revenus à partir de ces pratiques, mais s'est confrontée à un refus et à des procédures judiciaires de la part des majors du disque considérant ce mode de distribution comme une menace pour leur propre modèle économique. Par la suite, les modes de circulation illégale se sont multipliés : applications de partage de fichiers en pair-à-pair (Kazaa, Gnutella, eDonkey...), échanges de liens vers des fichiers hébergés en ligne sur des plateformes comme Megaupload, services de streaming illégal etc.
Face aux pratiques illégales, une autre solution a consisté à développer des propositions marchandes. Les offres proposées essentiellement par les acteurs numériques pure players sont relativement diversifiées : iTunes/Apple ou Amazon (vente d'exemplaires), Netflix (vidéo à la demande), Spotify, Deezer ou Rdio (diffusion en flux ou streaming). Leurs modèles de revenus diffèrent également, qui prévoient le paiement à l'unité, un système d'abonnement ou le financement par la publicité. Mais au-delà de cette diversité, deux grands modèles ont été identifiés par les économistes de la culture : le principe du best-seller et, plus récemment, la longue traîne (long tail). Tous deux partagent les deux traits principaux de la numérisation, soit l'accroissement de la variété produite et une capacité d'exposition spatiale et temporelle sans limites. La diversité des goûts des consommateurs n'en est pas pour autant appariée automatiquement avec la variété des biens produits. Tout dépend des modes de prescription.
Le best-seller est le modèle dominant actuel. Les éditeurs et les distributeurs, à la fois organisateurs et bénéficiaires de ce modèle, ont tout intérêt à le prolonger dans le monde numérique avec quelques adaptations à la marge. Ce modèle s'organise autour du vedettariat, du marketing de masse centré sur quelques biens préformatés et du turn-over rapide des biens culturels (cf. chapitre 14). Ces pratiques restreignent fortement la demande pour les œuvres « difficiles », celles qui ne correspondent pas aux goûts établis ou innovent par rapport à ces derniers (cf. chapitre 11). Pour ces dernières œuvres, le temps et la surface d'exposition sont insuffisants pour que le bouche-à-oreille élargisse le cercle des consommateurs au-delà d'un nombre initial de passionnés. Celles-ci sont alors le plus souvent oubliées ou laissées aux petits labels, tandis que leurs nombreux auteurs perçoivent des revenus faibles, insuffisants pour vivre pleinement de leur production. Leur survie et à travers eux la diversité culturelle dépendent dès lors pour une bonne part de financements publics et de mécénat privé, mais également des reversements de la part des producteurs dominants d'une partie des recettes qu'ils tirent des best-sellers selon leur stratégie de renouvellement de l'offre.
Dans le modèle du best-seller, les changements apportés par le numérique, théoriquement importants, demeurent somme toute marginaux. Les acteurs dominants (les stars, leurs éditeurs, les grands distributeurs) s'évertuent à en limiter les effets lorsqu'ils menacent leurs rentes (téléchargement illégal) et à valoriser ceux permettant de les accroître (vente en ligne, marketing viral...). Pour favoriser la vente en ligne présentée comme alternative au téléchargement illégal, les distributeurs ont adapté leur modèle, mais marginalement, en renonçant dans la musique aux formats propriétaires et en mettant en avant la vente à l'unité au détriment des albums. La prescription a également évolué, mais sans toucher non plus aux fondements du modèle, en associant au marketing de masse des systèmes de recommandation exploitant les avis des consommateurs organisés en communautés. Mais loin de contrarier la loi de Pareto, cette instrumentalisation du bouche-à-oreille aboutit aussi à faire converger les choix individuels autour d'une opinion moyenne.
Les modèles fondés sur la longue traîne sont présentés comme une alternative face au best-seller. Son principe est simple : si 80 % de la demande se concentre sur 10 % de biens culturels, il existe un potentiel de marché non exploité, à savoir les 90 % restants peu vendus ou non exposés dans le cadre du modèle du best-seller. Le modèle de la longue traîne consiste précisément à exploiter ce fonds en monétisant l'allongement de cette traîne. C'est donc a priori un modèle complémentaire du précédent, mais il pourrait a contrario se présenter comme un concurrent sérieux en « épaississant » la longue traîne (c'est-à-dire en permettant de vendre plus d'œuvres diverses) au détriment des best-sellers.
Contrairement au modèle du best-seller, la numérisation est davantage exploitée dans les modèles fondés sur la longue traîne. Tout d'abord, la réduction des coûts du stockage et du transport (électroniques ou physiques) permet une capacité d'exposition des œuvres sans limites (allongement de la queue de distribution, la « traîne »). Ensuite, les algorithmes ont amélioré significativement la recherche d'informations sur les œuvres et l'appariement avec les préférences des internautes à travers les systèmes de recommandation sociale mis en place par des acteurs comme Amazon et Netflix. Enfin, l'épaississement de la traîne qui en résulte est également alimenté à travers la captation par les acteurs de ce modèle des externalités positives générées par les revues en ligne, mais surtout les amateurs éclairés contribuant à la critique culturelle et la discussion des œuvres décentralisées (blogs, forums, réseaux de partage...). Ces prescripteurs numériques sont donc susceptibles d'attirer l'attention d'un public fragmenté sur des œuvres minoritaires, car exclus des circuits dominants (œuvres difficiles, échecs commerciaux etc.). Par conséquent, il devient économiquement rentable de distribuer et de valoriser les biens culturels qui en sont tirés en les agrégeant et en les mettant à disposition sur des plateformes numériques.
Par rapport au modèle du best-seller, la longue traîne introduit plus de bien-être à travers une visibilité et un accès nettement élargis à la variété de l'offre existante et un appariement mieux organisé avec l'hétérogénéité de la demande. Toutefois, ce modèle économique laisse ouvertes deux questions majeures : celle des mécanismes de prescription sur lesquels il repose et celle du financement des petites productions qu'il distribue.
D'une part, les systèmes de recommandation informatisés utilisés par des acteurs comme Amazon et Netflix peuvent avoir des effets ambivalents. S'ils permettent un meilleur appariement à partir des données divulguées par les consommateurs (avis postés, traces d'usage), ils peuvent aboutir à une certaine uniformisation des préférences via les suggestions et les sélections automatisées d'œuvres générées par leurs algorithmes. D'autre part, les recettes tirées des microventes ne garantissent a priori en rien le financement de nouvelles œuvres indépendantes ou difficiles d'accès et ne permettent pas non plus d'assurer la survie de petites structures de production. En l'état, ce modèle semble davantage orienté vers la valorisation de catalogues et l'écoulement des stocks d'invendus produits ou distribués par les majors. Et les grands gagnants de ce modèle sont avant tout les Amazon, Netflix, Spotify... qui ne financent pas les œuvres, les projets artistiques émergents... mais s'approprient une rente de situation sous la forme de commissions prélevées sur toute microvente réalisée sur leur plate-forme.
Une solution pourrait finalement provenir du financement participatif en ligne ou crowdfunding (cf. chapitre 5). Des artistes et des producteurs trouveraient là un moyen de financer leurs coûts fixes de création tout en bénéficiant de l'engagement des souscripteurs individuels, transformés en primo-marketeurs des œuvres qu'ils soutiennent financièrement. Associé aux réseaux sociaux numériques, ce mode de financement pourrait concilier les fonctions d'appariement et de financement de la culture en générant un nouvel écosystème de diversité créative dans lequel les plateformes accompagneraient les projets artistiques une fois produits ; elles pérenniseraient ainsi un ensemble de « réseaux artistiques locaux » reliés selon une logique de « petit monde » qui pourraient coexister avec, voire remettre en cause, les acteurs et modèles économiques dominants. À condition toutefois que le principe du crowdfunding puisse être étendu de manière significative à un plus grand nombre de projets à financer, que le financement des projets puisse atteindre un apport réellement significatif (plus importants que les micro-investissements de quelques milliers d'euros), et qu'il ne soit pas instrumenté par les grands distributeurs. Il ne jouerait alors qu'un simple rôle d'incubateur en structurant le vivier de création par une mise en visibilité plus grande de la création, l'organisation d'une présélection plus systématique des projets et le report des coûts inhérents sur l'ensemble des contributeurs.
Écosystèmes de la culture et stratégies de plateforme
L'arrivée des géants du numérique (le fameux quatuor Google-Apple-Facebook-Amazon) engendre indéniablement des opportunités indéniables en matière d'innovations de services et d'usages. Mais leurs stratégies globales pourraient déstructurer – à leur seul avantage – des écosystèmes de la culture (l'édition, le cinéma etc.) fondés sur des équilibres somme toute fragiles. Les secteurs d'activités liés aux mondes de la culture sont diversement affectés par la diffusion massive du numérique et les grandes manœuvres de ces acteurs transnationaux. Les arts plastiques et graphiques, de même que le spectacle vivant, connaissent des évolutions majeures liées à l'usage de leurs services : les visites de musées virtuels, les pages internet d'artistes, la création d'événements mondiaux autour d'expositions ou de ventes aux enchères, mais également l'utilisation de ces technologies dans les activités de création et de collaboration artistiques.
Toutefois, ce sont les industries culturelles qui semblent aiguiser le plus l'appétit des acteurs du Net. Elles se trouvent ainsi confrontées aux transformations les plus importantes et font face à des stratégies très variées, qui vont de la politique de numérisation massive des livres par Google à la stratégie d'intégration très poussée d'Amazon. Plusieurs raisons peuvent expliquer cet intérêt très fort. En premier lieu, les biens culturels reproductibles sont propices à des exploitations numériques très diversifiées (même si une pièce de théâtre et une peinture peuvent être « numérisées » et donner lieu à une circulation d'artefacts sur internet). À ce titre, ils peuvent alimenter en contenus les réseaux numériques tout en se pliant à des modèles d'affaires variés comme le versioning ou l'échantillonnage. En second lieu, ils permettent de différencier l'offre des acteurs du numérique à l'instar du rôle joué par les services iTunes et Appstore à l'égard des appareils produits par Apple. En troisième lieu, il s'agit de biens à haute valeur médiatique, valorisés sur des marchés de masse et occupant les esprits des individus au niveau tant de leur temps d'activité que de leur attention. Leur valorisation peut ainsi être couplée à des campagnes publicitaires, sources de revenus majeures pour des acteurs comme Google. Ces activités culturelles constituent, au même titre que la presse et les médias audiovisuels, des écosystèmes susceptibles de générer de l'audience et de valoriser l'offre des opérateurs de plateformes numériques. Pour comprendre ce phénomène, il convient de définir en premier lieu les notions d'écosystèmes et de plateformes.
Une stratégie récurrente : imposer sa plateforme
Une plateforme numérique est un système servant de support à la coordination entre des agents faisant partie d'un écosystème : plateforme logicielle (Microsoft, Google) ou terminaux (Apple). Elle remplit différentes fonctions logistiques permettant la création et le développement de produits complémentaires, tels que les applications, services et contenus. L'enjeu, pour son opérateur, consiste à attirer la base d'utilisateurs la plus large possible, si possible la verrouiller autour de l'usage des fonctions proposées. Imposer sa plateforme dans un écosystème donné confère ainsi à celui qui la possède une position privilégiée pour capter le revenu tiré de la valorisation des services et des contenus qui y sont associés. Les utilisateurs de la plateforme sont précisément les agents en interaction dans l'écosystème : développeurs d'applications, prestataires de services, fournisseurs de contenus, utilisateurs producteurs, simples consommateurs.
La clé du succès, pour un opérateur de plateforme, est de générer des effets de réseaux et des switching costs (des coûts liés au changement de plateforme) qui renforcent de manière cumulative la domination de sa plateforme vis-à-vis d'éventuelles concurrentes. Les nouveaux utilisateurs du magasin d'applications de Google peuvent ainsi attirer de nouveaux développeurs d'applications renforçant l'intérêt des services de Google pour les individus utilisateurs de ces applications. Dans le même temps, les individus apprennent à se servir de ces applications et à échanger des contenus à travers elles, ce qui peut accroître les coûts de changement et de migration vers une autre plateforme, comme celle d'Apple. Ces effets sont encore plus évidents avec Facebook où migrer sur une autre plateforme suppose d'emporter avec soi ses contenus et... ses amis.
Pour viabiliser son activité, un opérateur de plateforme doit définir un modèle d'affaires, soit une proposition de valeur, des modèles de revenu et d'investissement. Il peut proposer des prix différents à chaque groupe d'utilisateurs en fonction de leur sensibilité au prix pour maximiser les effets de réseau générés par leurs interactions et donc la valeur créée à travers l'usage collectif de la plateforme. Ainsi, la gratuité de l'accès aux programmes pour les téléspectateurs ou le paiement d'un prix élevé pour l'acquisition de jeux vidéo s'accompagnera de prix élevés de diffusion des messages publicitaires ou d'un partage de la valeur plus généreux avec les développeurs de jeux. L'opérateur de la plateforme va définir la contribution de chacun et le partage de la valeur selon ses compétences, son niveau d'investissement et de contribution, son pouvoir d'achat etc.
Au-delà de la diversité des modèles d'affaires, les opérateurs mondiaux de plateformes numériques poursuivent le même objectif stratégique : procéder à des investissements initiaux colossaux pour tenter de préempter des écosystèmes à l'échelle mondiale et de la sorte, obliger les acteurs de ces écosystèmes à accepter leur modèle de revenu en raison de l'utilisation de la plateforme par plusieurs catégories d'agents interdépendants. Ainsi, diffuser massivement une tablette numérique sous un système propriétaire oblige les fournisseurs de contenus et d'applications à être présents sur cette plateforme pour pouvoir accéder à leur client. Pour être en mesure d'imposer leur plateforme respective, ces acteurs doivent proposer continuellement de l'innovation à destination des utilisateurs de leur plateforme (d'une cartographie enrichie à des drones livreurs).
Si ce rythme rapide d'innovations permet de verrouiller (de « fidéliser ») progressivement les utilisateurs, une telle stratégie nécessite des investissements d'autant plus élevés que peu d'innovations ne s'imposent in fine. Cela pourrait poser un problème aux géants du numérique s'ils tiraient des revenus directement de ces innovations. Or, ce n'est pas le cas ; les revenus sont en fait de nature indirecte (publicité pour Google et Facebook, vente de terminaux pour Apple, commerce en ligne pour Amazon...).
Les plateformes numériques et les industries culturelles
Les écosystèmes de la culture, en particulier le livre, la musique et les productions audiovisuelles, constituent des exemples très pertinents pour comprendre les stratégies de plateforme et de captation de revenus indirects déployées par les géants du numérique.
La musique en ligne
Le format MP3 et internet ont provoqué un déséquilibre dans cet écosystème par l'entrée de nouveaux acteurs (réseaux pair-à-pair, radios en ligne, forums et blogs dédiés à la musique...) et le développement de nouvelles pratiques (partage de fichiers et de playlists, téléchargement etc.). Or, loin de résorber ce déséquilibre, les majors ont montré une incapacité à changer de modèle économique pour amorcer une reconversion numérique. L'apparition de nouveaux modèles est davantage le fait d'acteurs issus de l'informatique (Apple) ou des pure players (Spotify, Deezer...).
Ces nouveaux entrants transforment radicalement l'écosystème de la musique. Un exemple emblématique est celui d'iTunes/Apple. La valeur est certes générée par la mise à disposition de fichiers musicaux, mais elle est captée par Apple non pas tant directement par les commissions prélevées (les investissements pour imposer sa plateforme ont pesé longtemps sur la rentabilité de la vente de fichiers), mais indirectement par les ventes de terminaux sur lesquelles Apple dégage des marges commerciales très élevées. Cependant, si le téléchargement payant de musique représentait encore en 2013 la majorité des ventes numériques face à la montée du streaming, pour Apple, les recettes correspondantes ne représentent qu'environ 2 % de son chiffre d'affaires mondial. L'essentiel de ses recettes est tiré de la vente de matériel (ordinateurs, smartphones, tablettes numériques).
L'industrie musicale a souvent présenté Apple comme un sauveur face au téléchargement illégal en croyant être bénéficiaire du développement du marché de la musique en ligne. Mais d'une part, le sauveur est avare par rapport aux gains réels qu'il tire de cette opération et d'autre part, le développement d'un nouveau modèle commercial, la vente à l'unité, peut être jugé comme l'un des principaux accélérateurs de la chute des ventes de CD. Au lieu d'acheter un album, le consommateur n'acquiert qu'un ou deux titres. Les majors auraient pu légitimement revendiquer plus de revenus en se basant sur l'intégralité du chiffre d'affaires d'Apple et non sur ses seules ventes numériques de musique...
L'arrivée plus récente d'acteurs comme Deezer, Spotify et Rdio sur le marché de la musique en ligne peut a contrario s'analyser comme un modèle plus classique. Leurs chiffres d'affaires se basent plus directement sur les ventes d'abonnements (intermédiation) ou les revenus publicitaires (modèle à deux versants). Toutefois, les revenus artistiques demeurent faibles selon la même logique de partenariat « forcé ».
La vidéo à la demande
Le secteur de la télévision donne lieu actuellement à des mouvements stratégiques importants. Des groupes de communication tels que Time Warner ou HBO font des alliances pour contrer l'offensive de nouveaux acteurs tels que Netflix. Ce dernier ne se contente plus en effet d'être un intermédiaire, simple distributeur de contenus, mais offre des services complémentaires et surtout produit des contenus (des séries, mais également des films). Une telle intégration verticale peut en effet lui donner un pouvoir de négociation lors de l'acquisition de droits d'exploitation audiovisuels, ce qui constitue une des conditions pour atteindre des seuils de rentabilité à des niveaux plus élevés que les seules marges d'intermédiation sur internet. En cela, Netflix suit une stratégie similaire à celle de la société HBO à ses débuts. Cet acteur majeur sur le marché de la télévision payante outre-Atlantique était initialement un simple intermédiaire acquérant des droits de diffusion auprès des producteurs de films et payant des charges d'accès importantes pour pouvoir acheminer les contenus vers ses abonnés. HBO prêtait ainsi le flanc à des stratégies agressives de la part des câblo-opérateurs et des majors hollywoodiens pouvant la contourner en négociant directement la distribution de leurs films avec de nouveaux acteurs. Cela incita HBO à produire ses propres contenus et en particulier, des séries à succès.
Le même problème se pose à Netflix et à Amazon. Leur stratégie de production de séries peut s'interpréter comme une volonté de ne pas être confinés à un rôle de simple intermédiaire, mais au contraire d'acquérir une position de marché face aux acteurs opérant en aval de leurs activités et par ricochet, à l'égard des producteurs de films et de séries alimentant leurs catalogues. Et leur permettre une stratégie de verrouillage de leurs clients finaux.
Toutefois, sur ce dernier point, leurs objectifs sont différents. Pour Netflix, fondée en 1997, il s'agit de s'imposer comme acteur dominant sur le marché de la vidéo par abonnement. Netflix a opéré avec succès (50 millions d'abonnés en 2014) une stratégie consistant à cibler son offre davantage sur les films de catalogue et les séries, et non les sorties récentes de films – et à partir de 2012, à effectuer une remontée de la filière en produisant elle-même ses séries (House of Cards par exemple), mais également des programmes pour enfants, des documentaires etc. en misant sur l'originalité et la qualité du contenu. L'enjeu est non seulement de maîtriser son approvisionnement en contenus, mais également et surtout de différencier son offre par rapport à ses concurrents et d'élever des barrières à l'entrée.
Amazon s'inscrit dans une logique différente en ayant notamment établi un accord avec HBO, laquelle conserve l'exclusivité des programmes récents, attractifs et sources de revenus liés à des abonnements relativement onéreux, tandis qu'Amazon complète son fonds de catalogue avec des programmes plus anciens suivant ainsi une stratégie de longue traîne. Plus fondamentalement, Amazon décide en 2013 de produire des séries pour attirer et verrouiller ses clients sur sa plateforme de vente en ligne et d'infomédiation. En amont, Amazon suscite une forme d'engagement des clients en publiant en ligne un certain nombre de projets de séries et en mettant en place une procédure de vote pour sélectionner les meilleurs pilotes. Une fois produits, Amazon diffuse en accès libre les premiers épisodes pour finalement réserver les suivants aux abonnés de son service de vidéo en ligne. Sachant que la probabilité que ces derniers achètent des produits auprès d'Amazon est deux fois et demie plus élevée par rapport aux non-abonnés, la diffusion de la série (et donc l'entrée d'Amazon sur ce segment précis du marché audiovisuel) vise à attirer de l'audience vers ses services de base et améliorer son chiffre d'affaires global.
À cet égard, la stratégie d'Apple s'avère similaire à celle d'Amazon, même si sa plateforme est de nature différente. Il s'agit davantage de fournir des contenus vidéo pour ses tablettes et donc de différencier son offre par rapport à la concurrence. À l'instar de la musique en ligne, il ne s'agit pas de capter des revenus directs de la vente de fichiers vidéo, mais bien de capter cette valeur à travers la vente de matériel. Contrairement à Netflix et à Amazon, acteurs intégrés verticalement, Apple ne produit toutefois pas les contenus qu'il distribue à travers ses services.
Le livre numérique
Le livre a été affecté très tôt par la numérisation au niveau de la création, avec l'usage des machines à écrire électroniques, puis de la micro-informatique dans les années 1980. Toutefois, concernant sa valorisation, son dominant design est demeuré jusqu'à une période récente la lecture du livre papier façonnant son organisation industrielle. Un certain nombre d'expériences se sont développées rapidement après l'avènement d'internet : certaines ont réussi comme Lulu.com (plateforme d'auto-publication et de distribution en ligne créée en 2002), d'autres ont été des échecs comme les appareils de lecture de Gemstar ou Cytale au début des années 2000. Mais c'est davantage l'entrée d'Amazon et de Google qui a initié des changements majeurs. Comme dans la musique et les films, il s'agit de firmes dont la stratégie consiste à organiser les interactions entre des groupes d'agents autour de leur plateforme et à capter ensuite la valeur ainsi générée.
Fondée en 1994, Amazon.com fut longtemps l'entreprise emblématique du commerce électronique. Mais face à un problème récurrent de rentabilité, elle a dû modifier son modèle économique en mettant en place à partir de 2003 une plate-forme baptisée Marketplace. Elle est passée ainsi de la vente en ligne de biens culturels à l'infomédiation entre des vendeurs (souvent des particuliers) et des consommateurs. Amazon est l'un des rares pure players à avoir survécu à la bulle spéculative sur les valeurs internet, autour des années 2000. Cela s'explique notamment par des innovations logistiques importantes (organisation rationalisée à l'extrême d'entrepôts géants), mais coûteuses, pesant largement sur sa rentabilité longtemps négative et encore fragile aujourd'hui. Celle-ci est également affectée par la gratuité des frais d'envoi qui constitue une forme de dumping lui ayant permis de s'imposer face à ses concurrents. Mais sa survie s'explique davantage encore par l'évolution de son modèle économique, d'abord par la diversification des produits distribués (électronique grand public, outillage, mode, bijoux, jouets...), ensuite à travers l'intermédiation informationnelle en organisant sa plateforme de distribution autour du commerce entre particuliers et professionnels et enfin, en louant ses capacités de stockage informatique selon une logique de cloud computing.
Positionné initialement sur la vente en ligne de livres, Amazon a progressivement mené une intégration verticale en amont en offrant des outils de publication aux auteurs et en aval via ses terminaux de lecture. Sa stratégie a consisté à coupler une logique de longue traîne poussée à l'extrême avec des frais d'envoi gratuits, la mise en relation de vendeurs et d'acheteurs de livre via sa place de marché et un système de recommandation s'alimentant des avis et notes postés par ses clients. En janvier 2013, Amazon a obtenu un brevet sur le marché des livres numériques d'occasion traduisant une volonté de marchandisation des pratiques d'échange de livres entre particuliers. En moins d'une décennie, Amazon est ainsi devenu le plus grand libraire en ligne en imposant sa plateforme numérique dans l'écosystème du livre, au prix toutefois de faibles marges commerciales et d'un manque de rentabilité chronique.
Google représente un modèle très différent de plateforme. La diversification, la multiplication et le renouvellement incessant des innovations par Google correspondent à une stratégie de gestion d'audiences (recherche, captation et orientation vers sa plateforme). Il s'agit d'atteindre de nouveaux publics (lecteurs de la presse, utilisateurs d'applications mobiles etc.), de verrouiller les utilisateurs de ses services (suite bureautique, système de cartographie...) et finalement de diversifier les « lieux » (sites web, applications, services connectés...) où poster des liens commerciaux à travers son programme d'affiliation AdSense.
Son entrée dans l'écosystème du livre débute en 2004, lorsque l'entreprise introduit la recherche de livres en texte intégral dans son moteur de recherche et initie un programme de numérisation massive de livres (Library Project), aboutissant en 2012 à un catalogue de plus de 20 millions de livres scannés et entraînant en réaction la création de la plateforme (publique et nettement moins fournie) Europeana. Un certain nombre de conflits ont opposé Google aux éditeurs dans des pays comme les États-Unis et la France. Toutefois, le géant mondial est parvenu à établir des accords en s'imposant de facto comme une plateforme mondiale de distribution massive de livres. La stratégie semble récurrente : agir sans autorisation, s'imposer et négocier ensuite... Les revenus indirects sont tirés de publicités personnalisées affichées dans les pages de résultats de recherche. Plus récemment, Google a fait évoluer son modèle en incluant les livres gratuits en majorité et payants dans son service de distribution multimédia Google Play, qui joue davantage la fonction d'infomédiation (avec prélèvement de commissions) en renvoyant les consommateurs sur les sites de vendeurs en ligne. Il concurrence ainsi frontalement la place de marché d'Amazon tout en cherchant à conserver sa position dominante en matière d'accès à l'information sur internet.
En conclusion, une question fondamentale émerge de ces différentes stratégies de plateformes : annoncent-elles une destruction créatrice ou une création destructrice ? D'un côté, les innovations produites par les géants du numérique remplacent l'ancien par du nouveau, plus créateur de valeur, de richesse et de bien-être (accès à plus de diversité, plus rapidement, en interaction avec les autres consommateurs etc.). De l'autre, ces services aspirent la valeur produite par les écosystèmes sans en redistribuer davantage (faibles rémunérations des artistes sur les services de streaming) ni recréer des fonctions analogues (prescription de choix plutôt que lancement de goûts nouveaux). L'exemple du brevet d'Amazon sur le marché de l'occasion des biens culturels illustre finalement bien la manière dont ces modèles peuvent menacer certains fondamentaux de l'économie de la culture en marchandisant des pratiques de partage entre individus, pourtant essentielles à la découverte et à la formation des préférences.
. Von Hippel E., Democratizing innovation, Cambridge MA, The MIT Press, 2005.
. Rochelandet F., « The Internet: economics », in Towse R. (coord. par), A handbook of cultural economics, Cheltenham, Edward Elgar, 2011 (2e éd.), p. 254-260.
. Rallet A., « Commerce électronique ou électronisation du commerce ? », Réseaux, no 106, 2e trimestre, 2001, p. 17-72.
. De Long J. B., Froomkin A. M., « Speculative Microeconomics for Tomorrow's Economy », in Kahin B., Varian H. R. (coord. par), Internet Publishing and Beyond: The Economics of Digital Information and Intellectual Property, Cambridge, MIT Press, 2000, p. 6-44.
. Bailey J., « Intermediation and Electronic Markets: Aggregation and Pricing in Internet Commerce », Ph.D. Dissertation, Technology, Management and Policy, Massachusetts Institute of Technology, Cambridge, MA, 1998.
. Brynjolfsson, E. et Smith M., « Frictionless Commerce? A Comparison of Internet and Conventional Retailers », Management Science, vol. 46, no 4, 2000, p. 563-585 ; Zoonky L., Gosain S., « A Longitudinal price Comparison for Music CDs in Electronics and Brick-and-Mortar Markets: Pricing Strategies in Emergent Electronic Commerce », Journal of Business Strategies, vol. 19, no 1, 2002, p. 55-71 ; Bourreau M., Moreau F., Senellart P., « La diversité culturelle dans l'industrie de la musique enregistrée, 2003-08 », Culture études 2011- 4, Ministère de la Culture et de la Communication, 2011.
. Certains sites davantage orientés vers la publication ou l'édition en ligne de contenus (sites de journaux et magazines, pure players comme Critikat etc.) ou encore dans le commerce électronique (Apple/iTunes, Deezer, Spotifiy, Netflix, Artevod, Canalplay etc.) peuvent proposer également des services d'infomédiation, mais il ne s'agit pas de leur métier principal.
. Bourreau M., Gensollen M., « Communautés d'expérience et concurrence entre sites de biens culturels », Revue d'Économie Politique, vol. 113, 2003, p. 61-89.
. Banerjee A., « Simple model of herd behaviour », The Quarterly Journal of Economics, vol. 107, no 3, 1992, p. 797-817 ; Bikhchandani S., Hirshleifer D., Welch I., « Learning from the behavior of others: conformity, fads, and informational cascades », Journal of Economic Perspectives, vol. 12, no 3, 1998, p. 151-170.
. Anderson C., La longue traîne, Paris, Pearson, 2009 (2e éd.)
. Voir ainsi Benghozi P. J., Benhamou F., « Longue traîne : levier numérique de la diversité culturelle ? », Culture Prospective, 2008-1. Disponible sur : http://www2.culture.gouv.fr/deps/fr/traine.pdf.
. Konstan J. A., Riedl J., « Recommended for you », IEEE Spectrum, vol. 49, no 10, 2012, p. 54-61.
. Creton L., Kitsopanidou K. (dir.), Crowdfunding, industries culturelles et démarche participative. De nouveaux financements pour la création, Paris, Nouveau Monde / Labex ICCA, 2015 (à paraître).
. Rallet A., Rochelandet F., « Crowdfunding et valorisation des biens culturels : vers plus de diversité culturelle ? », in Creton, Kitsopanidou (2015), op. cit.
. Cette section se base sur des travaux menés par Alain Rallet et Fabrice Rochelandet. Rallet A., Rochelandet F., « Modèle d'affaires partenariaux et écosystèmes numériques », Document de travail ADIS, Université Paris-Sud, 2011.
. C'est toutefois leur forme matérielle qui a suscité au départ l'intérêt d'acteurs comme Amazon et Netflix : leur format (standard dans le cas du DVD) et leur manipulation relativement plus facile que d'autres biens se sont parfaitement intégrés aux innovations logistiques de ces acteurs.
. « Why Amazon's Original Series May Be More Successful (If Less Interesting) Than Netflix's », Indiewire, Celluloid Liberation Front, 12 mars 2013.
. Benhamou F., « Le livre et son double. Réflexions sur le livre numérique », Le Débat, vol. 3, no 170, 2012, p. 90-102.
. Jeanneney J.-N., Quand Google défie l'Europe, Paris, Fayard, 2010.
Conclusions
Intégrer l'économie dans la culture ?
Le mouvement en train de s'opérer, de nos jours, semble inexorablement conduire les contours de l'économie de la culture à s'étendre aux industries créatives. Nous avons évoqué l'intérêt, pour nombre de créateurs, de participer à ce mouvement qui leur permet de mieux justifier l'intervention publique dans leur secteur. Ceux-ci semblent donc avoir avantage à présenter la culture comme participant de manière importante à l'effort économique global, dans la logique de l'économie de la créativité : financer la culture, c'est investir dans l'un des secteurs les plus rentables et porteurs de croissance, à lire les différents rapports que l'on trouve aussi bien au sein de l'Union européenne qu'aux Nations unies. Nous avons déjà émis un certain nombre de doutes quant à cette vague d'optimisme économico-culturel.
Parallèlement, comme nous l'avons évoqué à travers la troisième partie, des tendances profondes transforment radicalement notre culture, au sens large : l'arrivée des nouveaux acteurs du numérique a déjà métamorphosé le monde des industries culturelles, mais son influence s'étend très largement aussi sur les secteurs historiques inscrits au cœur de l'économie de la culture : les arts de la scène, le patrimoine, les arts plastiques... On a commencé à émettre l'hypothèse, depuis déjà quelques années, d'une nouvelle culture et de son influence sur l'ensemble des institutions culturelles occidentales. Il est encore difficile de percevoir les contours de ces transformations dans lesquelles nous sommes totalement parties immergées, au même titre qu'il apparaissait absolument impossible, au début du xixe siècle, d'évaluer le potentiel des transformations à venir entraînées sur la production industrielle par la machine à vapeur. Diminution du temps de travail (voire diminution du travail) contre augmentation de celui des loisirs et allongement de la durée de vie, augmentation des vitesses de production, mais aussi de celle de consommation, distribution des produits sur l'ensemble du globe... Autant de facteurs, évoqués dans les chapitres précédents, qui ne sont pas sans influence sur la définition même de l'art et de la culture, ainsi que sur la manière de les pratiquer et les vivre. De nouveaux modèles économiques semblent se profiler à côté de celui du best-seller dans les industries culturelles et de la logique du star-system, tournés vers les principes de longue traîne et l'agrégation des marchés de niche, ainsi que sur le financement et le fonctionnement participatif et une certaine logique de gratuité. Pourrait-on imaginer que ces différents facteurs sonnent le glas de ce qui s'inscrit au cœur de l'économie des arts : le théâtre ou la musique sur scène, le patrimoine ou les arts plastiques ?
Nous savons que l'avènement de la salle de cinéma n'a pas mis fin aux théâtres ou aux musées et que l'essor de la télévision n'a pas empêché la poursuite du cinéma, mais nous savons aussi combien ces deux médiums ont influencé les pratiques, les demandes, ainsi que l'offre et la production elles-mêmes, de même que nous avons pu assister, dans chacun des cas, à la fermeture de nombreux théâtres ou de salles de cinéma, ainsi qu'à la création de nouveaux établissements ; tout comme nous avons pu voir, progressivement, le développement de nouveaux modèles économiques, liés partiellement à l'intervention publique (organisation du secteur, création de systèmes d'autofinancement ou de subventions, voire reprise en main par les pouvoirs publics), mais aussi à la logique de marché (merchandising, valorisation de la marque) ou fondée sur le don (associations d'amis, fondations, campagnes de levées de fonds, crowdfunding ou crowdsourcing).
À travers la notion même d'arts de la scène, celle de patrimoine et celle d'arts plastiques, se structurent trois principes intrinsèquement différents de ceux que l'on observe dans les modèles plus industriels visant à distribuer la création à partir d'un certain type de supports : (1) la communication directe et sensible (essentiellement l'audition et la vue) entre un créateur et son public, soit la logique de la scène, (2) la présentation directe (essentiellement la vue) d'un objet original par son créateur, sans support de reproduction, soit la logique de l'art plastique, (3) la notion de préservation, à travers le temps et dans l'espace tangible, d'objets ou d'immeubles présentant le monde et son histoire, soit la logique patrimoniale. Autant de notions qui déterminent des plans d'expression, de communication et de transmission irréductibles à d'autres et que l'arrivée du numérique ne peut influencer, même si elle transforme les institutions en charge de ce type particulier de communication et de transmission au sein de la société. La réflexion sur ce que le numérique (et de manière générale, toutes les tendances évoquées qui constituent l'évolution du monde) fait à l'œuvre d'art n'est pas sans rappeler la méditation de Walter Benjamin sur la reproduction technique. C'est le même hic et nunc évoqué par Benjamin à travers la notion d'aura que l'on retrouve dans l'approche directe de l'art par le biais du théâtre, de l'art et du patrimoine, et qui confine partiellement à la nature sacrée (les trois ont une origine religieuse) de la culture. À l'instar du philosophe de l'École de Francfort, nous ne pouvons que constater l'influence des rapports de production (et donc de l'économie, mais aussi de la technique) sur la manière de penser l'art et la culture.
En ce sens, la manière de concevoir l'économie et ses transformations – et notamment les rapports entre les logiques publiques, de marché ou de don – telle qu'elle s'applique indubitablement sur le champ de la culture, apparaît plus indispensable que jamais.
Si l'économie des arts et de la culture, à partir des nouvelles perspectives économiques (la culture comme domaine économique, l'économie créative) apparaît de nos jours comme un enjeu majeur, il convient encore d'évoquer les conséquences potentielles, au niveau des modes de fonctionnement, d'une telle intégration de la culture au sein de l'économie. Jusque durant les années 1980, en effet, le débat économique paraît hors de propos dans les milieux culturels. L'évolution que nous avons évoquée tout au long des chapitres montre ce qu'il en est actuellement. Nous voudrions insister ici sur quelques-unes des conséquences importantes de ce que Laurent Creton nomme de l'économisme : « En plaçant les valeurs d'échange au rang de but, l'économie marchande tend à inverser l'ordre des priorités. L'économie, simple système d'abstractions, devient le principe dominant d'organisation de la société, la vie et la culture étant réduites au rang d'instruments de son mode de valorisation. On tombe alors dans l'économisme. »
Le monde mis à prix et en chiffres
La question de la valeur, nous l'avons largement évoqué (cf. chapitre 1), est centrale dans l'économie. S'il est difficile de résumer cette dernière à la question du prix, a fortiori pour les biens culturels, force est de noter l'importance grandissante des informations liées aux prix de l'art et de la culture ou, quand la chose n'est pas possible, aux méthodes d'évaluation. Ainsi, le débat sur le prix des établissements culturels et la gratuité n'a jamais été aussi présent, de même que les techniques d'évaluation mises en place au sein des institutions culturelles.
Politique de prix et gratuité
Il convient de revenir quelques années en arrière pour saisir les changements considérables qui ont été opérés en matière de tarification, et qui résultent directement de la logique décrite dans cet ouvrage (cf. chapitre 4). Si, dans une logique de marché – le théâtre privé, les concerts de musique populaire – les questions d'argent apparaissent essentielles à la survie d'un établissement et doivent prioritairement être abordées au plus juste, tel n'est pas le cas dans la logique publique. Très rapidement, lorsque les pouvoirs publics ont pris en charge certaines institutions phares de la culture, comme l'opéra, les musées ou les bibliothèques, il est rapidement apparu que la part apportée par des recettes extérieures, et notamment par un droit d'entrée, apparaissait comme dérisoire au regard des subventions. Ainsi, la gratuité ou non de l'entrée, ou un droit d'entrée très faible, n'est pas étudiée pour rapporter de l'argent (mais parfois pour dissuader des importuns, par exemple).
C'est en fonction de cette même logique que certaines questions continuent à ne pas être abordées d'un point de vue financier, alors qu'elles pourraient tout à fait être envisagées comme telles par l'économiste. Ainsi en va-t-il de l'inaliénabilité dans les musées, déjà évoquée : puisque les œuvres sont dans le domaine public, elles perdent leur valeur financière et ne peuvent être vendues. Une telle prise de position a parfois de quoi surprendre l'homme de la rue, le politique ou l'économiste, mais repose sur un ensemble de valeurs qui nous font rejeter certains principes. De la même manière, un certain nombre de sujets continuent d'être rejetés hors du champ des échanges économiques, comme le don de sang, le don d'organes ou le don de la vie (mais il existe un trafic parallèle dans certains pays). La vente d'êtres humains, longtemps présentée comme une activité lucrative (l'esclavage), a été rejetée et est regardée de nos jours avec horreur. Et la mise à mort d'un être humain, pour des raisons économiques (il représente un coût pour la société et ne rapporte rien) n'est pas non plus (pour combien de temps ?) considérée comme un argument recevable par la même société.
L'incursion de la pensée économique néolibérale dans la culture a radicalement transformé de tels modes de raisonnement. « There is no free lunch », la phrase de Milton Friedman rappelle à juste titre que la gratuité parfaite n'existe pas et que quelqu'un doit toujours payer : en l'occurrence, l'État qui se finance par le biais de l'impôt, paye pour la gratuité des musées ou des lieux de patrimoine. Ne serait-il pas plus efficace que le consommateur participe plus au financement ? Aussi les musées, opéras et théâtres ou festivals ont-ils été chaudement encouragés à développer de nouvelles recettes, notamment par le droit d'entrée. C'est dans une telle perspective que des grilles tarifaires de plus en plus sophistiquées ont été mises au point, afin de diminuer les coûts d'opportunité des touristes ou des visiteurs aisés prêts à payer (cher), tout en favorisant les étudiants ou les professions disposant de moindres revenus. La fin du xxe siècle voit ainsi, un peu partout dans le monde, abandonner la gratuité ou les jours de visite gratuite. Il parut surprenant – et aberrant, pour nombre d'économistes – d'imaginer qu'au début du siècle suivant, des mesures de gratuité voient à nouveau le jour dans les musées français (parisiens, puis nationaux – à concurrence d'un jour par mois) et britanniques. Les études d'impact réalisées à cette occasion ont été largement discutées, les résultats étant interprétés, par les partisans et les adversaires, tantôt comme une mesure réelle de démocratisation, tantôt comme une action non profitable.
L'introduction d'un prix d'entrée plus ou moins élevé, faut-il le dire, transforme la relation qu'un établissement noue avec son public, qui peut dès lors entrer dans les habits du consommateur, se découvrir des droits, mais aussi évaluer son expérience (visite ou spectacle) à l'aune des coûts qu'il a subis (et dont le droit d'entrée n'est que l'une des composantes). Relation différente de la part du consommateur, mais aussi du personnel, qui dépend dès lors partiellement de son public, pour le meilleur (car il en tient compte), mais aussi pour le pire (la dépendance financière pouvant entraîner une course à la fréquentation).
Ainsi, à travers le droit d'entrée, nous trouvons-nous face à deux logiques apparemment incompatibles. Pour l'économiste, la gratuité appliquée à tous relève d'une sorte d'aberration, induisant des comportements de passager clandestin (ou free riding, comme les touristes qui paient l'entrée dans leur propre pays). S'il existe une disposition à payer pour un service, il serait ridicule de ne pas la concrétiser par un droit d'entrée fixé à partir de cette disposition. En revanche, pour l'homme politique, l'effort de démocratisation de la culture passe par la gratuité, toute tarification, même symbolique, constituant une barrière empêchant ce processus. Forcément, un tel discours, s'il peut présenter des relents populistes ou électoraux, n'envisage pas la culture comme un bien de consommation, mais comme une voie d'accès à la citoyenneté, par l'action et la médiation culturelle. Le raisonnement économique est imparable, mais l'action politique se situe sur un autre plan, qui ne voit dans le financement et sa rentabilité qu'une dimension d'un projet plus vaste.
L'évaluation
La manière la plus simple (ou la plus efficace) d'un point de vue économique pour déterminer la valeur d'un bien revient à s'interroger sur son prix, et c'est cette logique que l'on retrouve dans l'évaluation boursière des sociétés (à partir de leur profit) ou l'évaluation des biens de consommation. Le test du marché est aussi sans appel : une entreprise de mauvaise qualité ne fait pas de profit et perd de sa valeur, pour bientôt disparaître. Pour les biens publics ou mixtes et, de manière générale, pour une organisation sans but lucratif, notamment culturelle, la question doit être traitée de manière différente, puisqu'elle pourrait indéfiniment (dys)fonctionner, pourvu qu'elle bénéficie de subventions. C'est ainsi que de nombreux modèles d'évaluation ont été proposés, certains affinés par les économistes, afin de mieux cerner le fonctionnement adéquat ou idéal d'une organisation.
Parmi les évaluations les plus simples, celle qui tient lieu de premier outil est le rapport d'activité, moyen commode d'évoquer (souvent de manière littéraire) les réalisations d'une organisation. D'autres systèmes existent, notamment les systèmes d'évaluation par enquêtes de satisfaction des publics, visant à juger, auprès des visiteurs ou spectateurs, la qualité de la prestation qui a été présentée. Ce type d'évaluations, d'abord mises en place dans les systèmes éducatifs au début du xxe siècle, a progressivement été appliquée dans les lieux culturels (notamment les musées) à partir des années 1930. Plus récemment, depuis une quarantaine d'années, des systèmes d'évaluation par les pairs ont été instaurés, sous la forme de systèmes d'agrément ou d'accréditation, afin de garantir un certain niveau de qualité défini par la profession.
Les économistes ont opté, de manière plus spécifique, pour deux principes d'évaluation. Le premier part de la modélisation économique des fonctions de production des entreprises et vise à partir de mesures des inputs (subventions, personnel) à calculer les outputs à partir d'une fonction prédéfinie (de type Cobb-Douglas, par exemple) et à mesurer les écarts avec la production observée. D'autres méthodes (DEA et FDH) peuvent partir des résultats obtenus et les comparer avec les résultats d'autres établissements. La seconde méthode porte sur les mesures d'évaluation d'impact économique, déjà évoquées et discutées dans le chapitre 4, ou sur des évaluations de type contingentes, afin d'établir par voie d'enquête ce qu'une population est prête à payer pour le maintien d'un établissement (ce type d'évaluation est particulièrement sujet à caution).
De telles méthodes, utilisées dans l'analyse économique, n'influencent pas directement les organisations elles-mêmes. En revanche, les gestionnaires ont retenu le principe de critères mesurables pour établir un système d'évaluation plus objectif, mais aussi plus applicable à toutes les organisations. Cette logique, que l'on retrouve dans la nouvelle gestion publique, repose sur des principes à la base de toute approche stratégique (définition de la vision, des missions, objectifs et buts, dont les résultats doivent pouvoir être mesurés). Son application, dans le monde de la culture, est intimement liée aux transformations du modèle économique, à partir des années 1980. Le présupposé de telles méthodes est clair : « gérer l'État comme une entreprise est désormais le mot d'ordre de la Nouvelle gestion publique, et ce partout dans le monde ». Ce principe général, que l'on retrouve présenté comme une évidence, a été instauré dès 2001, en France, via la Loi organique relative aux lois de finances (LOLF) et mis en œuvre au sein de l'administration à partir de 2006. Ses buts sont certes louables : il s'agit de clarifier la situation pour le citoyen et préciser de manière optimale l'utilisation du budget de l'État, en l'orientant vers des résultats ; bref, des objectifs de transparence, de liberté et d'efficacité de gestion. L'État se voit donc confier un certain nombre de missions (32) par les citoyens, dont une mission « culture », cette mission étant déclinée en trois programmes et un certain nombre d'actions à réaliser, dont des batteries d'indicateurs visent à mesurer les résultats obtenus. Les indicateurs principaux pour le programme culture sont au nombre de quatre et comprennent l'accroissement de la fréquentation des institutions patrimoniales et architecturales, le renouvellement des bénéficiaires des dispositifs de soutien à la création, le taux d'insertion professionnelle des diplômés de l'enseignement supérieur de la culture et la part des enfants et adolescents ayant bénéficié d'une action d'éducation artistique et culturelle. Certes, d'autres batteries d'indicateurs existent, qui permettent d'affiner cette vision pour le moins réductrice. Mais il est permis de s'interroger sur de telles mesures, ces repères quantitatifs s'avérant utiles pour évaluer une situation, mais ne constituant pas la réalité. Le risque de confusion des indicateurs avec la réalité n'est pas mince, de même que le risque d'agir en fonction des indicateurs eux-mêmes pour l'efficacité en soi, et non pas en fonction de la réalité ; en témoigne l'audimat.
L'audimat
Même si le système utilisé pour mesurer l'audience est depuis plusieurs années le médiamat, c'est le nom du système précédent, l'audimat, qui continue d'être largement utilisé pour évoquer les audiences. Un tel principe vient directement du rapport que les chaînes de radio et de télévision entretiennent avec leurs annonceurs, l'audimat mesurant les audiences, donc les parts de marché, donc le nombre de téléspectateurs (essentiellement celui des ménagères de moins de cinquante ans, responsables des achats) pouvant être atteints par une annonce publicitaire. Il est difficile d'imaginer un rapport plus simple – mais aussi plus critiqué – à la performance ; il n'en reste pas moins que ce système continue de fournir la hiérarchie implicite des chaînes de télévision entre elles, mais aussi très largement des lieux de culture, et notamment des musées ou des théâtres. La logique du secteur artistique s'oppose à un tel principe : c'est d'abord la qualité qui doit être développée au théâtre, dans les musées ou à l'opéra. Ainsi, selon ces principes, des indices de type « qualimat » ont été développés par la télévision (notamment la BBC), procédant par enquête, afin de connaître la satisfaction des téléspectateurs. C'est sur le même modèle que les palmarès des festivals de cinéma ou les cérémonies des Molières, au théâtre, en privilégiant un jugement par les pairs, permettent d'évaluer d'autres aspects du métier. Il n'en demeure pas moins que la donnée de base, l'audience ou la fréquentation, constitue aussi, pour ces établissements, le critère de comparaison le plus souvent utilisé...
La référence continue à la gestion d'entreprise
La notion de croissance est devenue une norme dans notre manière de penser l'économie et l'ensemble des mesures prises au niveau politique est influencé par ce présupposé : tendre à la croissance la plus importante possible. La croissance économique, calculée par le PIB, induit une richesse répartie de manière plus ou moins équitable au sein de la société, mais profitant à tous (ne fût-ce que par la redistribution opérée par l'État, lui aussi mécaniquement plus riche). Si l'on évoque la culture comme moteur de la croissance, on sait par ailleurs que nombre d'établissements culturels ne sont pas pour autant bénéficiaires. Les règles de la gestion publique, pour cette raison, ont privilégié un autre axe, à partir du cadre missions-programmes-actions, contrôlés par des indicateurs de performance. Le principe de la performance, a priori, n'implique pas spécialement de la croissance. Au départ, le terme de performance évoque (notamment en anglais – et c'est à partir de cette littérature qu'il a été utilisé) plutôt les caractéristiques d'un résultat, comme on parle des performances d'un cheval ou d'une tondeuse à gazon. Mais c'est de plus en plus la notion d'exploit sportif (bonnes ou mauvaises performances d'un athlète) qui ramène insensiblement la logique de la performance vers le monde de la compétition et l'amélioration constante des résultats. On connaît mieux, de nos jours, les dégâts entraînés par la compétition sportive (et ses enjeux financiers), dont les affaires de dopage et les morts précoces défraient régulièrement la chronique. De nombreux essayistes ont souvent évoqué cette question à partir d'essais plus ou moins rigoureux sur le monde du travail.
Sur un plan plus scientifique, Luc Boltanski et Ève Chiapello exposaient voici déjà une quinzaine d'années, à travers la littérature managériale, le nouvel esprit du capitalisme, ayant incorporé les critiques artistes et présentant, après le modèle fordien, une vision du management plus flexible et autonome (individualiste). Quelques années plus tard, plusieurs sociologues du travail, à commencer par Vincent de Gaulejac, ont analysé les résultats au niveau des personnels et les risques que les nouvelles méthodes de gestion peuvent entraîner pour les gens qui les pratiquent. C'est en quelque sorte ces mêmes éléments qui, en s'installant dans la logique des organisations culturelles, peuvent apparaître comme des facteurs de risque pour le (dys)fonctionnement de la production culturelle. On peut ainsi, en suivant Gaulejac, présenter quelques « lois » inhérentes à la gestion entrepreneuriale, susceptibles de conséquences pour les secteurs de la culture.
Comprendre, c'est mesurer
Depuis de nombreuses années, le management privilégie le calcul et le nombre, dans un effort de se rapprocher des sciences exactes auxquelles les sciences économiques n'échappent pas non plus. La logique de la mesure vise à mettre en équation pour expérimenter des modèles, mais pour cela, il faut disposer de données quantifiables. Un tel dispositif privilégie le calcul plutôt que la recherche de sens : pour comprendre, il faut pouvoir calculer, mais surtout, il faut pouvoir trouver des données. La logique qui en découle est sans appel : ce qui n'est pas mesuré (ou ce qui n'est pas mesurable) n'existe pas. Le principe se retrouve dans les batteries d'indicateurs de performance, au risque de tenir pour négligeable ce qui ne peut être mesuré. C'est déjà contre ce principe que l'un des papes du management critiquait ouvertement le système des MBA formant l'essentiel des gestionnaires d'entreprises à partir de mesures déconnectées de la réalité industrielle. Mais que dire dès lors du monde de la culture ? Comment mesurer la qualité d'une exposition ou d'une pièce de théâtre ?
L'organisation est une donnée,
l'expert en est le connaisseur
La logique économique ou managériale suppose des modèles, au risque de les confondre avec la réalité. Le développement de ces modèles suppose qu'il existe un optimum pour une organisation, une forme parfaite, mathématique, et que les écarts par rapport à cette norme puissent être mesurés. Un tel raisonnement vise à développer un type spécial d'entreprises-modèles, reproductible dans le monde, au détriment de structures plus singulières, peut-être mieux adaptées à leur contexte, mais envisagées comme aberrantes en regard du modèle. Il consacre par ailleurs le rôle de l'expert-conseiller, dont la figure est apparue dès les années 1960 dans les organisations culturelles américaines, appliquant parfois sans trop connaître le contexte des recommandations standards et souvent pratiques (comment résoudre un conflit, gagner des parts de marché etc.) plutôt qu'en agissant sur le sens et les fins de l'organisation.
L'humain comme ressource de l'entreprise
Dans la perspective gestionnaire (et pour le capitalisme), l'humain constitue un facteur de production substituable (par d'autres humains ou par des machines). Le terme de gestion des ressources humaines, en ce sens, décrit bien les règles liant le travailleur à son entreprise : un stock doit se valoriser, se gérer, mais peut également être transféré ou vendu si cela s'avère plus profitable, moyennant la mobilisation psychologique du travailleur, qui doit s'identifier aux objectifs de l'organisation. Son énergie, son assiduité, son potentiel de créativité ne seront réellement identifiés à l'entreprise qu'à travers des règles de management appropriées, induisant la fusion de l'intérêt du travailleur et de celles des responsables (sinon actionnaires).
De l'anxiété au sens de la vie
Une telle culture de la croissance a permis, ces dernières années, une augmentation considérable de la productivité dans le monde des entreprises, et c'est bien ce qui est attendu dans celui des organisations culturelles. En revanche, elle induit aussi une pression considérable sur les travailleurs, l'augmentation de la performance s'avérant un processus sans fin – a fortiori dans les secteurs archaïques comme les arts de la scène et en grande partie les musées (cf. chapitre 6) – tout en rejetant la pression sur les personnels chargés de l'accomplir.
Culture de l'anxiété et inculture pour tous
Cette logique gestionnaire n'est par ailleurs pas seulement répandue dans le monde des entreprises, tant s'en faut. On peut l'observer aujourd'hui également dans la famille (présentée par Gary Becker comme construite à partir d'un raisonnement d'Homo œconomicus !), dans le secteur de l'éducation ou dans le monde hospitalier. Nous formons nos enfants en fonction d'objectifs, nous bénéficions de conseils spécialisés, dès les premiers niveaux du système scolaire, en fonction de principes liés à l'insertion professionnelle.
Quelle place la culture peut-elle occuper dans cette perspective ? À défaut de former les citoyens à la réflexion critique sur le sens et les enjeux de la société, comme le préconisaient nombre d'acteurs au début des années 1970, les organisations culturelles risquent bien de se présenter comme autant de reproducteurs du discours dominant, privilégiant l'excellence, l'efficience, l'efficacité et la performance. La logique d'une production guidée par les impératifs de croissance débouche inéluctablement sur des principes similaires, fondés sur l'augmentation de la production : dans le monde de la recherche, via le nombre d'articles scientifiques, dans le monde culturel, par celui des présentations théâtrales, d'expositions temporaires ou de prêts de livres.
Face à une telle pression, la culture risque bien d'être identifiée à la fonction de délassement qu'elle a souvent occupée, après un travail abrutissant ou anxiogène. C'est une critique similaire qu'adressaient déjà Adorno et Horkeimer à propos des industries culturelles ou Hannah Arendt sur la culture en général. Le principe d'une culture populaire facile à comprendre, mainstream, pouvant être appréciée par le plus grand nombre, s'accommode bien à la logique des industries culturelles et il est infiniment probable que les transformations opérées par le numérique suivent la même voie. Indique-t-elle pour autant un appauvrissement de la culture généralisé ? En tout état de cause, on peut gager que les productions de cette culture diffèrent fondamentalement de ce à quoi aspiraient Arendt, Malraux ou Adorno. Ce dernier présentait le cinéma, avec Horkheimer, comme un moyen supplémentaire d'asservir le prolétaire qui, en s'amusant de voir Charlot prendre des coups, se préparait psychologiquement à accepter ceux qu'il allait recevoir. Force est de remarquer que les nouvelles règles des industries culturelles n'incitent guère à l'optimisme, si l'on en juge notamment à la structure du jeu vidéo, en passe de devenir l'une des pratiques les plus importantes, ou à celle des jeux de téléréalité. Le jeu vidéo promeut largement la performance par les scores et l'auto-évaluation perpétuelle, tandis que les règles de la téléréalité semblent fondées sur l'expulsion des participants, décidée de commun accord ou par le public, en ce compris les meilleurs. S'agit-il de mieux préparer aux nouveaux types de licenciement dans le monde du travail ?
La question du sens
« La question des finalités ne relève pas de la science économique qui a pour vocation d'éclairer les choix, de répondre à des questions concernant la compatibilité des fins entre elles relativement aux moyens disponibles. Elle doit permettre de choisir les moyens les plus appropriés pour atteindre les objectifs poursuivis », souligne Laurent Creton. La critique de Gaulejac – et de tant d'autres – porte justement sur la question du sens, largement oublié dans le management ou l'économie, au profit de questions techniques, mais laissant désemparé le travailleur conduit à s'identifier à l'entreprise, et subitement licencié, ou traité comme partie négligeable.
Il ne fait guère de doute que l'économie s'inscrit dans une position centrale au sein de notre société et c'est à ce titre qu'il importe d'en connaître les règles et de comprendre les développements qu'elle entraîne sur le plan des arts et de la culture. Mais c'est en tant qu'outil fondé sur une pensée spécifique que l'économie est ici évoquée et ses hypothèses abordent bien peu les fondements les plus intimes de notre existence. Il revient justement à la culture, dans cette perspective, de formuler des réponses sur le sens de la vie, à que Malraux résumait de manière un peu grandiloquente : « ce que nous appelons la culture, c'est cette force mystérieuse des choses beaucoup plus anciennes et beaucoup plus profondes que nous et qui sont notre plus haut secours dans le monde moderne, contre la puissance des usines de rêve ». Près d'un demi-siècle plus tard, l'opposition entre l'un et l'autre univers trouve-t-elle encore un écho dans le monde actuel ?
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. Mairesse F., Le droit d'entrer au musée, Bruxelles, Labor, 2005.
. Pommerehne W. W., Frey B. S., « Les musées dans une perspective économique », Revue Internationale des Sciences Sociales, XXXII, 2, 1980, p. 345-362.
. Eidelman J., Céroux B., La gratuité dans les musées et monuments en France : quelques indicateurs de mobilisation des visiteurs, Paris, Culture études (Pratiques et publics), 2009-2. Disponible sur : <http://www.culture.gouv.fr/deps> (consulté en juillet 2011) ; Gombaut A., Petr C. et al., La gratuité des musées et des monuments côté publics, Paris, La Documentation française, 2006 ; Mbongo P. (dir.), Le prix de la culture. La gratuité au prisme du droit et de l'économie, Paris, Mare & Martin, 2011 ; Tobelem J. M., La culture mise à prix, Paris, L'Harmattan, 2005.
. Sur l'historique de ces méthodes, voir Mairesse F., Missions et évaluation des musées. Une enquête à Bruxelles et en Wallonie, Paris, L'Harmattan, 2004.
. Taalas M., « Costs of production », in Towse R. (dir.), A Handbook of Cultural Economics, Cheltenham, Edward Elgar, 2003, p. 152-160.
. L'une des premières tentatives d'application de ce principe est donnée par Martin F., Une méthode d'évaluation économique des musées, Montréal, HEC, Chaire de gestion des arts, 1993.
. Chong D., Arts Management, Londres, Routledge, 2010 (2e ed), p. 52 sq.
. Cohen A.-G., La nouvelle gestion publique. Concepts, outils, structures, bonnes et mauvaises pratiques. Contrôle interne et audits publics, Paris, Gualino, 2012, p. 5.
. Throsby D., The Economics of Cultural Policy, Cambridge, Cambridge University Press, 2010, p. 32 sq.
. Inglebert X., Manager avec la LOLF, Paris, Groupe Revue Fiduciaire, 2009.
. L'ensemble du budget et des indicateurs est disponible sur le Forum de la performance mis en œuvre par les pouvoirs publics : http://www.performance-publique.budget.gouv.fr/farandole/2012/rap/pdf/RAP_2012_BG_culture.pdf.
. Parmi les premiers essais, il convient de citer celui de l'écrivain Viviane Forrester, L'horreur économique (Paris, Fayard, 1996), prix Médicis qui a obtenu un grand succès de librairie. On peut également songer aux ouvrages de Naomi Klein, etc.
. Boltanski L., Chiapello È., Le nouvel esprit du capitalisme, Paris, Gallimard, 1999.
. Albert N., Gaulejac V. de, Le coût de l'excellence, Paris, Le Seuil, 1991, Gaulejac V. de, La société malade de la gestion, Paris, Le Seuil (Points), 2005. C'est ce dernier ouvrage dans lequel on retrouve les différents points évoqués dans les paragraphes qui suivent. Voir aussi Del Rey A., La tyrannie de l'évaluation, Paris, La Découverte, 2013.
. Mintzberg H., Des managers, des vrais ! Pas des MBA. Un regard critique sur le management et son enseignement, Paris, Éd. d'Organisation, 2005.
. Dujarier M.-A., L'idéal au travail, Paris, PUF, 2006.
. Jeanson F., L'action culturelle dans la cité, Paris, Le Seuil, 1973 ; Chaumier S., Mairesse F., La médiation culturelle, Paris, Armand Colin, 2013.
. Adorno T. W., Horkeimer M., (1944) Dialectique de la raison, Paris, Gallimard, 1974 (pour la trad. fr.) ; Arendt H. (1954), La crise de la culture, Paris, Gallimard, 1972 (pour la trad. fr).
. Chaumier S., L'inculture pour tous. La nouvelle utopie des politiques culturelles, Paris, L'Harmattan, 2010.
. Triclot M., Philosophie du jeu vidéo, Paris, Zones, 2011.
. Creton L., op. cit., p. 27.
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Tremblay G., « Industries culturelles, économie créative et société de l'information », Global Media Journal, vol. 1, no 1, 2008, p. 65-88.
Triclot M., Philosophie du jeu vidéo, Paris, Zones, 2011.
Ulibarri C. A., « Perpetual options: revisiting historical returns on paintings », Journal of Cultural Economics, 33, 2009, p. 135-149.
Unesco (Collectif), Les industries culturelles. Un enjeu pour l'avenir de la culture, Paris, Unesco, 1982.
Unesco (Collectif), Politiques pour la créativité. Guide pour le développement des industries culturelles et créatives. Paris, Unesco, 2011. Disponible sur : http://www.unesco.org/new/fr/culture/themes/cultural-diversity/diversity-of-cultural-expressions/tools/policy-guide/
Urfalino P., L'invention de la politique culturelle, Paris, Hachette Littératures, 2004.
Urrutiaguer D., Économie et droit du spectacle vivant en France, Paris, Sorbonne nouvelle, 2009.
Urrutiaguer D., Guide des études théâtrales, Paris, Armand Colin, 2012.
Van der Ploeg F., « Beyond the dogma of the fixed book price agreement », Journal of Cultural Economics, vol. 28, 2004, p. 1-20.
Van der Ploeg F., « The making of cultural policy : a European perspective », in Ginsburgh V. et Throsby D., Handbook of the Economics of Art and Culture, Amsterdam, Elsevier, vol. 1, 2006, p. 1183-1221.
Van de Sandt U., La Société des Amis des Arts (1789-1798). Un mécénat patriotique sous la Révolution, Paris, École nationale supérieure des Beaux-Arts, 2006.
Van Eijck K., « Social Differentiation in Musical Taste Patterns », Social Forces, vol. 79, no 3, 2001, p. 1163-1184.
Vany A. de et Walls D., « Bose – Einstein dynamics and adaptive contracting in the motion picture industry », Economic Journal, vol. 106, no 439, 1996, p. 1493-1514.
Vauclare C., « Les événements culturels, essais de typologie », Paris, Cultures études, 2009-3, 8 p.
Veblen T., Théorie de la classe des loisirs, Paris, Gallimard, 1970 (1899 pour l'éd. originale).
Vecco M., Économie du patrimoine monumental, Paris, Economica, 2007.
Veyne P., Le pain et le cirque : sociologie historique d'un pluralisme politique, Paris, Le Seuil, 1976.
Vital C., « Le Livre blanc des musées de France », Musées et collections publiques de France, numéro spécial, 260, 3, 2010, p. 1-127.
Vivant E., Qu'est-ce que la ville créative ? Paris, Presses universitaires de France, coll. « La ville en débat », 2009.
Von Hippel E., Democratizing innovation, Cambridge (Mass.), The MIT Press, 2005.
Walras L., Études d'économie appliquée, Corbaz, Lausanne [1898]. 2e édition, 1936, Paris, Pichon, OEC, vol. X, Paris, Economica, 1992.
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Wildestein G., « Le Musée permanent en France », La Gazette des Beaux-Arts, supplément, 1055, déc. 1956.
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Zallo R., Economia de la communicacion y de la cultura, Madrid, Akal, 1988.
Zoonky L. et Gosain S., « A longitudinal price comparison for music CDs in electronics and brick-and-mortar markets: pricing strategies in emergent electronic commerce », Journal of Business Strategies, vol. 19, no 1, 2002, p. 55-71.
Index
Académie , , , ,
Adorno (Theodor) , , , , , , ,
Aliénation ,
Altruisme , , ,
Ami des musées
Ancien Régime , , , , ,
Appariement , ,
Archive , ,
Art
de la scène , , , , ,
plastique
Artiste , , , , , , , , , , , , , , , , , , , , , ,
Audimat
Auteur
Avant-garde
Baumol (loi de)
Baumol (William) , , , , , , , , , , , , , , , , , , , , ,
Becker (Gary) , , , , , , , ,
Bénévolat ,
Bénévole , , ,
Benhamou (Françoise) , ,
Benjamin (Walter) , , ,
Best-seller , , , , ,
Bibliothèque , , , , , , , , , , , , , , , , ,
Bien ,
club ,
collectif ,
commun ,
culturel , , , , , , , , , , , , , , , , ,
artistique
reproductible
unique
d'expérience
de croyance
immatériel ,
matériel
mixte
non rival
privé ,
public , ,
Biennale
Blockbuster , ,
Bourdieu (Pierre) , , , , , ,
Capitale culturelle
Centre National du Cinéma ,
Centre National du Livre ,
Chromo ,
Chronologie des médias , ,
Cinéma , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,
Classe créative
Classement
Click and mortar
CNC , , , , , , ,
CNV
Collection
Collectionneur , , , , , , , ,
Commissaire-priseur
Compte de soutien
Concentration , , , , , , ,
horizontale
Concurrence , ,
monopolistique
parfaite
Conservateur
Consommateur , , , , , , , , ,
Consommation des biens culturels ,
Copyleft ,
Copyright ,
Copyright industries ,
Création , , ,
Créativité , , , , , , , , ,
Critique
Crowdfunding , , , , , ,
Crowdsourcing , , ,
Culture , , ,
Dation
Deaccessioning
Demande
Démocratie culturelle
Démocratisation de la culture
Détaillant
Diffuseur
Discrimination tarifaire
Disque ,
Distributeur
Distribution , , , , , , ,
Diversité culturelle , , , , , , , , , , , , , ,
Domaine public ,
Dominant design , , ,
Don , , , , , , , , , , , , , , , , , , , ,
Drive-in theaters
Droit
d'auteur , , , , , , , , , , , ,
de suite ,
Économétrie
Économie
créative (de la créativité) , ,
de l'expérience ,
de l'immatériel ,
des arts et de la culture
planifiée ,
Économisme ,
Éditeur
Édition ,
Église , , , , , , , ,
Élasticité ,
-croisée
-prix ,
-revenu
Endowment
Enquête
Équilibre du consommateur
État , , , , , , , , , , , , , , , , , , , , , , , , ,
Étude d'impact
Évaluation , ,
contingente
d'impact économique
économique
par analogie
Évergétisme
Expérimentation
Exploitation
Externalité , , ,
Fair use ,
Festival , , , , , , , , , ,
Foire
d'art
Fond de dotation , ,
Fondation , ,
Frange concurrentielle ,
Free riders
Fundraising
Gain de productivité
Galerie ,
Galeriste
Grande distribution alimentaire (GDA)
Grandes surfaces spécialisées (GSS)
Gratuité , , , , ,
Hadopi ,
Homo donator
Homo œconomicus , , , , , , , , , , , ,
Impact économique ,
Inaliénabilité ,
Indicateur , ,
Indice de Herfindahl-Hirschman
Industrie
créative , , , , , ,
culturelle , , , , , , , , , , , , , , , , , , , , , ,
musicale
Infomédiaire ,
Infomédiation
Innovation
Intégration verticale
Intermittence ,
Internet , , , , , , , , , , , , , , ,
Jeu vidéo , , , , ,
Keynes (John Meynard) , , ,
Kula
Lang (Jack) ,
Lang (loi)
Lecture
Levée de fonds
Libéralisme
Libraire ,
Librairie , ,
Livre , , , , , , , , , , , , , , , , , , , , , , , , ,
numérique ,
Logique
du don , ,
du marché , , , ,
publique , , ,
Loi
de l'offre et de la demande
de Pareto , , ,
de Rolland
sur le prix unique (loi Lang)
Longue traîne , ,
Mainstream , , , ,
Maison
de ventes
des artistes
Major , , , , , ,
Malraux (André) , , , , , , , , , , , ,
Mandeville (Bernard) , ,
Marché , , , , , , , , , , , , , , , , , , , , , ,
de l'art , , , , ,
des chromos
Marketing , , , , , , , , ,
Marx (Karl) , , , , , ,
Matthieu (effet) ,
Mauss (Marcel) , , ,
Mécénat , , , , , , ,
Ménage ,
Miami Model ,
Monde de l'art
Mondialisation , , , ,
Monopole , , , ,
Monument
historique , ,
philanthropique
Multiplicateur ,
Musée, museum , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,
superstar ,
Musique , , , , , , , , , , , , , , , , , , , , , ,
enregistrée
National Endowment for the Arts ,
Non-rivalité ,
Numérique , , , , , , , , , , , , , , , , , , , , ,
Numérisation
Œuvre d'art
Offre ,
et demande , ,
Oligopole , , , , , ,
Oligopsone ,
OMC
Omnivorité culturelle
Open end
Opéra , , , , , , , , ,
Passager clandestin (free riding) , ,
Patrimoine , , , , , ,
Payola
Performance ,
Philanthropie , , , , , , ,
Place de la culture au sein de l'économie
Plateforme , , , , , , , , ,
Politique
culturelle
de prix
tarifaire
Potlatch , ,
Pratique culturelle
Prescripteur , , , , ,
Prescription , ,
Prix , , , , , , , ,
unique du livre , ,
Producteur ,
Production , , , , , , ,
Productivité
Public choice ,
Pure player , ,
Radio , ,
Recommandation ,
Régulation
Rent seeking
Réseau social , , , , ,
Salon
Service ,
Smith (Adam) , , , , , , , , , , , , , , , , , ,
SNE
Société
d'amis
du spectacle
philanthropique
Spectacle
vivant , , ,
Star , , , , , , , , , , , , , ,
Star-system , , , , , ,
Statistique , ,
Studio system , ,
Subvention , , ,
Superstar , , , , ,
Surplus
du consommateur
total des consommateurs
SVOD
Téléchargement ,
Télévision , , , , , , , , , , , , , , ,
Test of time
Théâtre , , , , , , , ,
Théâtre , , , , , , , , , , , , , , , , , ,
amateur ,
privé ,
There is no free lunch ,
TIC
Tourisme , , , ,
culturel
Touriste , , , ,
Trésor national
Troisième République ,
Trustee
Unesco , , , , , , , , , ,
Utilitarisme
Utilité marginale ,
Valeur , ,
d'usage
Veblen (effet)
Veblen (Thorstein)
Vedettariat , , , , , , , , ,
Vente publique
Versionnage, versioning , ,
Vidéo , , , , , ,
à la demande ,
Ville créative
Walras (Léon) , , , , , , , , , , , , , , ,
Winner-take-all , , ,
|
{
"redpajama_set_name": "RedPajamaBook"
}
| 2,030
|
Ved Kongens Bord () é uma minissérie norueguesa de 2005 estrelada por Anneke von der Lippe e Dennis Storhøi. A série estreou no canal NRK em 28 de fevereiro de 2005.
Enredo
Tove Steen (Anneke von der Lippe) torna-se a nova ministra da Saúde da Noruega após o ex-ministro morrer misteriosamente em uma viagem de negócios a Rússia. A transição para a vida política é um fardo difícil a si mesma e para sua família.
Elenco
Anneke von der Lippe – Tove Steen
Dennis Storhøi – Arvid Gunnerud
Kim Haugen – Jørgen Gran
Sven Nordin – Harald Dahl
Lasse Kolsrud – Derek Thomassen
Lasse Lindtner – Einar Tangen
Gisken Armand – Ingunn Dahl
Nils Ole Oftebro – Tor Olav Jonsrud
Birgitte Victoria Svendsen – Bjørg Larsen
Stig Henrik Hoff – Odd Buene
Kim Sørensen – Morten Lindvik
Tone Danielsen – Anne Nystøen
Oda Solberg – Sigrid Steen Gunnerud
Janne Langaas – Politiinspektør Kviberg
Line Verndal – Oda Hagen
Ligações externas
Séries de televisão de drama da década de 2000
Programas de televisão que estrearam em 2005
Programas de televisão encerrados em 2005
Minisséries da Noruega
2005 na televisão na Noruega
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 1,731
|
#if X64
using System.Collections.Concurrent;
using System.ComponentModel.Composition;
using Evercoin.BaseImplementations;
using Evercoin.Util;
using LevelDb;
namespace Evercoin.Storage
{
[Export(typeof(IChainStore))]
[Export(typeof(IReadableChainStore))]
public sealed class LevelDBChainStore : ReadWriteChainStoreBase
{
private const string BlockFileName = @"C:\Freedom\blocks.leveldb";
private const string TxFileName = @"C:\Freedom\transactions.leveldb";
private readonly Database blockDB;
private readonly Database txDB;
private readonly Waiter<FancyByteArray> blockWaiter = new Waiter<FancyByteArray>();
private readonly Waiter<FancyByteArray> txWaiter = new Waiter<FancyByteArray>();
private readonly ConcurrentDictionary<FancyByteArray, bool> transactions = new ConcurrentDictionary<FancyByteArray, bool>();
public LevelDBChainStore()
{
Cheating.CopyLevelDbDll();
LevelDbFactory factory = new LevelDbFactory();
DatabaseOptions blockOptions = factory.CreateDatabaseOptions();
blockOptions.CompressionOption = CompressionOption.SnappyCompression;
blockOptions.CreateIfMissing = true;
DatabaseOptions txOptions = factory.CreateDatabaseOptions();
txOptions.CompressionOption = CompressionOption.SnappyCompression;
txOptions.CreateIfMissing = true;
this.blockDB = factory.OpenDatabase(BlockFileName, blockOptions);
this.txDB = factory.OpenDatabase(TxFileName, txOptions);
}
[Import]
public IChainSerializer ChainSerializer { get; set; }
protected override IBlock FindBlockCore(FancyByteArray blockIdentifier)
{
IBlock block;
while (!this.TryGetBlock(blockIdentifier, out block))
{
this.blockWaiter.WaitFor(blockIdentifier);
}
return block;
}
protected override ITransaction FindTransactionCore(FancyByteArray transactionIdentifier)
{
ITransaction transaction;
while (!this.TryGetTransaction(transactionIdentifier, out transaction))
{
this.txWaiter.WaitFor(transactionIdentifier);
}
return transaction;
}
protected override void PutBlockCore(FancyByteArray blockIdentifier, IBlock block)
{
byte[] serializedBlock = this.ChainSerializer.GetBytesForBlock(block);
this.blockDB.Put(blockIdentifier, serializedBlock);
this.blockWaiter.SetEventFor(blockIdentifier);
}
protected override void PutTransactionCore(FancyByteArray transactionIdentifier, ITransaction transaction)
{
byte[] serializedTransaction = this.ChainSerializer.GetBytesForTransaction(transaction);
this.txDB.Put(transactionIdentifier, serializedTransaction);
this.txWaiter.SetEventFor(transactionIdentifier);
this.transactions[transactionIdentifier] = true;
}
protected override bool ContainsBlockCore(FancyByteArray blockIdentifier)
{
return this.blockDB.Get(blockIdentifier) != null;
}
protected override bool ContainsTransactionCore(FancyByteArray transactionIdentifier)
{
return this.txDB.Get(transactionIdentifier) != null;
}
protected override bool TryGetBlockCore(FancyByteArray blockIdentifier, out IBlock block)
{
byte[] serializedBlock = this.blockDB.Get(blockIdentifier);
if (serializedBlock == null)
{
block = null;
return false;
}
block = this.ChainSerializer.GetBlockForBytes(serializedBlock);
return true;
}
protected override bool TryGetTransactionCore(FancyByteArray transactionIdentifier, out ITransaction transaction)
{
byte[] serializedTransaction = this.txDB.Get(transactionIdentifier);
if (serializedTransaction == null)
{
transaction = null;
return false;
}
transaction = this.ChainSerializer.GetTransactionForBytes(serializedTransaction);
return true;
}
protected override void DisposeManagedResources()
{
this.blockDB.Dispose();
this.txDB.Dispose();
this.blockWaiter.Dispose();
this.txWaiter.Dispose();
base.DisposeManagedResources();
}
}
}
#endif
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,372
|
package mt;
import java.util.ArrayList;
import java.util.List;
import java.util.concurrent.ExecutorService;
import java.util.concurrent.Executors;
import java.util.concurrent.TimeUnit;
import java.util.concurrent.atomic.AtomicInteger;
import redis.clients.jedis.HostAndPort;
import redis.clients.jedis.Jedis;
import redis.clients.jedis.JedisPoolConfig;
import redis.clients.jedis.Protocol;
import com.ericsson.jigsaw.redis.JedisTemplate;
import com.ericsson.jigsaw.redis.JedisTemplate.JedisAction;
import com.ericsson.jigsaw.redis.JedisTemplate.JedisActionNoResult;
import com.ericsson.jigsaw.redis.pool.ConnectionInfo;
import com.ericsson.jigsaw.redis.pool.JedisPool;
import com.ericsson.jigsaw.redis.pool.JedisSentinelPool;
/**
* Since most testing is about the thread and the real interaction with Jedis/Sentinel, use manual test instead of Unit
* test.
*
*
* Setup: start 1 master, 1 slave, 1/2 sentinels
*
* Case1: Stop master, the client print error message, after 30 seconds, the client print a master change message and
* stop print error message.
*
* Case2: Restart sentinel.
*
* Case3: No sentinel ready, the client throw an exception.
*
* Case4: Master name not in sentinel.conf, the client throw an exception.
*
*
* TearDown: Hit enter to stop client.
*/
public class SentinelPoolManualTest implements Runnable {
private static final String COUNTER_KEY = "test:counter";
private AtomicInteger counter = new AtomicInteger(0);
private JedisSentinelPool pool;
private JedisTemplate template;
public static void main(String[] args) throws Exception {
String hosts = System.getProperty("hosts", "127.0.0.1:26379");
String masterName = System.getProperty("masterName", "default");
SentinelPoolManualTest test = new SentinelPoolManualTest();
test.initPool(hosts, masterName);
ExecutorService threadPool = Executors.newFixedThreadPool(1);
threadPool.submit(test);
System.out.println("Press enter in console to stop the system");
while (true) {
char c = (char) System.in.read();
if (c == '\n') {
System.out.println("Shuting down");
test.shutdownPool();
threadPool.shutdownNow();
boolean poolExit = threadPool.awaitTermination(10, TimeUnit.SECONDS);
if (!poolExit) {
System.out.println("Thread pool stop fail, forcing shutdown");
System.exit(-1);
}
break;
}
}
System.out.println("System shutdown");
}
public void initPool(String hosts, String masterName) {
String[] hostAndPortArray = hosts.split(",");
List<HostAndPort> sentinelInfos = new ArrayList<HostAndPort>();
for (String hostAndPort : hostAndPortArray) {
HostAndPort sentinelInfo = new HostAndPort(hostAndPort.split(":")[0], new Integer(
hostAndPort.split(":")[1]));
sentinelInfos.add(sentinelInfo);
}
ConnectionInfo redisAddtionalInfo = new ConnectionInfo(Protocol.DEFAULT_DATABASE,
ConnectionInfo.DEFAULT_PASSWORD, Protocol.DEFAULT_TIMEOUT);
JedisPoolConfig poolConfig = JedisPool.createPoolConfig(10);
pool = new JedisSentinelPool(sentinelInfos.toArray(new HostAndPort[sentinelInfos.size()]),
masterName, redisAddtionalInfo, poolConfig);
template = new JedisTemplate(pool);
template.execute(new JedisActionNoResult() {
@Override
public void action(Jedis jedis) {
jedis.set(COUNTER_KEY, String.valueOf(0));
}
});
}
public void shutdownPool() {
System.out.println("JVM Counter is " + counter.get());
String redisCounter = template.execute(new JedisAction<String>() {
@Override
public String action(Jedis jedis) {
return jedis.get(COUNTER_KEY);
}
});
System.out.println("Redis Counter is " + redisCounter);
pool.destroy();
}
@Override
public void run() {
while (true) {
try {
template.execute(new JedisActionNoResult() {
@Override
public void action(Jedis jedis) {
jedis.incr(COUNTER_KEY);
counter.incrementAndGet();
}
});
Thread.sleep(100);
} catch (Exception e) {
if (e instanceof InterruptedException) {
System.out.println("thread intterupted");
break;
}
System.out.println(e.getMessage());
try {
System.out.println("Sleep 1 seconds");
Thread.sleep(1000);
} catch (InterruptedException e1) {
System.out.println("thread intterupted");
break;
}
}
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,149
|
\section{The ALICE Collaboration}
\begingroup
\small
\begin{flushleft}
S.~Acharya\Irefn{org141}\And
D.~Adamov\'{a}\Irefn{org95}\And
A.~Adler\Irefn{org74}\And
J.~Adolfsson\Irefn{org81}\And
M.M.~Aggarwal\Irefn{org100}\And
G.~Aglieri Rinella\Irefn{org34}\And
M.~Agnello\Irefn{org30}\And
N.~Agrawal\Irefn{org10}\textsuperscript{,}\Irefn{org54}\And
Z.~Ahammed\Irefn{org141}\And
S.~Ahmad\Irefn{org16}\And
S.U.~Ahn\Irefn{org76}\And
Z.~Akbar\Irefn{org51}\And
A.~Akindinov\Irefn{org92}\And
M.~Al-Turany\Irefn{org107}\And
S.N.~Alam\Irefn{org40}\textsuperscript{,}\Irefn{org141}\And
D.S.D.~Albuquerque\Irefn{org122}\And
D.~Aleksandrov\Irefn{org88}\And
B.~Alessandro\Irefn{org59}\And
H.M.~Alfanda\Irefn{org6}\And
R.~Alfaro Molina\Irefn{org71}\And
B.~Ali\Irefn{org16}\And
Y.~Ali\Irefn{org14}\And
A.~Alici\Irefn{org10}\textsuperscript{,}\Irefn{org26}\textsuperscript{,}\Irefn{org54}\And
N.~Alizadehvandchali\Irefn{org125}\And
A.~Alkin\Irefn{org2}\textsuperscript{,}\Irefn{org34}\And
J.~Alme\Irefn{org21}\And
T.~Alt\Irefn{org68}\And
L.~Altenkamper\Irefn{org21}\And
I.~Altsybeev\Irefn{org113}\And
M.N.~Anaam\Irefn{org6}\And
C.~Andrei\Irefn{org48}\And
D.~Andreou\Irefn{org34}\And
A.~Andronic\Irefn{org144}\And
M.~Angeletti\Irefn{org34}\And
V.~Anguelov\Irefn{org104}\And
C.~Anson\Irefn{org15}\And
T.~Anti\v{c}i\'{c}\Irefn{org108}\And
F.~Antinori\Irefn{org57}\And
P.~Antonioli\Irefn{org54}\And
N.~Apadula\Irefn{org80}\And
L.~Aphecetche\Irefn{org115}\And
H.~Appelsh\"{a}user\Irefn{org68}\And
S.~Arcelli\Irefn{org26}\And
R.~Arnaldi\Irefn{org59}\And
M.~Arratia\Irefn{org80}\And
I.C.~Arsene\Irefn{org20}\And
M.~Arslandok\Irefn{org104}\And
A.~Augustinus\Irefn{org34}\And
R.~Averbeck\Irefn{org107}\And
S.~Aziz\Irefn{org78}\And
M.D.~Azmi\Irefn{org16}\And
A.~Badal\`{a}\Irefn{org56}\And
Y.W.~Baek\Irefn{org41}\And
S.~Bagnasco\Irefn{org59}\And
X.~Bai\Irefn{org107}\And
R.~Bailhache\Irefn{org68}\And
R.~Bala\Irefn{org101}\And
A.~Balbino\Irefn{org30}\And
A.~Baldisseri\Irefn{org137}\And
M.~Ball\Irefn{org43}\And
S.~Balouza\Irefn{org105}\And
D.~Banerjee\Irefn{org3}\And
R.~Barbera\Irefn{org27}\And
L.~Barioglio\Irefn{org25}\And
G.G.~Barnaf\"{o}ldi\Irefn{org145}\And
L.S.~Barnby\Irefn{org94}\And
V.~Barret\Irefn{org134}\And
P.~Bartalini\Irefn{org6}\And
C.~Bartels\Irefn{org127}\And
K.~Barth\Irefn{org34}\And
E.~Bartsch\Irefn{org68}\And
F.~Baruffaldi\Irefn{org28}\And
N.~Bastid\Irefn{org134}\And
S.~Basu\Irefn{org143}\And
G.~Batigne\Irefn{org115}\And
B.~Batyunya\Irefn{org75}\And
D.~Bauri\Irefn{org49}\And
J.L.~Bazo~Alba\Irefn{org112}\And
I.G.~Bearden\Irefn{org89}\And
C.~Beattie\Irefn{org146}\And
C.~Bedda\Irefn{org63}\And
N.K.~Behera\Irefn{org61}\And
I.~Belikov\Irefn{org136}\And
A.D.C.~Bell Hechavarria\Irefn{org144}\And
F.~Bellini\Irefn{org34}\And
R.~Bellwied\Irefn{org125}\And
V.~Belyaev\Irefn{org93}\And
G.~Bencedi\Irefn{org145}\And
S.~Beole\Irefn{org25}\And
A.~Bercuci\Irefn{org48}\And
Y.~Berdnikov\Irefn{org98}\And
D.~Berenyi\Irefn{org145}\And
R.A.~Bertens\Irefn{org130}\And
D.~Berzano\Irefn{org59}\And
M.G.~Besoiu\Irefn{org67}\And
L.~Betev\Irefn{org34}\And
A.~Bhasin\Irefn{org101}\And
I.R.~Bhat\Irefn{org101}\And
M.A.~Bhat\Irefn{org3}\And
H.~Bhatt\Irefn{org49}\And
B.~Bhattacharjee\Irefn{org42}\And
A.~Bianchi\Irefn{org25}\And
L.~Bianchi\Irefn{org25}\And
N.~Bianchi\Irefn{org52}\And
J.~Biel\v{c}\'{\i}k\Irefn{org37}\And
J.~Biel\v{c}\'{\i}kov\'{a}\Irefn{org95}\And
A.~Bilandzic\Irefn{org105}\And
G.~Biro\Irefn{org145}\And
R.~Biswas\Irefn{org3}\And
S.~Biswas\Irefn{org3}\And
J.T.~Blair\Irefn{org119}\And
D.~Blau\Irefn{org88}\And
C.~Blume\Irefn{org68}\And
G.~Boca\Irefn{org139}\And
F.~Bock\Irefn{org96}\And
A.~Bogdanov\Irefn{org93}\And
S.~Boi\Irefn{org23}\And
J.~Bok\Irefn{org61}\And
L.~Boldizs\'{a}r\Irefn{org145}\And
A.~Bolozdynya\Irefn{org93}\And
M.~Bombara\Irefn{org38}\And
G.~Bonomi\Irefn{org140}\And
H.~Borel\Irefn{org137}\And
A.~Borissov\Irefn{org93}\And
H.~Bossi\Irefn{org146}\And
E.~Botta\Irefn{org25}\And
L.~Bratrud\Irefn{org68}\And
P.~Braun-Munzinger\Irefn{org107}\And
M.~Bregant\Irefn{org121}\And
M.~Broz\Irefn{org37}\And
E.~Bruna\Irefn{org59}\And
G.E.~Bruno\Irefn{org33}\textsuperscript{,}\Irefn{org106}\And
M.D.~Buckland\Irefn{org127}\And
D.~Budnikov\Irefn{org109}\And
H.~Buesching\Irefn{org68}\And
S.~Bufalino\Irefn{org30}\And
O.~Bugnon\Irefn{org115}\And
P.~Buhler\Irefn{org114}\And
P.~Buncic\Irefn{org34}\And
Z.~Buthelezi\Irefn{org72}\textsuperscript{,}\Irefn{org131}\And
J.B.~Butt\Irefn{org14}\And
S.A.~Bysiak\Irefn{org118}\And
D.~Caffarri\Irefn{org90}\And
A.~Caliva\Irefn{org107}\And
E.~Calvo Villar\Irefn{org112}\And
J.M.M.~Camacho\Irefn{org120}\And
R.S.~Camacho\Irefn{org45}\And
P.~Camerini\Irefn{org24}\And
F.D.M.~Canedo\Irefn{org121}\And
A.A.~Capon\Irefn{org114}\And
F.~Carnesecchi\Irefn{org26}\And
R.~Caron\Irefn{org137}\And
J.~Castillo Castellanos\Irefn{org137}\And
A.J.~Castro\Irefn{org130}\And
E.A.R.~Casula\Irefn{org55}\And
F.~Catalano\Irefn{org30}\And
C.~Ceballos Sanchez\Irefn{org75}\And
P.~Chakraborty\Irefn{org49}\And
S.~Chandra\Irefn{org141}\And
W.~Chang\Irefn{org6}\And
S.~Chapeland\Irefn{org34}\And
M.~Chartier\Irefn{org127}\And
S.~Chattopadhyay\Irefn{org141}\And
S.~Chattopadhyay\Irefn{org110}\And
A.~Chauvin\Irefn{org23}\And
C.~Cheshkov\Irefn{org135}\And
B.~Cheynis\Irefn{org135}\And
V.~Chibante Barroso\Irefn{org34}\And
D.D.~Chinellato\Irefn{org122}\And
S.~Cho\Irefn{org61}\And
P.~Chochula\Irefn{org34}\And
T.~Chowdhury\Irefn{org134}\And
P.~Christakoglou\Irefn{org90}\And
C.H.~Christensen\Irefn{org89}\And
P.~Christiansen\Irefn{org81}\And
T.~Chujo\Irefn{org133}\And
C.~Cicalo\Irefn{org55}\And
L.~Cifarelli\Irefn{org10}\textsuperscript{,}\Irefn{org26}\And
L.D.~Cilladi\Irefn{org25}\And
F.~Cindolo\Irefn{org54}\And
M.R.~Ciupek\Irefn{org107}\And
G.~Clai\Irefn{org54}\Aref{orgI}\And
J.~Cleymans\Irefn{org124}\And
F.~Colamaria\Irefn{org53}\And
D.~Colella\Irefn{org53}\And
A.~Collu\Irefn{org80}\And
M.~Colocci\Irefn{org26}\And
M.~Concas\Irefn{org59}\Aref{orgII}\And
G.~Conesa Balbastre\Irefn{org79}\And
Z.~Conesa del Valle\Irefn{org78}\And
G.~Contin\Irefn{org24}\textsuperscript{,}\Irefn{org60}\And
J.G.~Contreras\Irefn{org37}\And
T.M.~Cormier\Irefn{org96}\And
Y.~Corrales Morales\Irefn{org25}\And
P.~Cortese\Irefn{org31}\And
M.R.~Cosentino\Irefn{org123}\And
F.~Costa\Irefn{org34}\And
S.~Costanza\Irefn{org139}\And
P.~Crochet\Irefn{org134}\And
E.~Cuautle\Irefn{org69}\And
P.~Cui\Irefn{org6}\And
L.~Cunqueiro\Irefn{org96}\And
D.~Dabrowski\Irefn{org142}\And
T.~Dahms\Irefn{org105}\And
A.~Dainese\Irefn{org57}\And
F.P.A.~Damas\Irefn{org115}\textsuperscript{,}\Irefn{org137}\And
M.C.~Danisch\Irefn{org104}\And
A.~Danu\Irefn{org67}\And
D.~Das\Irefn{org110}\And
I.~Das\Irefn{org110}\And
P.~Das\Irefn{org86}\And
P.~Das\Irefn{org3}\And
S.~Das\Irefn{org3}\And
A.~Dash\Irefn{org86}\And
S.~Dash\Irefn{org49}\And
S.~De\Irefn{org86}\And
A.~De Caro\Irefn{org29}\And
G.~de Cataldo\Irefn{org53}\And
J.~de Cuveland\Irefn{org39}\And
A.~De Falco\Irefn{org23}\And
D.~De Gruttola\Irefn{org10}\And
N.~De Marco\Irefn{org59}\And
S.~De Pasquale\Irefn{org29}\And
S.~Deb\Irefn{org50}\And
H.F.~Degenhardt\Irefn{org121}\And
K.R.~Deja\Irefn{org142}\And
A.~Deloff\Irefn{org85}\And
S.~Delsanto\Irefn{org25}\textsuperscript{,}\Irefn{org131}\And
W.~Deng\Irefn{org6}\And
P.~Dhankher\Irefn{org49}\And
D.~Di Bari\Irefn{org33}\And
A.~Di Mauro\Irefn{org34}\And
R.A.~Diaz\Irefn{org8}\And
T.~Dietel\Irefn{org124}\And
P.~Dillenseger\Irefn{org68}\And
Y.~Ding\Irefn{org6}\And
R.~Divi\`{a}\Irefn{org34}\And
D.U.~Dixit\Irefn{org19}\And
{\O}.~Djuvsland\Irefn{org21}\And
U.~Dmitrieva\Irefn{org62}\And
A.~Dobrin\Irefn{org67}\And
B.~D\"{o}nigus\Irefn{org68}\And
O.~Dordic\Irefn{org20}\And
A.K.~Dubey\Irefn{org141}\And
A.~Dubla\Irefn{org90}\textsuperscript{,}\Irefn{org107}\And
S.~Dudi\Irefn{org100}\And
M.~Dukhishyam\Irefn{org86}\And
P.~Dupieux\Irefn{org134}\And
R.J.~Ehlers\Irefn{org96}\And
V.N.~Eikeland\Irefn{org21}\And
D.~Elia\Irefn{org53}\And
B.~Erazmus\Irefn{org115}\And
F.~Erhardt\Irefn{org99}\And
A.~Erokhin\Irefn{org113}\And
M.R.~Ersdal\Irefn{org21}\And
B.~Espagnon\Irefn{org78}\And
G.~Eulisse\Irefn{org34}\And
D.~Evans\Irefn{org111}\And
S.~Evdokimov\Irefn{org91}\And
L.~Fabbietti\Irefn{org105}\And
M.~Faggin\Irefn{org28}\And
J.~Faivre\Irefn{org79}\And
F.~Fan\Irefn{org6}\And
A.~Fantoni\Irefn{org52}\And
M.~Fasel\Irefn{org96}\And
P.~Fecchio\Irefn{org30}\And
A.~Feliciello\Irefn{org59}\And
G.~Feofilov\Irefn{org113}\And
A.~Fern\'{a}ndez T\'{e}llez\Irefn{org45}\And
A.~Ferrero\Irefn{org137}\And
A.~Ferretti\Irefn{org25}\And
A.~Festanti\Irefn{org34}\And
V.J.G.~Feuillard\Irefn{org104}\And
J.~Figiel\Irefn{org118}\And
S.~Filchagin\Irefn{org109}\And
D.~Finogeev\Irefn{org62}\And
F.M.~Fionda\Irefn{org21}\And
G.~Fiorenza\Irefn{org53}\And
F.~Flor\Irefn{org125}\And
A.N.~Flores\Irefn{org119}\And
S.~Foertsch\Irefn{org72}\And
P.~Foka\Irefn{org107}\And
S.~Fokin\Irefn{org88}\And
E.~Fragiacomo\Irefn{org60}\And
U.~Frankenfeld\Irefn{org107}\And
U.~Fuchs\Irefn{org34}\And
C.~Furget\Irefn{org79}\And
A.~Furs\Irefn{org62}\And
M.~Fusco Girard\Irefn{org29}\And
J.J.~Gaardh{\o}je\Irefn{org89}\And
M.~Gagliardi\Irefn{org25}\And
A.M.~Gago\Irefn{org112}\And
A.~Gal\Irefn{org136}\And
C.D.~Galvan\Irefn{org120}\And
P.~Ganoti\Irefn{org84}\And
C.~Garabatos\Irefn{org107}\And
J.R.A.~Garcia\Irefn{org45}\And
E.~Garcia-Solis\Irefn{org11}\And
K.~Garg\Irefn{org115}\And
C.~Gargiulo\Irefn{org34}\And
A.~Garibli\Irefn{org87}\And
K.~Garner\Irefn{org144}\And
P.~Gasik\Irefn{org105}\textsuperscript{,}\Irefn{org107}\And
E.F.~Gauger\Irefn{org119}\And
M.B.~Gay Ducati\Irefn{org70}\And
M.~Germain\Irefn{org115}\And
J.~Ghosh\Irefn{org110}\And
P.~Ghosh\Irefn{org141}\And
S.K.~Ghosh\Irefn{org3}\And
M.~Giacalone\Irefn{org26}\And
P.~Gianotti\Irefn{org52}\And
P.~Giubellino\Irefn{org59}\textsuperscript{,}\Irefn{org107}\And
P.~Giubilato\Irefn{org28}\And
A.M.C.~Glaenzer\Irefn{org137}\And
P.~Gl\"{a}ssel\Irefn{org104}\And
A.~Gomez Ramirez\Irefn{org74}\And
V.~Gonzalez\Irefn{org107}\textsuperscript{,}\Irefn{org143}\And
\mbox{L.H.~Gonz\'{a}lez-Trueba}\Irefn{org71}\And
S.~Gorbunov\Irefn{org39}\And
L.~G\"{o}rlich\Irefn{org118}\And
A.~Goswami\Irefn{org49}\And
S.~Gotovac\Irefn{org35}\And
V.~Grabski\Irefn{org71}\And
L.K.~Graczykowski\Irefn{org142}\And
K.L.~Graham\Irefn{org111}\And
L.~Greiner\Irefn{org80}\And
A.~Grelli\Irefn{org63}\And
C.~Grigoras\Irefn{org34}\And
V.~Grigoriev\Irefn{org93}\And
A.~Grigoryan\Irefn{org1}\And
S.~Grigoryan\Irefn{org75}\And
O.S.~Groettvik\Irefn{org21}\And
F.~Grosa\Irefn{org30}\textsuperscript{,}\Irefn{org59}\And
J.F.~Grosse-Oetringhaus\Irefn{org34}\And
R.~Grosso\Irefn{org107}\And
R.~Guernane\Irefn{org79}\And
M.~Guittiere\Irefn{org115}\And
K.~Gulbrandsen\Irefn{org89}\And
T.~Gunji\Irefn{org132}\And
A.~Gupta\Irefn{org101}\And
R.~Gupta\Irefn{org101}\And
I.B.~Guzman\Irefn{org45}\And
R.~Haake\Irefn{org146}\And
M.K.~Habib\Irefn{org107}\And
C.~Hadjidakis\Irefn{org78}\And
H.~Hamagaki\Irefn{org82}\And
G.~Hamar\Irefn{org145}\And
M.~Hamid\Irefn{org6}\And
R.~Hannigan\Irefn{org119}\And
M.R.~Haque\Irefn{org63}\textsuperscript{,}\Irefn{org86}\And
A.~Harlenderova\Irefn{org107}\And
J.W.~Harris\Irefn{org146}\And
A.~Harton\Irefn{org11}\And
J.A.~Hasenbichler\Irefn{org34}\And
H.~Hassan\Irefn{org96}\And
Q.U.~Hassan\Irefn{org14}\And
D.~Hatzifotiadou\Irefn{org10}\textsuperscript{,}\Irefn{org54}\And
P.~Hauer\Irefn{org43}\And
L.B.~Havener\Irefn{org146}\And
S.~Hayashi\Irefn{org132}\And
S.T.~Heckel\Irefn{org105}\And
E.~Hellb\"{a}r\Irefn{org68}\And
H.~Helstrup\Irefn{org36}\And
A.~Herghelegiu\Irefn{org48}\And
T.~Herman\Irefn{org37}\And
E.G.~Hernandez\Irefn{org45}\And
G.~Herrera Corral\Irefn{org9}\And
F.~Herrmann\Irefn{org144}\And
K.F.~Hetland\Irefn{org36}\And
H.~Hillemanns\Irefn{org34}\And
C.~Hills\Irefn{org127}\And
B.~Hippolyte\Irefn{org136}\And
B.~Hohlweger\Irefn{org105}\And
J.~Honermann\Irefn{org144}\And
D.~Horak\Irefn{org37}\And
A.~Hornung\Irefn{org68}\And
S.~Hornung\Irefn{org107}\And
R.~Hosokawa\Irefn{org15}\textsuperscript{,}\Irefn{org133}\And
P.~Hristov\Irefn{org34}\And
C.~Huang\Irefn{org78}\And
C.~Hughes\Irefn{org130}\And
P.~Huhn\Irefn{org68}\And
T.J.~Humanic\Irefn{org97}\And
H.~Hushnud\Irefn{org110}\And
L.A.~Husova\Irefn{org144}\And
N.~Hussain\Irefn{org42}\And
S.A.~Hussain\Irefn{org14}\And
D.~Hutter\Irefn{org39}\And
J.P.~Iddon\Irefn{org34}\textsuperscript{,}\Irefn{org127}\And
R.~Ilkaev\Irefn{org109}\And
H.~Ilyas\Irefn{org14}\And
M.~Inaba\Irefn{org133}\And
G.M.~Innocenti\Irefn{org34}\And
M.~Ippolitov\Irefn{org88}\And
A.~Isakov\Irefn{org95}\And
M.S.~Islam\Irefn{org110}\And
M.~Ivanov\Irefn{org107}\And
V.~Ivanov\Irefn{org98}\And
V.~Izucheev\Irefn{org91}\And
B.~Jacak\Irefn{org80}\And
N.~Jacazio\Irefn{org34}\textsuperscript{,}\Irefn{org54}\And
P.M.~Jacobs\Irefn{org80}\And
S.~Jadlovska\Irefn{org117}\And
J.~Jadlovsky\Irefn{org117}\And
S.~Jaelani\Irefn{org63}\And
C.~Jahnke\Irefn{org121}\And
M.J.~Jakubowska\Irefn{org142}\And
M.A.~Janik\Irefn{org142}\And
T.~Janson\Irefn{org74}\And
M.~Jercic\Irefn{org99}\And
O.~Jevons\Irefn{org111}\And
M.~Jin\Irefn{org125}\And
F.~Jonas\Irefn{org96}\textsuperscript{,}\Irefn{org144}\And
P.G.~Jones\Irefn{org111}\And
J.~Jung\Irefn{org68}\And
M.~Jung\Irefn{org68}\And
A.~Jusko\Irefn{org111}\And
P.~Kalinak\Irefn{org64}\And
A.~Kalweit\Irefn{org34}\And
V.~Kaplin\Irefn{org93}\And
S.~Kar\Irefn{org6}\And
A.~Karasu Uysal\Irefn{org77}\And
D.~Karatovic\Irefn{org99}\And
O.~Karavichev\Irefn{org62}\And
T.~Karavicheva\Irefn{org62}\And
P.~Karczmarczyk\Irefn{org142}\And
E.~Karpechev\Irefn{org62}\And
A.~Kazantsev\Irefn{org88}\And
U.~Kebschull\Irefn{org74}\And
R.~Keidel\Irefn{org47}\And
M.~Keil\Irefn{org34}\And
B.~Ketzer\Irefn{org43}\And
Z.~Khabanova\Irefn{org90}\And
A.M.~Khan\Irefn{org6}\And
S.~Khan\Irefn{org16}\And
A.~Khanzadeev\Irefn{org98}\And
Y.~Kharlov\Irefn{org91}\And
A.~Khatun\Irefn{org16}\And
A.~Khuntia\Irefn{org118}\And
B.~Kileng\Irefn{org36}\And
B.~Kim\Irefn{org61}\And
B.~Kim\Irefn{org133}\And
D.~Kim\Irefn{org147}\And
D.J.~Kim\Irefn{org126}\And
E.J.~Kim\Irefn{org73}\And
H.~Kim\Irefn{org17}\And
J.~Kim\Irefn{org147}\And
J.S.~Kim\Irefn{org41}\And
J.~Kim\Irefn{org104}\And
J.~Kim\Irefn{org147}\And
J.~Kim\Irefn{org73}\And
M.~Kim\Irefn{org104}\And
S.~Kim\Irefn{org18}\And
T.~Kim\Irefn{org147}\And
T.~Kim\Irefn{org147}\And
S.~Kirsch\Irefn{org68}\And
I.~Kisel\Irefn{org39}\And
S.~Kiselev\Irefn{org92}\And
A.~Kisiel\Irefn{org142}\And
J.L.~Klay\Irefn{org5}\And
C.~Klein\Irefn{org68}\And
J.~Klein\Irefn{org34}\textsuperscript{,}\Irefn{org59}\And
S.~Klein\Irefn{org80}\And
C.~Klein-B\"{o}sing\Irefn{org144}\And
M.~Kleiner\Irefn{org68}\And
A.~Kluge\Irefn{org34}\And
M.L.~Knichel\Irefn{org34}\And
A.G.~Knospe\Irefn{org125}\And
C.~Kobdaj\Irefn{org116}\And
M.K.~K\"{o}hler\Irefn{org104}\And
T.~Kollegger\Irefn{org107}\And
A.~Kondratyev\Irefn{org75}\And
N.~Kondratyeva\Irefn{org93}\And
E.~Kondratyuk\Irefn{org91}\And
J.~Konig\Irefn{org68}\And
S.A.~Konigstorfer\Irefn{org105}\And
P.J.~Konopka\Irefn{org34}\And
G.~Kornakov\Irefn{org142}\And
L.~Koska\Irefn{org117}\And
O.~Kovalenko\Irefn{org85}\And
V.~Kovalenko\Irefn{org113}\And
M.~Kowalski\Irefn{org118}\And
I.~Kr\'{a}lik\Irefn{org64}\And
A.~Krav\v{c}\'{a}kov\'{a}\Irefn{org38}\And
L.~Kreis\Irefn{org107}\And
M.~Krivda\Irefn{org64}\textsuperscript{,}\Irefn{org111}\And
F.~Krizek\Irefn{org95}\And
K.~Krizkova~Gajdosova\Irefn{org37}\And
M.~Kr\"uger\Irefn{org68}\And
E.~Kryshen\Irefn{org98}\And
M.~Krzewicki\Irefn{org39}\And
A.M.~Kubera\Irefn{org97}\And
V.~Ku\v{c}era\Irefn{org34}\textsuperscript{,}\Irefn{org61}\And
C.~Kuhn\Irefn{org136}\And
P.G.~Kuijer\Irefn{org90}\And
L.~Kumar\Irefn{org100}\And
S.~Kundu\Irefn{org86}\And
P.~Kurashvili\Irefn{org85}\And
A.~Kurepin\Irefn{org62}\And
A.B.~Kurepin\Irefn{org62}\And
A.~Kuryakin\Irefn{org109}\And
S.~Kushpil\Irefn{org95}\And
J.~Kvapil\Irefn{org111}\And
M.J.~Kweon\Irefn{org61}\And
J.Y.~Kwon\Irefn{org61}\And
Y.~Kwon\Irefn{org147}\And
S.L.~La Pointe\Irefn{org39}\And
P.~La Rocca\Irefn{org27}\And
Y.S.~Lai\Irefn{org80}\And
M.~Lamanna\Irefn{org34}\And
R.~Langoy\Irefn{org129}\And
K.~Lapidus\Irefn{org34}\And
A.~Lardeux\Irefn{org20}\And
P.~Larionov\Irefn{org52}\And
E.~Laudi\Irefn{org34}\And
R.~Lavicka\Irefn{org37}\And
T.~Lazareva\Irefn{org113}\And
R.~Lea\Irefn{org24}\And
L.~Leardini\Irefn{org104}\And
J.~Lee\Irefn{org133}\And
S.~Lee\Irefn{org147}\And
S.~Lehner\Irefn{org114}\And
J.~Lehrbach\Irefn{org39}\And
R.C.~Lemmon\Irefn{org94}\And
I.~Le\'{o}n Monz\'{o}n\Irefn{org120}\And
E.D.~Lesser\Irefn{org19}\And
M.~Lettrich\Irefn{org34}\And
P.~L\'{e}vai\Irefn{org145}\And
X.~Li\Irefn{org12}\And
X.L.~Li\Irefn{org6}\And
J.~Lien\Irefn{org129}\And
R.~Lietava\Irefn{org111}\And
B.~Lim\Irefn{org17}\And
V.~Lindenstruth\Irefn{org39}\And
A.~Lindner\Irefn{org48}\And
C.~Lippmann\Irefn{org107}\And
M.A.~Lisa\Irefn{org97}\And
A.~Liu\Irefn{org19}\And
J.~Liu\Irefn{org127}\And
S.~Liu\Irefn{org97}\And
W.J.~Llope\Irefn{org143}\And
I.M.~Lofnes\Irefn{org21}\And
V.~Loginov\Irefn{org93}\And
C.~Loizides\Irefn{org96}\And
P.~Loncar\Irefn{org35}\And
J.A.~Lopez\Irefn{org104}\And
X.~Lopez\Irefn{org134}\And
E.~L\'{o}pez Torres\Irefn{org8}\And
J.R.~Luhder\Irefn{org144}\And
M.~Lunardon\Irefn{org28}\And
G.~Luparello\Irefn{org60}\And
Y.G.~Ma\Irefn{org40}\And
A.~Maevskaya\Irefn{org62}\And
M.~Mager\Irefn{org34}\And
S.M.~Mahmood\Irefn{org20}\And
T.~Mahmoud\Irefn{org43}\And
A.~Maire\Irefn{org136}\And
R.D.~Majka\Irefn{org146}\Aref{org*}\And
M.~Malaev\Irefn{org98}\And
Q.W.~Malik\Irefn{org20}\And
L.~Malinina\Irefn{org75}\Aref{orgIII}\And
D.~Mal'Kevich\Irefn{org92}\And
P.~Malzacher\Irefn{org107}\And
G.~Mandaglio\Irefn{org32}\textsuperscript{,}\Irefn{org56}\And
V.~Manko\Irefn{org88}\And
F.~Manso\Irefn{org134}\And
V.~Manzari\Irefn{org53}\And
Y.~Mao\Irefn{org6}\And
M.~Marchisone\Irefn{org135}\And
J.~Mare\v{s}\Irefn{org66}\And
G.V.~Margagliotti\Irefn{org24}\And
A.~Margotti\Irefn{org54}\And
A.~Mar\'{\i}n\Irefn{org107}\And
C.~Markert\Irefn{org119}\And
M.~Marquard\Irefn{org68}\And
C.D.~Martin\Irefn{org24}\And
N.A.~Martin\Irefn{org104}\And
P.~Martinengo\Irefn{org34}\And
J.L.~Martinez\Irefn{org125}\And
M.I.~Mart\'{\i}nez\Irefn{org45}\And
G.~Mart\'{\i}nez Garc\'{\i}a\Irefn{org115}\And
S.~Masciocchi\Irefn{org107}\And
M.~Masera\Irefn{org25}\And
A.~Masoni\Irefn{org55}\And
L.~Massacrier\Irefn{org78}\And
E.~Masson\Irefn{org115}\And
A.~Mastroserio\Irefn{org53}\textsuperscript{,}\Irefn{org138}\And
A.M.~Mathis\Irefn{org105}\And
O.~Matonoha\Irefn{org81}\And
P.F.T.~Matuoka\Irefn{org121}\And
A.~Matyja\Irefn{org118}\And
C.~Mayer\Irefn{org118}\And
F.~Mazzaschi\Irefn{org25}\And
M.~Mazzilli\Irefn{org53}\And
M.A.~Mazzoni\Irefn{org58}\And
A.F.~Mechler\Irefn{org68}\And
F.~Meddi\Irefn{org22}\And
Y.~Melikyan\Irefn{org62}\textsuperscript{,}\Irefn{org93}\And
A.~Menchaca-Rocha\Irefn{org71}\And
C.~Mengke\Irefn{org6}\And
E.~Meninno\Irefn{org29}\textsuperscript{,}\Irefn{org114}\And
A.S.~Menon\Irefn{org125}\And
M.~Meres\Irefn{org13}\And
S.~Mhlanga\Irefn{org124}\And
Y.~Miake\Irefn{org133}\And
L.~Micheletti\Irefn{org25}\And
L.C.~Migliorin\Irefn{org135}\And
D.L.~Mihaylov\Irefn{org105}\And
K.~Mikhaylov\Irefn{org75}\textsuperscript{,}\Irefn{org92}\And
A.N.~Mishra\Irefn{org69}\And
D.~Mi\'{s}kowiec\Irefn{org107}\And
A.~Modak\Irefn{org3}\And
N.~Mohammadi\Irefn{org34}\And
A.P.~Mohanty\Irefn{org63}\And
B.~Mohanty\Irefn{org86}\And
M.~Mohisin Khan\Irefn{org16}\Aref{orgIV}\And
Z.~Moravcova\Irefn{org89}\And
C.~Mordasini\Irefn{org105}\And
D.A.~Moreira De Godoy\Irefn{org144}\And
L.A.P.~Moreno\Irefn{org45}\And
I.~Morozov\Irefn{org62}\And
A.~Morsch\Irefn{org34}\And
T.~Mrnjavac\Irefn{org34}\And
V.~Muccifora\Irefn{org52}\And
E.~Mudnic\Irefn{org35}\And
D.~M{\"u}hlheim\Irefn{org144}\And
S.~Muhuri\Irefn{org141}\And
J.D.~Mulligan\Irefn{org80}\And
A.~Mulliri\Irefn{org23}\textsuperscript{,}\Irefn{org55}\And
M.G.~Munhoz\Irefn{org121}\And
R.H.~Munzer\Irefn{org68}\And
H.~Murakami\Irefn{org132}\And
S.~Murray\Irefn{org124}\And
L.~Musa\Irefn{org34}\And
J.~Musinsky\Irefn{org64}\And
C.J.~Myers\Irefn{org125}\And
J.W.~Myrcha\Irefn{org142}\And
B.~Naik\Irefn{org49}\And
R.~Nair\Irefn{org85}\And
B.K.~Nandi\Irefn{org49}\And
R.~Nania\Irefn{org10}\textsuperscript{,}\Irefn{org54}\And
E.~Nappi\Irefn{org53}\And
M.U.~Naru\Irefn{org14}\And
A.F.~Nassirpour\Irefn{org81}\And
C.~Nattrass\Irefn{org130}\And
R.~Nayak\Irefn{org49}\And
T.K.~Nayak\Irefn{org86}\And
S.~Nazarenko\Irefn{org109}\And
A.~Neagu\Irefn{org20}\And
R.A.~Negrao De Oliveira\Irefn{org68}\And
L.~Nellen\Irefn{org69}\And
S.V.~Nesbo\Irefn{org36}\And
G.~Neskovic\Irefn{org39}\And
D.~Nesterov\Irefn{org113}\And
L.T.~Neumann\Irefn{org142}\And
B.S.~Nielsen\Irefn{org89}\And
S.~Nikolaev\Irefn{org88}\And
S.~Nikulin\Irefn{org88}\And
V.~Nikulin\Irefn{org98}\And
F.~Noferini\Irefn{org10}\textsuperscript{,}\Irefn{org54}\And
P.~Nomokonov\Irefn{org75}\And
J.~Norman\Irefn{org79}\textsuperscript{,}\Irefn{org127}\And
N.~Novitzky\Irefn{org133}\And
P.~Nowakowski\Irefn{org142}\And
A.~Nyanin\Irefn{org88}\And
J.~Nystrand\Irefn{org21}\And
M.~Ogino\Irefn{org82}\And
A.~Ohlson\Irefn{org81}\textsuperscript{,}\Irefn{org104}\And
J.~Oleniacz\Irefn{org142}\And
A.C.~Oliveira Da Silva\Irefn{org130}\And
M.H.~Oliver\Irefn{org146}\And
C.~Oppedisano\Irefn{org59}\And
A.~Ortiz Velasquez\Irefn{org69}\And
A.~Oskarsson\Irefn{org81}\And
J.~Otwinowski\Irefn{org118}\And
K.~Oyama\Irefn{org82}\And
Y.~Pachmayer\Irefn{org104}\And
V.~Pacik\Irefn{org89}\And
S.~Padhan\Irefn{org49}\And
D.~Pagano\Irefn{org140}\And
G.~Pai\'{c}\Irefn{org69}\And
J.~Pan\Irefn{org143}\And
S.~Panebianco\Irefn{org137}\And
P.~Pareek\Irefn{org50}\textsuperscript{,}\Irefn{org141}\And
J.~Park\Irefn{org61}\And
J.E.~Parkkila\Irefn{org126}\And
S.~Parmar\Irefn{org100}\And
S.P.~Pathak\Irefn{org125}\And
B.~Paul\Irefn{org23}\And
J.~Pazzini\Irefn{org140}\And
H.~Pei\Irefn{org6}\And
T.~Peitzmann\Irefn{org63}\And
X.~Peng\Irefn{org6}\And
L.G.~Pereira\Irefn{org70}\And
H.~Pereira Da Costa\Irefn{org137}\And
D.~Peresunko\Irefn{org88}\And
G.M.~Perez\Irefn{org8}\And
S.~Perrin\Irefn{org137}\And
Y.~Pestov\Irefn{org4}\And
V.~Petr\'{a}\v{c}ek\Irefn{org37}\And
M.~Petrovici\Irefn{org48}\And
R.P.~Pezzi\Irefn{org70}\And
S.~Piano\Irefn{org60}\And
M.~Pikna\Irefn{org13}\And
P.~Pillot\Irefn{org115}\And
O.~Pinazza\Irefn{org34}\textsuperscript{,}\Irefn{org54}\And
L.~Pinsky\Irefn{org125}\And
C.~Pinto\Irefn{org27}\And
S.~Pisano\Irefn{org10}\textsuperscript{,}\Irefn{org52}\And
D.~Pistone\Irefn{org56}\And
M.~P\l osko\'{n}\Irefn{org80}\And
M.~Planinic\Irefn{org99}\And
F.~Pliquett\Irefn{org68}\And
M.G.~Poghosyan\Irefn{org96}\And
B.~Polichtchouk\Irefn{org91}\And
N.~Poljak\Irefn{org99}\And
A.~Pop\Irefn{org48}\And
S.~Porteboeuf-Houssais\Irefn{org134}\And
V.~Pozdniakov\Irefn{org75}\And
S.K.~Prasad\Irefn{org3}\And
R.~Preghenella\Irefn{org54}\And
F.~Prino\Irefn{org59}\And
C.A.~Pruneau\Irefn{org143}\And
I.~Pshenichnov\Irefn{org62}\And
M.~Puccio\Irefn{org34}\And
J.~Putschke\Irefn{org143}\And
S.~Qiu\Irefn{org90}\And
L.~Quaglia\Irefn{org25}\And
R.E.~Quishpe\Irefn{org125}\And
S.~Ragoni\Irefn{org111}\And
S.~Raha\Irefn{org3}\And
S.~Rajput\Irefn{org101}\And
J.~Rak\Irefn{org126}\And
A.~Rakotozafindrabe\Irefn{org137}\And
L.~Ramello\Irefn{org31}\And
F.~Rami\Irefn{org136}\And
S.A.R.~Ramirez\Irefn{org45}\And
R.~Raniwala\Irefn{org102}\And
S.~Raniwala\Irefn{org102}\And
S.S.~R\"{a}s\"{a}nen\Irefn{org44}\And
R.~Rath\Irefn{org50}\And
V.~Ratza\Irefn{org43}\And
I.~Ravasenga\Irefn{org90}\And
K.F.~Read\Irefn{org96}\textsuperscript{,}\Irefn{org130}\And
A.R.~Redelbach\Irefn{org39}\And
K.~Redlich\Irefn{org85}\Aref{orgV}\And
A.~Rehman\Irefn{org21}\And
P.~Reichelt\Irefn{org68}\And
F.~Reidt\Irefn{org34}\And
X.~Ren\Irefn{org6}\And
R.~Renfordt\Irefn{org68}\And
Z.~Rescakova\Irefn{org38}\And
K.~Reygers\Irefn{org104}\And
A.~Riabov\Irefn{org98}\And
V.~Riabov\Irefn{org98}\And
T.~Richert\Irefn{org81}\textsuperscript{,}\Irefn{org89}\And
M.~Richter\Irefn{org20}\And
P.~Riedler\Irefn{org34}\And
W.~Riegler\Irefn{org34}\And
F.~Riggi\Irefn{org27}\And
C.~Ristea\Irefn{org67}\And
S.P.~Rode\Irefn{org50}\And
M.~Rodr\'{i}guez Cahuantzi\Irefn{org45}\And
K.~R{\o}ed\Irefn{org20}\And
R.~Rogalev\Irefn{org91}\And
E.~Rogochaya\Irefn{org75}\And
D.~Rohr\Irefn{org34}\And
D.~R\"ohrich\Irefn{org21}\And
P.F.~Rojas\Irefn{org45}\And
P.S.~Rokita\Irefn{org142}\And
F.~Ronchetti\Irefn{org52}\And
A.~Rosano\Irefn{org56}\And
E.D.~Rosas\Irefn{org69}\And
K.~Roslon\Irefn{org142}\And
A.~Rossi\Irefn{org28}\textsuperscript{,}\Irefn{org57}\And
A.~Rotondi\Irefn{org139}\And
A.~Roy\Irefn{org50}\And
P.~Roy\Irefn{org110}\And
O.V.~Rueda\Irefn{org81}\And
R.~Rui\Irefn{org24}\And
B.~Rumyantsev\Irefn{org75}\And
A.~Rustamov\Irefn{org87}\And
E.~Ryabinkin\Irefn{org88}\And
Y.~Ryabov\Irefn{org98}\And
A.~Rybicki\Irefn{org118}\And
H.~Rytkonen\Irefn{org126}\And
O.A.M.~Saarimaki\Irefn{org44}\And
R.~Sadek\Irefn{org115}\And
S.~Sadhu\Irefn{org141}\And
S.~Sadovsky\Irefn{org91}\And
K.~\v{S}afa\v{r}\'{\i}k\Irefn{org37}\And
S.K.~Saha\Irefn{org141}\And
B.~Sahoo\Irefn{org49}\And
P.~Sahoo\Irefn{org49}\And
R.~Sahoo\Irefn{org50}\And
S.~Sahoo\Irefn{org65}\And
P.K.~Sahu\Irefn{org65}\And
J.~Saini\Irefn{org141}\And
S.~Sakai\Irefn{org133}\And
S.~Sambyal\Irefn{org101}\And
V.~Samsonov\Irefn{org93}\textsuperscript{,}\Irefn{org98}\And
D.~Sarkar\Irefn{org143}\And
N.~Sarkar\Irefn{org141}\And
P.~Sarma\Irefn{org42}\And
V.M.~Sarti\Irefn{org105}\And
M.H.P.~Sas\Irefn{org63}\And
E.~Scapparone\Irefn{org54}\And
J.~Schambach\Irefn{org119}\And
H.S.~Scheid\Irefn{org68}\And
C.~Schiaua\Irefn{org48}\And
R.~Schicker\Irefn{org104}\And
A.~Schmah\Irefn{org104}\And
C.~Schmidt\Irefn{org107}\And
H.R.~Schmidt\Irefn{org103}\And
M.O.~Schmidt\Irefn{org104}\And
M.~Schmidt\Irefn{org103}\And
N.V.~Schmidt\Irefn{org68}\textsuperscript{,}\Irefn{org96}\And
A.R.~Schmier\Irefn{org130}\And
J.~Schukraft\Irefn{org89}\And
Y.~Schutz\Irefn{org136}\And
K.~Schwarz\Irefn{org107}\And
K.~Schweda\Irefn{org107}\And
G.~Scioli\Irefn{org26}\And
E.~Scomparin\Irefn{org59}\And
J.E.~Seger\Irefn{org15}\And
Y.~Sekiguchi\Irefn{org132}\And
D.~Sekihata\Irefn{org132}\And
I.~Selyuzhenkov\Irefn{org93}\textsuperscript{,}\Irefn{org107}\And
S.~Senyukov\Irefn{org136}\And
D.~Serebryakov\Irefn{org62}\And
A.~Sevcenco\Irefn{org67}\And
A.~Shabanov\Irefn{org62}\And
A.~Shabetai\Irefn{org115}\And
R.~Shahoyan\Irefn{org34}\And
W.~Shaikh\Irefn{org110}\And
A.~Shangaraev\Irefn{org91}\And
A.~Sharma\Irefn{org100}\And
A.~Sharma\Irefn{org101}\And
H.~Sharma\Irefn{org118}\And
M.~Sharma\Irefn{org101}\And
N.~Sharma\Irefn{org100}\And
S.~Sharma\Irefn{org101}\And
O.~Sheibani\Irefn{org125}\And
K.~Shigaki\Irefn{org46}\And
M.~Shimomura\Irefn{org83}\And
S.~Shirinkin\Irefn{org92}\And
Q.~Shou\Irefn{org40}\And
Y.~Sibiriak\Irefn{org88}\And
S.~Siddhanta\Irefn{org55}\And
T.~Siemiarczuk\Irefn{org85}\And
D.~Silvermyr\Irefn{org81}\And
G.~Simatovic\Irefn{org90}\And
G.~Simonetti\Irefn{org34}\And
B.~Singh\Irefn{org105}\And
R.~Singh\Irefn{org86}\And
R.~Singh\Irefn{org101}\And
R.~Singh\Irefn{org50}\And
V.K.~Singh\Irefn{org141}\And
V.~Singhal\Irefn{org141}\And
T.~Sinha\Irefn{org110}\And
B.~Sitar\Irefn{org13}\And
M.~Sitta\Irefn{org31}\And
T.B.~Skaali\Irefn{org20}\And
M.~Slupecki\Irefn{org44}\And
N.~Smirnov\Irefn{org146}\And
R.J.M.~Snellings\Irefn{org63}\And
C.~Soncco\Irefn{org112}\And
J.~Song\Irefn{org125}\And
A.~Songmoolnak\Irefn{org116}\And
F.~Soramel\Irefn{org28}\And
S.~Sorensen\Irefn{org130}\And
I.~Sputowska\Irefn{org118}\And
J.~Stachel\Irefn{org104}\And
I.~Stan\Irefn{org67}\And
P.J.~Steffanic\Irefn{org130}\And
E.~Stenlund\Irefn{org81}\And
S.F.~Stiefelmaier\Irefn{org104}\And
D.~Stocco\Irefn{org115}\And
M.M.~Storetvedt\Irefn{org36}\And
L.D.~Stritto\Irefn{org29}\And
A.A.P.~Suaide\Irefn{org121}\And
T.~Sugitate\Irefn{org46}\And
C.~Suire\Irefn{org78}\And
M.~Suleymanov\Irefn{org14}\And
M.~Suljic\Irefn{org34}\And
R.~Sultanov\Irefn{org92}\And
M.~\v{S}umbera\Irefn{org95}\And
V.~Sumberia\Irefn{org101}\And
S.~Sumowidagdo\Irefn{org51}\And
S.~Swain\Irefn{org65}\And
A.~Szabo\Irefn{org13}\And
I.~Szarka\Irefn{org13}\And
U.~Tabassam\Irefn{org14}\And
S.F.~Taghavi\Irefn{org105}\And
G.~Taillepied\Irefn{org134}\And
J.~Takahashi\Irefn{org122}\And
G.J.~Tambave\Irefn{org21}\And
S.~Tang\Irefn{org6}\textsuperscript{,}\Irefn{org134}\And
M.~Tarhini\Irefn{org115}\And
M.G.~Tarzila\Irefn{org48}\And
A.~Tauro\Irefn{org34}\And
G.~Tejeda Mu\~{n}oz\Irefn{org45}\And
A.~Telesca\Irefn{org34}\And
L.~Terlizzi\Irefn{org25}\And
C.~Terrevoli\Irefn{org125}\And
D.~Thakur\Irefn{org50}\And
S.~Thakur\Irefn{org141}\And
D.~Thomas\Irefn{org119}\And
F.~Thoresen\Irefn{org89}\And
R.~Tieulent\Irefn{org135}\And
A.~Tikhonov\Irefn{org62}\And
A.R.~Timmins\Irefn{org125}\And
A.~Toia\Irefn{org68}\And
N.~Topilskaya\Irefn{org62}\And
M.~Toppi\Irefn{org52}\And
F.~Torales-Acosta\Irefn{org19}\And
S.R.~Torres\Irefn{org37}\And
A.~Trifir\'{o}\Irefn{org32}\textsuperscript{,}\Irefn{org56}\And
S.~Tripathy\Irefn{org50}\textsuperscript{,}\Irefn{org69}\And
T.~Tripathy\Irefn{org49}\And
S.~Trogolo\Irefn{org28}\And
G.~Trombetta\Irefn{org33}\And
L.~Tropp\Irefn{org38}\And
V.~Trubnikov\Irefn{org2}\And
W.H.~Trzaska\Irefn{org126}\And
T.P.~Trzcinski\Irefn{org142}\And
B.A.~Trzeciak\Irefn{org37}\textsuperscript{,}\Irefn{org63}\And
A.~Tumkin\Irefn{org109}\And
R.~Turrisi\Irefn{org57}\And
T.S.~Tveter\Irefn{org20}\And
K.~Ullaland\Irefn{org21}\And
E.N.~Umaka\Irefn{org125}\And
A.~Uras\Irefn{org135}\And
G.L.~Usai\Irefn{org23}\And
M.~Vala\Irefn{org38}\And
N.~Valle\Irefn{org139}\And
S.~Vallero\Irefn{org59}\And
N.~van der Kolk\Irefn{org63}\And
L.V.R.~van Doremalen\Irefn{org63}\And
M.~van Leeuwen\Irefn{org63}\And
P.~Vande Vyvre\Irefn{org34}\And
D.~Varga\Irefn{org145}\And
Z.~Varga\Irefn{org145}\And
M.~Varga-Kofarago\Irefn{org145}\And
A.~Vargas\Irefn{org45}\And
M.~Vasileiou\Irefn{org84}\And
A.~Vasiliev\Irefn{org88}\And
O.~V\'azquez Doce\Irefn{org105}\And
V.~Vechernin\Irefn{org113}\And
E.~Vercellin\Irefn{org25}\And
S.~Vergara Lim\'on\Irefn{org45}\And
L.~Vermunt\Irefn{org63}\And
R.~Vernet\Irefn{org7}\And
R.~V\'ertesi\Irefn{org145}\And
L.~Vickovic\Irefn{org35}\And
Z.~Vilakazi\Irefn{org131}\And
O.~Villalobos Baillie\Irefn{org111}\And
G.~Vino\Irefn{org53}\And
A.~Vinogradov\Irefn{org88}\And
T.~Virgili\Irefn{org29}\And
V.~Vislavicius\Irefn{org89}\And
A.~Vodopyanov\Irefn{org75}\And
B.~Volkel\Irefn{org34}\And
M.A.~V\"{o}lkl\Irefn{org103}\And
K.~Voloshin\Irefn{org92}\And
S.A.~Voloshin\Irefn{org143}\And
G.~Volpe\Irefn{org33}\And
B.~von Haller\Irefn{org34}\And
I.~Vorobyev\Irefn{org105}\And
D.~Voscek\Irefn{org117}\And
J.~Vrl\'{a}kov\'{a}\Irefn{org38}\And
B.~Wagner\Irefn{org21}\And
M.~Weber\Irefn{org114}\And
S.G.~Weber\Irefn{org144}\And
A.~Wegrzynek\Irefn{org34}\And
S.C.~Wenzel\Irefn{org34}\And
J.P.~Wessels\Irefn{org144}\And
J.~Wiechula\Irefn{org68}\And
J.~Wikne\Irefn{org20}\And
G.~Wilk\Irefn{org85}\And
J.~Wilkinson\Irefn{org10}\textsuperscript{,}\Irefn{org54}\And
G.A.~Willems\Irefn{org144}\And
E.~Willsher\Irefn{org111}\And
B.~Windelband\Irefn{org104}\And
M.~Winn\Irefn{org137}\And
W.E.~Witt\Irefn{org130}\And
J.R.~Wright\Irefn{org119}\And
Y.~Wu\Irefn{org128}\And
R.~Xu\Irefn{org6}\And
S.~Yalcin\Irefn{org77}\And
Y.~Yamaguchi\Irefn{org46}\And
K.~Yamakawa\Irefn{org46}\And
S.~Yang\Irefn{org21}\And
S.~Yano\Irefn{org137}\And
Z.~Yin\Irefn{org6}\And
H.~Yokoyama\Irefn{org63}\And
I.-K.~Yoo\Irefn{org17}\And
J.H.~Yoon\Irefn{org61}\And
S.~Yuan\Irefn{org21}\And
A.~Yuncu\Irefn{org104}\And
V.~Yurchenko\Irefn{org2}\And
V.~Zaccolo\Irefn{org24}\And
A.~Zaman\Irefn{org14}\And
C.~Zampolli\Irefn{org34}\And
H.J.C.~Zanoli\Irefn{org63}\And
N.~Zardoshti\Irefn{org34}\And
A.~Zarochentsev\Irefn{org113}\And
P.~Z\'{a}vada\Irefn{org66}\And
N.~Zaviyalov\Irefn{org109}\And
H.~Zbroszczyk\Irefn{org142}\And
M.~Zhalov\Irefn{org98}\And
S.~Zhang\Irefn{org40}\And
X.~Zhang\Irefn{org6}\And
Z.~Zhang\Irefn{org6}\And
V.~Zherebchevskii\Irefn{org113}\And
Y.~Zhi\Irefn{org12}\And
D.~Zhou\Irefn{org6}\And
Y.~Zhou\Irefn{org89}\And
Z.~Zhou\Irefn{org21}\And
J.~Zhu\Irefn{org6}\textsuperscript{,}\Irefn{org107}\And
Y.~Zhu\Irefn{org6}\And
A.~Zichichi\Irefn{org10}\textsuperscript{,}\Irefn{org26}\And
G.~Zinovjev\Irefn{org2}\And
N.~Zurlo\Irefn{org140}\And
\renewcommand\labelenumi{\textsuperscript{\theenumi}~}
\section*{Affiliation notes}
\renewcommand\theenumi{\roman{enumi}}
\begin{Authlist}
\item \Adef{org*}Deceased
\item \Adef{orgI}Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), Bologna, Italy
\item \Adef{orgII}Dipartimento DET del Politecnico di Torino, Turin, Italy
\item \Adef{orgIII}M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear, Physics, Moscow, Russia
\item \Adef{orgIV}Department of Applied Physics, Aligarh Muslim University, Aligarh, India
\item \Adef{orgV}Institute of Theoretical Physics, University of Wroclaw, Poland
\end{Authlist}
\section*{Collaboration Institutes}
\renewcommand\theenumi{\arabic{enumi}~}
\begin{Authlist}
\item \Idef{org1}A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia
\item \Idef{org2}Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine
\item \Idef{org3}Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India
\item \Idef{org4}Budker Institute for Nuclear Physics, Novosibirsk, Russia
\item \Idef{org5}California Polytechnic State University, San Luis Obispo, California, United States
\item \Idef{org6}Central China Normal University, Wuhan, China
\item \Idef{org7}Centre de Calcul de l'IN2P3, Villeurbanne, Lyon, France
\item \Idef{org8}Centro de Aplicaciones Tecnol\'{o}gicas y Desarrollo Nuclear (CEADEN), Havana, Cuba
\item \Idef{org9}Centro de Investigaci\'{o}n y de Estudios Avanzados (CINVESTAV), Mexico City and M\'{e}rida, Mexico
\item \Idef{org10}Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche ``Enrico Fermi', Rome, Italy
\item \Idef{org11}Chicago State University, Chicago, Illinois, United States
\item \Idef{org12}China Institute of Atomic Energy, Beijing, China
\item \Idef{org13}Comenius University Bratislava, Faculty of Mathematics, Physics and Informatics, Bratislava, Slovakia
\item \Idef{org14}COMSATS University Islamabad, Islamabad, Pakistan
\item \Idef{org15}Creighton University, Omaha, Nebraska, United States
\item \Idef{org16}Department of Physics, Aligarh Muslim University, Aligarh, India
\item \Idef{org17}Department of Physics, Pusan National University, Pusan, Republic of Korea
\item \Idef{org18}Department of Physics, Sejong University, Seoul, Republic of Korea
\item \Idef{org19}Department of Physics, University of California, Berkeley, California, United States
\item \Idef{org20}Department of Physics, University of Oslo, Oslo, Norway
\item \Idef{org21}Department of Physics and Technology, University of Bergen, Bergen, Norway
\item \Idef{org22}Dipartimento di Fisica dell'Universit\`{a} 'La Sapienza' and Sezione INFN, Rome, Italy
\item \Idef{org23}Dipartimento di Fisica dell'Universit\`{a} and Sezione INFN, Cagliari, Italy
\item \Idef{org24}Dipartimento di Fisica dell'Universit\`{a} and Sezione INFN, Trieste, Italy
\item \Idef{org25}Dipartimento di Fisica dell'Universit\`{a} and Sezione INFN, Turin, Italy
\item \Idef{org26}Dipartimento di Fisica e Astronomia dell'Universit\`{a} and Sezione INFN, Bologna, Italy
\item \Idef{org27}Dipartimento di Fisica e Astronomia dell'Universit\`{a} and Sezione INFN, Catania, Italy
\item \Idef{org28}Dipartimento di Fisica e Astronomia dell'Universit\`{a} and Sezione INFN, Padova, Italy
\item \Idef{org29}Dipartimento di Fisica `E.R.~Caianiello' dell'Universit\`{a} and Gruppo Collegato INFN, Salerno, Italy
\item \Idef{org30}Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy
\item \Idef{org31}Dipartimento di Scienze e Innovazione Tecnologica dell'Universit\`{a} del Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy
\item \Idef{org32}Dipartimento di Scienze MIFT, Universit\`{a} di Messina, Messina, Italy
\item \Idef{org33}Dipartimento Interateneo di Fisica `M.~Merlin' and Sezione INFN, Bari, Italy
\item \Idef{org34}European Organization for Nuclear Research (CERN), Geneva, Switzerland
\item \Idef{org35}Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia
\item \Idef{org36}Faculty of Engineering and Science, Western Norway University of Applied Sciences, Bergen, Norway
\item \Idef{org37}Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic
\item \Idef{org38}Faculty of Science, P.J.~\v{S}af\'{a}rik University, Ko\v{s}ice, Slovakia
\item \Idef{org39}Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universit\"{a}t Frankfurt, Frankfurt, Germany
\item \Idef{org40}Fudan University, Shanghai, China
\item \Idef{org41}Gangneung-Wonju National University, Gangneung, Republic of Korea
\item \Idef{org42}Gauhati University, Department of Physics, Guwahati, India
\item \Idef{org43}Helmholtz-Institut f\"{u}r Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universit\"{a}t Bonn, Bonn, Germany
\item \Idef{org44}Helsinki Institute of Physics (HIP), Helsinki, Finland
\item \Idef{org45}High Energy Physics Group, Universidad Aut\'{o}noma de Puebla, Puebla, Mexico
\item \Idef{org46}Hiroshima University, Hiroshima, Japan
\item \Idef{org47}Hochschule Worms, Zentrum f\"{u}r Technologietransfer und Telekommunikation (ZTT), Worms, Germany
\item \Idef{org48}Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania
\item \Idef{org49}Indian Institute of Technology Bombay (IIT), Mumbai, India
\item \Idef{org50}Indian Institute of Technology Indore, Indore, India
\item \Idef{org51}Indonesian Institute of Sciences, Jakarta, Indonesia
\item \Idef{org52}INFN, Laboratori Nazionali di Frascati, Frascati, Italy
\item \Idef{org53}INFN, Sezione di Bari, Bari, Italy
\item \Idef{org54}INFN, Sezione di Bologna, Bologna, Italy
\item \Idef{org55}INFN, Sezione di Cagliari, Cagliari, Italy
\item \Idef{org56}INFN, Sezione di Catania, Catania, Italy
\item \Idef{org57}INFN, Sezione di Padova, Padova, Italy
\item \Idef{org58}INFN, Sezione di Roma, Rome, Italy
\item \Idef{org59}INFN, Sezione di Torino, Turin, Italy
\item \Idef{org60}INFN, Sezione di Trieste, Trieste, Italy
\item \Idef{org61}Inha University, Incheon, Republic of Korea
\item \Idef{org62}Institute for Nuclear Research, Academy of Sciences, Moscow, Russia
\item \Idef{org63}Institute for Subatomic Physics, Utrecht University/Nikhef, Utrecht, Netherlands
\item \Idef{org64}Institute of Experimental Physics, Slovak Academy of Sciences, Ko\v{s}ice, Slovakia
\item \Idef{org65}Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India
\item \Idef{org66}Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic
\item \Idef{org67}Institute of Space Science (ISS), Bucharest, Romania
\item \Idef{org68}Institut f\"{u}r Kernphysik, Johann Wolfgang Goethe-Universit\"{a}t Frankfurt, Frankfurt, Germany
\item \Idef{org69}Instituto de Ciencias Nucleares, Universidad Nacional Aut\'{o}noma de M\'{e}xico, Mexico City, Mexico
\item \Idef{org70}Instituto de F\'{i}sica, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil
\item \Idef{org71}Instituto de F\'{\i}sica, Universidad Nacional Aut\'{o}noma de M\'{e}xico, Mexico City, Mexico
\item \Idef{org72}iThemba LABS, National Research Foundation, Somerset West, South Africa
\item \Idef{org73}Jeonbuk National University, Jeonju, Republic of Korea
\item \Idef{org74}Johann-Wolfgang-Goethe Universit\"{a}t Frankfurt Institut f\"{u}r Informatik, Fachbereich Informatik und Mathematik, Frankfurt, Germany
\item \Idef{org75}Joint Institute for Nuclear Research (JINR), Dubna, Russia
\item \Idef{org76}Korea Institute of Science and Technology Information, Daejeon, Republic of Korea
\item \Idef{org77}KTO Karatay University, Konya, Turkey
\item \Idef{org78}Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France
\item \Idef{org79}Laboratoire de Physique Subatomique et de Cosmologie, Universit\'{e} Grenoble-Alpes, CNRS-IN2P3, Grenoble, France
\item \Idef{org80}Lawrence Berkeley National Laboratory, Berkeley, California, United States
\item \Idef{org81}Lund University Department of Physics, Division of Particle Physics, Lund, Sweden
\item \Idef{org82}Nagasaki Institute of Applied Science, Nagasaki, Japan
\item \Idef{org83}Nara Women{'}s University (NWU), Nara, Japan
\item \Idef{org84}National and Kapodistrian University of Athens, School of Science, Department of Physics , Athens, Greece
\item \Idef{org85}National Centre for Nuclear Research, Warsaw, Poland
\item \Idef{org86}National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India
\item \Idef{org87}National Nuclear Research Center, Baku, Azerbaijan
\item \Idef{org88}National Research Centre Kurchatov Institute, Moscow, Russia
\item \Idef{org89}Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
\item \Idef{org90}Nikhef, National institute for subatomic physics, Amsterdam, Netherlands
\item \Idef{org91}NRC Kurchatov Institute IHEP, Protvino, Russia
\item \Idef{org92}NRC «Kurchatov Institute» - ITEP, Moscow, Russia
\item \Idef{org93}NRNU Moscow Engineering Physics Institute, Moscow, Russia
\item \Idef{org94}Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom
\item \Idef{org95}Nuclear Physics Institute of the Czech Academy of Sciences, \v{R}e\v{z} u Prahy, Czech Republic
\item \Idef{org96}Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States
\item \Idef{org97}Ohio State University, Columbus, Ohio, United States
\item \Idef{org98}Petersburg Nuclear Physics Institute, Gatchina, Russia
\item \Idef{org99}Physics department, Faculty of science, University of Zagreb, Zagreb, Croatia
\item \Idef{org100}Physics Department, Panjab University, Chandigarh, India
\item \Idef{org101}Physics Department, University of Jammu, Jammu, India
\item \Idef{org102}Physics Department, University of Rajasthan, Jaipur, India
\item \Idef{org103}Physikalisches Institut, Eberhard-Karls-Universit\"{a}t T\"{u}bingen, T\"{u}bingen, Germany
\item \Idef{org104}Physikalisches Institut, Ruprecht-Karls-Universit\"{a}t Heidelberg, Heidelberg, Germany
\item \Idef{org105}Physik Department, Technische Universit\"{a}t M\"{u}nchen, Munich, Germany
\item \Idef{org106}Politecnico di Bari, Bari, Italy
\item \Idef{org107}Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum f\"ur Schwerionenforschung GmbH, Darmstadt, Germany
\item \Idef{org108}Rudjer Bo\v{s}kovi\'{c} Institute, Zagreb, Croatia
\item \Idef{org109}Russian Federal Nuclear Center (VNIIEF), Sarov, Russia
\item \Idef{org110}Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India
\item \Idef{org111}School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom
\item \Idef{org112}Secci\'{o}n F\'{\i}sica, Departamento de Ciencias, Pontificia Universidad Cat\'{o}lica del Per\'{u}, Lima, Peru
\item \Idef{org113}St. Petersburg State University, St. Petersburg, Russia
\item \Idef{org114}Stefan Meyer Institut f\"{u}r Subatomare Physik (SMI), Vienna, Austria
\item \Idef{org115}SUBATECH, IMT Atlantique, Universit\'{e} de Nantes, CNRS-IN2P3, Nantes, France
\item \Idef{org116}Suranaree University of Technology, Nakhon Ratchasima, Thailand
\item \Idef{org117}Technical University of Ko\v{s}ice, Ko\v{s}ice, Slovakia
\item \Idef{org118}The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland
\item \Idef{org119}The University of Texas at Austin, Austin, Texas, United States
\item \Idef{org120}Universidad Aut\'{o}noma de Sinaloa, Culiac\'{a}n, Mexico
\item \Idef{org121}Universidade de S\~{a}o Paulo (USP), S\~{a}o Paulo, Brazil
\item \Idef{org122}Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil
\item \Idef{org123}Universidade Federal do ABC, Santo Andre, Brazil
\item \Idef{org124}University of Cape Town, Cape Town, South Africa
\item \Idef{org125}University of Houston, Houston, Texas, United States
\item \Idef{org126}University of Jyv\"{a}skyl\"{a}, Jyv\"{a}skyl\"{a}, Finland
\item \Idef{org127}University of Liverpool, Liverpool, United Kingdom
\item \Idef{org128}University of Science and Technology of China, Hefei, China
\item \Idef{org129}University of South-Eastern Norway, Tonsberg, Norway
\item \Idef{org130}University of Tennessee, Knoxville, Tennessee, United States
\item \Idef{org131}University of the Witwatersrand, Johannesburg, South Africa
\item \Idef{org132}University of Tokyo, Tokyo, Japan
\item \Idef{org133}University of Tsukuba, Tsukuba, Japan
\item \Idef{org134}Universit\'{e} Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
\item \Idef{org135}Universit\'{e} de Lyon, Universit\'{e} Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne, Lyon, France
\item \Idef{org136}Universit\'{e} de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France, Strasbourg, France
\item \Idef{org137}Universit\'{e} Paris-Saclay Centre d'Etudes de Saclay (CEA), IRFU, D\'{e}partment de Physique Nucl\'{e}aire (DPhN), Saclay, France
\item \Idef{org138}Universit\`{a} degli Studi di Foggia, Foggia, Italy
\item \Idef{org139}Universit\`{a} degli Studi di Pavia, Pavia, Italy
\item \Idef{org140}Universit\`{a} di Brescia, Brescia, Italy
\item \Idef{org141}Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India
\item \Idef{org142}Warsaw University of Technology, Warsaw, Poland
\item \Idef{org143}Wayne State University, Detroit, Michigan, United States
\item \Idef{org144}Westf\"{a}lische Wilhelms-Universit\"{a}t M\"{u}nster, Institut f\"{u}r Kernphysik, M\"{u}nster, Germany
\item \Idef{org145}Wigner Research Centre for Physics, Budapest, Hungary
\item \Idef{org146}Yale University, New Haven, Connecticut, United States
\item \Idef{org147}Yonsei University, Seoul, Republic of Korea
\end{Authlist}
\endgroup
\section*{Acknowledgements}
\input{fa_2020-05-04.tex}
\end{acknowledgement}
\bibliographystyle{utphys}
|
{
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\section{Introduction}
Capturing the semantic relationship between two concepts is a fundamental operation for many semantic interpretation tasks. This is a task which humans perform rapidly and reliably by using their linguistic and commonsense knowledge about entities and relations. Natural language processing systems which aspire to reach the goal of producing meaningful representations of text must be equipped to identify and learn semantic relations in the documents they process.
The automatic recognition of semantic relations has many applications such as information extraction, document summarization, machine translation, or the construction of thesauri and semantic networks. It can also facilitate auxiliary tasks such as word sense disambiguation, language modeling, paraphrasing, and recognizing textual entailment \cite{hendrickx2009semeval}.
However it is not always possible to establish a direct semantic relation given two entity mentions in text. In the Semeval 2010 Task 8 test collection \cite{hendrickx2009semeval} for example 17.39\% of the semantic relations mapped within sentences were assigned with the label \textit{"OTHER"}, meaning that they could not be mapped to the set of 9 direct semantic relations \footnote{Cause-Effect, Instrument-Agency, Product-Producer, Content-Container, Entity-Origin, Entity-Destination, Component-Whole, Member-Collection, Communication-Topic}.
In many cases, the semantic relations between two entities can only be expressed by a composition of two or more operations. This work aims at improving the description and the formalization of the semantic relation classification task by introducing the concept of composite semantic relation classification, in which the relations between entities can be expressed using the composition of one or more relations.
This paper is organized as follows: Section \ref{csrc} describes the semantic relation classification problem and the related work followed by the proposed composite semantic relation classification (Section \ref{proposed}), Section \ref{baseline} describes the
existing baseline models; while Section \ref{evaluation} describes the experimental setup and analyses the results, providing a comparative analysis between the proposed model and the baselines. Finally, Section \ref{Conclusion} provides the conclusion.
\section{Composite Semantic Relation Classification}\label{csrc}
\subsection{Semantic Relation Classification}
Semantic relation classification is the task of classifying the underlying abstract semantic relations between target entities (terms) present in texts \cite{qin2016empirical}. The goal of relation classification is defined as follows: given a sentence $S$ with the pairs of annotated target nominals $e_1$ and $e_2$, the relation classification system aims to classify the relations between $e_1$ and $e_2$ in given texts within the pre-defined relation set \cite{hendrickx2009semeval}. For instance, the relation between the nominal \textbf{burst} and \textbf{pressure} in the following example sentence is interpreted as \textbf{Cause-Effect($e_2, e_1$)}.
\begin{displayquote}
The $<e_1>burst</e_1>$ has been caused by water hammer $<e_2>pressure</e_2>$.
\end{displayquote}
\subsection{Existing Approaches for Semantic Relation Classification}
Different approaches have been explored for relation classification, including unsupervised relation discovery and supervised classification. Existing literature have proposed various features to identify the relations between entities using different methods.
Recently, {Neural network-based approaches} have achieved significant improvement over traditional methods based on either human-designed features\cite{qin2016empirical}. However, existing neural networks for relation classification are usually based on shallow architectures (e.g., one-layer convolutional neural networks or recurrent networks). In exploring the potential representation space at different abstraction levels, they may fail to perform\cite{xu2016improved}.
The performance of supervised approaches strongly depends on the quality of the designed features \cite{zeng2014relation}. With the recent improvement in Deep Neural Network (DNN), many researchers are experimenting with unsupervised methods for automatic feature learning. \cite{xu2015classifying} introduce gated recurrent networks, in particular, Long short-term memory (LSTM), to relation classification. \cite{zeng2014relation} use Convolutional Neural Network (CNNs). Additionally, \cite{dos2015classifying} replace the common Softmax loss function with a ranking loss in their CNN model. \cite{xu2015semantic} design a negative sampling method based on CNNs. From the viewpoint of model ensembling, \cite{liu2015dependency} combine CNNs and recursive networks along the Shortest Dependency Path (SDP), while \cite{nguyen2015combining} incorporate CNNs with Recurrent Neural Networks (RNNs).
Additionally, much effort has been invested in relational learning methods that can scale to large knowledge bases. The best performing neural-embedding models are Socher(NTN)\cite{socher2013reasoning} and Bordes models (TransE and TATEC) \cite{bordes2013translating,garcia2016combining}.
\section{From Single to Composite Relation Classification} \label{proposed}
\subsection{Introduction}
The goal of this work is to propose an approach for semantic relation classification using one or more relations between term mentions/entities.
\begin{displayquote}
"The $<e_1>child</e_1>$ was carefully wrapped and bound into the $<e_2>cradle</e_2>$ by means of a cord."
\end{displayquote}
In this example, the relationship between $Child$ and $Cradle$ cannot be directly expressed by one of the nine abstract semantic relations from the set described in \cite{hendrickx2009semeval}.
However, looking into a commonsense KB (in this case, ConceptNet V5.4) we can see the following set of composite relations between these elements:
\begin{displayquote}
$<e_1>child</e_1>$ $createdby \circ causes \circ atlocation$ $<e_2>cradle</e_2>$
\end{displayquote}
As you increase the number of edges that you can include in the set of semantic relations compositions (the size of the semantic relationship path), there is a dramatic increase in the number of paths which connect the two entities. For example, for the words $Child$ and $Cradle$ there are 15 paths of size 2, 1079 paths of size 3 and 95380 paths of size 4. Additionally, as the path size grows many non-relevant relationships (less meaningful relations) will be included.
The challenge in \textit{composite semantic relation classification} is to provide a classification method that provides the most meaningful set of relations for the context at hand. This task can be challenging because, as previously mentioned, a simple KB lookup based approach would provide all semantic associations at hand.
To achieve this goal we propose an approach which combines \textit{sequence machine learning models}, \textit{distributional semantic models} and \textit{commonsense relations knowledge bases} to provide an accurate method for composite semantic relation classification.
The proposed model (Fig \ref{fig:proposed_model}) relies on the combination of the following approaches:
\begin{enumerate}[label=\roman*]
\item Use existing structured commonsense KBs define an initial set of semantic relation compositions.
\item Use a pre-filtering method based on the Distributional Navigational Algorithm (DNA) as proposed by \cite{freitas2014distributional}
\item Use sequence-based Neural Network based model to quantify the sequence probabilities of the semantic relation compositions. We call this model Neural Concept/Relation Model, in analogy to a Language Model.
\end{enumerate}
\begin{figure}[ht]
\centering
\includegraphics[height=6.2cm]{CSRC_Chart.eps}
\caption{Depiction of the proposed model relies on the combination of the our three approaches}
\label{fig:proposed_model}
\end{figure}
\subsection{Commonsense KB Lookup}\label{commensense_KB}
The first step consists in the use of a large commonsense knowledge base for providing a reference for a sequence of semantic relations. ConceptNet is a semantic network built from existing linguistic resources and crowd-sourced. It is built from nodes representing words or short phrases of natural language, and labeled abstract relationships between them.
1094 paths were extracted from ConceptNet with two given entities (e.g. $child$ and $cradle$) with no corresponding semantic relation from the Semeval 2010 Task 8 test collection (Figure \ref{fig:proposed_model}(i)). Examples of paths are:
\begin{itemize}
\item \textbf{child/canbe/baby/atlocation/cradle}
\item child/isa/animal/hasa/baby/atlocation/cradle
\item child/hasproperty/work/causesdesire/rest/synonym/cradle
\item child/instanceof/person/desires/baby/atlocation/cradle
\item child/desireof/run/causesdesire/rest/synonym/cradle
\item \textbf{child/createdby/havesex/causes/baby/atlocation/cradle}
\end{itemize}
\subsection{Distributional Navigational Algorithm (DNA)}
The Distributional Navigational Algorithm (DNA) consists of an approach which uses distributional semantic models as a relevance-based heuristic for selecting relevant facts attached to a contextual query. The approach focuses on addressing the following problems: (i) providing a semantic selection mechanism for facts which are relevant and meaningful in a particular reasoning \& querying context and (ii) allowing coping with information incompleteness in a huge KBs.
In \cite{freitas2014distributional} DSMs are used as a complementary semantic layer to the relational model, which supports coping with semantic approximation and incompleteness.
For large-scale and open domain commonsense reasoning scenarios, model completeness, and full materialization cannot be assumed. A commonsense KB would contain vast amounts of facts, and a complete inference over the entire KB would not scale to its size. Although several meaningful paths may exist between two entities, there are a large number of paths which are not meaningful in a specific context. For instance, the reasoning path which goes through (1) is not related to the goal of the entity pairs (the relation between $Child$ of human and $Cradle$) and should be eliminated by the application of the Distributional Navigation Algorithm (DNA) \cite{freitas2014distributional}, which computes the distributional semantic relatedness between the entities and the intermediate entities in the KB path as a measure of semantic coherence. In this case the algorithm navigates from $e1$ in the direction of $e2$ in the KB using distributional semantic relatedness between the target node $e2$ and the intermediate nodes $en$ as a heuristic method.
\begin{figure}[ht]
\centering
\includegraphics[height=5.2cm]{DNA.eps}
\caption{Selection of meaningful paths}
\label{exampleKB}
\end{figure}
\subsection{Neural Entity/Relation Model}
The Distributional Navigational Algorithm provides a pre-filtering of the relations maximizing the semantic relatedness coherence. This can be complemented by a predictive model which takes into account the likelihood of a sequence of relations, i.e. the likelihood of a composition sequence. The goal is to systematically compute the sequence of probabilities of a relation composition, in a similar fashion to a language model. For this purpose we use a Long short-term memory (LSTM) recurrent neural network architecture (Figure \ref{fig:LSTM}) \cite{hochreiter1997long}.
\begin{figure}[ht]
\centering
\includegraphics[height=12.2cm]{LSTM.eps}
\caption{The LSTM-CSRC architecture}
\label{fig:LSTM}
\end{figure}
\begin{algorithm}[ht]
\caption{Composite Semantic Relation Classification}
\label{euclid}
\begin{algorithmic}
\State $I : $ \textit{sentences of semeval 2010-Task 8 dataset}
\State $O : $ \textit{predefined entity pairs ($e_1$, $e_2$)}
\State $W :$ \textit{words in I}
\State $R :$ \textit{related relations of $w$}
\ForAll{$s \in I$}:
\State $S \gets $ \textit{If entities of} $s$ \textit{are connected in a } $OTHER$ \textit{ relation}
\EndFor
\ForAll{$s \in S$}:
\State $ ep \gets$ \textit{predefined entity pairs of }$ s $
\State $ p \gets $ \textit{find all path of} $ ep $ \textit{in ConceptNet (with maximum paths of size 3)}
\ForAll{$i \in p$}:
\State $sq_i \gets $ \textit{avg similarity score between each word pairs \cite{barzegar2015dinfra} }
\EndFor
\State $ msq \gets$ \textit{find max } $sq$
\ForAll{$i \in p$}:
\State \textit{filter } $i$ \textit{ If } $sq_i <$ $msq$ - $\frac{msq}{2}$
\EndFor
\State $ dw \gets $ \textit{convert } $s$ \textit{ into suitable format for deep learning}
\EndFor
\State $ model \gets$ \textit{learning LSTM with } $dw$ \textit{ dataset}
\end{algorithmic}
\end{algorithm}
\section{Baseline Models}\label{baseline}
As baselines we use bigram language models which define the conditional probabilities between a sequence of semantic relations $r$ after entities $e$, i.e. $P(r \mid e)$.
The performance of baselines systems is measured using the \textit{CSRC\footnote{Composite Semantic Relation Classification} $Cloze$ task}, as defined in section \ref{cloze} where we hold out the last relation and rate a system by its ability to infer this relation.
\begin{itemize}
\item \textbf{Random Model: } This is the simplest baseline, which outputs randomly selected relation pairs.
\item \textbf{Unigram Model: } Predicts the next relation based on unigram probability of each relation which was calculated from the training set. In this model, relations are assumed to occur independently.
\item \textbf{Single Model: }
The single model is defined by \cite{jans2012skip}:
\begin{equation} \label{eq1}
\begin{split}
P(r\mid e) = \frac{P(r, e)}{P(e)}
\end{split}
\end{equation}
where $P(r \mid e)$ is the probability of seeing $e$ and $r$, in order.
Let $A$ be an ordered list of relations and entities, $\left | A \right |$ is the length of R, For $i = 1, .., \left | A \right |$, define $a_i$ to be the $ith$ element of A. We rank candidate relations r by maximizing F(r,a), defined as
\begin{equation} \label{eq2}
\begin{split}
F(r,a)= \sum_{i=1}^{\left | A \right |-1} log P(r \mid a_i) \end{split}
\end{equation}
where the conditional probabilities $P(r \mid a_i)$ calculated using (1).
\item \textbf{Random Forest: } is an ensemble learning method for classification and other tasks, that operate by constructing a multitude of decision trees at training time and outputting the class that is the mode of the classes. Random decision forests correct for decision trees' habit of overfitting to their training set.
\end{itemize}
\section{Experimental Evaluation}\label{evaluation}
\subsection{Training and Test Dataset} \label{cloze}
The evaluation dataset was generated by collecting all pairs of entity mentions in the Semeval 2010 task 8 \cite{hendrickx2009semeval} which had no attached semantic relation classification (i.e. which contained the relation label \textit{"OTHER"}).
For all entities with unassigned relation labels, we did a $Conceptnet$ lookup \cite{speer2012representing}, where we generated all paths from sizes 1, 2 and 3 (number of relations) occurring between both entities($e_1$ and $e_2$) and their relations ($R$).
For example:\\
$\textbf{e1} - R1_i - \textbf{e2}$ \\
$\textbf{e1} - R1_i - \textbf{X1}_n - R2_j - \textbf{e2}$ \\
$\textbf{e1} - R1_i - \textbf{X1}_n -R2_j - \textbf{X2}_m - R3_k - \textbf{e2}$
where $X$ contains the intermediate entities between the target entity mentions \textbf{e1} and \textbf{e2}.
In next step, the Distributional Navigational Algorithm (DNA) is applied over the entity paths\cite{freitas2014distributional}. In the final step of generating training \& test datasets, the best paths are selected manually out of filtered path sets.
From 602 entity pairs assigned to the \textit{"OTHER"} relation label in Semeval, we found $27,415$ paths between $405$ entity pairs in ConceptNet. With the Distributional Navigation Algorithm (DNA), meaningless paths were eliminated, and after filtering, we have $2,514$ paths for $405$ entity-pairs.
Overall we have $41$ relations and $964$ entities. All paths were converted into the following format which will be input into the neural network: $\textbf{e}_1 - R1_i - \textbf{X1}_n -R2_j - \textbf{X2}_m - R3_k - \textbf{e}_2 $ (Table \ref{Training1}).
\begin{table}[ht]
\caption{Training data-set for CSRC model}
\label{Training1}
\begin{center}
\begin{tabular}{|l|l|}
\hline
input & Classification \\ \hline
$\textbf{e}_1$ $\textbf{e}_2$ $\textbf{X1}_n $ & $\textcolor{blue}{\textbf{R1}_i}$ \\ \hline
$\textbf{e}_1$ $\textbf{e}_2$ $\textbf{X2}_m$ $\textbf{X1}_n$ $\textcolor{blue}{\textbf{R1}_i}$ & $\textcolor{blue}{\textbf{R2}_i}$ \\ \hline
$\textbf{e}_1$ $\textbf{e}_2$ $\textbf{X2}_m$ $\textcolor{blue}{\textbf{R2}_i}$ $\textbf{X1}_n$ $\textcolor{blue}{\textbf{R1}_i} $ & $\textcolor{blue}{\textbf{R3}_i}$ \\ \hline
\end{tabular}
\end{center}
\end{table}
We provide statistics for the generated datasets in the Tables \ref{test-baseline} and \ref{Trainingdataset}. In Table \ref{Trainingdataset} our dataset is divided into a training set and a test set with scale ($75-25\%$), also we used $25$ percent of the training set for cross-validation, $3120$ examples for training, $551$ for validation and $1124$ for testing. Table \ref{test-baseline} shows statistics for test dataset of baseline models.
\begin{table}[ht]
\caption{Number of different length in the test dataset for baseline models}
\label{test-baseline}
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
Test Dataset & \# Length 2 & \# Length 4 & \# Length 6 \\ \hline
Baselines & 245 & 391 & 432 \\ \hline
\end{tabular}
\end{center}
\end{table}
\begin{table}[ht]
\caption{Dataset for LSTM model}
\label{Trainingdataset}
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
Dataset & \# Train & \# Dev & \# Test \\ \hline
CSRC & 3120 & 551 & 1124 \\ \hline
\end{tabular}
\end{center}
\end{table}
\subsection{Results}
To achieve the classification goal, we generated a LTSM model for the composite relation classification task. In our experiments, a batch size 25, and epoch 50 was generated. An embedding layer using Word2Vec pre-trained vectors was used.
In our experiment, we optimized the hyperparameters of the LSTM model. After several experiments, the best model is generated with:
\begin{itemize}
\item Inputs length and dimension are $6$ and $303$, respectively.
\item Three hidden layers with $450$, $200$ and $100$ nodes and $Tanh$ activation,
\item Dropout technique ($0.5$),
\item $Adam$ optimizer.
\end{itemize}
We experimented our LSTM model with three different pre-training embedding word vector models:
\begin{itemize}
\item Word2Vec (Google News) with 300 dimensions
\item Word2Vec (Wikipedia 2016) with 30 dimensions
\item No pre-training word embedding
\end{itemize}
The accuracy for the configuration above after 50 epochs is shown in the table below.
\begin{table}[ht]
\caption{Validation Accuracy}
\label{Accuracy}
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
CRSC & W2V Google\_News & W2V Wikipedia & No Pre Training \\ \hline
Accuracy & 0.4208 & 0.3841 & 0.2196 \\ \hline
\end{tabular}
\end{center}
\end{table}
Table \ref{evaluation_results} contains the Precision, Recall, F1-Score and Accuracy.
\begin{table}[!htbp]
\caption{\label{evaluation_results}Evaluation results on baseline models and our approach, with four metrics}
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
Method & Recall & Precision & F1 Score & Accuracy \\ \hline
Random & 0.0160 & 0.0220 & 0.0144 & 0.0234 \\ \hline
Unigram & 0.0270 & 0.0043 & 0.0074 & 0.1606 \\ \hline
Single & 0.2613& 0.2944 & 0.2502 & 0.3793 \\ \hline
Random Forest & 0.2476 & \textbf{0.3663} & 0.2766 & 0.3299 \\ \hline
\textbf{LSTM-CSRC} & \textbf{0.3073} & 0.3281 & \textbf{0.3119} & \textbf{0.4208} \\ \hline
\end{tabular}
\end{center}
\end{table}
Between the evaluated models, the LSTM-CSRC achieved the highest F1 Score and Accuracy. The Single model achieved the second highest accuracy $0.3793$ followed by Random forest model $0.3299$. The LSTM approach provides an improvement of 9.86 \% on accuracy over the baselines, and 11.31 \% improvement on the F1-score. Random Forest achieved the highest precision, while LSTM-CSRC achieved the highest recall.
The extracted information from confusion matrix show in Tables \ref{ConfusionPart1} and \ref{ConfusionPart2}.
\begin{table}[ht]
\caption{The extracted information from Confusion Matrix - Part 1}
\label{ConfusionPart1}
\begin{center}
\resizebox{\textwidth}{!}{
\begin{tabular}{|l|l|l||l|l|l|}
\hline
Relation & \shortstack{ \# Correct \\ Predicted} & \shortstack{\# Correct \\Predicted Rate} & Relation & \shortstack{ \# Correct \\ Predicted}& \shortstack{\# Correct \\Predicted Rate} \\ \hline
notisa & 2 & 1 & memberof & 1 & 0.5 \\ \hline
atlocation & 172 & 0.67 & hasa & 24 & 0.393 \\ \hline
notdesires & 6 & 0.666 & hassubevent & 12 & 0.378 \\ \hline
similar & 5 & 0.625 & partof & 16 & 0.374 \\ \hline
desires & 36 & 0.593 & haspropertry & 12 & 0.375 \\ \hline
hasprerequest & 23 & 0.547 & sysnonym & 54 & 0.312 \\ \hline
causesdesire & 17 & 0.548 & derivedfrom & 20 & 0.307 \\ \hline
isa & 147 & 0.492 & etymologicallyderivedfrom & 6 & 0.3 \\ \hline
antonym & 68 & 0.492 & capableof & 13 & 0.26 \\ \hline
instandof & 46 & 0.479 & motivationbygoal & 3 & 0.25 \\ \hline
usedfor & 47 & 0.475 & receivsection & 5 & 0.238 \\ \hline
desireof & 5 & 0.5 & createdby & 4 & 0.2 \\ \hline
hascontext & 2 & 0.5 & madeof & 3 & 0.16 \\ \hline
haslastsubevent & 2 & 0.5 & causes & 3 & 0.15 \\ \hline
nothasa & 1 & 0.5 & genre & 1 & 0.11 \\ \hline
\end{tabular}}
\end{center}
\end{table}
\begin{table}[ht]
\caption{The extracted information from Confusion Matrix - Part 2}
\label{ConfusionPart2}
\begin{center}
\resizebox{\textwidth}{!}{\begin{tabular}{|l|l|l|||l|l||l|l||l|l|}
\hline
Relation & \shortstack{\# Correct \\ Predicted} & Rate &\shortstack{Wrong\\ Relation 1} & \shortstack{\# False\\ Predicted \\ for \\Relation 1}&\shortstack{Wrong \\Relation 2} & \shortstack{\# False \\Predicted\\ for \\Relation 2 }& \shortstack{Wrong \\Relation 3 } & \shortstack{\# False \\Predicted \\for\\ Relation 3} \\ \hline
atlocation & 172 & 0.67 & antonym & 20 & Usedfor & 17 & & \\ \hline
desire & 36 & 0.593 & isa & 6 & Capableof & 6 & Usedfor & 5 \\ \hline
hasprerequest & 23 & 0.547 & sysnonymy & 4 & antonym & 3 & atlocation & 2 \\ \hline
causesdesire & 17 & 0.548 & usedfor & 7 & & & & \\ \hline
isa & 147 & 0.492 & atlocation & 26 & antonym & 22 & instanceof & 22 \\ \hline
antonym & 68 & 0.492 & isa & 17 & atlocation & 9 & & \\ \hline
instandof & 46 & 0.479 & isa & 27 & atlocation & 8 & & \\ \hline
usedfor & 47 & 0.475 & atlocation & 26 & isa & 18 & & \\ \hline
hasa & 24 & 0.393 & antonym & 11 & usedfor & 6 & & \\ \hline
hassubevent & 12 & 0.378 & causes & 5 & antonym & 4 & & \\ \hline
partof & 16 & 0.374 & synonym & 12 & antonym & 3 & hasproperty & 3 \\ \hline
haspropertry & 12 & 0.375 & isa & 8 & & & & \\ \hline
sysnonym & 54 & 0.312 & isa & 31 & hasproperty & 17 & atlocation & 12 \\ \hline
derivedfrom & 20 & 0.307 & isa & 10 & sysnonym & 8 &\shortstack{etymologically-\\derivedfrom} & 8 \\ \hline
\shortstack{etymologically-\\derivedfrom} & 6 & 0.3 & derivedfrom & 6 & & & & \\ \hline
capableof & 13 & 0.26 & usedfor & 13 & isa & 7 & & \\ \hline
motivatedbygoal & 3 & 0.25 & causes & 3 & hassubevent & 2 & & \\ \hline
receivsection & 5 & 0.238 & atlocation & 9 & usedfor & 3 & & \\ \hline
createdby & 4 & 0.2 & antonym & 6 & isa & 5 & & \\ \hline
madeof & 3 & 0.16 & isa & 7 & antonym & 3 & hsaa & 2 \\ \hline
causes & 3 & 0.15 & causesdesire & 6 & hassubevent & 4 & derivedfrom & 3 \\ \hline
\end{tabular}}
\end{center}
\end{table}
At table \ref{ConfusionPart1} \textit{'Correctly Predicted'} column indicates the proportion of relations are predicted correctly, and \textit{'Correct Prediction Rate'} column indicates the rate of correct predicted. For instance, our model predicts the relation $notisa$ 100 percent correct.
Table \ref{ConfusionPart2} shows the relations which are wrongly predicted (\textit{'Wrongly Predicted'} columns).
Based on the results, the most incorrectly predicted relation is $'isa'$, which accounts for a large proportion of relations of the dataset (around 150 out of 550). In the second place is $'atlocation'$ relation (172 out of 550). The third place is the $'antonym'$ relation. On the other hand, some relations which are correctly unpredicted, can be treated as semantically equivalent to their prediction, where the assignment is dependent on a modelling decision. The same situation occurs for $'etymologicallyderivedfrom'$ and $'derivedfrom'$ relations. \\ Another issue is the low number of certain relations expressed int he dataset.
\section{Conclusion}\label{Conclusion}
In this paper we introduced the task of composite semantic relation classification. The paper proposes a composite semantic relation classification model which combines \textit{commonsense KB lookup}, a \textit{distributional semantic based filter} and the application of a \textit{sequence machine learning model} to address the task. The proposed LSTM model outperformed existing baselines with regard to f1-score, accuracy and recall. Future work will focus on increasing the volume of the training set for under-represented relations.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 965
|
\section{Introduction}
\label{Introduction}
Cadmium telluride (CdTe) is becoming an increasingly important II-VI semiconductor that can be obtained
with both $n$- and $p$-type conductivity \cite{Segall63,Khattak91,Basol87,Hofmann92}. Its main applications include room temperature $x$-ray and $\gamma$-ray detectors, medical imaging, nuclear safeguards, and thin-film solar cells \cite{Szeles04,Schlesinger01,Shah99}. CdTe has a high optical absorption coefficient and a near-ideal direct band gap of $\sim$1.5 eV at room temperature, which is optimum for solar energy conversion. However, native defects and impurities usually form compensating donors and acceptors that decrease both carrier concentration, and lifetime \cite{hage1992,fiederle1994,Krsmanovic00}. Consequently, controlled doping with Cu \cite{Kranz13,Korevaar14,Yang16_1} and Cl \cite{Metzger06,Li13} is commonly used to enhance hole density and carrier lifetime. Furthermore, deep levels may act as recombination centers that are detrimental to electron transport, thereby degrading the performance of solar cells and high-energy radiation detectors.
High resistivity of undoped CdTe has been associated with the Fermi level pinning near midgap by a native deep donor, which is usually assumed to be tellurium antisite $(\text{Te}_\text{Cd})$ or interstitial tellurium $(\text{Te}_\text{i})$ \cite{Chu01,Fiederle04,Babentsov09,Ma13}, considering that CdTe is normally grown in a Te-rich environment. However, theoretical results show that $(\text{Te}_\text{Cd})$ induces a gap level that is too shallow to pin the Fermi level close to the midgap \cite{Chu01,Fiederle98,Du08}, whereas $(\text{Te}_\text{i})$ has higher formation energy than $(\text{Te}_\text{Cd})$ in the Te-rich limit \cite{Yang14}. Moreover, the 1.1-eV band usually observed in luminescence and absorption experiments, remains as an unresolved issue. In 1968, Bryant and Webster \cite{Bryant68} associated it to the Te vacancy, but theory has not yet confirmed this.
The theoretical description of defects and impurities in semiconductors is currently performed in the framework of the density functional theory (DFT), which reduces the many-electron problem to an effective single-electron problem. In principle, DFT provides an exact formulation to calculate ground-state properties, but it fails to predict the band gaps of semiconductors and insulators as there is no theoretical support for interpreting the eigenvalues from the Kohn-Sham equations as quasiparticle energies. Moreover, neglecting correlation effects can give qualitatively incorrect results for systems with partially filled electronic $d$ or $f$ shells. Additionally, the self-interaction error artificially raises the position of the valence band maximum (VBM) \cite{Gruneis14,Du15,Freysoldt16} and may lead to unreliable defect-level positions in the band gap. This is particularly severe for deep defect levels such as $(\text{Te}_\text{Cd})$. All these limitations involved in DFT calculations make them not reliable to evaluate defect properties, such as formation energies and charge transition levels \cite{Biswas11,Petretto15}. On the other hand, the \emph{GW} formalism \cite{Hedin65,Hybertsen85}, which describes the interaction of weakly correlated
quasiparticles by means of a nonlocal energy-dependent self-energy, can give accurate quasiparticle band structures of solids \cite{Zakharov94,Klimes14}.
Early DFT calculations of native defects in CdTe suggest that $(\text{Te}_\text{Cd})$ is stable in $(+2)$, $(+1)$, and neutral charge states \cite{Berding99,S-Huai02}. Du \emph{et al.} \cite{Du08_2} have found that (Te$_\text{Cd}$) exhibits a negative-U behavior with a (+2/0) transition level at VBM + 0.35 eV. On the other hand, Carvalho \emph{et al.} \cite{Carvalho10} using the local spin density approximation (LSDA) found no negative-U effect. More recent calculations employing hybrid functionals that mix a fraction of Hartree-Fock (HF) exchange with local or semilocal exchange-correlation functionals also show serious discrepancies. Yang and co-workers \cite{Yang14}, Lordi \cite{Lordi13}, and Lindstr\"{o}m \emph{et al.} \cite{Lindstrom16} have found a negative-U behavior in (Te$_\text{Cd}$). In contrast, Biswas and Du \cite{Biswas12} have pointed out that $(\text{Te}_\text{Cd})$ is a deep donor with (+2/+) and (+/0) transition levels at VBM + 0.38 eV and VBM + 0.58 eV, respectively.
In order to investigate these large discrepancies among theoretical calculations, in the present work we investigate the formation energies, charge transition levels and quasiparticle defect states of $(\text{Te}_\text{Cd})$ in CdTe using the state-of-the-art DFT$\hspace{0.05cm}+\hspace{0.05cm}$\emph{GW} formalism \cite{Hedstrom06,Rinke09,Malashevich14,Flores15_1}, which is free of the well-known band gap error of DFT. According to our results, $(\text{Te}_\text{Cd})$ induces a deep level at VBM + 0.99 eV, exhibiting a negative-U effect. Moreover, the optical excitation of the $(\text{Te}_\text{Cd})^0$ configuration to the positively charged state, followed by the capture of an electron from the conduction bands is consistent with the 1.1-eV center observed in both absorption \cite{Davis93} and photoluminescence (PL) \cite{Bryant68} measurements at cryogenic temperatures.
\section{Methods}
\vspace{0.1cm}
\subsection{Computational methods}
\vspace{0.3cm}
Our DFT calculations were performed using the Quantum-ESPRESSO code \cite{Giannozzi2009}. Electron-ion interactions were described by GBRV ultrasoft pseudopotentials \cite{Garrity2014}, whereas the generalized gradient approximation to the exchange and correlation functional of Perdew, Burke, and Ernzerhof (PBE) \cite{Perdew96} was employed. A kinetic energy cutoff of 36 Ry for the plane-wave basis set expansion and 200 Ry to represent the charge density were used. To avoid finite-size effects as much as possible, the defect calculations were performed within large 512-atom cubic supercells. The atomic structures were relaxed until the Hellmann-Feynman forces were less than 0.001 Ry/bohr. The \textbf{k}-point sampling was restricted to the $\Gamma$ point.
Many-body $G_0W_0$ calculations with defect supercells were performed using the WEST code \cite{Pham13,Govoni15}, which avoids an explicit sum over empty orbitals by using a technique called projective eigendecomposition of the dielectric screening (PDEP) \cite{Pham13}, evaluating the correlation self-energy by a Lanczos-chain algorithm \cite{Rocca08}. In our calculations we used 200 projective dielectric eigenpotential basis vectors to represent the inverse of the Hermitian dielectric matrix and 30 Lanczos steps to evaluate the irreducible polarizability. Our tests show that these parameters are sufficient to obtain a well-converged band gap within 0.1 eV. For the absolute position of the VBM we used $\Delta E_\text{VBM} = -0.74$ eV as obtained in Ref. \cite{Gruneis14} employing the \emph{GW}$\Gamma$ approximation, that includes a first-order vertex correction in the self-energy and the effect of spin-orbit coupling. Optimized norm-conserving Vanderbilt pseudopotentials (ONCV) \cite{Hamann13} with 20 and 16 valence electrons for Cd and Te atoms, respectively, and a plane-wave energy cutoff of 70 Ry were employed. A considerable improvement in computational efficiency was obtained employing ONCV pseudopotentials, as the plane-wave cutoff requirements with semicore states are modest compared to the conventional Kleinman-Bylander \cite{Kleinman82} representation.
The $G_0W_0$ band gap of bulk CdTe is calculated to be 1.56 eV, in excellent agreement with the room temperature band gap of 1.5 eV, as well as with previous calculations \cite{Klimes14}. Quasiparticle corrections to Kohn-Sham (KS) eigenvalues were obtained using 64-atom supercells at the $\Gamma$ point only. These corrections were then applied to the KS eigenvalues obtained from DFT calculations employing 512-atom supercells.
\vspace{0.1cm}
\subsection{Defect formation energies}
\vspace{0.3cm}
The formation energy of a defect in charge state $q$ and arbitrary ionic configuration \textbf R can be expressed as \cite{Jain11}
\begin{eqnarray}
\hspace{1.5cm}E^f_q[\textbf{R}] = E_q[\textbf{R}] - E_\text{ref} + qE_F,
\end{eqnarray}
\begin{eqnarray}
\hspace{1.5cm}E_\text{ref} \equiv E^\text{CdTe}_\text{bulk} + \sum_i n_i\mu_i,
\end{eqnarray}
where $E_q[\textbf{R}]$ is the total energy of the system in charge state $q$ and atomic positions $\textbf{R}$, and $E_\text{ref}$ is the energy of a reference system with the same number of atoms as the supercell containing an isolated defect. The integer $n_i$ indicates the number of $i$ elements (Cd or Te) that have been added ($n_i > 0$) or removed ($n_i < 0$) from the supercell, and $\mu_i$ is the chemical potential of the element $i$, and $E_F$ is Fermi energy.
The chemical potentials are defined by the experimental growth conditions. For the case of CdTe, the Cd-rich limit is defined by imposing an equilibrium between the system and a reservoir of bulk Cd, whereas for the Te-rich limit $\mu_\text{Te} $ is equivalent to the energy of bulk Te. Therefore, $\mu_{\text{Cd}}$ and $\mu_{\text{Te}}$ are assumed under Cd-rich conditions to be $\mu_\text{Cd} $ = $\mu_\text{Cd (bulk)} $ and $\mu_\text{Te} $ = $\mu_\text{CdTe} - \mu_\text{Cd}$. Similarly, under Te-rich conditions, $\mu_\text{Te} $ = $\mu_\text{Te (bulk)} $ and $\mu_\text{Cd} $ = $\mu_\text{CdTe} - \mu_\text{Te}$. The stability condition for CdTe requires $E^f[\text{CdTe}] < \Delta\mu_{\text{Te}} < 0$, and $E^f[\text{CdTe}] < \Delta\mu_{\text{Cd}} < 0$, where $E^f[\text{CdTe}] $ is the formation energy of CdTe, which is calculated to be $-0.91$ eV, in good agreement with the experimental value of $-0.96$ eV \cite{Haynes14}, and $\Delta\mu_{\text{i}}$ is the relative chemical potential referenced to their respective reservoirs, e.g., $\Delta\mu_{\text{Te}} = \mu_\text{Te}- \mu_\text{Te (bulk)}$.
\vspace{0.1cm}
\subsection{DFT$\hspace{0.05cm}+\hspace{0.05cm}$GW formalism}
\vspace{0.3cm}
The formation energy of a defect in charge state $q\hspace{-0.05cm}-\hspace{-0.07cm}1$ is given by
\begin{eqnarray}
E^f_{q-1}[\textbf{R}_{q-1}] = E_{q-1}[\textbf{R}_{q-1}] - E_\text{ref} + (q-1)E_F.
\end{eqnarray}
By adding and substracting first $E_{q-1}[\textbf{R}_{q}]$ and then $E_{q}[\textbf{R}_{q}]$, we have \cite{Flores15_1}
\begin{equation}
\begin{split}
E^f_{q-1}[\textbf{R}_{q-1}] &= \left \{ E_{q-1}[\textbf{R}_{q}] - E_{q}[\textbf{R}_{q}] \right \} \\
&+ \left \{ E_{q-1}[\textbf{R}_{q-1}] - E_{q-1}[\textbf{R}_{q}]\right \} \\
&+ E^f_{q}[\textbf{R}_{q}] - E_F \\
&\equiv E_\text{QP} + E_{\text{relax}} + E^f_{q}[\textbf{R}_{q}] - E_F,
\end{split}
\end{equation}
where $\textbf{R}_{q}$ corresponds to the minimum energy configuration for the charge state $q$. The first term is a quasiparticle energy (i.e., an electron addition or removal energy) and may be calculated using the many-body perturbation theory based on the $GW$ approximation \cite{Hedin65, Hybertsen85}. The second term corresponds to a relaxation energy and may be evaluated at DFT level, since we only calculate energy differences between configurations with the same number of electrons.
Using Kohn-Sham wave functions $\psi_{n,k}^{\text{KS}} $ and energies $\epsilon_{n,k}^{\text{KS}} $ as mean-field starting points for the construction of G and W ($G_0W_0$ approximation), we calculate the quasiparticle energies $E^\text{QP}_{n,k}$ within a first-order perturbation theory approximation as
\begin{equation}
E^\text{QP}_{n,k} = \epsilon_{n,k}^{\text{KS}} + \left< \psi_{n,k}^{\text{KS}} |\Sigma (E^{\text{QP}}_{n,k}) - V_\text{xc}| \psi_{n,k}^{\text{KS}}\right>,
\end{equation}
which comes from replacing the KS exchange-correlation potential $V_{xc}$ with the self-energy operator $\Sigma$. When the reference state is an open-shell system, wave functions and energies from spin-polarized DFT calculations were used as mean-field starting points.
Considering the computational demands, we employed a cubic 64-atom supercell to calculate the quasiparticle corrections to the DFT eigenvalues at the $\Gamma$ point only. These corrections were then applied to the KS eigenvalues of 512-atom supercells to obtain the quasiparticle energies referenced to the average electrostatic potential of bulk CdTe. This approach is justified because we consider finite-size effects at the DFT level. Moreover, quasiparticle corrections are largely invariant with respect to the supercell size \cite{Flores15_1,Choi09,Chen13} and, at the high-symmetry points their differences are up to 0.1 eV. The relaxation energies were calculated using 512-atom supercells.
\section{Results and discussion}
Starting from the ground state configuration $(\text{Te}_\text{Cd})^{+2}$, we can obtain the formation energies for different charge states using Eq. (4). A key observation is that the self-interaction error will mostly cancel in the first difference of Eq. (1), since it has all the valence bands full and all the conduction bands empty.
We should note that the absolute position of the VBM of bulk CdTe obtained using the PBE exchange-correlation functional was corrected by $\Delta E_\text{VBM} = -0.74$ eV. Hence, the energy change due to the exchange of electrons and holes with the carrier reservoirs for the $(\text{Te}_\text{Cd})^{+2}$ configuration differs by $+2 \times \Delta E_\text{VBM} = -1.48 $ eV, as compared to PBE. Moreover, in the case of CdTe, the widely used screened hybrid functional of Heyd, Scuseria and Ernzerhof (HSE) \cite{Heyd05} only partially corrects the self-interaction error, lowering the energy of the VBM by 0.51 eV with respect to PBE \cite{Gruneis14}, resulting in a formation energy $0.46$ eV higher than our results (an illustrative comparison between LDA and HSE06 can be found in Fig. 4 of Ref. \cite{Lindstrom16}). Du \cite{Du15} has recently stressed the importance of the correct absolute positions of VBM and CBM for reliable predictions of charge transition levels. It deserves noting that corrections for electron and chemical reservoirs have been recently proposed \cite{Freysoldt16}.
\begin{figure}[h]%
\centering
\vspace{0.4cm}
\includegraphics[width=3.5cm]{Figure1}
\label{tab:f1}
\hspace{0.5cm}
\includegraphics[width=3.5cm]{Figure2}
\caption{Calculated formation energies of $(\text{Te}_\text{Cd})$ in various charge states as a function of the Fermi level inside the band gap. The stable charge states are shown by solid lines.}
\end{figure}
The calculated defect formation energies are plotted as a function of the Fermi level in Figure 1. Table I shows the contributions to the formation energies coming from quasiparticle and relaxation energies according to Eq. (4). The formation energy of $(\text{Te}_\text{Cd})$ in the neutral charge state is found to be 1.45 eV for the Te-rich limit, and 3.27 eV for the Cd-rich limit. Our results indicate that $(\text{Te}_\text{Cd})$ exhibits a negative-U behavior that causes the $(+1)$ charge state to be unstable. The $(+2/0)$ charge transition level is found to be deep in the band gap, at VBM + 0.99 eV. For low values of the Fermi energy, the Te antisite will be in a double positive charge state, whereas for $n$-type CdTe, the neutral charge state will be favored.
\begin{table}[h]
\centering
\vspace{0.2cm}
\begin{tabular*}{0.60\textwidth}{@{\extracolsep{\fill}}ccc}
\hline \hline
\T & $E_\text{QP} - E_\text{VBM}$ (eV) & $E_{\text{relax}}$ (eV)\B\\
\hline
\T \T $E^f_{+1}$ & $1.53$ & $-0.21\hspace{0.25cm}$ \\
\T $E^f_{0}$ & $1.05$ & $- 0.23\hspace{0.25cm}$\\
\T $E^f_{-1}$ & $1.56$ & $0.01$\\
\T $E^f_{-2}$ & $1.56$ & $0.00$\B\\
\hline \hline
\end{tabular*}
\caption{\label{tab:table1}Contributions to the formation energies of $(\text{Te}_\text{Cd})$ coming from quasiparticle and relaxation energies, according to Eq. (4).}
\end{table}
\begin{figure}[h]%
\centering
\vspace{0.1cm}
(a)\hspace{-0.4cm}
\includegraphics[width=3.3cm]{Figure3.pdf}
\hspace{0.7cm}
(b)\hspace{-0.4cm}\includegraphics[width=3.3cm]{Figure4.pdf}
\caption{Theoretical band structure of (a) $(\text{Te}_\text{Cd})^{+2}$, and (b) $(\text{Te}_\text{Cd})^{+1}$, calculated by using 512-atom supercells. In (b), the arrow indicates the occupation of the energy level in the band gap.}
\label{f2}
\end{figure}
Figure 2 shows the electronic band structures of $(\text{Te}_\text{Cd})$ in (+1), and (+2) charge states calculated by using large 512-atom supercells. A scissors operator, consisting in a shift to the defect level and a rigid shift to the conduction bands so as to recover the $G_0W_0$ quasiparticle band gap, was applied to correct the KS band structure. In the ideal $T_d$ symmetry, the Te antisite induces a triple-degenerate energy level inside the band gap, and it would be unstable with respect to symmetry-lowering distortions that minimize the total electronic energy. However, the ground state configuration $(\text{Te}_\text{Cd})^{+2}$ maintains the $T_d$ symmetry, because the triple-degenerate energy level is unoccupied [Figure 2 (a)]. On the other hand, $(\text{Te}_\text{Cd})^{+1}$ [Figure 2 (b)] and $(\text{Te}_\text{Cd})^{0}$ [Figure 3] undergo static Jahn-Teller distortions \cite{Opik57}. Two A$_1$ and one E double-degenerate level can be identified (labeled $u, v$, and $e$, respectively). A $T_d$ to $C_{3v}$ distortion gives a $u^2v^2e$ ground state configuration, where $u$ is located below the VBM, $v$ remains isolated in the band gap, and the double-degenerate level E is resonant with the conduction bands.
\begin{figure}[h]%
\centering
\vspace{0.3cm}
\includegraphics[width=6.55cm]{Figure5}
\hspace{0.1cm}
\includegraphics[width=3.6cm]{Figure6}
\caption{(Color online) Theoretical band structure and charge density isosurface ($\rho =$ 0.0005 $e$/Bohr$^3$) of the energy level in the band gap of (Te$_\text{Cd}$)$^0$, calculated by using a 512-atom supercell. Dark spheres are Te atoms and light spheres are Cd atoms. The crystal is oriented along the $\langle 111 \rangle$ direction.}
\label{f3}
\end{figure}
The ground state $(\text{Te}_\text{Cd})^{+2}$ configuration has an empty triple-degenerate energy level very close to the CBM, as shown in Figure 2 (a). The addition of one electron induces a Jahn-Teller distortion, lifting the degeneracy. As the system has now a partially occupied highest energy level [Figure 2 (b)], it is expected to increase its energy if an additional electron is captured, due to the Coulombic repulsion. However, the presence of a second electron induces an energy-lowering structural distortion that supply a net effective attractive interaction (negative-U effect) that overcome Coulombic repulsion. Therefore, electrons are likely to be trapped by pairs at the defect. Our calculated value of U = $\epsilon (+|0) - \epsilon (+2|+) $ is found to be $-0.38$ eV.
According to Figure 1, in $p$-type conditions, the Te antisite is favorable to be in a double positive charge state. It should tend to transfer its electrons to uncompensated acceptors such as Cd vacancies, which are present at significant concentrations in CdTe \cite{Szeles04,Shepidchenko15}. Although the $(+2/0)$ level is deep in the band gap, the unoccupied triple-degenerate energy level close to the CBM may easily capture a pair of electrons from the conduction bands. If so, a $T_d$ to $C_{3v}$ Jahn-Teller distortion would lift the degeneracy, leaving a fully occupied isolated energy level in the band gap at VBM + 0.3 eV [Figure 3].
\begin{figure}[h]%
\centering
\vspace{0.3cm}
\includegraphics[width=7.5cm]{Figure7}
\caption{Configuration-coordinate diagram for the excitation cycle of $(\text{Te}_\text{Cd})^{0}$ .}
\label{fig4}
\vspace{0.3cm}
\end{figure}
As noted above, the Te antisite is energetically favorable to be in the neutral charge state in $n$-type CdTe. However, this configuration may also be metastable when the position of the Fermi level is near the middle of the gap. Moreover, the optical excitation of $(\text{Te}_\text{Cd})^{0}$ to the positively charged state, followed by the capture of an electron from the conduction bands is consistent with the observed absorption peak near 1.1 eV \cite{Davis93,Simonds06}, as well as with the 1.1-eV band generally found in PL measurements \cite{Bryant68,Bowman88,Krustok96,Zazvorka16}. The former was attributed to localized defect states within the band gap \cite{Davis93}, whereas the latter has been associated with donor-acceptor pair (DAP) transitions \cite{Krustok96}. More recently, it was proposed that the PL band could be caused by a transition from an excited state activated by carrier capture (component 9 in Ref. \cite{Zazvorka16}).
To gain further understanding on this issue, we calculate the energy of the zero-phonon line (ZPL), which allows us to compare our calculations to experimental results at low temperatures. The zero-point vibration states will raise the energies of the ground state and excited configurations by a value of the order of a few tens meV, called zero-point energy (ZPE). The difference between the ZPE of the ground state and excited configurations is expected to be even smaller, of the order on a a few meV. Therefore, the ZPL can be well approximated by the sum of the excitation energy for promoting one electron from the localized energy level of $(\text{Te}_\text{Cd})^{0}$ (the gap-state in Fig. 3) to the conduction bands (transition A $\rightarrow$ B in Fig. 4), and the subsequent relaxation energy of the excited configuration (transition B $\rightarrow$ C in Fig. 4); the latter produces a shift in the absorption energy (a Stoke shift). We use constrained DFT \cite{Dederichs84} to calculate the Stokes shift. This method allows one to define constraints on the charge density, and has been successfully applied to Nitrogen-Vacancy \cite{Gali09_1,Gali09,Choi12}, and Silicon-Vacancy \cite{Gali13} color centers in diamond. The expected error in this approach is small, as the Stokes shift corresponds to the energy difference between two different ionic configurations with the same electronic configuration \cite{Gali09}; the same principle is used in the DFT$\hspace{0.05cm}+\hspace{0.05cm}$\emph{GW} formalism \cite{Flores15_1}.
Our calculated energies for the vertical absorption (A $\rightarrow$ B) and the Stokes shift (B $\rightarrow$ C) are 1.26 eV and $-0.14$ eV, respectively; thus, the ZPL is calculated to be 1.12 eV. This result agrees well with the 1.1-eV center observed in both absorption \cite{Davis93} and emission \cite{Davis93,Bryant68} at cryogenic temperatures.
\begin{figure*}[!ht]%
\vspace{0.4cm}
\centering
(a)\hspace{-0.35cm}\includegraphics[width=3.2cm]{Figure8}
\hspace{-0.2cm}
\includegraphics[width=2.76cm]{Figure9}
\hspace{0.5cm}
(b)\hspace{-0.35cm}\includegraphics[width=3.2cm]{Figure10}
\hspace{-0.2cm}
\includegraphics[width=2.76cm]{Figure11}
\vspace{0.5cm}\\
(c)\hspace{-0.35cm}\includegraphics[width=3.2cm]{Figure12}
\hspace{-0.2cm}
\includegraphics[width=2.74cm]{Figure13}
\caption{(Color online) Theoretical band structure and charge density isosurfaces ($\rho =$ 0.0005 $e$/Bohr$^3$) of the energy levels in the band gap for the neutral complexes: (a) $(\text{Se}_{\text{Te}}\hspace{-0.05cm}-\hspace{-0.05cm}\text{Te}_\text{Cd})^0$, (b) $(\text{S}_{\text{Te}}\hspace{-0.05cm}-\hspace{-0.05cm}\text{Te}_\text{Cd})^0$, and (c) $(\text{O}_{\text{Te}}\hspace{-0.05cm}-\hspace{-0.05cm}\text{Te}_\text{Cd})^0$, calculated by using 512-atom supercells. The arrows indicate the occupation of the energy level in the band gap. Dark spheres are Te atoms and light spheres are Cd atoms. The crystals are oriented along the $\langle 111 \rangle$ direction.}
\vspace{0.1cm}
\end{figure*}
Having identified the Te antisite in the neutral charge state as hole trap, we should note that in order to limit any potential deleterious impact to carrier transport, Te-poor grown conditions are desirable. However, most polycrystalline CdTe films require high growth temperatures resulting in a Te-excess material (due to the lost of Cd during the growth process) \cite{Yujie03,Moure-Flores12}. To solve this problem, it was recently proposed that the incorporation of oxygen passivates the gap states associated with $(\text{Te}_\text{Cd})^0$, by forming $(\text{O}_\text{Te}-\text{Te}_\text{Cd})$ complexes \cite{Flores15_1}.
To investigate more deeply the beneficial effects of oxygen incorporation, we perform DFT calculations considering three distinct isovalent impurities: selenium, sulfur, and oxygen. For the cases of selenium [Figure 5 (a)] and sulfur [Figure 5 (b)], the electronegativity of the impurity atom is reflected in the size of its antibonding molecular orbital; as consequence, the energy of the $(\text{Te}_\text{Cd})^0$ gap state, located at VBM + 0.3 eV, is lowered by 0.13 eV and 0.18 eV, respectively. Remarkably, isovalent oxygen completely removes the antibonding interaction along the $C_{3v}$ rotation axis, lowering the position of the gap state by $0.24$ eV [Figure 5 (c)]. In the case of $(\text{O}_\text{Te}-\text{Te}_\text{Cd})$, the localized energy level is located at VBM + 0.06 eV; thus, hole trapping is unlikely to occur.
\section{Conclusions}
In summary, we have investigated the formation energies, charge transition levels and quasiparticle defect states of the Te antisite in CdTe within the DFT$\hspace{0.05cm}+\hspace{0.05cm}$\emph{GW} formalism. We find that $(\text{Te}_\text{Cd})$ is a negative-U defect, inducing a deep donor level at VBM + 0.99 eV. In addition, our results suggest that the $\sim$1.1 eV band, visible in both luminescence and absorption experiments can be associate with the $(\text{Te}_\text{Cd})^0$ defect, which acts as a hole trap.
\section*{Acknowledgment}
This work was supported by the FONDECYT Grant No. 1130437. Powered@NLHPC: This research was partially supported by the supercomputing infrastructure of the NLHPC (ECM-02).
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 5,138
|
require "json"
require 'google/api_client'
require 'active_support'
require 'active_support/core_ext/time'
module Ruboty
module GoogleCalendar
class CalendarClient
APPLICATION_NAME = 'ruboty-google_calendar'
def initialize(env)
# Initialize OAuth 2.0 client
# authorization
@client = Google::APIClient.new(application_name: APPLICATION_NAME)
@client.authorization.client_id = env["GOOGLE_CALENDAR_CLIENT_ID"]
@client.authorization.client_secret = env["GOOGLE_CALENDAR_CLIENT_SECRET"]
@client.authorization.scope = env["GOOGLE_CALENDAR_SCOPE"]
@client.authorization.refresh_token = env["GOOGLE_CALENDAR_REFRESH_TOKEN"]
@client.authorization.access_token = env["GOOGLE_CALENDAR_ACCESS_TOKEN"]
@cal = @client.discovered_api('calendar', 'v3')
end
def search id, day=Time.now
# 時間を格納
min = day.beginning_of_day.iso8601
max = day.end_of_day.iso8601
# イベントの取得
params = {'calendarId' => id,
'orderBy' => 'startTime',
'timeMin' => min,
'timeMax' => max,
'singleEvents' => 'True'}
result = @client.execute(:api_method => @cal.events.list,
:parameters => params)
# 結果を返却
result.data.items
end
end
end
end
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 4,418
|
By Robert Burleigh
Read by Susan Pelosi
Category: Children's Picture Books
Category: Audiobooks | Children's Picture Books
Jan 27, 1997 | 32 Pages | 4-8 years
*This format is not eligible to earn points towards the Reader Rewards program
Audiobook Download $5.00
Jan 22, 2019 | 19 Minutes | 4-8 years
Jan 27, 1997 | 32 Pages
Jan 22, 2019 | 19 Minutes
About Flight
Winner of the Orbis Pictus Award for Nonfiction and Publishers Weekly Best Book of the Year.
Flight. Loneliness. Fear. Danger. Courage. Charles Lindbergh considered all these things and more when he set out for Paris on the morning of May 20, 1927, with only two compasses and the stars for his guides. Experience all the drama of Lindbergh's history-making flight with startling intimacy as you travel along with the first pilot to fly solo across the Atlantic, and follow the courage and endurance of one man who dared to make his dream come true.
"(A) glorious re-creation of an epic adventure."–Publishers Weekly
"Brings new life to one of the stories of the century."–Kirkus Reviews
Also by Robert Burleigh
See all books by Robert Burleigh
About Robert Burleigh
Robert Burleigh has published poems, reviews, essays, many filmstrips and videos, and more than 40 children's picture books. Born and raised in Chicago, he graduated from DePauw University (Greencastle, Indiana) and later received an MA in humanities from the University of… More about Robert Burleigh
Paperback | $7.99
Published by Puffin Books
Jan 27, 1997 | 32 Pages | 10-1/4 x 8 | 4-8 years | ISBN 9780698114258
Audiobook Download | $5.00
Published by Listening Library (Audio)
Jan 22, 2019 | 19 Minutes | 4-8 years | ISBN 9780525628538
People Who Read Flight Also Read
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 1,501
|
El HP-75C y el HP-75D eran computadoras de mano programables en BASIC, hechos por Hewlett-Packard desde 1982 a 1986.
El HP-75 tenía un pantalla de cristal líquido de una sola línea, 48 KB de ROM del sistema y 16 KB RAM, un teclado comparativamente grande, aunque sin el teclado numérico separado (keypad), un lector de tarjeta magnética manual (2×650 bytes por tarjeta), un puerto de enchufe para la expansión de memoria, y una interfaz HP-IL que podía ser usada para conectar impresoras, almacenamiento y el equipo de prueba electrónico. El interpretador BASIC incluyó capacidades para manejar archivos, usando para almacenamiento de programa, la memoria RAM, tarjetas, o casetes/disquetes (vía HP-IL).
Otras características incluyeron un editor de textos así como un recordador de citas con alarmas, similar a funciones de PDAs modernos.
El HP-75D (1984-1986) agregó un puerto para un lector de código de barras manual, usado a menudo para tareas de control de inventario.
El HP-75 era comparativamente costoso en $995 MSRP para el 75C, o $1095 MSRP para el 75D, haciéndolo menos popular que el más barato modelo sucesor, el HP-71B.
Miscellanea
En HP, el nombre código interno para el 75C era Kangaroo (canguro), y el 75D fue apodado Merlin.
Notas
Enlaces externos
HP-75 at the MoHPC
HP Journal, June 1983 Article about the HP-75C design, the IL interface and the card reader
75
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 2,453
|
Q: Error: Can't assign to the final variable 'color'. assert(color = null || decoration == null, ^^^^^ I can't run even a simple code. I think the problem is with the container. dart
This is the full picture in debug console. I am doing flutter for 1 month. Can someone help me out?
A: Somehow you've corrupted your Flutter install. That line 274 is meant to say color == null not color = null
assert(color == null || decoration == null,
'Cannot provide both a color and a decoration\n'
'To provide both, use "decoration: BoxDecoration(color: color)".',
),
You can just correct that back, but you may want to remove and reinstall Flutter, just in case there are other corruptions.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,509
|
Alexeï Mikhaïlovitch Tchali, ou Tchaly, selon les transcriptions (en russe : Алексей Михайлович Чалый ; en ukrainien: Олексі́й Миха́йлович Ча́лий ; aussi traduit: Aleksei Mikhailovich Chaliy ), né le à Sébastopol (république socialiste soviétique ukrainienne, URSS), est un homme politique russe, ancien maire de Sébastopol (du jusqu'au ), qui a fait office de gouverneur de la ville-territoire de Sébastopol en république de Crimée (rattachée à la Russie depuis le ), du avril au .
Biographie
Alexeï Tchali naît dans la famille d'un scientifique soviétique spécialiste de construction d'appareils électroménagers, Mikhaïl Vassilievitch Tchali et de son épouse Alevtina Tikhonovna Tchalaïa, professeur en cybernétique et titulaire d'un doctorat. Alexeï Tchali est le petit-fils du vice-amiral Vassili Tchali (1911-1979), dernier commandant de l'escadre de la Flotte de la mer Noire (1939-1961) de 1956 à 1961, puis premier commandant-adjoint de la flotte de la mer Noire.
Alexeï Tchali poursuit ses études à l'université technique nationale de Sébastopol dont il obtient un doctorat en sciences techniques. À la fin de ses études en 1987, il dirige un laboratoire d'études de cette université à propos d'appareils de commutation. En 1990, le laboratoire est transformé à la fin de la perestroïka en entreprise nommé Tavrida Elektrik (Tavrida signifiant Tauride, ancien nom de la Crimée). Quelques mois plus tard, lorsque l'URSS s'effondre ainsi que toute l'économie du pays, cette entreprise est en mesure de sauver quelques bureaux d'études de la région. Aujourd'hui Tavrida Elektrik, dont le siège est à Sébastopol, regroupe une soixantaine de compagnies spécialisées dans l'électro-technologie et employant environ trois mille personnes. Ses filiales sont implantées dans environ cinquante villes de Russie: Moscou, Saint-Pétersbourg, Votkinsk, Oriol, Lipetsk, Nijni Novgorod, etc. Elle a aussi des bureaux de représentations à Pékin, Tallinn, Vancouver, Johannesburg, et d'autres villes.
En tant qu'entrepreneur de Sébastopol, Tchali est à l'initiative de la restauration de plusieurs sites historiques rappelant l'histoire militaire de la ville et de sa résistance aux diverses occupations étrangères, notamment pendant la Seconde Guerre mondiale et l'offensive de Manstein.
Alexeï Tchali fait l'objet depuis la sécession de la Crimée, en tant que signataire du rattachement à la Russie à la suite du référendum populaire du , d'une interdiction de pénétrer aux États-Unis et dans autres pays alliés des États-Unis. Il fait partie des trente-trois personnes interdites de séjours dans l'Union européenne visées par les sanctions depuis l'annexion de la Crimée, suite à son inscription le .
Il est marié et père de famille.
Carrière politique
Deux semaines avant les élections municipales de Sébastopol, Tchali s'est exprimé à la télévision locale :
Le , une première manifestation d'envergure a lieu à Sébastopol dans le centre-ville, place Nakhimov, contre la révolution de Maïdan (qualifiée de par ses opposants). Elle regroupe plus de vingt mille personnes. On remarque des drapeaux russes, de la croix de saint André (emblème de la flotte russe) et même du parti communiste ukrainien ou de la Biélorussie, tandis que les slogans de la foule font état de demandes d'appui de la Russie, de l'organisation de nouvelles élections municipales pour le rétablissement de l'ordre, et de la non-reconnaissance du gouvernement de Kiev issu de la révolution de Maïdan. Cependant, l'organisation d'élections municipales contrevient à la loi ukrainienne qui prévoit que le maire de Sébastopol doit être uniquement nommé par les autorités centrales de Kiev et non pas élu.
Deux personnalités se présentent en premier plan pour des élections, l'ancien maire Vladimir Iatsouba (élu le ) et l'entrepreneur Alexeï Tchali. Le , le nouveau ministre de l'Intérieur ukrainien, Arsen Avakov, arrive en Crimée, ainsi que le chef des services secrets intérieurs ukrainiens, Valentin Nalivaïtchenko. Le , le maire de Sébastopol, Iatsouba, donne sa démission, expliquant que les , en effet depuis 1992, le maire de Sébastopol est directement nommé par le pouvoir de Kiev. Il ajoute qu'il Il démissionne également du parti des régions.
Ce même jour, l'administration de la ville de Sébastopol déclare comme illégale toute tentative issue d'organisations radicales de la révolution de Maïdan d'imposer une nouvelle administration à Sébastopol. En même temps, un rassemblement a lieu à Sébastopol en faveur de Tchali, alors que Fiodor Roubanov (ancien adjoint de Vladimir Iatsouba) est de fait président par intérim de l'administration. Des rumeurs selon lesquelles Roubanov serait soutenu par Kiev et que Tchali serait passible de poursuites légales de la part de Kiev provoquent l'indignation d'une grande partie de la population locale. Roubanov promet une réunion du comité exécutif pour le . Mais dans la soirée, un procureur avec un mandat d'arrêt contre Tchali et un groupe des services de sécurité intérieure ukrainiens sont forcés par la foule de quitter les lieux.
Simultanément, le conseil municipal se prononce en faveur d'Alexeï Tchali par 49 voix sur les 75 conseillers présents. Cette élection n'est pas reconnue par Kiev.
Au conseil exécutif
Arrivé à la tête du conseil exécutif, Tchali désavoue les autorités centrales issues de Maïdan, tandis que sur la route de Yalta et celle d'Inkerman apparaissent des points de contrôle et que sur les ponts des hommes du parti Bloc russe et des milices populaires assurent la surveillance des accès et n'arrêtent selon leurs déclarations . Le 26, Tchali annonce que son territoire n'appliquera pas les mesures exigées par le ministère de l'Intérieur ukrainien à l'encontre des membres des forces du Berkout.
Le matin du mars, le nouveau chef de la police nommé par Kiev, Vitaly Malikov, est empêché par une foule d'environ 600 personnes d'entrer dans les locaux de la police. Le nouveau chef de l'administration, Dmitri Belik, est élu et il se prononce pour l'inclusion de Sébastopol dans la Fédération de Russie. Le , Tchali annonce que son territoire ne participera pas aux élections présidentielles ukrainiennes anticipées du , mais que la ville continue à verser ses impôts et maintient ses relations économiques avec Kiev, jusqu'au référendum prévu le 16 mars 2014, sur la question du rattachement ou non de Sébastopol à la Fédération de Russie comme sujet de la Fédération de Russie. Le , Dmitri Belik annonce que le russe est désormais langue officielle pour les documents administratifs et que cette mesure sera appliquée à partir du . Le , Alexeï Tchali est inclus à la liste des personnes frappées de sanction par l'Union européenne (gel des avoirs éventuels et interdiction de visa). Cette mesure est une réponse au résultat du référendum donnant 96 % de voix favorables au rattachement de la Crimée et du territoire de Sébastopol à la Russie que l'Union européenne suivant les États-Unis refuse de reconnaître.
Le , Alexeï Tchali, ainsi que Sergueï Axionov et Vladimir Konstantinov signent avec Vladimir Poutine dans la salle Saint-Georges du palais du Kremlin le rattachement des territoires qu'ils représentent à la Russie.
Le , Alexeï Tchali signe un accord de coopération économique avec le maire de Moscou, Sergueï Sobianine.
Gouverneur par intérim
Le , il est élu à l'unanimité par les députés de l'assemblée législative de Sébastopol, gouverneur par intérim, avant qu'une nouvelle charte du territoire soit adoptée en conformité avec la législation russe avant la fin du mois. Il est prévu que ce soit le vice-amiral Sergueï Méniaïlo, ancien commandant-adjoint de la flotte de la mer Noire; Alexeï Tchali se réservant le poste de directeur de la nouvelle agence de développement stratégique de Sébastopol. La nomination du vice-amiral Meniaïlo intervient le .
Notes et références
Liens externes
Site de l'assemblée législative de Sébastopol
Naissance à Sébastopol
Naissance en juin 1961
Sébastopol
Personnalité politique russe
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Русское Сиренькино — это деревня в Альметьевском районе, входящая в состав Сиренькинского сельского поселения.
География
Находится в юго-восточной части Татарстана на расстоянии приблизительно 34 км по прямой на запад от районного центра города Альметьевск.
История
Основано около 1744 года. До 1920-х годов название было Большой Сосновый Багряш. В 1888 году была построена Михайло-Архангельская церковь.
Население
Постоянных жителей было: в 1782 году — 83, в 1795 — 97, в 1816—126, в 1834—174, в 1859—204, в 1870—230, в 1884—318, в 1897—409, в 1905—450, в 1912—544, в 1920—556, в 1926—347, в 1938—362, в 1949—293, в 1958—133, в 1970 — 51, в 1979 — 87, в 1989 — 83, в 2002 − 112 (чуваши 81 %), 105 в 2010.
Примечания
Населённые пункты Альметьевского района
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